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## Scientific Summary

## SUMMARY OF |

Figure 1. |

As Santilli puts it: *Stars initiate their lives as being mostly composed of Hydrogen; they first synthesize the neutron as a "compressed Hydrogen atom" according to Rutherford; and then, only thereafter, there is the initiation of the majestic production of light with the nuclear synthesis first of the Deuteron and then the synthesis of heavier elements. Therefore, I personally had no interest in studying nuclear syntheses until we had achieved some understanding of the most fundamental fusion in nature, that of the Hydrogen atom into the neutron. The decades needed for these studies are due to the fact that 20th century methods resulted to be inapplicable for the synthesis of the neutron, and suitable covering theories had to be built.*

**I.2. Inapplicability of 20th century theories to nuclear syntheses**

On strict scientific grounds, theories at large, thus including quantum mechanics and quantum chemistry, can be considered as being "exactly" valid for given physical conditions if and only if they represent "all" related experimental data from unadulterated first principles. In the event experimental data are not exactly represented, theories are only "approximately" valid for the conditions considered. In the event the theories provide representations of events violating physical laws, or the theories are unable to produce quantitative representation of the problem considered, said theories are "inapplicable" on strict scientific grounds, rather than "violated" because not built for the event considered.

Along the above lines, *quantum mechanics* is indeed "exactly" valid for the atomic structure because it represents all experimental data without the addition of arbitrary parameters or ad-hoc functions. By contrast, Santilli's central view is that, when applied to nuclear physics and its various processes, quantum mechanics is, in general, only "approximately" valid and "inapplicable" in a number of specific events, particularly for nuclear syntheses, as established by the following evidence (see, e.g., Vol. I of refs. [14]):

Figure 2. |

*massive points,*thus being approximately valid in nuclear physics because the nuclear constituents have large dimensions for the particle world (Fig. 2). As shown by extensive studies in the field (see below), the inability to represent protons and neutrons (nucleons) with their actual, non-spherical and deformable shape has implied the known inability by quantum mechanics to represent a number of nuclear experimental data.

2.2. Despite one century of efforts and the use of large research funds, quantum mechanics has been unable to represent nuclear magnetic moments since we still have 1% deviation of experimental values from the prediction of the theory for the simplest possible nucleus, the Deuteron, with embarrassing deviations for large nuclei, such as the Zirconium or the Uranium (Fig. 3). Studies in the field have established that the representation of nucleons as extended and deformable charge distributions when members of a nuclear structure has permitted an "exact" representation of all nuclear magnetic moments (see, e.g., Ref. [11]).

Figure 3. |

*nuclei do not possess nuclei*(Fig. 2). In the absence of exactly valid Galileo and Poincare' symmetries, any claim that nonrelativistic and relativistic quantum mechanics are exactly valid in nuclear physics have no scientific value.

2.4. Despite about one century of efforts, quantum mechanics has been unable to explain the stability of the neutron when a member of stable nuclides. In fact, the neutron is naturally unstable (when isolated) and decays spontaneously into the proton and an electron originally used for its synthesis. Yet, when a member of the deuteron or of other stable isotopes, the neutron becomes permanently stable, thus implying rather deep structural processes in the transition from the free state to the bound state beyond any clue from quantum mechanics.

2.5. Despite additional research protracted for about one century, quantum mechanics has been unable to represent nuclear spins without internal inconsistencies. As an example, quantum mechanics predicts that a stable bound state of one proton and one neutron has to be a singlet state with spin zero, while the deuteron has spin one. The spin of the deuteron is attempted via a "mixture" of orbits for the "ground state," with easily provable internal inconsistencies. Much more embarrassing deviations exist between spin predictions and experimental data for heavy nuclei for which deuteron-type attempts at using a variety of states for the stable ground state pass the boundary of scientific credibility.

2.6. Quantum mechanics is inapplicable for the most fundamental synthesis in the core of a star, the synthesis of the neutron from the Hydrogen atom, because, as reviewed in detail in Part II, the rest energy of the neutron is 0.782 MeV *bigger* then the sum of the rest energies of the proton and of the electrons, in which case the Schrodinger and Heisenberg equations of quantum mechanics no longer admit physically consistent solutions. In fact, all consistent quantum mechanical bound states are characterized by a "negative binding energy" that results in the well known "mass defect," while for the synthesis of the Hydrogen atom into the neutron (as well as for all other hadrons) we would need a "positive binding energy" resulting in a "mass excess" that is anathema for quantum mechanics.

2.7. Quantum mechanics is inapplicable for nuclear syntheses because its axioms have no "arrow of time," thus being reversible over time, while nuclear syntheses are strictly irreversible over time. Consequently, quantum mechanics predicts with finite probabilities not only the synthesis of two nuclei into a third, but also the spontaneous disintegration of the third nucleus into the original two nuclei,

(1) N_{1} + N_{2} → N_{3}, N_{3} → N_{1} + N_{2}

in violation of causality, energy conservation and other laws. These violations cannot be resolved via the generally adopted position of ignoring the event backward in time because the lack of representation of the irreversible character of nuclear fusions has been shown to prevent the industrial achievement of new clean nuclear energies.

According to a rather general view, all the above insufficiencies for the quantum description of nuclear physics are resolved by passing to the conjecture that the hypothetical quarks are the constituents of protons and neutrons. While accepting the SU(3)-color as well as the standard model for the *classification* of particles into families, Santilli does not accept quarks as physical particles in our spacetime for various reasons outlined in Section II.3, including: A) The lack of achievement to date of a serious confinement of quarks due to the uncertainty principle; B) The technical impossibility of even defining quarks in our spacetime; C) The impossibility for quarks to have "point-like wavepackets" (as necessary for the exact validity of quantum mechanics), resulting in interior non-linear, non-local and non-Hamiltonian effects preventing the very definition of quarks as quantum mechanical particles; and various other reasons.

Even assuming that the hypothetical quarks are the physical constituents of nucleons, Santilli has shown that quantum mechanics remains inapplicable in nuclear physics for various reasons, such as the fact that the orbits of the hypothetical quarks are very small, thus preventing the polarizations needed to achieve an exact representation of nuclear magnetic moments, spins and other data.

Additionally, the assumption that the hypothetical quarks are the physical constituents of protons and neutrons prevents any quantitative description of the synthesis of the neutron from the Hydrogen atom inside a star (see also Section II.3). As Santilli puts it: *I believe that the conjecture that the undetectable and uncontainable quarks are the physical constituents of hadrons, while effective to maintain the validity of relativistic quantum mechanics in nuclear physics, constitutes the biggest obstacle against the search and development of much needed new clean nuclear energies.*

It should be finally stressed that the No Reduction Theorem I.2.1 establishes that the irreversibility of nuclear syntheses simply cannot be resolved via the reduction of nucleons to the hypothetical quarks because, by basic assumption, quarks are believed to be stable and reversible entities.

Since a covering of quantum mechanics under the name of *hadronic mechanics* [14] has already shown the capability of resolving insufficiencies 2.1 to 2.7, any continued sole use of quantum mechanics and quark conjectures for publicly funded research in nuclear syntheses raises evident accountability issues, not only in the use of public funds, but also vis-a-vis the need by society of new clean nuclear energies.

Figure 4. |

*quantum chemistry*is unable to represent energy releasing processes, such as the simple coal combustion (Fig. 4), again, because the theory is strictly reversible over time, while coal combustion is irreversible. Hence, quantum chemistry predicts with finite probabilities that smoke and ashes spontaneously recombine themselves to reconstitute the original coal, again in violation of physical laws.

The above occurrences establish the need for a covering mathematics possessing a time direction in their very basic axioms as a prerequisite for the construction of irreversible coverings of quantum mechanics and chemistry.

When facing an irreversible event, a rather general view is that the irreversible character is "illusory" (sic) because it disappears (sic) when reducing the macroscopic event to its elementary particle constituents. This view was disproved by Santilli during his Ph. D. studies at the University of Torino, Italy, in the mid 1960s via the proof of the following:

*NO REDUCTION THEOREM I.2.1: A macroscopic irreversible process cannot be consistently reduced to a finite number of elementary particles all in reversible conditions. Vice-versa, a finite number of particles all in reversible conditions cannot consistently yield a macroscopic irreversible process under the correspondence or other principles.*

Figure 5. |

An alternative proof of the theorem was based on the fact that entropy and thermodynamical laws are not "illusory", as needed to maintain quantum mechanics, because in reality they originate at the most elementary level of nature. As an illustration, the contact, nonconservative and irreversible forces experienced by a spaceship during reentry (Fig. 5) are due to non-linear, non-local and non-Hamiltonian interactions between the electron orbitals of peripheral atoms of the spaceship with corresponding electron orbitals of atmospheric atoms.

As it was the case for the sole continued use of quantum mechanics for nuclear syntheses, since a manifestly irreversible covering of quantum chemistry under the name of *hadronic chemistry* [15] has already shown the capability of resolving the above serious insufficiencies, any sole use of the manifestly reversible quantum chemistry for manifestly irreversible energy releasing processes, particularly when conducted under public financial support, raises again serous accountability issues.

**I.3. Genomathematics and genomechanics**

Santilli has dedicated his research life to mathematical, physical and chemical studies of energy releasing processes as well as their industrial applications. The research initiated with his graduate studies at the University of Torino, Italy, in the mid 1960s, during which Santilli became aware of the inapplicability of 20th century theories for the quantitative representation of irreversible energy-releasing processes for reasons outlined in the preceding section.

To begin, Santilli first studied the representation of reversible processes via the historical Lagrange and Hamilton equations, not those used in the 20th century, but those with external terms that were intended by Lagrange and Hamilton precisely to represent irreversibility, but he discovered that external terms cause the loss of all algebras in the brackets of the time evolution law (see Vol. I of Refs. [14]). Hence, he passed to the search of irreversible dynamical equations characterizing a generalized algebra by the brackets of the time evolution law as a condition to construct coverings of 20th century theories.

In so doing Santilli noted that 20th century theories are reversible over time because based on *Lie's theory* whose brackets between two Hermitean operators A, B are invariant under anti-Hermiticity, thus being invariant under time reversal, [A, B] = AB - BA = - [A, B]^{†}. Consequently, Santilli proposed in 11967 [1] the construction of generalized mathematical and physical formulations based on Albert's covering notion of *Lie-admissible algebras* with the proposal in 1967 of the first known (p, q)-deformation of Lie algebras into Lie-admissible algebras with brackets (for brevity, see Ref. [1] for original references and definitions)

(2) (A, B) = qAB - qBA = n(AB - BA) + m(AB + BA) = n[A, B] + m{A, B}

where p = n + m, q = - n + m and p± q are non-null scalars.

Jointly, Santilli proposed the *Lie-admissible generalization of Heisenberg equation* for the time evolution of an observable A in the infinitesimal form [2,3]

(3) i dA/dt = (A, H) = qAH - q HA,

and integrated finite form

(4) A(t) = exp(Hwti) A(0) exp(-itpH),

where H is the usual Hamiltonian and the representation of irreversibility is assured for p ≠ q.

Because of his studies in irreversibility, Santilli was invited by NASA and moved in 1967 to the U.S.A. to continue his research in irreversibility at the *Center for Theoretical Physics* of the *University of Miami* in Coral Gables, Florida, because spaceship re-entry (Figure 5) is an irreversible event not reducible to an ideal collection of conservative elementary particles (No Reduction Theorem I.2.1).

In 1977, when he joined the *Lyman Laboratory of Physics* of *Harvard University,* Santilli was invited by the *U. S. Department of Energy* (then called ERDA) to continue his studies on irreversibility under contract ER-78-S-02-4742.A000 because, as stressed in section 2, all energy releasing processes are irreversible over time thus not admitting a consistent representation with 20th century mathematics, physics and chemistry.

In 1978, Santilli published memoirs [4,5] under said DOE grant (see monographs [6] also of 1978 under said grant for the formal treatment), the first [4] establishing the foundations of the *Lie-admissible generalization of 20th century mathematics,* today known as *Santilli geno-Mathematics* (where the prefix "geno" was proposed in the Greek sense of "inducing new axioms") via the following *two* generalizations of the associative algebra of a Lie algebra for motion forward and backward in time,

(5) A<B = AR*B, B >A = B S*A,

with the general Lie-admissible product first introduced in ref. [4]

(6) (A, B)* = A <B - B>A = AR*B - BS*A = [A, B]* + {A, B}* =

= (AT*B - BT*A) + (AW*B + BW*A),

where R* = T*+ W* and S* = - T* + W* are called *genotopic elements* (the asterisk denoting formulation in a *bimodular Hilbert space* identified below) and consists of matrices or operators that, besides being non-singular, have an unrestricted functional dependence on all needed local; variables, such as time t, coordinates r, momenta p, wave-functions ψ, etc., R = R(t, r, p, ψ, ...), S = S(t, r, p, ψ, ...).

It should be recalled that Santilli's Lie-admissible algebra with product (A, B)* has been proved to be universal in the sense of admitting as particular cases all known algebras (over a field of characteristic zero), such as: associative, Lie, Jordan, supersymmetric, nilpotent, flexible and any other known algebras.

In the second memoir [5], Santilli put the foundation of an *irreversible Lie-admissible covering of quantum mechanics* under the name of *hadronic mechanics,* specifically conceived for the quantitative treatment of the structure of strongly interacting particles (hadrons) and of energy releasing processes at large in accordance with the DOE request, with central equations in their infinitesimal form today known as *Heisenberg-Santilli genoequations*

(7) i dA/dt = (A, H)* = A<H - H >A = AR*H - HS*A = [A, H]* + {A, H}*

with exponentiated form to a *Lie-Santilli genogroup*

(8) A(t) = exp(HS*ti) A(0) exp(-itR*H)

where irreversibility is evidently assured for R* ≠ S*, with corresponding genotopies of Schrodinger equations, today known as *Schrodinger-Santilli forward and backward genoequations*

(9a) H >|ψ*) = HS|ψ*) = E^{> } |ψ*)

(9b) (*ψ|<H = (*ψ|RH = (*ψ|^{ <}E,

(9c) E^{> } ≠ ^{ <}E.

Note that quantum mechanics has a modular associative structure with equivalent actions to the right H|ψ) = E|ψ) and to the left (ψ|H = (ψ|E due to the Hermiticity of H. In Santilli Lie-admissible covering the theory becomes nontrivially *bimodular* in the sense that the right and left modular actions are no longer equivalent, Eqs. (9), even though the Hamiltonian remains Hermitean to be observable [14]. This is the central *mathematical* feature of hadronic mechanics assuring a *physically* consistent representation of irreversible processes.

**I.4. Isomathematics and isomechanics**

As a particular case of the above Lie-admissible formulations, Santilli proposed in memoir [4] (see again monographs [6] for the formal treatment) the isotopies of the various branches of Lie's theory, today known as the *Lie-Santilli IsoTheory* (where the prefix "iso" was suggested to indicate the preservation of Lie axioms). The Lie-Santilli IsoTheory occurs in the classification of the Lie-admissible theory for R* = S* = T* = T*^{†} = T*(t, r, p, ψ, ...) > 0, in which case T* is called the *isotopic element,* with consequential single generalized associative product

(10) A⊗B = AT*B,

that characterizes the universal enveloping isoassociative algebra ξ*(L*) of the *Lie-Santilli IsoAlgebra* L* with Isocommutation rules

(11) [J_{i}, J_{j}]* = J_{i} T* J_{j} - J_{j} T* J_{i} = C_{ij}^{k} J_{k}

and related *Lie-Santilli IsoGroups and IsoSymmetries* (see Refs. [6] for detailed presentations).

In the subsequent memoir [5] Santilli proposed the construction of the *Lie-isotopic generalization of quantum mechanics* also known as *isomechanics,* with *Heisenberg-Santilli isoequations* in the infinitesimal form

(12) i dA/dt = [A, H]* = A⊗H - H ⊗A = AT*H - HT*A,

and corresponding finite *Lie-Santilli isoGroup*

(13) A(t) = exp(HTti) A(0) exp(-itTH)

and compatible *Schrodinger-Santilli isoequation*

(14) H ⊗ |ψ*) = H(r, p) T*(t, r, p, ψ, ...) |ψ*) = E|ψ*)

where one should note the embedding of non-linear interactions in the isotopic element T*(t, r, p, ψ...}. This allows the preservation of the superposition principle and, consequently, a consistent representation of composite systems with non-linear internal interactions, something basically impossible for quantum mechanics (because non-linear interactions must be embedded in the Hamiltonian, H(r, p, ψ |ψ) = E|ψ) ...), with consequential violation of the superposition principle).

As one can see, Eqs. (14) show *two* operators for the representation of dynamical systems, the Hamiltonian H(r, p) for the representation of action-at-a-distance potential interactions (all known to be strictly reversible over time) and the isotopic operator T*(t, r, p, ψ ...) for the representation of internal non-Hamiltonian effects at short distances due to the overlapping of wavepackets or charge distributions. In this case, despite the conservation of the total energy idH/dt = [H, H]* = 0, irreversibility is assured for T*(t, ...) = T*^{†} ≠ T*(-t, ...).

Following these foundations, Santilli (Refs. [12,14]) noted that the above generalized dynamical equations are *non-unitary* by conception, yet they are elaborated via the mathematics of unitary theories. As such, they are afflicted by series inconsistencies, such as the lack of preservation over time of the base numeric field, inability to predict the same numerical values under the same conditions at different times, lack of preservation of Hermiticity over time, and have other "catastrophic" inconsistencies expressed by the following

*THEOREM I.3.1: Non-canonical or non-unitary theories elaborated via the mathematics of canonical and unitary theories (conventional fields, metric spaces, functional analysis, etc), respectively, are catastrophically inconsistent on mathematical and physical grounds.*

Consequently, Santilli had to embark in laborious studies for the construction of new mathematics capable of resolving the above inconsistencies for the isotopic and genotopic cases, that required the isotopies and, separately, genotopies of the totality of 20th century applied mathematics with no exclusion known to the author to avoid insidious inconsistencies.

