Ruggero Maria Santilli

P. O. Box 1577, Palm Harbor, FL 34682

Curriculum Vitae

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Last revision April 14, 2003

THE NEUTRON AS A HADRONIC BOUND STATE OF AN ISOELECTRON AND AN ISOPROTON, INDUSTRIAL UTILIZATION OF THE INEXHAUSTIBLE CLEAN ENERGY INSIDE THE NEUTRON, AND THE APPARENT LACK OF EXISTENCE OF NEUTRINOS FOR EXTENDED HADRONS.

**DEDICATION
This section is dedicated to
MICHAEL McDONNOUGH,
President
Betavoltaic Industries, Inc,
because his leadership, vision and dedication to the pursuit of qualified basic advances in the new, clean, and inextinguishable energy contained in the neutron have been instrumental in the continuation of my studies in the field.**

2. RUTHERFORD'S CONCEPTION OF THE NEUTRON AND ITS HISTORICAL INCONSISTENCIES FOR QUANTUM MECHANICS

4. NONRELATIVISTIC, EXACT AND INVARIANT REPRESENTATION OF THE NEUTRON SPIN VIA HADRONIC MECHANICS

7. COMPATIBILITY OF THE RUTHERFORD-SANTILLI NEUTRON STRUCTURE WITH SU(3) CLASSIFICATIONS

8. PHYSICAL LAWS PREDICTED BY HADRONIC MECHANICS FOR NEW HADRONIC ENERGIES OF CLASS I

9. DON BORGHI'S EXPERIMENT ON THE SYNTHESIS OF THE NEUTRON FROM PROTONS AND ELECTRONS

10. INDUSTRIAL UTILIZATION OF THE INEXTINGUISHABLE CLEAN ENERGY INSIDE THE NEUTRON

11. TSAGAS' EXPERIMENTAL VERIFICATION OF THE STIMULATED DECAY OF THE NEUTRON

12. RECYCLING OF RADIOACTIVE NUCLEAR WASTE VIA STIMULATED BETA DECAYS

14. LACK OF NEED OF THE NEUTRINO HYPOTHESIS FOR EXTENDED HADRONS

16. GENERAL REFERENCES ON HADRONIC MECHANICS

**1. REDUCTION OF THE STRUCTURE OF MATTER TO ELECTRONS AND PROTONS VERIFYING HADRONIC MECHANICS**

As stated in the original proposal (38) of 1978, *hadronic mechanics has been constructed for the reduction of the strutture of all matter (antimatter) in the universe to the only known stable and massive particles, electrons and protons (their antiparticles).* The main assumption is that in the transition from their condition in vacuum at large mutual distances, as exactly represented by quantum mechanics, to conditions of deep mutual penetration of their wavepackets at short distances, we have new contact effects that are **nonunitary,** thus not representable with a Hermitean (observable) Hamiltonian. As such, these effects are beyond the descriptive capacities of quantum mechanics, with the consequential applicability of the covering hadronic mechanics in view of its nonunitary structure.

Since hadrons are considered as isolated from the rest of the universe for the scope here considered, they verify conventional, Galilean or Einsteinian, total conservation laws, yet admit non-Hamiltonian internal effects. Under these conditions, the applicable discipline is the **isotopic branch of hadronic mechanics,** or **isomechanics** for short, with fundamental time evolution law in finite and infinitesimal form for a Hermitean operator (observable) A(t), first introduced in Ref. (38),

(1.1a) A(t) = [Exp(ixHxTxt)] x A(0) x [Exp(-ixTxH)],

(1.1b) i x dA/dt = A x T x H - H x T x A = A*H - H*A = [A, H]*,

(1.1c) I^ = 1/T, I^*|s> = (1/T) x T x |s> = |s>,

with corresponding generalized Schroedinger equations (Part II), where: "x" represents the conventional associative product of numbers, matrices, operators, etc.; "*" represents its isotopic covering; the Hamiltonian H = H(r, p) = p^{2}/2m + V = H^{+} represents conventional action-at-a-distance, potential interactions; the Hermitean, everywhere invertible, and positive-definite isounit I^ = I^(r, p, ...) = 1/T(r, p, ...) = (I^)^{+} > 0 represents said nonunitary/non-Hamiltonian effects; and Eqs. (1.1) are defined on the *iso-Hilbert space over the isofield* C^ of isocomplex numbers (12) with isostates and inner isoproduct, respectively,

(1.2a) I^ = U x U^{+} > 0, I^ ≠ I,

(1.2b) |s*) = U x |s), (s*| = (s| x U^{+},

(1.2c) (s*|*|s*) x I^ = (s*| x T x |s*) = U x (s| x |s) x U^{+},

where |s) and (s|x|s) are states and inner product, respectively of a conventional quantum mechanical Hilbert space over the field of complex numbers C.