The *invariant* formulation of Lie-Santilli isoTheory requires its elaboration via *Santilli IsoMathematics* here referred to the axiom-preserving generalization of *all* aspects of 20th century mathematics into a form admitting generalized multiplicative units I* as the inverse of the isotopic element T* of Eq. (10), I* = 1/T*, called *Santilli isounit*, with realizations of the type

(15a) I* = 1/T* = Π_{k=1,..,N} Diag. (n_{k1}^{2}, n_{k2}^{2}, n_{k3}^{2}) exp Γ_{k}(t, r, p, ψ, ...) > 0,

(15b) I* >> 1, T* << 1 ,

where, as one can see, the actual extended and deformable shape of the particles is represented by the n^{2}-quantities, irreversible non-Hamiltonian interactions are represented by the Γ's, and conventional potential interactions are represented with the Hamiltonian.

Since physical theories need to be formulated over a numeric field as a condition to conduct measurements, Santilli achieved in Ref. [7] of 1993 the isotopic lifting of conventional numbers n (real, compleX and quaternionic numbers) into *isonumbers* n* = nI* that verify the axioms of a field under the assumption of isoproduct (10) for generalized LEFT AND RIGHT unit (15).

Additionally, the achievement of invariance required Santilli to generalize the Newton-Leibnitz differential calculus into a generalized form first presented in memoir [8] of 1996 (see monographs [13] for detailed studies), today known as *Santilli's isoDifferential calculus* (IDC), wIth basic rules

(16a) d*r* = T*d(rI*) = dr + r TdI*,

(16b) ∂*f*(r*)/∂*r* = I* ∂f*(r*)/∂r*

where f* is an *isofunction* with structure f* = fI* as a condition for its value to be isonumbers. As one can see, the IsoDifferential calculus coincides with the conventional calculus for all isounits I* that are constant or independent from the differentiation variable, and this may explain the reason for the lack of detection of the IsoDifferential calculus for centuries until Santilli's seminal memoir [8] of 1996 (see also the mathematical studies [24]).

It should be recalled that *hadronic mechanics admits no divergences because of strongly convergent perturbation series under isounit (15),* thus providing an additional reason for the development of the theory. This is due to the fact that, in all applications, the value of Santilli's isounit has resulting to be much bigger than 1 and, consequently, the value of the isotopic element is much smaller than 1, Eqs. (15b). Therefore, perturbative expansions that are divergent (or weakly convergent) in quantum mechanics, becomes strongly convergent in hadronic mechanics,as in the case (see monographs [13,14] for detailed studies)

(17) A(w) = I* + w (AT*H - HT*A) / 1! + .... < ∞, w > 1, T* < < w.

Recall that the notion of *point-like particles* originated with Newton's equations because inherent in the local character of the differential calculus. The same notion was then adopted by Galileo, Einstein, Schrodinger, Heisenberg and the other founders of 20th century knowledge and eventually resulted in the limitations of quantum mechanics in nuclear physics indicated in Section I.2.

**I.5. The Newton-Santilli isoequations**

Perhaps the most important advance permitted by the novel isomathematics has been *the first known generalization of Newton's equations in about four centuries for the representation of the extended character of bodies, thanks to the isodifferential calculus with isounits of type (15).* This generalization is a necessary condition to admit contact non-potential interactions for bodies moving within physical media. The generalized equations were proposed for the first time by Santilli in memoir [8] of 1996, are today called *Newton-Santilli isoequations* and can be written in the form

(18) m*⊗d*v*/d*t* = F^{SA}(t*, r*, p*),

where SA stands for *variational selfadjointness* [6], namely, the verification of the conditions to admit a potential, in which case all non-potential forces are embedded in the isodifferential of the velocity by therefore admitting the representation via a variational principle, unique and unambiguous map of non-potential interactions to operator theories and other basic advances [13,14].

The potentially historical character of Eqs. (19) is that they are the first known to the authors achieving a consistent representation of *extended bodies* in mechanics, thus being the ultimate foundations of the representation of the extended nuclear constituents that, in turn are at the foundation of nuclear syntheses without harmful radiations.

**I.6 Invariance of hadronic mechanics**

The invariant formulation of santilli's Lie-admissible formulations require their elaboration via the broader *Forward and Backward GenoMathematics* that are characterized by two generalizations of all aspects of 20th century mathematics admitting the following forward and backward generalized multiplicative units at all levels

(19) I^{>} = 1/S*, ^{<}I = 1/R*,

each having realizations of the type (15). Additionally, genomathematics requires *forward and backward genofunctions, genofields and genodifferential calculi* [8] we cannot possibly review here for brevity.

*HyperMathematics* is the most general mathematics conceivable nowadays by the human mind characterized by the hyperformulation in terms of generalized operations of genounits (20) under the axioms of *Vougiouklis Hv-hyperstructures* [26]. Hypermathematics is particularly recommended for the study of biological structures and other systems of large complexity requiring, in general, multi-valued characterizations.

*Iso-, Geno- and Hyper-Mechanics and chemistry* [14] are branches of hadronic mechanics and Chemistry, respectively, and are characterized by the lifting of conventional mechanical and chemical theories via Iso-, Geno- and Hyper-mathematics, respectively, with realizations of the generalized units (15) verifying the condition

(20) Lim Γ_{r> 1fermi}= 1

as a result of which, by central conception, *hadronic mechanics and chemistry solely hold at mutual distances of particles of the order of 1 Fermi, while recovering conventional mechanics and chemistry for bigger distances.*

**I.7. Simple construction of hadronic mechanics**

For the limited mathematical needs of this workshop, it is sufficient to note that all needed isomechanical models can be easily constructed via the simple non-unitary transform of conventional quantum models [7,8]

(21a) UU^{†} ≠ I, A → A* = UAU^{†},

(21b) 1 → I* = UU^{†},

(21c) AB → A* T* B*, T* = (UU^{†})^{-1},

(21d) ) [A, B] → [A*, B*]*, etc.

The central Schrodinger-Santilli isoequation of isomechanics, Refs. (14), can then be constructed via a simple nonunitary transformation of the conventional Schrodinger equation

(22a) U(H |ψ)U^{†} = H* T* |ψ*) = U(E |ψ)U^{†} = E |ψ*),

(22b) U(ψ| A |ψ)U^{† = (ψ*| T* A T* |ψ*)
(22c) H* = UHU†, |ψ*) = U |ψ)U†}

where in Eq. (22b) one can see the new vacuum isoexpectation values of the iso-Hilbert space with isostates |ψ*). For the all crucial invariance over time of hadronic mechanics under additional non-unitary transforms identically reformulated as isounitary transforms, we refer the interested reader to memoir [10] or monograph [14].

Forward genomathematics, genomechanics and genochemistry can be constructed by subjecting the totality of conventional formulations, including all quantities and all their operations, to the dual non-unitary map [9]

(23) A → A* = WAZ^{†}, WW^{†} ≠ I, ZZ^{†} ≠ I, WZ^{†} ≠ I

under which

(24a) AB → W(AB)Z^{†} = A* > B*,
AB → Z(AB)W^{†} = A* < B*,

(24b) R* = (ZW^{†})^{†})^{-1}

(24c) [A, B] → (A*, B*)* = A*<B* - B*>A*.

Ref. [12] provides the latest account in the formulation of Lie-admissible theories and their invariance, while Ref. [26] provides their lifting into hyperstructures. Technical studies on Iso-, Geno- and Hypermathematics will be conducted at specialized ma mathematical meetings.

Following seminal works [1-5,6], Santilli conducted comprehensive mathematical, physical and chemical studies (see representative memoirs [7-9] and monographs [10-12]). Numerous scholars have contributed to the development of the new mathematics, among which I indicate H. C. Myung, M. L. Tomber, Gr. T. Tsagas, D. S. Sourlas, K. M. MacCrimmon, J. V. Kadeisvili, A. K. Aringazin, A. Kirhukin, R. H. Ohemke, G. F. Wene, G. J. Lohmus, E. L. Sorgsepp, D. B. Lin, J. V. Voujouklis, P. Broadbridge, P. R. Chernoff, J. Sniatycki, S. Guiasu, E. Prugovecki, C.X. Jiang, R. M. Falcon Ganfornina, J. Nunez Valdes, A. Davvaz, N. Lygeros, B. Davvaz, P. Nikolaidou, A. S. Muktibodh, N. Schmidt, R. Katebi, and others. Among the physicists who have contributed to the development and application of the new mathematics, I recall S. Okubo, S. Adler, J. Fronteau, A Tellez-Arenas, A. O. E. Animalu, J. A. Kobussen, Y. Ylamed, N. Salingaros, T. Giill, A. J. Kalnay, H. Rauch, G. Eder, P. Caldirola, R. Trostel, A. Schober, R. J. Slobodrian, J. Sun, A. de Wet, A. D. Jannussis, G. Brodimas, D. S. Sourlas, N. Salingaros, N. Tsagas, D. P. K. Ghikas, E. Kapushik, F. Rohrlich, J. Snyaticki, G. Cassinelli, G. Lochak, D. Y. Kim, J. Salmon, M. Grmela, E. Tonti, J. G. Gilson, V. K. Agrawala, W. H. Steeb, M. Mijatovich, R. Broucke, and others (see monographs [13-21], with comprehensive bibliography up to 2006 available in Volume I of Refs. [11] and update in ref. [21]).

A knowledge of hadronic mechanics and chemistry is necessary for the understanding of the lectures and discussions in this workshop, since they will be assumed as being known due to lack of time for their review.

**PART II: APPLICATION OF HADRONIC MECHANICS TO THE
SYNTHESIS OF THE NEUTRON FROM THE HYDROGEN ATOM**

**II.1. Historical notes**

H. Rutherford [27] proposed in 1920 the synthesis in the core of a star of the Hydrogen atom into a neutral particle he called the

*neutron*according to the reaction

(25) p^{+} + e^{-} → n.

J. Chadwick [28] confirmed in 1932 the existence of the neutron, but W. Pauli [29] indicated that the above reaction violates the quantum mechanical principle of conservation of the angular momentum.

Therefore, E. Fermi [30] conjectured that, jointly with the synthesis of the neutron, there is the emission of a particle he called *neutrino* (meaning "little neutron" in Italian) denoted with the symbol "ν" with spin 1/2 and null mass, according to the reaction

(26) p^{+} + e^{-} → n + ν,

by initiating the theory of weak interactions that eventually led to the current standard model of elementary particles.

R. M. Santilli [4-6] re-examined in 1978 synthesis (25) with the conclusion that Pauli and Fermi * did not* salvage quantum mechanics with the neutrino hypothesis because the rest energy of the neutron is 0.782 MeV *bigger* than the sum of the rest energies of the proton and of the electron

(27a) p^{+} + e^{-} → n + ν,

(27b) E_{p} = 938.272 MeV, E_{e} = 0.511 MeV, E_{n} = 939.565 MeV, E_{v} = ?

(27c) E_{n} - (E_{p} + E_{e}) = 0.782 MeV

under which conditions there is the need for a *positive binding energy* resulting in a *mass excess* that is anathema for quantum mechanics. In fact, all consistent quantum mechanical bound states require a "negative binding energy" resulting in the well known "mass defect". Under a "positive binding energy", Schrodinger's and Heisenberg's equations of quantum mechanics no longer admit physically meaningful solutions.

In particular, Santilli noted that the missing energy of 0.782 MeV cannot be supplied by the relative kinetic energy of the proton and the electron because, in this case, the cross section of electron-proton scattering is so small (of about 10^{-20} barns) to prevent any bound state.

Additionally, Santilli noted that the 0.782 MeV are *missing* in the neutron synthesis, thus requiring the hypothesis of a new particle *in the left hand side* of the reaction, rather than in the right hand side as per Pauli-Fermi's hypothesis. However, the reformulation of synthesis (25) with the anti-neutrino (here denoted ν^) in the left

(28) p^{+} + ν^ + e^{-} → n

does not allow a physically meaningful synthesis of the Hydrogen atom into the neutron on various counts, such as the fact that the cross section of the anti-neutrino and the electron or the proton is essentially null, anti-neutrinos are expected to have negative energy, thus *requiring* rather than providing energy for the synthesis, and other reasons.

**II.2. The birth of hadronic mechanics**

In view of the above insufficiencies, Santilli suggested the construction of *hadronic mechanics* as a covering of quantum mechanics for the specific purpose of achieving a consistent representation of the synthesis of the neutron from the Hydrogen atom as well as for hadrons at large. Already in 1978, it was clear that the achievement of a consistent representation of the neutron synthesis under data (27) required a *non-unitary* covering of quantum mechanics representing internal non-linear, non-local and non-Hamiltonian effects caused by the total penetration of the wavepacket of the electron within the hyperdense medium in the interior of the proton.

In Section 5 of the 1978 originating memoir [5], Santilli proved the validity of hadronic mechanics for the representation of *all* characteristics (and not solely the rest energy) of the π^{o} meson in its synthesis from the positronium (see also the review in Chapter 6 of Refs. [23,26]). However, as stated in the introductory comments of Ref. [5], the π^{o} meson has spin zero and, consequently, the study of its synthesis is not applicable to that of the neutron due to the Pauli-Fermi spin problem.

In this way, Santilli was forced to conduct comprehensive mathematical studies on the isotopies of Lie's theory [4-8] with particular reference to the isotopies of the rotational O(3), SU(2)-spin and Lorentz symmetries [9] as well as the study of numerous collateral aspects, including the experimental verification of hadronic mechanics in various fields (see Vol. IV of Ref. [14] or Chapter 5 of Refs. [23,25]).

Thanks to all these preparatory studies, Santilli finally achieved in 1990 [31] (see also the 1992 ICTP Communication [32] written during his visit to the *International Center for Theoretical Physics,* in Trieste, Italy, in summer 1992, following one of the last invitations issued by the late Abdus Salam) the non-relativistic representation of *all* characteristics of the neutron (and not only its mass) in synthesis (27).

In particular, one single non-unitary covering of the Schrodinger equation provided the exact representation of the neutron rest energy, mean-life, charge radius, while the spin and the anomalous magnetic moment of the neutron were represented in Ref. [31] via the IsoAlgebras O*(3) and SU*(2) (see also the excellent review by the late Jerdsay V. Kadeisvili [40]).

Santilli achieved the relativistic representation of the synthesis of the neutron from the Hydrogen atom in 1993 in the JINR Communication [33] (see its publication in ref. [34]) written during his visit to the *Joint Institute for Nuclear Research* in Dubna, written there in summer 1993, following systematic studies on the isotopies of Dirac's equation to represent the transition from the Hydrogen atom for large mutual distances to the neutron for mutual distances of the order of 1 Fermi.

**II.3. The dichotomy of classification vs structure of hadrons**

Perhaps, the biggest historical implication of the Pauli-Fermi hypothesis of the neutrino, and the inability by quantum mechanics to represent the synthesis the neutron from the Hydrogen atom inside stars, has been the restriction of particle physics to *one* single model for the representation of both, the *classification* of particles into families, as well as the representation of the *structure* of each individual hadron of a given family.

Santilli [5,36] accepts the SU(3)-color model as well as the standard model for the *classification* of particles into families, but rejects their joint representation of the structure of particles on numerous counts, such as:

1. As it was the case for nuclei, atoms and molecules, the classification and structure required *two* different, yet compatible models, one for the classification and one for the structure. For instance, we had first the Mendeleev classification of atoms into families and then the structure model of each atom of a given Mendeleev family. In particular, the transition from the classification to the structure required the transition from classical to quantum mechanics. Santilli contends that a similar dichotomy is needed for hadrons, especially for the development of new clean nuclear energies, including the generalization, this time, of quantum into hadronic mechanics due to large differences in physical conditions between classification and structure, such as point-particles in vacuum for the former and particles in conditions of total mutual penetration for the latter.

2. On strict technical grounds, quarks are purely mathematical representations of a purely mathematical unitary symmetry defined on a purely mathematical complex-valued space. As such, these representations are indeed necessary for the elaboration of the classification model, but Santilli does not accept that quarks are physical particles in our spacetime for various reasons, such as: the impossibility of the technical definition of quarks as particles in the Minkowski space due to departures from the Poincare' symmetry; the absence of a rigorous confinement of quarks due to the uncertainty principle; the inability by quark conjectures to represent the spin, anomalous magnetic moments and other features of hadrons; and other reasons. By contrast, the structure model with physical constituents in our spacetime according to hadronic mechanics, represents *all* characteristics of hadrons in a way compatible with the current classification [10,23,25] (see also below).

3. Even assuming that quarks exist as physical particles with a point-like charge (as necessary to maintain the validity of special relativity and quantum mechanics for the structure problem), Santilli contends that quarks cannot be consistently treated via quantum mechanics because, in his words, *there exist no point-like wavepackets in nature.* Since all hadrons have approximately the same size as that of wavepackets, a necessary condition to be hadronic constituents, is that the wavepackets of quarks must be in condition of total mutual penetration, resulting in the *hadronic medium,* namely, the medium, inside hadrons, which is the densest medium measured by mankind in laboratory to date. Under these conditions, we have the emergence of internal non-linear, non-local and non-Hamiltonian effects under which special relativity and quantum mechanics are inapplicable for numerous reasons. In any case, deviations from the predictions of special relativity and quantum mechanics within the hyperdense hadronic medium have been confirmed by the fit of all particle physics experiments without the a priori assumption of special relativity and quantum mechanics (see Vol. IV of Ref. [14], and Chapter 6 of Refs. [23,25]).

Participants of this workshop should be made aware of the fact that studies in the synthesis of the Hydrogen atom into the neutron herewith outlined are part of the new approach to particle physics consisting of the acceptance of the standard model for the *exterior* dynamical description of point-like particles in vacuum according to special relativity and quantum mechanics, and the *interior* dynamical description of the structure of individual particles according to hadronic mechanics under the condition for the latter to achieve compatibility with the former, as in fact done in Ref. [10] (see also Refs. [23,25]).

**II.4. Non-relativistic representation of the neutron mass, mean-life and charge radius.**

Santilli states: *I simply cannot accept that the permanently stable proton and electron "disappear" at the time of the synthesis of the Hydrogen atom into the neutron and certain hypothetical quarks "appear" by academic fiat and, then, at the time of the spontaneous decay of the neutron, certain hypothetical quarks "disappear" while the permanently stable proton and electron "reappear" again by academic fiat. Under these evident doubts, I have studied the most plausible hypothesis that the proton and the electron are actual physical constituents of the neutron in our spacetime, not in their conventional quantum mechanical states, but in generalized states due to the total penetration of the wavepacket of the electron within the hyperdense proton, for which I have suggested the names of "isoproton,"* here denoted p*, * and "isoelectron," * here denoted e*, * which new states are technically realized as irreducible isorepresentation of the Lorentz-Poincare'-Santilli isosymmetry. Hence, I have studied the representation of "Rutherford's compression" of the Hydrogen atom into a neutron inside a star via a non-unitary transform of the conventional structure of the Hydrogen atom* (HA)

(29) HA = (e^{-}_{↑}, p^{+}_{↓})_{qm} → U(e^{-}_{↑}, p^{+}_{↓})U^{†}
= (e*^{-}_{↑}, p^{+}_{↓})_{hm} = n, UU^{†} ≠ I,

where qm stands for elaboration via quantum mechanics and hm stands for elaboration via hadronic mechanics and its fundamental isosymmetries.

Note the assumption of one single non-unitary transform used for the regular isotopies of Lie's theory (rather than two non-unitary transforms as used for the covering Lie-admissible theory) because the synthesis of the neutron is reversible over time due to its spontaneous decay, thus requiring antisymmetric brackets, although with non-Hamiltonian internal effects represented by the Lie-Santilli isotheory.

The transition from protons p and electrons e in vacuum to their corresponding states p* and e* when in conditions of total mutual penetration is called a *mutation* according to terminology introduced in 1967 [1] and today fully appropriate in order to distinguish these studies from known deformations. Note also that the proton is about 2,000 times heavier than the electron. Therefore, Santilli assumes in model (29) that the proton is not mutated, and only the electron experiences a mutation.

Santilli then selects the following realization of the fundamental isounit (15)

(30) I* = 1/T* = UU^{†} = Diag. (1, 1, 1) exp{ [r e^{- r / R} / (1 - e^{- r / R})] ∫ e^{*-}_{up} x p^{+}_{down} d^{3}r} =

= exp{[|e) / |e*)] ∫ e*^{-}_{up} p^{+}_{down} d^{3}r},

where |e) and |e*) represent the wave-functions (in first approximation) of the electron in the Hydrogen atom and when immersed inside the proton, respectively. Note the emergence of non-linear, non-local/integral and non-Hamiltonian interactions represented by the isounit, exactly as desired.

By recalling representation (15) of the actual size and shape of particles via the n^{2}-quantities, note that in isounit (30) Santilli assumes that the proton charge distribution is perfectly spherical with radius of 1 Fermi abstracted to 1. The inclusion of the actual non-spherical shape due to the spin of the proton is expected to provide only contributions of higher order.

Note also that, by central assumption, the isounit recovers the unit for null values of the integral, that is, when there is no appreciable overlapping of the wavepackets of the electron and the proton. This implies that, by conception, excited states of the neutron recover conventional quantum states of the Hydrogen atom. Note finally that the value of the isounit I* = 1/T* is much bigger than 1, the value of the isotopic element T* is, consequently, much smaller than 1, and model (29) admit *no divergencies* with rapidly convergent perturbative series as in Eq. (17).

Via the use of the above non-unitary transform, Santilli maps the conventional Schrodinger equation of the Hydrogen atom into the isoequation (22) of hadronic mechanics (with h-bar = 1)

(31) H |e) = [(-1/m)∂_{k}∂_{k} - e^{2}/r] |e) = E |e) →

→ U[H |e)]U^{†} = U[(-1/m)∂_{k}∂_{k} - e^{2}/r] |e)U^{†} =

= [(-1/m)∂*_{k}∂*_{k} - e^{2}/r] (UU^{†})^{-1} |e*)

where m is the usual reduced mass, ∂* = I*∂ represents Santilli's isoderivative [16], and is the sum over the k-indices.

Under the approximation that the neutron is fully stable (since the 15 minutes mean-life is very large for particle standards), and therefore the orbit of the electron within the proton is stable, Santilli assumes that the isounit can be approximated into a constant. By replacing expression (30) into (31), we have

(32a) [- (1 / m') Δ + V_{Coulomb} + V_{Hulten}] |e*) =

= [- (1 / m') Δ - e^{2}/r - K e^{- r / R} / (1 - e^{- r / R}) ] |e*) = E' |e*),

(32b) m' ≈ m / | I*^{2}|

By reducing the above equation to the radial form and by adding the constraints for the 15 minutes mean-like and the charge radius of the neutron, we have the following *Santilli non-relativistic structure model of the neutron with physical constituents* first achieved in Ref. [390] of 1990

(33a) [(1/r^{2}(d/dr)r^{2}(d/dr) + (4 π^{2}m')(E + N e^{- r / R} / (1 - e^{- r / R}) ] |e*) = 0,

(33b) τ_{n} = 2 λ^{2} | e^{*}(0)|^{2} α E_{e*}/h = 10^{3} sec,

(33c) R_{n} = 10^{-13 } cm,

that do indeed admit physically and mathematically consistent solutions for the representation of the rest energy, mean-like and charge radius of the neutron we cannot possibly review here for brevity (see Ref. [30] with first detailed solutions available in Section 5 of Ref. [5] and reviews [23,25]).

The following comments are here in order. The conventional Coulomb potential of the Hydrogen atom is absorbed in Eq. (33) by the Hulten potential since it is known to behave like the Coulomb potential at short distances, said absorption merely implying a shift of the constant N; the Coulomb binding energy is ignored in first approximation because much smaller than the Hulten binding energy; and the solution for the rest energy of the neutron is given by

(34) E_{n} = E_{p} + E_{e*} - | E' | = 939 MeV, E_{e*} = 1.293 MeV, E' ≈ 0.

Non-expert in the field should not be surprised at the fact that E' ≈ 0 because we are dealing with a binding mechanism caused by contact interactions that, as such, have *no* potential energy by assumption.

Figure 6. |

*finite*number of energy levels. Intriguingly, Eqs. (33) admit one and only one energy level, the neutron, since all excited states imply the transition from hadronic to quantum mechanics. Hence, the excited states of the above structure model of the neutron are given by the conventional states of the Hydrogen atom (Fig. 6).

Santilli calls this single energy level the *hadronic mass spectrum suppression* to emphasize the transition from the *classification* of hadrons where a mass spectrum is indeed needed, and the *structure* of individual hadrons preventing the joint study of different hadrons. In fact, when the hadronic constituents are assumed as being physical particles in our spacetime generally produced in the spontaneous decays with the lowest mode, different hadrons have emerged as having different constituents and, therefore, different structures [10,23,25].

It is important to identify the mechanism used by Santilli for the achievement of a consistent synthesis of the neutron and appraise its implications for particle physics for discussions at this workshop. Recall that the missing energy of 0.782 MeV cannot be provided by the relative kinetic energy of the proton and the electron when dealing with quantum mechanics, that is, when the proton and the electron are assumed as being point-like particles.

Note that the crucial consistency of model (33) is due to the increase of the value of the electron energy of the electron, from 0.511 MeV to 1.293 MeV (see also Eq. (32b)), which is called *mass isorenormalization* to stress that we are not dealing with a conventional renormalization. The new isorenormalization was fully identified by Santilli in the originating memoir [5], Section 5, Eq. (5.11.4a), p. 836 (with the notation ρ for I*).

This new isorenormalization is inherent in all non-unitary coverings of quantum mechanics or, equivalently, whenever considering dynamics of extended particles or wavepackets within physical media, and it is today technically and invariantly treated via the transition from the Lorentz-Poincare' symmetry to the covering Lorentz-Poincare'-Santilli isosymmetry [9].

Discussions are invited at this workshop on the implications of Santilli's mass isorenormalization for all high energy scattering processes since they all imply a hyperdense scattering region in which special relativity and quantum mechanics cannot be consistently defined, let alone directly tested. Specifically, an open problem suggested for discussions at the workshop is whether the Higgs boson should or should not be subjected to Santilli's mass isorenormalization.

**II.5. Non-relativistic representation of the neutron spin**

Santilli's main contentions for the representation of the spin of the neutron are the following [31] (Fig. 7):

I. Under quantum mechanical treatment, the proton is a massive point in which case Pauli and Fermi had no other option than that of conjecturing the existence of the hypothetical neutrino. However, when the proton is represented as it is in nature, i.e., as an extended particle permitted by the covering hadronic mechanics, there is the emergence of the *orbital* motion of the electron within the proton which is completely absent in the quantum treatment.

Figure 7. |

III. As it is well known, half-odd-integer angular momenta are known to be impossible for quantum mechanics (they violate causality). However, it is easy to see that half-odd-integer angular momenta M are fully admitted by hadronic mechanics thanks to the new degrees of freedom offered by the three-dimensional isounit of the Lie-Santilli O*(3) isosymmetry [31].

It then follows that *the total angular momentum of the isoelectron is null and the spin 1/2 of the neutron coincides with that of the proton*

(35) J_{n} = J_{p} - J_{e*} + M_{e*} = J_{p}, J_{e*} = M_{e*} = 1/2, J^{tot}_{e*} = 0.

For details on the derivation via the Lie-Santilli isoalgebras O*(3), we refer for brevity to Ref. [31] or reviews [23,25,48].

**II.6. Non-relativistic representation of the neutron magnetic moment**

A notorious insufficiency of the standard model, as well as of quantum mechanics at large for the structure of hadrons, is the inability to represent the anomalous magnetic moment of the neutrons as well as of hadrons at large.

Santilli contends that this insufficiency is due to the to the representation of the the proton as a massive point, in which case quantum mechanics can solely use the conventional magnetic moments of the proton and the electron, resulting in deviations between the prediction of the theory and experimental data.

However, when the proton is represented as an extended particle, the exact representation of the anomalous magnetic moment of the neutron is simple and immediate, because the missing contribution is the magnetic moment of the *orbital* motion of the electron inside the proton.

Simple calculations then yield the exact representation first achieved in Ref. [31] of 1990 (see reviews [23,25,48])

(36a) μ_{n} =
μ_{p} + μ_{e*,Intrinsic} - μ_{e*,Orbital} = -1,913 μ_{N},

(36b) μ_{p*} = μ_{p} = + 2.793 μ_{N},
μ_{e*} = μ_{e} = - 1.001 μ_{B} = 1,837.987 μ_{N}, μ_{p} + μ_{e*} = 1,835 μ_{N},

(36c) μ_{e*Orbital} = +1.004 μ_{B}, μ_{e*Total} = 3 x 10^{-3} μ_{B}, μ_{n} = -1,913 μ_{N}.

This completes our review of Santilli's non-relativistic representation of the neutron characteristics. Note that the small value of the total magnetic moment of the isoelectron is fully in line with the small value of its total angular momentum (that is null only in first approximation due to the assumed lack of mutation of the proton).

**II.7. Relativistic representation of the synthesis of the neutron from the Hydrogen atom**

Of course, the non-relativistic representation of the neutron synthesis was merely preparatory to the full relativistic treatment on which Santilli conducted comprehensive studies over three decades, including: the isotopies of Lie's theory [4-6]; the geometrization in 1983 [37] of inhomogeneous and anisotropic physical media via the isotopies of the Minkowskian spacetime with conventional metric η = Diag. (1, 1, 1, -1) and isotopic line element

(37a) x*^{2} = x^{μ}T*_{μ}^{ρ} η _{ρν} x^{ν} = x^{μ} η*_{μν} x^{ν} ,

(37b) η * = T*η , I* = 1/T*, μ, ν, ρ = 1, 2, 3, 4;

its universal isosymmetry achieved in the same 1983 paper [37]; the isotopies of all aspects of the conventional Poincare' symmetry resulting in the *Lorentz-Poincare'-Santilli isosymmetry* [9]; the isotopies of Galileo's and Einstein's special relativities [38]; the isotopies of the Minkowski geometry [39]; and the study of other aspects (see monographs [13] for comprehensive treatments).

Following these preparatory studies, Santilli proposed in Refs. [33,34] of 1993 the isotopies of the spinorial covering of the Poincare' symmetry, and then the isotopies of Dirac's equation, today known as the *Dirac-Santilli isoequation* that we write in the form

(38a) [γ*^{μ}(p*_{μ} - ieA_{μ}) - (imc)*] T* |e*) = 0,

(38b) γ*^{μ} = U_{4x4}γ^{μ}U^{†}_{4x4},

(38c)
γ*^{μ} T* γ*^{ν} + γ*^{ν} T* γ*^{μ} = η*^{μν}

where the γ* are called the *Dirac-Santilli isogamma matrices.*

Eqs. (38) are based on the isotopies of the four-dimensional Minkowski spacetime for the orbital motion and the isotopies of the two-dimensional unitary space for the spin, with related fundamental isounits

(39a) I*_{orb} = 1/T*_{orb} = Diag. (n_{1}^{2}, n_{2}^{2}, n_{3}^{2}, n_{4}^{2}) = U_{4x4} U^{†}_{4x4},

(39b) I_{spin} = 1/T_{spin} = Diag. (s_{1}^{2}, s_{2}^{2}) = U_{2x2} U^{†}_{2x2}.

Eq. (38a) permitted Santilli to achieve the relativistic, invariant, and exact representation of *all* characteristics of the neutron in its synthesis from a Hydrogen atom inside a star, and not solely the representation of the mass via a mass spectrum linked to other hadrons according to quark conjectures.

Note the remarkable appearance of the isometric η* of the Minkowski-Santilli isospacetime, Eqs. ( 33), in the isoanticommutators of the γ* matrices, thus confirming the deep interconnection between geometry and dynamics that exists at the conventional level and persists in full under isotopies.

Figure 8. |

The most important outcome of the model is that *a necessary condition for the exact and invariant relativistic representation of the synthesis of the neutron from the Hydrogen atom inside a star is that the isoelectron must orbit with a tangential superluminal speed.* In fact the fit of all characteristics of the neutron requires that the isoelectron tangential speed is given by

(40) V_{e*} = c/n_{4} > c, n_{4} = 0,605.

There is no violation of special relativity here because such a theory cannot be even defined within the hyperdense medium inside the proton. Additionally, the speed limit c set by special relativity solely holds for point-like particles moving in empty space under action-at-a distance interactions derivable from a potential energy.

These special relativity conditions are inapplicable for the speed of the isoelectron inside the proton because, in this case, the particle is accelerated by contact interactions having no potential energy under which the maximal causal speed is arbitrary, as anticipated by Santilli since 1981 [40], now characterized by the Lorentz-Poincare'-Santilli isosymmetry, and verified in all fits of particle experiments without the a priory assumption of relativistic quantum mechanics (Vol. IV of Refs. [14 and Chapter 5 of Refs. [23,25]).

Note incidentally that maximal causal speed (40) is referred to a particle with *real mass* in spacetime. As such, *the isoelectron is not a tachyon.* For interior conditions, Santilli has introduced the notion of *isotachyon* with imaginary mass which is a hypothetical particle outside the interior light cone with speed bigger than the local maximal causal speed (see monographs [13] for technical treatments).

**II.8. Santilli etherino**

As indicated earlier, under the a priory assumption of the exact validity of quantum mechanics and the consequential approximation of the proton as a massive point, the Pauli-Fermi *emission* at the time of the synthesis of the neutron from a proton and an electron is unavoidable, to our knowledge.

However, Santilli contends that, when the proton is represented with its actual extended dimensions thanks to the covering hadronic mechanics, the missing energy of 0.782 MeV and the structure equations of the neutron offer no possibility of identifying additional energy for the creation of the hypothetical neutrino. Additionally, under the indicated conditions, the emission of the neutrino would *violate,* rather than verify, the conservation of the total angular momentum due to the necessary emergence of a constrained angular momentum of the isoelectron when immersed inside the hyperdense proton.

Figure 9. |

However, when nuclei and their constituents are represented via the covering hadronic mechanics, the bell-shaped behavior of the energy of the emitted electron is easily explained as being dependent on the direction of emission of the electron because of the dependence of its energy on the *attractive* Coulomb interaction between the electron and the nucleus, resulting in an energy emission which is maximal for the radial emission and minimal for the tangential one.

In summary, while working on the synthesis of the neutron from a proton and an electron, Santilli was forced to dismiss the Pauli-Fermi hypothesis of the neutrino as a physical particle in our spacetime. In his words: *I was quite embarrassed in writing my papers of the 1990s on the structure of the neutron because, on one side, my devotion for my mentors Pauli and Fermi forced me to maintain the presence of the neutrino in the r.h.s. of the reaction while, on the other side, I knew that the emission of the neutrino was inconsistent with the fusion process.*

Santilli further states: *I had a reverence for the original Pauli-Fermi hypothesis of "one" neutrino and "one" anti-neutrino. However, I simply cannot accept the recent series of implausible neutrino conjectures ventured for the specific intent of maintaining the validity of the standard model for all of particle physics, such as: first, the multiplication of neutrino into three different particles without well identified physical distinctions; then the further multiplication of neutrinos due to color, again, without clearly identified physical distinctions; then the conjecture that these neutrinos have mass; then the conjecture that they "oscillate"; and so on. Under such a chain of far reaching conjectures, I simply cannot accept that the hypothetical numerous neutrinos and anti-neutrinos exist as physical particles in our spacetime.* Hence, Santilli was forced to search for an alternative to the neutrino hypothesis.

Following decades of studies of the problem, Santilli's main contention is that the missing energy of 0.782 MeV cannot originate from the interior of a star because, at the initiation of the production of light, small stars synthesize from the primordial Hydrogen atoms about 10^{30} neutrons *per second* with bigger stars synthesizing neutrons at the rate of up to 10^{50} per seconds. Santilli contends that, in the event the missing energy originates from their interior, stars would never initiate producing light because they would *lose* from 10^{30} to 10^{50} MeV *per seconds,* thus becoming cold.

As indicated earlier, in the event the missing energy is provided by the relative kinetic energy between protons and electrons, their synthesis is rendered impossible by the extremely low value of the cross section of their scattering, while hypothetical neutrinos cannot possibly be the source of the missing energy due to their virtually null cross section with protons and electrons.