In this way, hadronic models can be constructed quite simply via a nonunitary transform of conventional quantum models (see Parts I and II for details). The fundamental isounit of the theory for the case of two particles, here denoted 1 and 2, interacting at short distances is given by

(1.3) I^ = U x U^{+} = [ Diag. (n_{1}^{2}, n_{2}^{2}, n_{3}^{2}, n_{4}^{2})_{particle 1} x Diag. (n_{1}^{2}, n_{2}^{2}, n_{3}^{2}, n_{4}^{2})_{particle 2} ] x

x Exp[F(r, p,...) (1*|x|2*)]

where: n_{1}^{2}, n_{2}^{2}, n_{3}^{2} represent the actual, extended and deformable **shape** of hadrons (here assumed to be ellipsoids due to their general spinning character); n_{4}^{2} represents the **density** of the medium inside the hadron considered with normalization to 1 for the vacuum. [note that the density of hadrons varies from hadron to hadron due to the preservation of the size under the increase of the mass]; F(r, p, ...) is a function representing contact **non-potential interactions;** and (1*|x|2*) represents the volume integral of state |2*> and |1*>^{+}, namely,
the **wave overlappings** of the constituents.

It should be noted that the shapes and densities of the two particles 1 and 2 are generally assumed to be the same in first approximation. This is the reason why the isounit actually used in specific models only generally has only one matrix, rather than the product of two.

<
As one can see, the new interactions permitting the reduction of matter to electrons and protons are: **nonpotential,** in the sense of being of contact/zero-range type not representable with an additive term in the Hamiltonian; **nonlinear,** in the sense of depending on the isowavefunctions/isostates in a nonlinear way; and **nonlocal,** in the sense of depending on a volume that is not reducible to a finite set of isolated points, as necessary for the exact applicability of quantum mechanics. Note that, whenever the overlappings of the wavepackets of the constituents is ignorable, i.e., (s*|x|s*) = 0, and the particles are assumed to be perfectly spherical, I^ = I hadronic mechanics recovers quantum mechanics identically.

Since hadronic mechanics coincides with quantum mechanics at the abstract, realization-free level (because I and I^ are both positive-definite, AxB and A*B are both associative, etc.), the transition from quantum to hadronic mechanics is called an *isotopy* (23) in the sense of being axiom preserving. Therefore, **hadronic mechanics is a mere broader realization of the same abstract axioms of quantum mechanics.**

The fundamental mathematical methods for the reduction of matter to electrons and protons are given by: the **iso-Minkowskian space** ; the **Poincare'-Santilli isosymmetry,** and **isospecial relativity,** all introduced for the first time in Ref. (26) of 1983 (see Ref. (15) for a recent treatment of the iso-Minkowskian geometry, Ref. (29) for the Poincare'-Santilli isosymmetry, and Refs. (30,52-55) for isospecial relativity).

The transition of particles from motion in vacuum at large mutual distances to the condition of deep mutual penetrations is represented by the transition from irreducible representations of the Poincare' symmetry to irreducible isorepresentations of the covering Poincare'-Santilli isosymmetry. Such a transition is also called a **mutation** (16) because of certain algebraic reasons connected to Albert's notion of Lie- and Jordan admissibility (7). The resulting particles are called **isoparticles** and denoted with the symbols e^, p^, etc., to distinguish them from conventional quantum particles such as e, p, ...

In Part IV we reviewed the important result that* hadronic mechanics achieved since the original proposal by R. M. Santilli (38) of 1978 the exact and invariant representation of all characteristics of mesons and unstable leptons via a hadronic bound state at short distances of electrons and positrons, although in the mutated form of isoparticles obeying isospecial relativity and underlying Poincare'-Santilli isosymmetry.* The reduction was achieved via suitable nonunitary transforms of conventional quantum models. For instance the structure model of p

(1.4) p^{o} = (e^^{-},e^^{+})_{hm} = U x (e^{-},e^{+})_{qm} x U^{+} = U x (positronium) x U^{+}.