Santilli agrees with Pauli and Fermi on the need for a third unknown particle in the synthesis of the Hydrogen atom into the neutron. However, he contends that the primary function of this particle is to *supply the missing energy,* without any need for a contribution to the spin. Also, the missing particle should appear in the *left hand side* of the reaction, rather than in its right hand side as per Eq. (26).

In view of the above aspects, Santilli has submitted in Ref. [41] of 2007 the hypothesis of the *etherino* represented with the symbol "a" (from the Latin "aether") delivering the missing 0.782 MeV energy to the proton and the electron according to the reaction

(41) p^{+} + a + e^{-} → n.

In particular, the etherino is *not* suggested to be a particle, but rather a *longitudinal impulse* originating from the ether as a universal substratum with extremely high energy density for the characterization and propagation of electromagnetic waves as well as particles.

Santilli contends that, contrary to a rather popular belief, the ether as a universal substratum *does not* cause any violation of Einstein special relativity in vacuum because the absolute reference frame hypothetically at rest with the universal substratum cannot be identified in our laboratory.

Participants to this workshop should keep in mind the remark of Ref. [41] that the Hilbert space of quantum mechanics *cannot* represent exchanges of energy between the ether and our world, while such exchanges are indeed quantitatively representable via the covering iso-Hilbert space of hadronic mechanics.

Figure 10. |

Yet an additional aspect to be discussed at the workshop is the contention that an energy input from the ether is needed for stars not only at their initiation of production of light, but also at the time of their death, because nuclear syntheses are insufficient to represent the immense energy of supernovae by a factor believed by some to be of about 1,000,000 for the very reason that, at the time of the supernovae explosions, all primary nuclear syntheses have been exhausted by central assumption.

A further suggestive aspect open for discussion at the workshop is *Santilli's revival of the steady state cosmology with continuous creation of matter* which is implicit in the etherino hypothesis, especially when combined with recent experimental evidence that the universe is not expanding [42].

Figure 11. |

**II.9. Laboratory synthesis of the neutron from a Hydrogen gas**

The first laboratory synthesis of the Hydrogen atom into the neutron was conducted in 1965 by the Italian priest-physicist Don Carlo Borghi (Fig. 10) and his colleagues and published later on in Refs. [43,44]. With reference to Fig. 11, a klystron was filled up with Hydrogen gas, maintained in its ionized state by an electric discharge and traversed by a microwave. The klystron was surrounded by fissionable substances that apparently showed nuclear transmutations following several hours of operation.

With reference to Fig. 12, the laboratory synthesis of the neutron was confirmed by Santilli [45-47] in 1997 via the use of a klystron with transparent walls (to visually assure proper internal events) filled up with a Hydrogen gas and solely exposed to a 10 kW DC arc between internal Tungsten electrodes. Three different neutron detectors were placed in the vicinity of the klystron. Apparently, the tests confirmed that a particle with zero charge and the dimension of the order of 1 Fermi (as necessary to traverse walls) had apparently been produced inside the klystron.

Figure 12. |

** II.10. The hypothesis of the neutron**

Both Don Borghi and Santilli agree that the emitted particle is not necessarily the neutron, but an intermediate state with the mass, size and charge of the neutron but zero spin, called *neutron* and denoted with the symbol ñ. Santilli reported that unequivocal detections of true neutrons by all three neutron detectors occurred only under the addition of special events he called "triggers", e. g., when the Hydrogen was contaminated with air resulting in an explosion at the activation of the electric arc.

In fact, Santilli had to evacuate the lab three different times when testing with the indicated trigger due to all neutron detectors entering into maximal sonic and vibrational alarms (see Fig. 13)

Figure 13. |

** II.11. The apparent new class of nucleoids**

Santilli [45-47] has reported cases in which neutron detectors showed no signal following the activation of the arc in the klystron, but clear detections did occur later on when the detectors were at large distance from the klystron. In one case, Santilli reported that the neutron detector manufactured by Polimaster entered into sonic and vibrational alarm, about 15 minutes following its exposure to the operating klystron while being miles away from the klystron.

The sole rational explanation of this occurrence is that the experimental set up produced neutroids ñ, rather than neutrons n, which was absorbed by the nuclei of the plastic casing of the detector that, as such, became unstable with a mean-life of about 15 minutes. Therefore, Santilli submitted the following:

*HYPOTHESIS II,11: In addition to the well known class of tabulated nuclides, there exists an additional class of anomalous nuclides, submitted with the name of nucleoids, characterized by the absorption of a neutroid ñ by a conventional nuclide N according to the reaction (where A is the atomic number, Z the nuclear charge, J the spin, and M the mass)*

(42) N(A, Z, J, M) + ñ(1, 0, 0, 1.008) ⇒ N^{*}(A + 1, Z, J, M + 1.006).

The study of Santilli's apparent new class of nucleoids is an important task of this workshop due to their evident relevance for new nuclear energies.

**PART III: APPLICATION OF HADRONIC MECHANICS FOR THE
REDUCTION OF MATTER TO PROTONS AND ELECTRONS**

**III.1. Implications of the neutron synthesis**

It is evident that the reduction of the neutron to a generalized bound state of one proton and one electron implies that all nuclei and, therefore, all matter at large, are solely composed of protons and electrons under the covering laws of hadronic mechanics.

In particular, the exact representation of all characteristics of the neutron in its synthesis from the Hydrogen atom via the Dirac-Santilli isoequation outlined in Part II establishes the validity for the nuclear structure of the covering *Lorentz-Poincare'-Santilli (LPS) isosymmetry* [9] according to which, when constituents of a nucleus, protons and electrons are not the same as when member of the Hydrogen atom but are mutated by their wave overlapping into forms technically described by irreducible isorepresentations of the LPS isosymmetry, are called *isoprotons* and ^{+} and e*^{-}, respectively.

Needless to say, the conception of nuclei as quantum mechanical bound states of protons and neutrons remains indeed valid, but only as a first approximation. The nuclear structure most important for nuclear syntheses is the deeper conception of nuclei as bound states of isoprotons and isoelectrons under the covering laws of hadronic mechanics.

The technical understanding of the conception, mathematical treatment and engineering realization of nuclear syntheses without radiations requires a technical knowledge of the notions of isoprotons and isoelectrons as nuclear constituents and a technical knowledge on their novel NSA interactions.

**III.2. The Deuteron as a three-body system**

According to a widespread belief for about one century, the Deuteron D is a *two-body system* consisting of a quantum mechanical (qm) bound state of one proton and one neutron

(43) D = (p^{+}, n)_{qm}.

The reduction of the neutron to one isoproton and one isoelectron implies instead that the Deuteron is a *three-body system* composed by the bound state of two isoprotons and one isoelectron under the the covering hadronic mechanics (hm) illustrated to Fig. 14,

(44) D = (p*_{1}, e*, p*_{2})_{hm}.

Figure 14. |

**III.2A. Deuteron spin**

For model (43), quantum mechanics requires that the proton and the neutron are coupled in singlet to avoid the large repulsive forces existing for triplet couplings at short mutual distances. Under these conditions, the sole possibility to represent the spin 1 is that the Deuteron consists of a kind of continuous, hypothetical, excited state with orbital angular momentum 1.

In turn, this hypothetical excited state implies the lack of existence of true ground states in nuclear structures with a number of inconsistencies, such as the violation of the principle of conservation of the energy due to the lack of identification of the energy needed to maintain a continuously excited state angular momentum 1.

Figure 15 |

Fig. 15 depicts the "gear model" introduced by Santilli since the original memoir [5] of 1978 to illustrate the only possible stable couplings of three spinning particles when in conditions of mutual penetration, by therefore confirming the direct and invariant representation of the Deuteron spin 1 in a ground state with null angular momentum which is absent for model (43).

**III.2B. Deuteron magnetic moment **

Model (43) and underlying quantum mechanics have prohibited the achievement of an exact representation of the magnetic moment of the Deuteron for about one century. In fact, following all possible relativistic corrections as well as the use of the hypothetical assumption that the Deuteron is composed by six conjectural quarks, quantum mechanics still misses about 1% of the Deuteron magnetic moments.

Assuming that a representation of the magnetic moment of the Deuteron is reached via manipulations, such as the use of arbitrary functions fitted from the data, embarrassing deviations exist between the predictions of quantum mechanics and the experimental data on magnetic moments for large nuclei.

Let us recall the following experimental values on magnetic moments

(45a) μ_{p} = 14.106067 μ_{N}, μ_{n} = -9.66236 μ_{N},

(45b) μ_{D} = 4.3307346 μ_{N},

(45c) μ_{e} = -9284.764 μ_{N}, μ_{N} = 10^{-27} JT^{-1}

It is then easy to see that model (43) *cannot* achieve an exact representation of the magnetic moment of the Deuteron because quantum mechanics is incompatible with the deformation theory. As a result, the proton and the neutron are considered to be perfectly rigid, thus preserving the value of their magnetic moment when members of a nuclear structure.

By contrast, hadronic mechanics has been constructed from its foundations, the Lie-Santilli isotheory theory in general and the isorotational symmetry in particular [13b], to be compatible with the deformation theory precisely to represent expected deformations of the charge distributions of protons and neutrons when members of a nuclear structure. This objective is achieved via the central element of the hadronic mechanics, Santilli isounit (15), whose space components n_{k2 are functions representing variable semi-axes of charge distributions depending on the conditions at hand,}

(46) I* = 1/T* = Π_{k=1,..,n} Diag. (n_{k1}^{2}, n_{k2}^{2}, n_{k3}^{2}).

But a deformation of a spinning charge distribution is known to imply a mutation of its magnetic moment. Therefore, the exact representation of nuclear magnetic moment is reduced to the identification of the deformation of the charge distribution of protons and neutrons when members of a nuclear structure [11].

When the Deuteron is considered as being in first approximation to be a bound state of a proton and a neutron, 1% deformation of their charge distribution is sufficient to achieve a numerically exact and invariant representation of the Deuteron magnetic moment, first achieved by Santilli in Ref. [57] of 1994 when visiting the JINR in Dubna, Russia, and then extended to all nuclei in details in memoir [11].

(47) μ_{D} = μ_{p*} + μ_{n*} = 4.3307346 μ_{N}

When the Deuteron is considered more realistically as being the three-body structure of model (44), besides the deformation of the charge distribution of the proton into the isoproton, we have the additional contribution of the magnetic moment of the isoelectron. The ensuing exact representation of the magnetic moment of the Deuteron when in its ground state then holds according to the law

(48) μ_{D} = 2 μ_{p*} + μ_{e*, tot} = 4.3307346 μ_{N.}

It should be indicated that the assumption of the Deuteron as being composed by six hypothetical quarks does not allow the exact representation of the magnetic moment of the simplest nucleus, let alone of larger nuclei, because the hypothetical orbits of the hypothetical quarks are so small to prevent meaningful magnetic contributions from their polarization.

For detailed elaborations, see the above quoted Ref. [13]b] on the study of the isorotational symmetry, and Refs. [57,13,50] for the exact and invariant treatment.

**III.2C. Deuteron binding energy **

Recall that, boeing based on the conventional Lie theory, quantum mechanics is a purely Hamiltonian theory in the sense that the sole admitted forcers are those derivable from a potential. The direct and immediate consequence is then the impossibility of a *quantitative* representation of the deuteron binding energy

(49) E_{D} = - 2.26 MeV.

that is, a *representation via equations,* rather than via the existing epistemological arguments.

Said impossibility is compounded by the fact that the mathematics underlying quantum mechanics, being local-differential, can only represent the proton and the neutron of model (43) as being *point-like particles.* Under these approximations, quantum mechanics admits no binding energy at all for the Deuteron, including the absence of binding energy of Coulomb type, because the neutron is abstracted as a neutral massive point.

On rigorous scientific grounds, the lack of a quantum mechanical binding energy for the Deuteron persists even under the assumption that the Deuteron is composed by six hypothetical quarks because attractive and repulsive contributions between the hypothetical quarks of the proton and those of the neutron cancel out, resulting in no force at all between the proton and the neutron, irrespective of whether attractive or repulsive.

Model (44) under the covering laws of hadronic mechanics has permitted the achievement of the first quantitative representation of the binding as well as the total energy of the Deuteron in scientific history, thus illustrating the validity of Santilli's original proposal of 1978 [5] to build the covering hadronic mechanics.

Let us consider first model (43) under the laws of hadronic mechanics. This means that, in first approximation, the Deuteron is a bound state of one isoproton and one isoneutron,

(50) D = (p*, n*)_{hm.}

The most important feature of the above model is that it implies the necessary emergence of *contact interactions,* namely, interactions without any potential energy, whose sole representation invariant over time (as a condition to predict the same numerical values under the same conditions at different times) is that via Santilli fundamental isounit (15), i.e.,

(51) I* = 1/T* = Π_{k=1,..,2} Diag. (n_{k1}^{2}, n_{k2}^{2}, n_{k3}^{2}) exp Γ_{k}(t, r, p, ψ, ...) > 0.

Consequently, *hadronic mechanics can represent the binding energy (49) of the Deuteron in its first approximation (50) even in the absence of any potential interaction.*

In fact, the structure equations of the Deuteron for model (50) are given by the Schrodinger-Santilli isoequation for isounit (51) with input values given by the deuteron binding energy (49), infinite mean-life (stability) and charge radius (where h = h-bar)

(52a) [(1/r^{2}(d/dr)r^{2}(d/dr) + (4 π^{2}m*)(E + N e^{- r / R} / (1 - e^{- r / R}) ] |ψ*) = 0,

(52b) E_{D} = - E = - 2.26 MeV,

(52c) τ_{D} = 2 λ^{2} |ψ*(0)|^{2} α E_{e*}/h → ∞,

(52d) R_{D} = R = 1.41 x 10^{-13 } cm,

(52e) m* = m/\I*2|.

The best solution of the above equations with boundary conditions remain Santilli's 1978 original solution given in Ref. [5] of 1978, Section 5. This solution applies for Eqs. (52) yielding the desired first quantitative representation of the Deuteron binding energy, stability and charge radius via one single structure equation.

A first important feature of the solution of Eqs. (52) is the *isorenormalization of the mass,* Eq. (52d), where m is the reduced mass for model (43). This feature is inherent in non-potential interactions and technically originates from the lifting of the Lorentz symmetry into the Lorentz-Santilli isotopic covering [9].

The implications of the hadronic isorenormalization are rather serious because it implies that masses of intermediate particles predicted by quantum mechanics, such as the conventionally believed mass of the Higgs boson, are not necessarily the actual masses whenever said masses occur within hyperdense media, such as those in the structure of hadrons, nuclei, stars as well as high energy interacting regions.

A second important feature of Eqs. (52) is the *admission of only one state, the Deuteron,* because the contact interactions originating the structure, Eq. (51), are null for mutual distances of the isoproton and the isoneutron bigger than the range of the nuclear forces, 1 fm, at which distances bound state (50) reduces to a free proton and a free neutron.

The above feature is permitted by the finite number of energy levels admitted by the Hulten potential that are reduced to one for the assumed values (52b), (52c) and (52d). The feature was called by Santilli in Ref. [5] *mass spectrum suppression* and was indicated as being necessary for the consistency of structure models of hadrons and their bound states. Hence, the analytic confirmation of the suppression of the mass spectrum by Eqs. (52) is important for the very consistency of the model.

The extension of model (50) to the full three-body model (44) is an instructive exercise for readers interested in learning new sciences. The problem is significant since the three-body model (44) admits exact analytic solutions under the approximation of being a reduced three-body system (much similar to the structure of the Hydrogen molecule indicated in Part IV).

**III.2D. Deuteron stability**

For model (43), there has been no known possibility to represent the stability of the Deuteron since the neutron is naturally unstable and no mechanism has been identified to our knowledge that turns the neutron into a stable state when a member of the Deuteron.

For model (44), the representation of the stability of the Deuteron is direct and immediate since protons and electrons, whether in the r conventional or mutated state, are the only massive permanently stable particles existing in nature. Hence, the reduction of the unstable neutron to the permanently stable isoproton and isoelectron provides a direct and immediate interpretation of the stability of the Deuteron which is basically absent for quantum mechanics.

It is rewarding to see that, besides the above considerations, the stability of the Deuteron is analytically represented in Eqs. (52) via value (52c).

**III.2E. Deuteron charge radius**

The quantitative representation of the size of the deuteron is also not possible for quantum mechanics without often used adulterations because of the assumption that the Deuteron is in a kind of permanent excited state with angular momentum 1, under which the mutual distance of the proton and neutron is necessarily bigger than value (52d), as the serious scholar can independently verify.

It is rewarding to see that the charge radius of the Deuteron is analytically represented by the solution of Eqs. (52), Eq. (52d) in particular.

**III.2F. Deuteron electric dipole moment and parity**

The electric dipole moment of the proton, neutron and Deuteron are null according to current knowledge. The preservation of these values by hadronic mechanics is assured by the general property that axiom-preserving liftings preserve the original numeric values, and the same holds for parity (see Ref. [13b] for details).

**III.2G. Deuteron charge **

At a first glance, model (44) trivially represents the Deuteron positive charge +e. However, a quantitative representation of the charge of the Deuteron is not trivial at a deeper inspection. This is due to the fact that hadronic mechanics implies the isorenormalization of all intrinsic characteristics of particles, thus including the mutation of the charge Q → Q*.

Therefore, the representation of the charge +e of model (44) requires the study of the isorenormalization of the charges of all three constituents

(53) Q_{D} = Q*_{p*1} + Q*_{e*} + Q*_{p*2} = + e,

which is expected to be possible since, by conception, isorenormalizations are purely internal effects not detectable outside dense hadronic media. This study is left as an instructive exercise for the interested reader.

In closing we should indicate that the structure of the Deuterium *atom* should be solely treated via *quantum* (and not hadronic) mechanics (because all non-potential effects are null at atomic distances).

**III.2H. Nuclear forces **

By far, the most important contribution of hadronic mechanics in nuclear physics is a deeper understanding of the nuclear force.