The reduction of the remaining mesons and unstable leptons to hadronic bound states of isoelectrons and isopositron was then consequential. For instance, the representation of all characteristics of charged pions is achieved via the model
p^{ħ} = (p^^{o},e^^{ħ})_{hm}, with similar models for the remaining particles, as first proposed and worked out in all numerical details in the original proposal (38).

As proposed in Ref. (31), full compatibility between the above structure models and the SU(3) color model of Mendeleev-type classification was easily achieved via the hypermechanics, e.g., by forming an octet of isounits I_{8} = (I^_{po}, I^_{pħ}, ...) and then constructing the SU(3) hypersymmetry with respect such 8-multi-valued unit. Since both, the conventional trivial unit I = Diag. (1, 1,,1,...) currently used in unitary models and the hyperunit I^_{8} are positive-definite, the hypersymmetry SU^_{8}(3) is isomorphic to the conventional symmetry, in which case all conventional results persist under the above lifting, with intriguing added degrees of freedom to resolve open vexing problems of SU(3) symmetries, e.g., the still missing representation of of the spin of hadrons.

According to the above view, quarks do remain applicable and useful. However, *hadronic mechanics identified quarks for what they are outside academic politics, purely mathematical representations of a purely mathematical symmetry realized on the purely mathematical complex unitary spaces, as a consequence of which quarks cannot be even defined, let alone exist as physical particles in our spacetime.*

A primary objective of this web site is to show that the theoretically and experimentally unsubstantiated belief that quarks are actual physical particles PREVENTS the study of new clean energies, thus raising problems of scientific ethics and accountability by quark believers, because scholar opposing the clear evidence on the purely mathematical nature of quarks actually oppose a scientific process aimed at industrial applications of hadron physics for personal gains.

In this Part 5 we show that *hadronic mechanics permits an exact and invariant representation of all characteristics of unstable baryons via hadronic bound states at short distances of protons, electrons and their antiparticles, again in the mutated form of isoparticles obeying isospecial relativity and its underlying Poincare'-Santilli isosymmetry.*

The fundamental model is the representation of ALL characteristics of the neutron n as a hadronic bound state of one isoelectron e^ and one isoproton p^ (214) via a nonunitary transform of the structure model of the hydrogen atom,

(1.5) n = (e^^{-},p^^{+})_{hm} = U x (e^{-},p^{+})_{qm} x U^{+} = U x (hydrogen atom) x U^{+}.

The reduction of the structure of all remaining unstable baryons to hadronic bound states of isoelectron, isoprotons and their antiparticles is then consequential, as we shall see. Full compatibility with SU(3) Mendeleev-type classifications are achieved as for the case of mesons via hyper-liftings of conventional unitary models.

The exact and invariant representation of all characteristics of the neutron via the above hadronic model was achieved for the first time at the nonrelativistic level by R. M. Santilli in Ref. (214) of 1990. The full relativistic extension via the isotopies of Dirac's equation representing precisely the electron inside the proton, was achieved by R. M. Santilli in Ref. (30) of 1996. Additional important studies based on hadronic mechanics were done by R. Driscol, S. Smith, J. V. Kadeisvili, as we hope the authors will outline in Part VIII of this web site.

Due to the limitations of the current htlm format for mathematical symbols, the need for the original derivations for a serious study, and the possible lack of general availability of the quoted papers, Refs. (30,214) will be reproduced in pdf format at the end of this Part V.

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Since quantum mechanics can only represent point particles moving in vacuum, the covering hadronic mechanics becomes mandatory to represent the extended wavepackets of the electron when moving within the hyperdense medium in the proton structure, as well as to resolve the several historical objections against Rutherford's model (such as the inability to represent the rest energy, spin, meanlife, charge radius, anomalous magnetic moment and other features of the neutron).

It should be noted that recent experiments conducted at Virginia's Jefferson Laboratory appear to confirm that the neutron is indeed composed of the proton surrounded by a negative charge. The latter is generally interpreted as being given by the p^{-} for the evident intent of adapting physical data to quantum mechanics (since the assumption of the electron mandates the use of the covering hadronic mechanics to resolve said historical inconsistencies).