Santilli has indicated his * distress* caused by the inability of quantum mechanics in about one century of attempts to reach a representation of the nuclear force compatible with experimental data. Quantum mechanics is strictly Hamiltonian, thus solely admitting potential interactions. Since various initial potentials turned out to be insufficient to represent nuclear forces, additional potentials in the Hamiltonian of nuclear models were added with the passing of time, by recently reaching a disproportionate number of potentials of the type one can see in recent nuclear physics papers

(54) H = p^{2}/2m + V_{1} + V_{2} + V_{3} + V_{4} + V_{5} + V_{6} + V_{7} + V_{8} + V_{9} + V_{10} +

+ V_{11} + V_{12} + V_{13} + V_{14} + V_{15} + V_{16} + V_{17} + V_{18} +

+ V_{19} + V_{20} + V_{21} + V_{22} + V_{23} + V_{24} + V_{25} +

+ V_{26} + V_{27} + V_{28} + V_{29} + V_{30} + V_{31} + V_{32} +

+ V_{33} + V_{134} + V_{35} + ...

Hadronic mechanics has terminated this endless addition of potentials, and represented nuclear forces via the Coulomb potential V_{Coul} for all electric and magnetic interactions between isoprotons and isoelectrons, and the contact interactions of type (15), resulting in the *hadronic representation of nuclear forces*

(54a) H = Σ_{k=1,...,N}p^{2}_{k}/2m + V_{k, Coul},

(54b) I* = 1/T* = Π_{k=1,..,N} Diag. (n_{k1}^{2}, n_{k2}^{2}, n_{k3}^{2}) exp Γ_{k}(t, r, p, ψ, ...) > 0.

As an illustration, the celebrated "exchange potential" is indeed necessary for a quantum mechanical representation of the nuclear forces under the assumption that protons and neutrons can change one into the other. Hadronic mechanics can actually provide the still missing quantitative interpretation of such an exchange which is merely given by the isoelectron in Fig. 14 passing from one isoproton to the other.

However, at the full level of hadronic mechanics, the "exchange potential" has no mathematical or physical meaning because isoprotons and isoelectrons are permanently stable when members of a nuclear structure. Therefore, there is no possibility of exchanging isoprotons with isoprotons, or isoelectrons with isoelectrons, or isoprotons with isoelectrons, and this illustrates the absence of "exchange potentials" in the representation of the nuclear force of Eqs. (54). The occurrence also illustrates that the "exchange potential" used for about one century in nuclear physics are purely mathematical since there is no actual
"potential energy" that can be rigorously associated with the exchange.

According to the above view, *the strong nuclear forces are entirely of contact, non-potential character* as invariantly represented in Eq. (54), since the remaining forces, (those of Coulomb type) are repulsive. As indicated in Part V, this novel conception of the nuclear forces allows the conception and engineering realization of a variety of novel nuclear applications, including new syntheses without radiations, new mechanisms for the stimulated disintegration of radioactive nuclear waste, and other applications depending on the appropriate understanding of the nuclear forces.

Note that the reduction of nuclei to the hypothetical and unconfinable quarks turns nuclear physics into a kind of philosophy since quarks cannot be consistently represented in our spacetime, are not directly detectable by conception, and are point-like as a central condition to preserve Einstein's special relativity in the interior of the hyperdense nuclei, namely, a medium in which said theories cannot be even properly formulated and are disproved by large experimental evidence (see Vol. IV of Ref. [14].

Note also that, as we shall see better in Part V, the reduction of nuclei to the hypothetical quarks prevents any quantitative studies of novel nuclear energies, such as nuclear reactions without radiations, the reduction of nuclei to the hypothetical quarks prevents studies on the stimulated decay of the neutron, prevents the recycling of radioactive nuclear waste via their stimulated decay, and cause additional serious harm to nuclear physics as well as science at large.

**III-3. Reduction of nuclei and matter to protons and electrons**

It is hoped the above outline illustrates the credibility of a main synthesis permitted by hadronic mechanics, the reduction of neutrons to hadronic bound states of protons and electrons, thus implying the reduction of nuclei to protons and electrons, with the consequential reduction of all matter in the universe to protons and electrons under laws depending on physical conditions.

For mutual distances of protons and electrons bigger than their wavepackets, we assume the validity of quantum mechanics, while for mutual distances of the order of or smaller than said wavepackets. we assume the validity of the isotopic, genotopic and hyperstructural branches of hadronic mechanics depending on whether we have reversible, irreversible or multi-valued events, respectively.

**PART IV: OUTLINE OF HADRONIC CHEMISTRY**

**IV.1. Insufficiencies of quantum chemistry**

To have practical value, controlled nuclear synthesis must be achieved from natural elements generally contained in molecular structures, namely, structures described by chemistry. Therefore, any idea that controlled nuclear syntheses can be achieved without a correct chemical description of molecular structures may eventually result to be futile.

With all due respect to the historical chemical achievement during the 20th century, Santilli never accepted that quantum chemistry as a final theory, and searched for a more adequate *covering* theory, namely, a broader theory admitting quantum chemistry in first approximation. Following half a century of studies, this search eventually lead to the construction and verification of *hadronic chemistry* outlined in this Part IV (see monograph [63] for a comprehensive presentation, lecture, Ref. [64] as an excellent introduction, Ref. [65] for an independent review, Ref. [66] for an independent summary, and Refs. [67-93] for various experimental verifications and novel industrial applications).

Figure 16 |

Santilli rejected the notion of valence according to quantum chemistry because *identical electrons repel each other according to quantum mechanics* (see Fig. 16). Therefore, *the sole possibility to achieve a quantitative representation of valence bonds is that the pairing of identical valence electrons in singlet couplings (as requested by Pauli principle) creates a basically new force which is so strongly attractive to overcome the repulsive Coulomb force.*

Alternatively, Santilli showed that the sum of all conventional quantum mechanical forces in a simple molecule such as H2 is identically null, including all possible Coulomb interactions between peripheral electrons as well as their nuclei (Fig. 17). This feature mandated the identification of new *non-potential* interactions as being responsible for the bond of the Hydrogen atoms in the H2 molecule, as it happened for the Deuteron structure, Section III.2.4.

Figure 17 |

The achievement of an exact representation of the binding energy of the H2 molecule suggested the introduction of the so-called "screened Coulomb potentials" essentially given by the multiplication of the conventional potential by an arbitrary function f(r) which is then fitted from the data

(55) V(r) = e^{2}/r → V'(r) = f(r) e^{2}/r.

Santilli never accepted the above screenings as a final description because:

A) Quantized energy exchanges solely exist for the conventional Coulomb potential V(r) and do not exist for the screened potential V'(r), thus rendering questionable the use of the name "quantum chemistry";

B) The map V(r) → V'(r) is strictly non-unitary, thus causing screened Coulomb potentials to exit from the class of unitary equivalence of quantum chemistry with a host of ensuing problems (including the hidden violation of causality) that generally remain unaddressed;

C) Even assuming that the above problems can be manipulated into some acceptable form, screened Coulomb potentials violate the basic symmetries of quantum mechanics, the rotational, Galileo and Lorentz symmetries, with ensuing violation of Von Newman imprimitivity theorem under which quantum theories cannot be credibly voiced.

Moreover, the "loose" character of the valence of quantum chemistry (in any of its various forms) implies the prediction that all substances are paramagnetic, as illustrated in Fig. 18 for the case of the H2 molecule, in dramatic disagreement with experimental evidence according to which H2 is fully diamagnetic and so is the case for the majority of known molecules in nature.

Figure 18 |

*pairs,*but it is generically referred to

*correlations between electron orbitals.*In the absence of a clearly identified

*attractive*force, specifically, between

*valence electron pairs,*it is easy to prove that all electron orbitals can be oriented under a sufficiently strong external magnetic field, resulting in the unavoidable prediction that all substances in nature are paramagnetic, with dramatic disagreements with experimental evidence.

It is hoped the reader can se the starting point of this Part IV to the effect that, in the absence of a more adequate chemistry for a deeper understanding of molecular structures, any attempts to achieve nuclear synthesis may well turn out to be sterile. This also explains the reason Santilli spent decades in the study of a more appropriate chemistry before even considering the problem of nuclear syntheses.

Readers without a knowledge of Part I of this summary are discouraged from reading this Part IV prior to acquiring the necessary knowledge from from the specialized literature to prevent inevitable misconceptions.

**IV.2. Hadronic chemistry.**

According to Santilli conception [63], the *isotopic branch of hadronic chemistry,* also called *isochemistry,* is a single-valued step-by-step non-unitary covering of quantum chemistry that : 1) Has to be elaborated via isomathematics as a condition to avoid the inconsistencies of nonunitary theories; 2) Holds for permanently stable chemical structures, as a condition to verify the time reversal invariance of isochemistry; and 3) Is solely valid at mutual distances of valence electron bonds (of the order of 1 fm), while recovering quantum chemistry uniquely and identically for all mutual distances bigger than 1 fm. As such, isochemistry is ideally suited for the study of molecular structures.

Also according to Santilli conception [loc. cit.], the *genotopic branch of hadronic chemistry,* also called *genochemistry,* is a single-valued covering of quantum chemistry generated by two non-unitary transformations as in Eqs. (22) which covering : 1) Has to be elaborated via genomathematics as a condition to avoid the inconsistencies of nonunitary theories; 2) Holds for open-irreversible chemical structures, as a condition to violate the time reversal invariance of isochemistry; and 3) Is solely valid at mutual distances of valence electron bonds (of the order of 1 fm), while recovering quantum chemistry uniquely and identically for all mutual distances bigger than 1 fm. As such, genochemistry is ideally suited for the study of energy releasing processes at large, and nuclear syntheses in particular.

Also according to Santilli conception [63], the *hyperstructural branch of hadronic chemistry,* also called *hyperchemistry,* is a multi-valued (3+1)-dimensional covering of quantum chemistry generated by two multi-valued non-unitary transformations as in Eqs. (xxx) which covering: 1) Has to be elaborated via hypermathematics as a condition to avoid the inconsistencies of nonunitary theories; 2) Holds for multi-valued, (3+1)-dimensional open-irreversible chemical structures, as a condition to violate the time reversal invariance of isochemistry; and 3) Is solely valid at mutual distances of valence electron bonds (of the order of 1 fm), while recovering quantum chemistry uniquely and identically for all mutual distances bigger than 1 fm. As such, hyperchemistry is ideally suited for the study of biological structures.

**IV.3. Santilli-Shillady strong valence bond**

Thanks to Santilli isomathematics and the basic axioms of the novel isochemistry, R. M. Santilli and Don Shillady, Professor of Chemistry at Virginia Commonwealth University, did indeed achieve in 1999 [67] the first quantitative formulation of the valence in scientific history, consisting of a mathematical representation producing a force between identical valence electron pairs in singlet couplings capable of an exact representation of experimental data on molecules. The model is today known as *Santilli-Shillady strong valence bond.*

The main principles are the same as those for the synthesis of the hydrogen atom into the neutron or for the reduction of the deuterium to two isoprotons and one isoelectron, namely, the strong valence bond originates from the contact non-potential interactions caused by the deep mutual penetration of the electron wavepackets. The resulting deeply bonded pair of valence electrons was called by Santilli and Shillady the *isoelectronium.*

Figure 19 |

**IV.4. Santilli-Shillady isochemical model of the Hydrogen molecule**

Thanks to their strong valence bond, Santilli and Shillady achieved in the 1999 paper [67] (se also the review in Ref. [63])the first and only known exact representation of the binding energy and other basic features on the Hydrogen molecule.

Note from Fig. 19 that the representation of the paramagnetic character of the H2 molecule was crucially dependent on the strong valence bond of the valence electron pairs with resulting primary orbitals of the oo-type for which the total magnetic field the H2 is null.

An important feature of the Santilli-Shillady isochemical model of the Hydrogen molecule is that it can be approximated as a restricted three-body problem, again in view of the strong bond between valence pairs, thus admitting exact analytic solutions that have been investigated in Refs. [68,69]. Apparently, the same principles and techniques can be used for a possible exact analytic solution of Santilli's model of the Deuteron as a restricted three-body problem (Figs. 14, 15).

We should indicate that the above achievement followed a similar quantitative representation of the bond of identical electrons in the Cooper pair in superconductivity by Animalu and Santilli [35].

**IV.5. Santilli-Shillady model of the water molecule**

In their paper of 2000 [70] (see also the detailed review in monograph [63]), Santilli and Shillady achieved the first and only known exact representation from unadulterated first principle of the binding energy and other characteristics of the hydrogen atom, including its diamagnetic and dielectric characters.

Figure 20 |

**IV.6. The new chemical species of Santilli magnecules**

In Santilli's view, the first fundamental problem for the realistic achievement of a *controlled* nuclear synthesis is *the systematic exposure of nuclei from their electron orbitals.* Th argument is that nuclei are naturally shielded from the environment by electron orbitals that, at ambient temperature, have a spherical distribution. Until nuclei are exposed out of this electron cloud, no systematic nuclear syntheses are plausible.

Therefore, as part of his long term research program initiated when he was at Harvard University under DOE support in the late 1970s, Santilli addressed the problem of achieving a systematic control in the exposure of nuclei from their electron clouds.

It soon became evident that the solution of this problem requires a *new chemical species* since electron could instantly regain their spherical distributions following the termination of any external action. the only possibility seen by Santilli was then that of achieving a permanent coupling of atoms with their exposed nuclei.

Following, and only following a deeper understanding of the conventional chemical species of molecules, Santilli initiated comprehensive studies for a new chemical species specifically conceived and developed as a necessary premise of Intermediate Controlled syntheses without harmful radiations.

In memoir [71] of 1998 (see the comprehensive review in monograph [63]), Santilli presented mathematical, theoretical and experimental evidence on the existence of the new chemical species of what he called * magnecules* defined as * clusters of individual atoms (H, O, C, etc.), dimers (HO, CH, etc.) and ordinary molecules (H_2, CO, H_2O, etc.) bonded together by attractive forces between opposing magnetic polarities of toroidal polarizations of atomic orbitals, as well as the polarization of the magnetic moments of nuclei and electrons* (see a conceptual rendering in Fig. 21).

Figure 21 |

The main theoretical argument of Ref.[71] is that the toroidal polarization of the electron orbitals creates a magnetic field (due to the rotation of the electrons within said toroid) which does not exist for the same atom when the electron orbitals have the conventional spherical distribution.

When two so polarized atoms are at a sufficiently close distance, the resulting total force between the two atoms is attractive because all acting forces are attractive except for the repulsive forces due to nuclear and electron charges. However, the latter forces can be averaged to zero in first approximation since the individual atoms have a null total charge.

Alternatively, Santilli argues that, in their natural state, the total electric and magnetic fields of two atoms is identically null (Section UV.zzzz). Therefore, when a new magnetic field is created in the atomic structure via the toroidal polarization of the electron orbitals, resulting *attraction* between said atoms is beyond scientific doubt.

Memoir [71] then provides means for the actual creation of a gas with the new magnecular chemical structure. In essence, Santilli recalled the well known property that the polarization of the electron orbitals from their natural spherical distribution to the needed toroidal form requires extremely high magnetic fields (expected to be of the order of 10^{10} Gauss or more) that, as such, are not available in our macroscopic environment.

For the creation of the new magnecular species, Santilli suggested the use of a DC electric arc between graphite electrodes submerged within a liquid (such as distilled water). As it is well known, the arc decomposes the liquid molecules into mostly ionized atoms by creating between the tip of the electrodes plasma composed of H, C, and O individual atoms, C-H and O-H dimers, and ordinary molecules such as C-O, H_{2}O and others.

Figure 22 |

^{-8}cm) and directly proportional to the electric current (of the order of 10

^{3}A or more), thus having a strength of the order of 10

^{11}Gauss which is sufficient to achieve the desired toroidal polarizations of the electron orbitals (see the conceptual rendering of Fig zzzz).

Additionally, the strong magnetic field surrounding a DC arc naturally aligns polarized atoms in the needed sequence of magnetic polarities South-North-South-North, etc. resulting in the configuration of Fig. 22. As shown in Part V, this configuration is truly fundamental for controlled nuclear syntheses.

It is evident that, as soon as the arc is disconnected, atoms return to their natural spherical distribution due to collisions and other reasons. Santilli's main chemical argument is that the spherical distribution is indeed recovered but for the bonded pairs of polarized atoms as in Fig.1, since said spherical distribution cannot be achieved for each individual atom of the bonded pair due to insufficient energies to break said bond.

Figure 23 |

The only possibility available at the time of memoir [71] to ascertain the existence of the new species of magnecules was that of subjecting the same gas injection, first for the detection via the GC-MS and then the detection via the IRD. The identification of clear clusters in the GC-MS that have no IR signature for large clusters establishes the existence of magnecules since their bond is stable at ambient temperature, but have no IR signature. The magnecular nature of the bond was then confirmed by the arc method for its creation.

Figure 24 |

Gas chromatographic analyses reported in memoir [71] were conducted via a GC-MS/IRD consisting of a HP GC model 5890, a HP MS model 5972, and a HP IRD model 5965 operated in rather unusual conditions described in details in Ref. [71], such as: largest available feeding line of at least 0.3 mm ID; cryogenic cooling of the feeding line; lowest available column temperature of 100 C; longest available elusion time of about 25m; and other conditions.

Representative chromatographs out of a considerable number of scans of memoir [71] are reported in Figs. 23-25. Memoir [71] also reported the confirmation of the results (here not reproduced for brevity) obtained via an identical GC-MS/IRD located at a different laboratory.

Memoir [1] also provided considerable experimental evidence for the existence of magnecules in liquids, and comments on the expected existence of magnecular bonds in solids.

Figure 25 |

**IV.7. Confirmations of Santilli magnecules**

Following the appearance of memoir [71], M. G. Kucherenko and A. K. Aringazin confirmed in Ref.[72] of 1998 the numerical value computed by Santilli for the magnetic field along the axial symmetry of a toroidal polarization of the electron orbital of the Hydrogen atom as being about 1,347 times stronger than the nuclear magnetic field, thus confirming the presence of a magnetic field sufficiently strong to create a bond of the type of Fig. 21.

A. K. Aringazin conducted in Ref. [73] of 2001 an in depth theoretical analysis of the strong magnetic fields needed to achieve the toroidal polarization of electron orbitals, thus confirming Santilli's use of a submerged DC electric arc in order to achieve a magnetic field of the needed strength.

In 2001, Santilli released monograph [63] on a systematic presentation of the status of the knowledge in the new field in early 2000. In particular, magnecules were presented in their proper technical environment, that of a nonunitary covering of quantum chemistry nowadays known under the name of isotopic branch of hadronic chemistry.

Monograph [63] also detailed the first industrial realization of the new species of magnecules consisting of the gaseous fuel produced and sold world-wide under the trade name of *MagneGas ^{TM}* (MG) by

*Magnegas Corporation,*a U. S. corporation initiated by Santilli and now publicly traded at NASDAQ under the symbol MNGA (see www.magnegas.com for details).

*Santilli Magnegas technology* essentially consists of completely automatic equipment capable of converting liquids via a submerged electric arc into the gaseous fuel MagneGas that possesses anomalous features, such as a combustion flame temperate double that of natural gas, metal cutting faster than acetylene, combustion exhaust without hydrocarbons thanks to a full combustion (because the magnecular bond is weaker than the valence bond), and other features.

Santilli presented in Ref. [74] of 2003 theoretical and experimental evidence for the second industrial application of the new species of magnecules, consisting of the synthesis of heavy Hydrogen and Oxygen, nowadays denoted with the chemical symbols MH and MO, respectively, and consisting of magnecular clusters of Hydrogen or Oxygen atoms, respectively.

When detected via GC-TCD equipment operated at high temperature (so as to destroy the magnecular bond), MH and MO can be constituted by conventional Hydrogen or Oxygen up to 99% pure, yet their specific weight is a multiple that of conventional molecular Hydrogen and Oxygen.

The new species MH and MO were presented in Ref. [5] as evidence on the very existence of magnecules since the Hydrogen has only one valence electron to share and, as such, cannot possibly achieve valence bonds for more than two Hydrogen atoms (see the forthcoming paper [16] for details).

Santilli then provided in Ref. [75] of 2006 theoretical and experimental evidence on a third industrial application of the new species of magnecules that he called the *HHO gas,* here referred to the gas commercially produced via certain electrolyzers and essentially consisting of 2/3 Hydrogen and 1/3 Oxygen (a similar gas produced via a different electrolyzer is known as Brown's gas).

M. O. Cloonan presented in Refs.[76-78] of 2006 to 2009 applications of Santilli magnecules and its underlying hadronic chemistry to particular forms of pericyclic reactions and related new structures, thus illustrating the expected capability of the new species of Santilli magnecules to produce new chemical substances (i.e., chemical substances not entirely based on valence bonds).

In monograph [79] of 2008, R. M. Santilli presented an update on the first industrial application of the new species of magnecules via the combustible gas MagneGas indicated earlier, as well as an update of the additional industrial applications for MH, MO, and HHO.

In ref [80] of 2013, Y. Yang, J. V. Kadeisvili, and S. Marton, presented systematic experimental confirmation of the new chemical species of MagneHydrogen MH, and in Ref. [81] of the same year they presented systematic experimental verifications of the existence of the new species of Santilli magnecules.

Additional, yet unpublished contributions we believe deserve a mention are:

1) Santilli's [82] three independent experimental detections of H_{3}O, COH, COH and anomalous species solely possible under a magnecular bond;

2) Santilli's proposal to verify or dismiss experimentally (rather than theoretically) the hypothesis that the Avogadro number increases with the increase of the temperature for gases with magnecular structure [82]; and

3) The new class of fuels consisting of a magnecular bond of Hydrogen and conventional fossil fuels (such as gasoline, diesel and coal), known as *Santilli�s HyFuels* with consequential combustion of hydrocarbons, CO and other contaminants in the exhaust due to their combustion by magnecular Hydrogen (see the industrial website oof Magnegas Corporation).

We should indicate that *all* anomalous characteristics of Magnegas identified by Santilli in the original memoir [71] were systematically confirmed in Ref. [81] by Y. Yang, J. V. Kadeisvili, and S. Marton, such as:

1. Characterization of magnecules by weakly bonded individual atoms, dimers, and conventional molecules;

2. Stability of magnecules at ambient temperature;

3. Progressive reduction of magnecules with the increase of the temperature;

4. Termination of magnecules at a suitable Curie temperature;

5. Detection of magnecular clusters under a suitably selected and operated GC-MS;

6. Transparency of magnecules to infrared detectors for the a.m.u. of the clusters (and not at a smaller a.m.u. characterizing constituents);

7. Dependence of detected magnecules on the elusion time;

8. Dependence of magnecular species on filtration and compression;

9. Anomalous adhesion of magnecular gases to disparate materials;

10. Anomalous mutation of magnecular clusters in time and under different detection procedures or equipment;

11. Anomalous accretion of magnecular clusters by individual atoms; and other features.

To complete the review of magnecules, we should indicate that Santilli has introduced in monograph [63] *three* forms of magnecules with increasing complexity under the names of *iso-, geno- and hyper-magnecules* based on the corresponding chain of *iso-, geno-, and hyper-mathematics* [13].

According to this classification, the magnecules reviewed in this Part IV, and applied to controlled *nuclear syntheses* in the Part V are isomagnecules. Genomagnecules are specifically used to represent irreversible chemical reactions under magnecular bonds. Hypermagnecules are ideally suited for the representation of *biological structures,* such as the DNA, since its conception as a "molecule" is known to be afflicted by numerous insufficiencies or sheer inconsistencies.

**IV.8. Conventional molecular combustion**

Following twenty century of experience, chemistry has identified several types of *combustion* easily identifiable in the related vast literature, and generally classified as complete, incomplete, rapid, explosive and other combustions, although without any structural study the atomic or molecular level capable of achieving a numerical representation of the experimental evidence, including the still missing representation of the irreversibility of all energy releasing processes.

Santilli points out that, at the *microscopic / structural level, all types of conventional combustion are reducible to dissociation of valence bonds among atomic constituents of the original fuels and the creation of new valence bonds among the atomic constituents of the combustion exhaust.* As a representative case, we have the well known the combustion of Hydrogen in Oxygen into water

>(56) H_{2} + O_{2}/2 → H_{2}O + heat (61,000 BTU/lb = 57.5 Kcal/mole).

Similarly, we have the complete combustion of methane in air

(57) CH_{4} + 2 O_{2} → 2 CO + 2 H_{4}O + heat (23,000 BTU/lb);

the incomplete combustion of propane in air

(58) 2 C_{3}H_{8} + 7 O_{2} → 2C + 2 CO + 8 H_{2}O + 2 CO_{4} + heat (21,000 BTU/lb)

and numerous other combustions.

In all cases, quantum chemistry has identified rather precise *rules and data,* combustion by combustion. However, according to Santilli, we are essentially dealing with "nomenclatures" in the sense that the descriptions are mainly conceptual/mnemonic,since they lack a quantitative representation of the rather complex processes occurring at the level of individual valence couplings.

After all, as recalled in Section IV.1, the very quantum notion of valence coupling lacks a quantitative identification of the *attractive force* between identical valence electrons, by always keeping in mind that *identical electrons repel each other according to quantum mechanics, and certainly they do not attract each other to form any bond.*

**IV.9. Santilli's magnecular combustion**

In Santilli's view, a main insufficiency of the quantum chemical notion of combustion is the following. In A necessary condition for combustion (56) to occur is the separation of the molecular bonds H-H and O-O since the water molecule contains only one Oxygen atoms and the two Hydrogen atoms are separated in the two dimers H-O and O-H. This implies that the process of combustion must first provide the energy necessary for the molecular separations

(59a) O_{2} → O + O - 119.1/ Kcal/mole

(59b) H_{2} → H + H - 104.2 Kcal/mole,

Consequently, the combustion of Hydrogen and oxygen *does not* produce 57.5 Kcal/mole because, in order not to violate the principle of conservation of the energy, said combustion must produce

p>
(60) 57.5 + 59.5 + 104.2 Kcal/mole = 221.2 Kcal/mole,

the measured amount of 57.5 Kcal./mole being the mere residue following the use of 163.7 Kcal/mole for the separation of the Hydrogen and Oxygen molecules in whose absence the creation of the water molecule H2O = H-O-H is manifestly impossible.
Once the true energy balance in combustion law has been understood, it is easy to see the
environmental and industrial importance of *Santilli's fuels with
magnecular structure* because they contain individual atoms under a bond
*weaker* than the valence bond. Therefore, *magnecular fuels
yield an energy output greater than that of molecular fuels with the
same atomic constituents.* To clarify these new notion,
Santilli has introduced the following definitions [79]:

*MOLECULAR COMBUSTION: is that for fuels whose atoms are entirely
under a molecular bonds, such as Hydrogen. methane, propane, gasoline, diesel, etc.*

*
MAGNECULAR COMBUSTION: is that for fuels whose atoms are at least in
part under a magnecular bond, and the rest under a molecular bond, such
as MagneGas, HHO, MagneHydrogen and other fuels.*

The bigger energy output of magnecular fuels with respect to molecular
fuels with the same atomic composition is beyond scientific doubt. Consider, for instance,
MagneGas produced by an arc between graphite electrodes submerged within
distilled water. This type of MagneGas contains about 66% H-atoms, 16% O-atoms and 16% C-atoms,
plus impurities here inessential.

Recall that H_{2}
contains about 300 BTU/scf, while CO contains about 89 BTU/scf.
Consequently, under the assumption of a conventional molecular structure, the thermal content of MagneGas should be

(61) (0.7 x 300 + 0.3 x 89) BTU/scf = 236 BTU/scf.

But Magnegas cute metal slabs up to 12: thick faster than acetylene that contains 2,400 BTU/scf and has a certified flame temperature more of 10,400 F which is more than double the flame temperature of natural gas. Similar occurrences hold got HHO, MH and other fuels with magnecular structure. Therefore, the evidence disproves the molecular interpretation (61) in favor of the magnecular one.
To initiate a quantitative analysis, assume that the H-atom is bonded magnecularly with a yet unknown value of "s" Kcal/mole. We then have the following data for the combustion
of MH_{2} = HxH in Oxygen

(62a) HxH → H + H - s Kcal/mole,

(62b) O_{2}/2 → (O + O)/2 - 59.55
Kcal/mole,

(62c) HxH + O_{2}/2 → H_{2}O + (161.7 - s) Kcal/mole,

namely, *the combustion of magnecular Hydrogen HxH and atomic oxygen O is predicted to yield about three times the value predicted by molecular structures with the same atomic constituents,* under the approximation s = 0 at the
combustion temperature.

It is easy to see that all mixtures of molecular H_{2} and
magnecular MH_{2} yield a combustion energy output bigger than
57.5 Kcal/mole. As an example, a mixture of 10% MH_{2} and 90%
H_{2} would yield (62.71 - s) Kcal/mole.

It should be indicated that much remains to be studied in Santilli's magnecular
combustion. In fact, despite its novelty, the magnecular combustion alone appears as being insufficient for a quantitative representation of large energy outputs, such as the instantaneous melting of tungsten and other metal by Magnegas, HHO, MH and other magnecular gases, that require additional novel notions, such as the toroidal polarization of at least some of the orbitals for fast and deep penetration within metal structures.

**PART V: NUCLEAR ENERGIES WITHOUT RADIATIONS****V.1. Introduction**

Santilli's 50 years of mathematical, physical, chemical and experimental studies *prior* to the addressing of controlled nuclear syntheses without radiations illustrates the complexity of the problems to be identified and solved for the achievement of: truly controlled nuclear syntheses; nuclear syntheses without the emission of harmful radiations and without the release of radioactive nuclear waste; industrial reactors capable of implementing the preceding requirements; and other needs.

Figure 26 |

*"The protracted lack of solution of physical or chemical problems is generally due to insufficiencies of the used mathematics. The lack of achievement to date of industrially available, controlled nuclear syntheses is due, in my view, to the insufficiencies of the local-differential mathematics underlying quantum mechanics and chemistry, with consequential insufficiencies of quantum physical or chemical laws.*

In fact, such a mathematics solely allows the abstraction of particles to dimensionless points and the abstraction of physical or chemical; events to processes reversible over time. These abstractions are clearly effective for the atomic structure due to the large mutual distances of the constituents, as well as the known reversibility of the atomic structure. However, the same abstractions are manifestly insufficient for the nuclear structure due to actual contact of the charge distributions of the nuclear constituents as established by nuclear data. The lack of exact validity of quantum mechanics and chemistry for irreversible processes, such as nuclear syntheses, is evident to all serious scholars.

Hence, before addressing problems related to triggering and control of notoriously irreversible nuclear syntheses, I had to spent decades for constructing a mathematics suitable for the representation of nuclear constituents as extended, non-spherical and deformable charge distributions. Additionally, for such a representation to have real values for nuclear syntheses, the needed broader mathematics had to be structurally irreversible, that is, irreversible in the basic mathematical axioms

These (and other) needs lead first to the construction of isomathematics with a Lie-isotopic algebraic structure defined on isospaces over isofields with consequential isotopic branches of hadronic mechanics and chemistry. These isotopic methods did provide an invariant characterization of extended, non-spherical and deformable nucleons, but only in a form reversible over time. The removal of the latter insufficiency (as well as others) mandated the further lifting of isomathematics into the irreversible genomathematics with a covering Lie-admissible structure defined on forward genospaces over forward genofields with consequential genotopic branches of hadronic mechanics and chemistry.

*
Following, and only following the achievement of mathematical maturity for the invariant representation of irreversible processes among extended nucleons, initial applications to specific nuclear syntheses were rather simple and direct with the understanding that so much remains to be understood and developed. As an illustration I believe that, by far, the most important new vistas in nuclear physics yet to be initiated are expected from the novel invariant representation of nuclear forces as being constituted by Coulomb interactions plus strongly attractive, non-linear, non-local and non-Hamiltonian interactions among extended nuclear constituents.*

Figure 27 |

Among the new industrial developments in nuclear physics, we shall provide particular attention to *Santilli's Intermediate Nuclear Syntheses* (ICNS - patented and International Patents pending), simply called *intermediate
syntheses,* but also indicate other forms of nuclear energies without harmful radiations currently under development, including ongoing research on the stimulated decay of the neutron and of radioactive nuclear waste.

The reader without a technical knowledge of *all* preceding methods and their experimental verifications is discouraged from venturing any judgment, whether in favor or against nuclear energies without radiations, so as to prevent the illusion of science. Additionally, readers should be aware that this is the corporate website of a U. S. publicly traded company that, as such, requires secrecy on ongoing developments, and the restriction of the disclosure to scientific papers published in refereed journals, thus explaining the paucity of engineering details. Finally, the reader should be aware that this Part V is restricted to nuclear synthesis and processes that have been treated via Santilli genomathematics and genomechanics. The extension of the results to other nuclear energies presented in the large literature on cold and hot syntheses, is left to the interested reader.

Figure 28. |

**5.2. Physical laws of intermediate syntheses without radiations**

The central objective of Santilli's ICNF is the achievement of the controlled synthesis of two, properly selected, light, natural and stable nuclei into a third nucleus under a number of conditions, such as:

1) The systematic and controlled exposure of the original nuclei from their electron clouds and their coupling via magnecular bonding presented in Part IV;

2) The systematic and controlled triggering of said exposed and coupled nuclei to mutual distances of the order of the nuclear forces (1 Fermi) via engineering means called the *trigger* (TR) under which the synthesis is unavoidable;

3) The selection of the original nuclei in such a way that the synthesized third nucleus is also light, natural and stable without any emission of harmful radiations or release of radioactive waste.

All quantitative studies are conducted via the use of hadronic mechanics and chemistry. The light, natural and stable nuclei meeting the above requirements are then called *hadronic fuels.* The reactor providing the engineering implementation of the above conditions are then called *Santilli hadronic reactors* (and friendly referred to as "Dragons" since they do spit fire).

Figure 29. |

**Law V.1: Threshold Energy:**

The energies activating ICNF must be "intermediate" between the energies of cold and hot syntheses and have the minimal possible ("threshold") values needed to verify all necessary physical, chemical and engineering requirements, because excess energies over the indicated threshold values cause instabilities and other uncontrollable effects. Note that the release in the hadronic reactor of energy below the indicated threshold provides a first mean for the disconnection of ICNF.

**Law V.2: Nuclear Exposure:**

The nuclei of hadronic fuels must be subjected to systematic and controlled exposure out of their electron clouds via the toroidal polarization of atomic orbitals and then coupled via the industrially available technologies of Santilli magnecules (see Part IV and Fig. 21). Note that the disconnection of the engineering means for the polarization of the orbitals into toroids and then coupling under magnecular bonds implies the instantaneous termination of any systematic nuclear synthesis (since the electron orbital instantly reacquire their spherical distribution), thus offering an additional mean for terminating ICNF via the disconnection in the hadronic reactor of the magnecular polarizations and bonding since the natural electron shielding of a nucleus prevents any systematic "contact" with another nucleus.

**Law V.3: Spin Alignment:**

With reference to Fig. 26, exposed nuclei must be coupled either according to *planar anti-parallel spins* (planer singlet) or *axial parallel spins* (axial triplet). Santilli has shown that different types of spin couplings cause strongly repulsive forces that prevent any systematic and controlled nuclear syntheses. Therefore, the disconnection in the hadronic reactors of the engineering means for the indicated spin coupling causes the instantaneous halting of nuclear syntheses. Note that Santilli. Magnegas Technology and its basic magnecular coupling outlined in Part IV and illustrated in Fig. 21, does indeed industrial equipments, the magnegas hadronic reactors, for the industrial verification now of the crucial Laws V.2 and V2 and V.3, and this explains the reason Santilli devoted a decade of his life to development the Magnegas Technology prior to initiating tests of ICNF.

**Law V.4: Triggering Nuclear Forces:**

Following systematic and controlled engineering implementations of the preceding laws, hadronic reactors must have engineering means to implement the *trigger* (TR), namely, the mechanism that forces the properly exposed and coupled nuclei at one Fermi mutual distance at which there is the activation of the strongly attractive nuclear forces and the nuclear synthesis becomes unavoidable. Note that the engineering means for the trigger allow a fourth control of nuclear syntheses independent from the preceding ones since the disconnection of the trigger implies the instantaneous termination of any possible synthesis.