*
It is important for the reader outside academic politics to know that the above quantum mechanical structure model of the neutron is fundamentally flawed because the p ^{-} is an UNSTABLE particle with a meanlife of about 10^{-16} seconds, thus being fundamentally unable to represent the stability of the neutron in ordinary stable matter. In view of its stability, only the assumption of the electron as originating the negative cloud around the proton can represent recent experimental data on the neutron structure, while achieving an exact and invariant representation of all known phenomenology of the neutron. However, such a resolution can only be achieved with the reverse attitude, that of adapting and modifying the theory to the problem at hand.*

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A reason for the considerable period of time elapsed from the achievement of the hadronic model for mesons of the original proposal (38) of 1978 and the hadronic structure model of the neutron (214) of 1990 was the need of prior studies on the isotopies of the fundamental rotation and spin symmetries, that are briefly outlined in the following sections.

As we shall see in this Part V and in the following Part VI, *the admission that quarks are purely mathematical objects, and the consequential reduction of all matter in the universe to electrons and protons permits the prediction and quantitative treatment of basically new clean energies, thus deserving serious attention by the scientific community at large.*

**2. RUTHERFORD'S CONCEPTION OF THE NEUTRON AND ITS HISTORICAL INCONSISTENCIES FOR QUANTUM MECHANICS**

E. Rutherford conceived the neutron in 1920 as a "compressed hydrogen atom in the core of a star," namely, as an electron compressed all the way inside a proton. As it is well known since Rutherford's time, stars initiate their lives as being solely composed of hydrogen, and end their lives by releasing all natural elements. This implies the synthesis in the interior of stars, first, of the neutron from protons and electrons, then of the deuteron and then of all other natural elements.

In 1932 J. Chadwick confirmed experimentally Rutherford's hypothesis on the *existence* of the neutron. However, Rutherford's *conception* of the structure of the neutron was rejected by W. Pauli, E. Fermi, W. Heisenberg, and all other leading scientists of the time, because **quantum mechanics does not permit a consistent representation of the neutron as a bound state of a proton and an electron.**Recall that:

1) **The main characteristics of the neutron are:**: rest energy 939.565 MeV; charge 0; spin 1/2; charge radius of about one Fermi (F = 10^{-13} cm); meanlife of about 916 sec (when isolated in vacuum); magnetic dipole moment -1.913 m_{N}; and electric dipole moment essentially null;

2) **The main characteristics of the proton are:** rest energy 938.273 MeV; charge +e; spin 1/2; charge radius of about one Fermi; meanlife essentially infinite; magnetic dipole moment 2.793 m^{N}; and electric dipole moment essentially null.

3) **The main feature of the electron are:** rest energy 0.511 MeV; charge -e; spin 1/2; classical radius of the order of Fermi; meanlife essentially infinite; ; magnetic dipole moment 1.001 m_{B}; and electric dipole moment essentially null;

In view of the above characteristics, we have the following **historical difficulties of Rutherford's conception of the neutron:**

HISTORICAL DIFFICULTY # I: Quantum mechanics does not permit the representation of the neutron rest energy because its value (939.565 MeV) is *bigger* than the sum of the rest energies of the proton and of the electron (938.784 MeV), thus requiring *positive binding energy,* a mere anathema for quantum mechanics because in this case Schroedinger's equation becomes inconsistent (in fact, all binding energies predicted by quantum mechanics are negative).

HISTORICAL DIFFICULTY # II: Quantum mechanics does not permit the representation of the spin 1/2 of the neutron, because the two constituents both have spin 1/2, thus implying that all possible quantum mechanical bound states have integer spin.

HISTORICAL DIFFICULTY # III: Quantum mechanics does not permit the representation of the size (charge radius) of the neutron, because the smallest radius predicted by quantum mechanics for a bound state of a proton and an electron is Bohr's radius, that is about 10^5 times *bigger* than the neutron charge radius.

HISTORICAL DIFFICULTY # IV: Quantum mechanics does not permit a representation of the neutron meanlife (916 sec) because it predicts that an electron can be trapped inside the proton only for nanoseconds.