**Law V.5: No Harmful Radiations or Radioactive Waste:**

The fifth and perhaps most important law of Santilli ICNF is that the original and final
nuclei have to be light, natural and stable elements selected in such a way to prevent the emission of neutrons and other harmful radiations and to avoid the release of radioactive waste. As an illustration, Hydrogen *cannot* be a hadronic fuel for ICNF under the use of an electric arc for the activation of the reactions due to the production of a flux of neutrons according to the measurements reported in Section II.9.

**V.3. Intermediate nuclear syntheses under industrial development**

Following the preceding laborious journey, Santilli finally initiated in early 2010 systematic experimentation of ICNF verifying the above five basic laws. By using standard nuclear terminologies and symbols with A, Z,J^{p}, u and τ denoting the atomic number, the nuclear charge, the nuclear spin, the parity, the nuclear energy in a.m.u., and the mean life, respectively, the intermediate nuclear syntheses verifying Laws V.1-V-5 can be expressed via the nuclear synthesis

(63a) N_{1}(A_{1},Z_{1}, J^{p}_{1}, u_{1}, τ_{1}) + N_{2}(A_{2}, Z_{2}, J^{p}_{2}, u_{2}, τ_{2}) +TR →

→ N_{3}(A_{3}; Z_{3}; J^{p}_{3}; u_{3}, τ_{3}) + Heath,

(63b) A_{1} + A_{2} = A_{3}; Z_{1} + Z_{2} = Z_{3}; J_{1} + J_{2} = J_{3}; p_{1} + p_{2} = p_{3},

(63c) ΔE = (E_{1} + E_{2}) -E_{3} > 0,

where: all initial and final nuclei must be light, natural and stable isotopes, thus having infinite mean life τ; ΔE measured in a.m.u. must be positive; TR denotes the trigger identified in the preceding section; the heat is produced by the de-excited states of the synthesized nucleus N_{3}; and the used threshold energies must be basically insufficient to produce neutron or other harmful radiations and be basically insufficient to disintegrate any nucleus as an evident prerequisite for the release of radioactive nuclear waste.

Since 2010, Santilli has constructed seven hadronic reactors with increasing power and complexities for the industrial developed of systematic and controlled intermediate nuclear syntheses (56), which reactors are now owned and operated by Thunder Fusion Corporation (see Figs. 36 to 30 for partially illustrations).

Following two years of testing, the first known intermediate controlled nuclear synthesis without radiations was published by Santilli in Ref. [85] of 2011 and consists of the synthesis of Deuterium and Carbon into Nitrogen according to the synthesis

(64a) D(2, 1, 1^{+}, 2.0141, stable) + C(12; 6, 0^{+}, 12.0000, stable) + TR →

→ N(14, 7, 1^{+}, 14.0030, stable) + ΔE;

(64b) ΔE = (E_{carb} + E_{deut}) - E_{nitr} = 0.0111 u > 0,

that verifies all physical laws of the preceding section. The above synthesis was achieved via the hadronic reactor depicted in Fig. 27 powered by a 50 kW Miller Electric Dimension 1000 AC-DC converter suitably used to release a special kind of electric arc between carbon electrodes in a Deuterium atmosphere at pressure, which arc is capable of: A) polarizing the orbitals of the Deuterium and Carbon as in Fig. 22, B) coupling said polarized atoms into a DxC magnecules as in Fig. 21, and C) forcing their mutual distance of the polarized Deuterium and Carbon atoms to the mutual distance of 1 Fermi via a trigger TR than cannot be disclosed in this website.

Note in synthesis (57) that, either Nitrogen is synthesized (in which case there cannot possibly be any emission of harmful radiations or release of radioactive waste), or the synthesis into Nitrogen does not occur (in which case the energy available is one million times short of the energy needed to disintegrate the Deuterium or the Carbon nucleus as a condition to produce harmful radiations or release radioactive waste). Hence, D-2 and C-12 are indeed acceptable hadronic fuels.

Particular attention was devoted in Ref. [85], not only to various chemical analyses signed by laboratory directors [91-95] establishing the production of anomalous Nitrogen, but above all to the verification via three different detectors of the lack of any neutron or other particle radiations in the outside f the reactor (Fig. 27). Needless to say, electric arcs release beta and gamma (but *not* alpha) radiations in the interior of the hadronic reactors, but they are known to have low energy, are easily captured by the thick wall of the reactor and cannot escape to the outside.

Figure 30. |

Following the positive results presented in Ref. [85], Santilli invited Drs. Robert Brenna, Theodore Kuliczkowski, Leong Ying of the

*Princeton Gamma Tech Instruments*, Princeton, NJ, to conduct an independent re-run of all measurements via the use of exactly the same equipment and under the same conditions as those of the original measurements. The results of these re-runs were confirmatory and were published in Ref. [86]. Particular attention was devoted in these re-runs to the confirmation of the absence of neutron or other harmful radiations and the lack of any release of radioactive waste (Fig. 28).

In addition to the re-runs of Ref. [86], comprehensive, independent confirmatory measurements on the ICNF of Deuterium and Carbon into Nitrogen were conducted by Drs. J. V. Kadeisvili, C. Lynch and Y. Yang, of *Magnegas Corporation,* Tarpon Springs, Florida, and presented in Ref. [87] (see also Ref. [88] by Prof. Cai Wei of City College of New York).

Subsequently, Santilli published in Ref. [89] evidence on the ICNF of Oxygen and Carbon into Silica according to the synthesis

(65a) O(18, 8, 0^{+}; 17.9991, stable) + C(12, 6, 0^{+}; 12.0000, stable) + TR →

→ Si(30, 14, 0^{+}, 29:9737, stable) + ΔE;

(65b) ΔE = 0.0254 u > 0,

that also verifies all physical laws for the preceding section and also cannot emit neutron radiations or release radioactive wastes.

To avoid un-necessary length, we recommend for details to inspect the original papers [85-89] as well as the individual chemical analyses signed by laboratory directors, Refs. [91-100].

The chemical show that, in addition to the considered *primary ICNF,* there also exist *secondary ICNF* currently under investigation, such as the ICNF of Carbon and Helium into Nitrogen

(66a) C(12, 6, 0^{+}, 12:0000, stable) + He(4, 2; 0^{+}; 4:0026, stable) + TR →

→ O(16, 8, 0^{+}, 15:9949, stable) + ΔE,

(66b) ΔE = 0:0077 u > 0,

the apparent ICNF of O-18 and SI-30 into Ti-44

(67a) O(18, 8, 0^{+}; 17.9991, stable) + Si(30, 14, 0^{+}; 29.9737, stable) + TR →

→ Ti(30, 14, 0^{+}; 29.9737, 63 y) + ΔE,

(67b) ΔE = 0.0254 u;

that verify all needed physical laws.

In reaction (67), Ti-44 is unstable with a mean life of 63 years, but it decays via two successive electron captures first into Sc-44 and then into Ca-44, the latter being stable. Hence, syntheses (60) are acceptable ICNF.

The reader should keep in mind that, as in the opening statement of this Summary, the primary aim of Thunder Fusion Corporation is to develop a new form of environmentally clean combustion of fossil fuels. The primary industrial use of the technologies underlying ICNF, such as the use of high voltage arcs, is that of triggering a full combustion of fossil fuels. the actual future use of ICNF outlined in this website are merely intended to enhance, in due time and under sufficient funding, the energy output via the controlled nuclear synthesis of atmospheric Oxygen with the Carbon content of fossil fuels into Silica, Eq. (60), or other intermediate nuclear syntheses without radiations.

*In closing this section, we should indicate the impossibility for the above ICNF to produce a bomb since the nuclear syntheses can solely occur in the small cylindrical volume surrounding the electric arc, each synthesis disrupting the arc due to the very high local energy density, with ensuing need for the continuous resetting of the conditions for said syntheses.*

**V.4. Stimulated decay of the neutron**

According to Santilli [90], the neutron is the biggest and cleanest reservoir of energy available to mankind because it is naturally unstable and decays (when isolated) with the emission of a highly energetic electron, thus allowing in principle a double form of clean energy, the first given by heat resulting from the capture of the emitted electron and the second resulting from the ensuing electric potential.

By part the biggest obstacle for the study and development of these new and clean energies is the century old quantum mechanical interpretation of the synthesis and consequential of the neutron based on the Pauli-Fermi conjecture of the hypothetical neutrino

(68) p^{+} + e^{-} → n + ν → p^{+} + e^{-}

because the neutrino hypothesis prevents any structure model of the neutron with actual physical particles that can be clearly defined in our spacetime, let alone having no quantitative representation via quantum mechanics due to the need of a "positive binding energy" studied in Part II.

By contrast, the achievement of the quantitative, numerical and exact representation of "all" characteristics of the neutron in its synthesis from the Hydrogen atom via the etherino hypothesis

(69) p^{+} + a + e^{-} → n → p^{+} + a + e^{-}

does allow the representation of the neutron as a hadronic bound state of one (iso)-proton and one (iso)-electron.

In turn, the admission of the electron as an actual constituents of the neutron in a suitably mutated form does indeed allow the conception and test of a variety of means to stimulated the decay of the neutron via the excitation of the electron in its structure whose study was initiated in Ref. [90] of 1994 and shall be continued by Thunder Fusion Corporation.

Needless to say, industrially meaningful possibilities for this new clean form of nuclear energy must be referred to the stimulated decay of the neutron when a member of selected nuclei, thus leading to nuclear transmutations of the type

(70) N_{1}(A_{1}, Z_{1}, J^{p}_{1}, u_{1}, stable) + TR →

→ N_{2}(A_{1}, Z_{2} + 1, J^{p}_{1} - 1/2, u_{2} < u_{1}, stable) + gammas + electrons + heat,

where TR is the trigger stimulating the decay of one or more peripheral neutrons of the original nucleus that has to be selected in such a way to verify reaction (73).
the initial hadronic fuel has to be selected in such a way to prohibit the emission of neutron or other harmful radiations, the emission of electrons being easily trapped by the reactor.

A first possibility identified by Santilli is given by the nuclear transmutation stimulated by a photon with the particular energy of 0.0014 expected to be the
resonating frequency for the isoelectron plus additional means represented by the trigger [90]

(71) Tc(100, 43, 1^{+}, 99.9076, stable) + γ + TR → Ru(100, 44, 0^{+}, 99.9042, stable) + ΔE.

with positive energy output without any possible radiations

(72) ΔE = 0.0085 > 0,

where we included the 0.0014 a.m.u of the incident gamma.

According to quantum mechanics, the probability amplitude for the above transmutation is essentially null for ll gamma frequencies. Hadronic mechanics recovers this behavior, but provides a sharp peak in the amplitude at 0.0014 which is typical of all resonating effects.

Due to the notorious insufficiency of quantum mechanics for the nuclear structure (Part III), l;et alone for irreversible transmutation (66), it is hoped that serious scholars will provide priority to new knowledge and the environment by contributing to collegial studies of transmutations of type (66), rather than giving priority to a preferred old theory.

**V.5. Stimulated decay of radioactive wastes**

Radioactive nuclear waste consists of large nuclei that, being naturally unstable, must admit engineering means to stimulating the decay. In this way rather than waiting tens of thousands of years for the natural decay, radioactive nuclear waste can be stimulated to decay in a short period of time depending on the collection of used engineering means.

As an illustration, conventional quantum mechanics predicts that, under a sufficiently intense external electric field, radioactive nuclei can be deformed into spheroids admitting positive charges at the terminals such to trigger the decay. Numerous additional mechanisms exist for triggering the decay of naturally unstable radioactive nuclei, and some of them have been patented (se the list in Ref. [101].

Thunder Fusion Corporation is studying basically new methods and mechanisms for the stimulated decay of radioactive nuclear waste primarily based on Santilli's conception of the neutron (Part II) and of the nuclear forces (Part III), resulting in the expected stimulated decay

(73) N(A, Z, J^{p}, u, unstable) + TR →

→ Σ_{k}N_{k}(A_{k}, Z_{k}, J^{p}_{k}, u_{k}, stable) + gammas + electrons + heat,

Since engineering means for the stimulated decay of radioactive waste are not expected to be very large, Santilli [103] indicate the possibility, in due time and under due funding, that stimulated decays (69) can be performed in the pool of nuclear reactors, thus rendering more environmentally acceptable current nuclear power plants.

Thunder Fusion Corporation will solely release technical presentation on the stimulated decay of radioactive nuclear wastes published in refereed journals following due authorization by the Board of Directors.

**REFERENCES**

**Part I: References on Hadronic Mechanics**

[1] R. M. Santilli, "Embedding of Lie-algebras into Lie-admissible algebras," Nuovo Cimento {\bf 51}, 570 (1967),

http://www.santilli-foundation.org/docs/Santilli-54.pdf

[2] R. M. Santilli, "An introduction to Lie-admissible algebras," Suppl. Nuovo Cimento, {\bf 6}, 1225 (1968).

[3] R. M. Santilli, "Lie-admissible mechanics for irreversible systems." Meccanica, {\bf 1}, 3 (1969).

[4] R. M. Santilli, "On a possible Lie-admissible covering of Galilei's relativity
in Newtonian mechanics for nonconservative and Galilei form-non-invariant systems," Hadronic J. Vol. 1, 223-423 (1978), available in free pdf download from

http://www.santilli-foundation.org/docs/Santilli-58.pdf

[5] R. M. Santilli, "Need of subjecting to an experimental verification the validity within a hadron of Einstein special relativity and Pauli exclusion principle," Hadronic J. Vol. 1, 574-901 (1978), available in free pdf download from

http://www.santilli-foundation.org/docs/santilli-73.pdf

[6] R. M. Santilli, *Foundation of Theoretical Mechanics,* Volume
(a) I (1978) and (b) II (1982) Springer-Verlag, Heidelberg, Germany,

http://www.santilli-foundation.org/docs/Santilli-209.pdf

http://www.santilli-foundation.org/docs/santilli-69.pdf

[7] R. M. Santilli, "Isonumbers and Genonumbers of Dimensions 1, 2, 4,
8, their Isoduals and Pseudoduals, and ;Hidden Numbers; of Dimension
3, 5, 6, 7," Algebras, Groups and Geometries Vol. 10, 273 (1993),

http://www.santilli-foundation.org/docs/Santilli-34.pdfbr>

[8] R. M. Santilli, "Nonlocal-Integral Isotopies of Differential
Calculus, Mechanics and Geometries," in Isotopies of Contemporary
Mathematical Structures, P. Vetro Editor, Rendiconti Circolo
Matematico Palermo, Suppl. Vol. 42, 7-82 (1996),

http://www.santilli-foundation.org/docs/Santilli-37.pdf

[9] R. Anderson, "Main references on the Lorentz-Poincare'-Santilli Isosymmetry,"

http://www.santilli-foundation.org/LPS-references.php

[10] R. M. Santilli, "Relativistic hadronic mechanics: nonunitary, axiom-preserving completion of relativistic quantum mechanics," Found. Phys. Vol. 27, 625-729 (1997)

http://www.santilli-foundation.org/docs/Santilli-15.pdf

[11] Thunder Fusion Corporation, "Reduction of matter to protons and electrons," website

http://www.thunder-fusion.com/santilli-scientific-discoveries-6.php

,p>
[12] R. M. Santilli, "Lie-admissible invariant representation of
irreversibility for matter and antimatter at the classical and
operator levels," Nuovo Cimento B 121, 443 (2006),

http://www.santilli-foundation.org/docs//Lie-admiss-NCB-I.pdf

s
[13] R. M. Santilli, *Elements of Hadronic Mechanics, *Volumes I
and II Ukraine Academy of Sciences, Kiev, second edition 1995,

http://www.santilli-foundation.org/docs/Santilli-300.pdf

http://www.santilli-foundation.org/docs/Santilli-301.pdf

[14] R. M. Santilli, *Hadronic Mathematics, Mechanics and
Chemistry,*, Vol. I [a], II [b], III [c], IV [d] and [e],
International Academic Press, (2008), available as free downlaods
from

[ 15] R. M. Santilli, *Isotopic, Genotopic and Hyperstructural Methods in Theoretical Biology,*
Ukraine Academy of Science, first edition (1997),

http://www.santilli-foundation.org/docs/santilli-67.pdf

[16] A. K. Aringazin, A. Jannussis, F. Lopez, M. Nishioka and B. Vel-janosky, *Santilli�s Lie-Isotopic Generalization of Galilei and Einstein Relativities,* Kostakaris Publishers, Athens, Greece (1991),

http://www.santilli-foundation.org/docs/Santilli-108.pdf

[17] D. S. Sourlas and G. T. Tsagas, *Mathematical Foundation of the Lie-Santilli Theory,* Ukraine Academy of Sciences 91993),

http://www.santilli-foundation.org/docs/santilli-70.pdf

[18] J. Lohmus, E. Paal, and L. Sorgsepp, *Non-associative Algebras in Physics,* Hadronic Press, Palm Harbor, 1994),

http://www.santilli- foundation.org/docs/Lohmus.pdf

[19] J. V. Kadeisvili, *Santilli�s Isotopies of Contemporary Algebras, Geometries and Relativities,* Ukraine Academy of Sciences, Second edition (1997),

http://www.santilli-foundation.org/docs/Santilli-60.pdf

[20] Chun-Xuan Jiang, *Foundations of Santilli Isonumber Theory,* Inter- national Academic Press (2001),

http://www.i-b-r.org/docs/jiang.pdf

[21] Raul M. Falcon Ganfornina and Juan Nunez Valdes, *Fundamentos de la Isoteoria de Lie-Santilli,* International Academic Press (2001),

http://www.i-b-r.org/docs/spanish.pdf

[22] B. Davvaz, *Hyperings Theory and Applications,* International Academic Press (2007),

http://www.santilli-foundation.org/docs/Davvaz.pdf

[23] I. Gandzha and J Kadeisvili, {\it New Sciences for a New Era:
Mathematical, Physical and Chemical Discoveries of
Ruggero Maria Santilli,} Sankata Printing Press, Nepal (2011),

http://www.santilli-foundation.org/docs/RMS.pdf

[24] S. Georgiev, *Foundation of the IsoDifferential Calculus,* Volume I, to appear (2014). preliminary and partial version available from the link
http://www.santilli-foundation.org/docs/isohandbook.pdf

[25] Thunder Fusion Corporation, *Mathematical, Physical and Chemical Sciences underlying Santilli's Intermediate nuclear Fusions without harmful Radiations,* website

http://www.thunder-fusion.com/science.html

[26] R. M. Santilli and T. Vougiouklis, (a) "Isotopies, Genotopies, Hyperstructures and their Applications,*Prooc. Int. Workshop in Monderoduni: New Frontiers in Hyperstructures and Related Algebras,* Hadronic Press (1996), 177-188; and (b) "Lie-admissible hyper
algebras," Italian Journal of Pure and Applied Mathematics, Vol. 31, pages 239-254 (2013)

http://www.santilli-foundation.org/Lie-adm-hyperstr.pdf

**Part II: References on the Fusion of the Hydrogen Atom into the Neutron**

[27] H. Rutherford, Proc. Roy. Soc. A, ** 97**, 374 (1920)

.
[28] J. Chadwick, Proc. Roy. Soc. A, **136**, 692 (1932).

[29] W. Pauli, *Handbuch der Physik,* Vol. 24, Springer-Verlag, Berlin (1933).

[30] E. Fermi, * Nuclear Physics,* University of Chicago Press (1949).

[31] R. M. Santilli, "Apparent consistency of Rutherford's hypothesis on the neutron as a compressed hydrogen atom, Hadronic J. ** 13**, 513 (1990).

http://www.santilli-foundation.org/docs/Santilli-21.pdf

[32] R. M. Santilli, "Apparent consistency of Rutherford's hypothesis on the neutron structure via the hadronic generalization of quantum mechanics - I: Nonrelativistic treatment",
ICTP communication IC/91/47 (1992)

http://www.santilli-foundation.org/docs/Santilli-150.pdf

[33] R. M. Santilli, "Recent theoretical and experimental evidence on the apparent synthesis of neutrons from protons and electrons.", Communication of the Joint Institute for Nuclear Research, Dubna, Russia, number JINR-E4-93-352 (1993)

[34] R.M. Santilli, "Recent theoretical and experimental evidence on the apparent synthesis of neutrons from protons and electrons," Chinese J. System Engineering and Electronics Vol. 6, 177-199 (1995)

http://www.santilli-foundation.org/docs/Santilli-18.pdf

[35] A. O. E. Animalu and R. M. Santilli, "Nonlocal isotopic representation of the Cooper pair in superconductivity," Intern. J. Quantum Chemistry Vol. 29, 185 (1995)

http://www.santilli-foundation.org/docs/Santilli-26.pdf

[36] R. M. Santilli, "An intriguing legacy of Einstein, Fermi, Jordan and others: The possible invalidation of quark conjectures," Found. Phys. Vol. 11, 384-472 (1981)

http://www.santilli-foundation.org/docs/Santilli-36.pdf

[37] R. M. Santilli, "Lie-isotopic Lifting of Special Relativity for Extended Deformable Particles," Lettere Nuovo Cimento Vol. 37, 545 (1983),

http://www.santilli-foundation.org/docs/Santilli-50.pdf

[38] R. M. Santilli, *Isotopic Generalizations of Galilei and
Einstein Relativities,* Volumes (a) I and (b) II, International
Academic Press (1991) ,

http://www.santilli-foundation.org/docs/Santilli-01.pdf

http://www.santilli-foundation.org/docs/Santilli-61.pdf

[39] R. M. Santilli, "Isominkowskian Geometry for the Gravitational Treatment of Matter and its Isodual for Antimatter," Intern. J. Modern Phys. D {\bf 7}, 351 (1998),

http://www.santilli-foundation.org/docs/Santilli-35.pdf

[40] R. M. Santilli, "Can strong interactions accelerate particles faster than the speed of light?" Lettere Nuovo Cimento {\bf 33}, 145 (1982)

www.santilli-foundation.org/docs/Santilli-102.pdf

[41] R. M. Santilli, "The etherino and/or the neutrino hypothesis," Foundation of Physics **37**, 670 (2007).

http://www.santilli-foundation.org/docs/EtherinoFoundPhys.pdf

[42] R. M. Santilli, "Confirmations of the lack of expansion of the universe in five recent scientific meetings and from space."

http://www.santilli-foundation.org/Conf-2013-No-Univ-Exp.php

[43] C. Borghi, C. Giori C. and A.~ Dall'Olio, Communications of CENUFPE, Number 8 (1969) and 25 (1971),

[44] C. Borghi, C. Giori C. and A.~ Dall'Olio,(Russian) Phys. Atomic Nuclei, ** 56**, 205 (1993).

[45] R. M. Santilli, "Apparent confirmation of Don Borghi's experiment toward the synthesis of neutron from protons and electrons," Hadronic Journal **30**, 709 (1997).

http://www.santilli-foundation.org/docs/Santilli-21.pdf

46] R. M. Santilli, "Confirmation of Don Borghi's experiment on the synthesis of neutrons from protons and electrons," website

http://www.neutronstructure.org/neutron-synthesis.htm

[47] R. M. Santilli, The synthesis of the neutron according to hadronic mechanics and chemistry," Journal Applied Sciences, in press

[48] J. V. Kadeisvili, The Rutherford-Santilli Neutron," Hadronic J. Vol. 31, Number 1, pages 1-125, 2008
pdf version of the publisghed paper

http://www.i-b-r.org/Rutherford-Santilli-II.pdf

also available in in htlm format at
http://www.i-b-r.org/Rutherford-Santilli-neutron.htm

[49] R. M. Santilli, "The structure of the neutron as predicted by hadronic mechanics" website (2006)

http://www.neutronstructure.org/

**Part III: References on the the reduction of Nuclei to Protons and Electrons.**

[50] R. M. Santilli, "Nuclear realization of hadronic mechanics and the exact representation of nuclear magnetic moments,"
R. M. Santilli, Intern. J. of Phys. Vol. 4, 1-70 (1998)

http://www.santilli-foundation.org/docs/Santilli-07.pdf

[51] R. M. Santilli, "The nuclear structure according to hadronic mechanics,"
R. M. Santilli, Intern. J. of Phys. Vol. 4, 1-70 (1998)

http://www.santilli-foundation.org/docs/Santilli-07.pdf

[52] R. M. Santilli, "Closed systems with non-Hamiltonian internal forces,"
ICTP preprint # IC/91/259 (1991)

http://www.santilli-foundation.org/docs/Santilli-143.pdf

[54] R. M. Santilli, "Generalized two-body and three-bodies systems with non-Hamiltonian internal forces," ICTP preprint # IC/91/264 (1991)

http://www.santilli-foundation.org/docs/Santilli-139.pdf

[55] R. M. Santilli, "Theory of mutation of elementary particles and its application to Rauch's experiment on the spinorial symmetry," ICTP preprint # IC/91/265 (1991)

http://www.santilli-foundation.org/docs/Santilli-141.pdf

[56] R. M. Santilli, "The notion of nonrelativistic isoparticle," ICTP preprint # IC/91/265 (1991)

http://www.santilli-foundation.org/docs/Santilli-145.pdf

[57] R. M. Santilli, "A quantitative isotopic representation of the deuteron magnetic moment," in *Proceedings of the International Symposium 'Dubna Deuteron-93,* Joint Institute for Nuclear Research, Dubna, Russia (1994)

http://www.santilli-foundation.org/docs/Santilli-134.pdf

[58] R. M. Santilli, "Theory of mutation of elementary particles and its application to Rauch's experiment on the spinorial symmetry," ICTP preprint # IC/91/46 (1991)

http://www.santilli-foundation.org/docs/Santilli-141.pdf

[59] R. M. Santilli, "Isorepresentation of the Lie-isotopic SU(2) algebra with application to nuclear physics and local realism,

Acta Appliucandae Mathematicae Vol. 50, 177-190 (1998)

http://www.santilli-foundation.org/docs/Santilli-27.pdf

[60] C. Ktorides, H. C. Myung and R. M. santilli, "Elaboration of the recently proposed test of Pauli's principle under strong interactions," Physical Review D, Vol. 22, 892 (1980)

http://www.santilli-foundation.org/docs/Santilli-16.pdf

[61] R. M. Santilli, "Possible implications of nonlocal-integral effects for new methods of recycling nuclear waste," in the *Proceedings of "Large Scale Collective Motion of Atomic Nuclei",* G. Giardina, G. Fazio and M. Lattuada, Editors, World Scientific pages 549-556 (1996)

http://www.santilli-foundation.org/docs/Santilli-132.pdf

[62] R. M. Santilli, *The Physics of New Clean Energies and Fuels According to Hadronic Mechanics,* ICTP preprint # IC/91/47 (1992)

http://www.santilli-foundation.org/docs/Santilli-114.pdf

**PPart IV: References on Hadronic Chemistry**

[63] ]R. M. Santilli, *Foundations of Hadronic Chemistry, with Applications to New Clean Energies and Fuels,* Kluwer Academic Publishers (2001),

http: //www.santilli-foundation.org/docs/Santilli-113.pdf.

Russian translation

http://i-b-r.org/docs/Santilli-Hadronic-Chemistry.pdf

[64] R. M. Santilli, "An Introduction to Hadronic Chemistry," Keynote Lecture at the
*2013 Indian Conference on hadronic Chemistry*

http://www.santilli-foundation.org/Santilli-India-2013.php

[65] E. Trell, "Review of Santilli�s Foundations of Hadronic Chemistry," Intern. J. Hydrogen Energy 28, 251 (2003),

http://www.santilli-foundation.org/docs/Trell-review-HC.pdf

[66] V. Tandge, "Hadronic Chemistry Applied to Hydrogen and Water Molecules," AIP Conf. Proc. 1479, 1013 (22012)

http://www.santilli-foundation.org/docs/Tandge-AIP.pdf

[67] R. M. Santilli and D. D. Shillady,, "A new isochemical model of the hydrogen molecule," Intern. J. Hydrogen Energy Vol. 24, pages 943-956 (1999)

http://www.santilli-foundation.org/docs/Santilli-135.pdf

[68] R. Perez-Enriquez and R. Riera, "Exact analytic solution of the restricted three-body Santilli-Shillady model of the hydrogen molecule, " Progress in Physics Vol. 2, 34-41 (2007) (physics/0001056)

www.santilli-foundation.org/docs/3body2.pdf

[69] A. K. Aringazin and M.G. Kucherenko, "Exact variational solution of the restricted three-body Santilli-Shillady model of the hydrogen molecule," Hadronic J. Vol. 23, 1-56 (2000) (physics/0001056)

www.santilli-foundation.org/docs/3body.pdf

[70] R. M. Santilli and D. D. Shillady, , "A new isochemical model of the water molecule," Intern. J. Hydrogen Energy Vol. 25, 173-183 (2000)

http://www.santilli-foundation.org/docs/Santilli-39.pdf

[71] R. M. Santilli, "Theoretical prediction and experimental verification of the new chemical species of magnecules," Hadronic J. 21, 789 (1998),

http://www.i-b-r.org/docs/estimate.pdf

[72] M.G. Kucherenko and A.K. Aringazin, "Estimate of the polarized magnetic moment of the isoelectronium in the hydrogen molecule" Hadronic J. 21, 895 (1998),

http://www.i-b-r.org/docs/landau.pdf

[73 ] A. K. Aringazin, "Toroidal configuration of the orbit of the electron of the hydrogen atom under strong external magnetic fields," Hadronic J. 24, 134 (2001),

http://www.santilli-foundation.org/docs/landau.pdf

[74] R. M. Santilli, "The novel magnecular species of hydrogen and oxygen with increased specific weight and energy content," Intern. J. Hydrogen Energy 28, 177-196 (2003),

http://www.santilli-foundation.org/docs/Santilli-38.pdf

[ 75] R. M. Santilli, "A new gaseous and combustible form of water," Intern. J. Hydrogen
Energy 31, 1113 (2006),

http://www.santilli-foundation.org/docs/Santilli-138.pdf

[76] M. O. Cloonan,"Application of the Cplex-isoelectronic theory to electrocyclisations, sigmatropic rearrangements, cheletropic reactions and antiaromaticity: Consistent with Santilli�s hadronic chemistry," Int. J. Hydrogen Energy 32 , 3026 (2006),

http://www.santilli-foundation.org/docs/Cloonan-Paper2.pdf

[77] M. O. Cloonan, "A new electronic theory of pericyclic chemistry and aromaticity is proposed: The Cplex-isoelectronic theory. Consistent with Santilli�s hadronic chemistry," Int J Hydrogen Energy, 32, 159 (2007),

http://www.santilli-foundation.org/docs/Cloonan-Paper1.pdf

[ 78] M. O. Cloonan, "Origin of the endoselectivity observed in pericyciclic reactions based on the CPlex-Isoelectronic theory,� Hadronic J, 32, 125 (2009),

http://www.santilli-foundation.org/docs/Cloonan-Paper3.pdf

[ 79] R. M. Santilli, *The New Fuels with Magnecular Structure, * International Academic
Press (2008),

http://www.i-b-r.org/docs/Fuels-Magnecular-StructureF.pdf,

Italian translation available from the link

http://www.i-b-r.org/docs/Carb-Strutt-Magnecolare.doc

[80] Y. Yang, J. V. Kadeisvili, and S. Marton, "Experimental Confirmations of the New Chemical Species of Santilli MagneHydrogen,"
International Journal Hydrogen Energy Vol. 38, page 5002 (2013)

http://www.santilli-foundation.org/docs/MagneHydrogen-2012.pdf

[81] Y. Yang, J. V. Kadeisvili, and S. Marton, "Experimental Confirmations of the New Chemical Species of Santilli Magnecules,"
The Open Physical Chemistry Journal Vol. 5, 1-16 (2013)

pdf available from the link
http://www.santilli-foundation.org/docs/Magnecules-2012.pdf

82] R. M. Santilli, "Apparent detection of H3O, COH, CO2H and other anomalous species," submitted for publication (2014)

http://www.santilli-foundation.org/docs/H3O-paper.pdf

**Part V: References on Nuclear Energies Without Radiations**

(83) R. M. Santilli, * The Physics of New Clean Energies and Fuels According to Hadronic Mechanics,* Special issue of the Journal of New Energy, 318 pages (1998)

http://www.santilli-foundation.org/docs/Santilli-114.pdf

[84] R. M. Santilli. "The novel ``Controlled Intermediate Nuclear Fusion:" A report on its industrial realization as predicted by hadronic mechanics," Hadronic J. Viol.31, page 1, 2008

http://www.i-b-r.org/CNF-printed.pdf

[85] R. M. Santilli, "Experimental Confirmation of Nitrogen Synthesis from deuterium and Carbon without harmful radiations," New Advances in Physics Vol. 4, page 29, 2011

http://www.santilli-foundation.org/docs/ICNF-1.pdf

[86] Robert Brenna, Theodore Kuliczkowski, Leong Ying, "Verification of Santilli intermediate Controlled Nuclear Fusions without harmful radiations a and the production of magnecular clusters," New Advances in Physics, Vol. 5, page 9 (2011)

http://www.santilli-foundation.org/docs/ICNF-2.pdf

[87] J. V. Kadeisvili, C. Lynch and Y. Yang, "Confirmations of Santilli Intermediate Nuclear Fusions of Deuteron and Carbon into Nitrogen without Radiations." The Open Physical Chemistry HJournal Vol. 5, page 17, 2013

http://www.santilli-foundation.org/docs/ICNF-Conf-2013.pdf

[88] L. Ying, W. Cai, J. Kadeisvili3, C. Lynch, S. Marton, S. Elliot and Y. Yang, "Experimental verification for Intermediate Controlled Nuclear Fusion," City College of New York Preprint, to appear,

http://www.santilli-foundation.org/docs/ICNF-Cai-paper-Ying.pdf

[89] R. M. Santilli, "Additional Confirmation of the "Intermediate Controlled Nuclear Fusions"
without harmful radiation or waste," *Proceedings of the Third International Conference on the Lie-Admissible Treatment of Irreversible Processes,* C. Corda, Editor, Kathmandu University (2011) pages 163-177

http://www.santilli-foundation.org/docs/ICNF-3.pdf

[90] R. M. Santilli, "Hadronic energies,"
Hadronic Journal, Vol. 17, 311 (1994)

http://www.santilli-foundation.org/docs/Santilli-23.pdf

[91] D. Rossiter, Director, "IVA Report 184443 on comparative Nitrogen counts" (for Ref. [78]),

http://www.santilli-foundation.org/docs/IVA-Report-184443.pdf

[92] Daniel Rossiter, Director, "IVA Report 184445 on comparative Nitrogen counts on five samples" (for ref. [79]),

http://www.santilli-foundation.org/docs/Spectral-analysis-Ref-[79].png

[93] R. Brenna, T. Kuliczkowski and L. Ying, "Report on Test for Silica" (for Ref. [80]),

http://www.santilli-foundation.org/docs/PGTI-Anal-test1.pdf
[94] D. Rossiter, Director, "IVA Report 189920 on comparative Silica counts," (for ref. [80]).

http://www.santilli-foundation.org/docs/IVAReport 189920.pdf

[95] D. Rossiter, Director, "IVA Report 189920 on comparative Silica counts," (for ref. [80]).

http://www.santilli-foundation.org/docs/IVAReport 189920.pdf

[96] D. Rossiter, Director, "IVA Report 200010 on comparative Nitrogen counts," (for Ref. [81]).

http://www.santilli-foundation.org/docs/Oneida-analyses-2013.zip

[97] D. Swartz, "Constellation Technologies first report on comparative Silica counts,"
http://www.santilli-foundation.org/docs/Constellation-Si-10-13.zip

[98] D. Swartz, "Constellation technologies second report on comparative Silica counts,"
http://www.santilli-foundation.org/docs/Constellation-Rep-Si-2.zip

[99] D. Swartz, "Constellation technologies Third report on comparative Silica counts,"
http://www.santilli-foundation.org/docs/Constell-Si-3.pdf

[100] A. Nas, "Data on Constellation technologies tests 1 and 2 on comparative Silica counts,"

http://www.santilli-foundation.org/docs/Data-Constell-tests.docx

[101] R. M. Santilli, "Teh problem of recycling nuclear waste," Web site 2008

http://www.nuclearwasterecycling.com/