HISTORICAL DIFFICULTY # V: Quantum mechanics does not permit a representation of the magnetic moment of the neutron (-1.913 m_{N}) from the magnetic moment of the proton (2.793 m_{N}) and of the electron (1.001 m_{B}) since 1 m_{B} = 1836.151 m_{N}, as a result of which the magnetic moment predicted by quantum mechanics would be - 1,883. 358 m_{N} rather than -1.913 m_{N} since all these paticles are assumed to be pointlike.

The abandonment of Rutherford conception of the neutron structure caused a major historical change in physics that has not yet been appraised by historians. In fact, we first saw the proposal in 1943 by W. Heisenberg of the *mathematical unification* of protons and neutrons via the SU(2)-isospin symmetry, to be followed in the second half of the 20-st century by the well known SU(3)-color classification and structure of hadrons, the latter implying an even greater departures from Rutherford's teaching for physically constituents, that is, constituents directly and unequivocally detectable in our laboratory contrary to what had been the preceding cases for the structure of molecules, nuclei and atoms.

Moreover, the abandonment of Rutherford's conception of the neutron forced the conjecture of the various neutrinos, which conjecture, as we shall see later on in this Part V, is un-necessary for the structure of the neutron according to Rutherford while preserving ALL conventional conservation laws, provided that the proton and neutron are NOT assumed to be point-like, as necessary for quantum mechanics, and are instead admitted and represented as they are in the physical reality, expended particles.

The expectation of the universal validity of quantum mechanics was understandable during Pauli's, Fermi's and Heisenberg's times. However, **nowadays, the assumption that quantum mechanics is exactly valid within the hyperdense medium in the interior of the proton is considered a purely political-nonscientific posture,** due to the dramatic physical differences between the orbiting of an electron in vacuum around the proton, and the orbiting of the same electron within the hyperdense medium inside the proton. While quantum mechanics is exactly valid in the former case, the sole open scientific issue for the latter case is the identification of the appropriate more adequate mechanics.

For the latter reasons, studies on Rutherford's conception of the neutron as a bound state of a proton and an electron were never halted (see various contributions in Proceedings (91)). After all, the neutron decays spontaneously into a proton, an electron and the hypothetical antineutrino,

(2.1) n => p + e + antineutrino,

thus providing a *prima facie* major intuitional support for Rutherford's conception.

Moreover, currently preferred conjectures on the structure of the neutron imply that, **at the time of the synthesis of the neutron in the core of stars, the proton and the electron completely disappear to be replaced by the hypothetical quarks,**

(2.2) p + e => n + neutrino, n = quark bound state.

However, *the proton and the electron are the only known permanently stable, massive particles. The idea that they disappear at the time of the neutron synthesis to be replaced by the hypothetical and undetectable quarks, is contrary to common sense and will never be accepted as physical reality by the entire scientific community.*

The SU(3)-color model can be safely assumed as providing the final Mendeleev-type classification of hadrons into families, while the assumption that the same classification model also provides the structure of each individual hadron of an SU(3)-multiplet is afflicted by a plethora of major unresolved problems. After all, for the case of atomic, nuclear, molecular and other systems, *history has established the need for two models, one for the classification of structures into families, and a different, yet compatible model for the structure of each member of a given family.*

In the final analysis, ** the neutron constitutes the largest reservoir of clean energy available to mankind,** because it is naturally unstable and releases a very energetic electron that can be easily trapped by thin metal shields, thus permitting the conception of clean new energies. As we shall see, *the utilization of the clean energies inside the neutron is prohibited by quark conjectures because of the impossibility of producing quarks free, contrary to what has been the case for atomic, nuclear and all other energies. On the contrary, as we shall see in this Part V, the utilization of the energy contained inside the neutron is permitted by Rutherford's original conception. *

In view of the above open scientific problems and societal implications, we have an ethical duty to submit Rutherford's conception of the neutron to serious conceptual, theoretical and experimental scrutinies. All scholars who worked at the construction of hadronic mechanics (see a partial list in Section I.3) have fulfilled well this duty because the new mechanics was constructed primarily for the resolution of the historical difficulties of Rutherford's conception of the neutron, and the consequential return of the physics of strong interactions to more concrete grounds admitting significant industrial applications as it had been the case for the physics of electromagnetic interactions.

We are now equipped to review the exact and invariant representation of ALL characteristics of the neutron as a hadronic bound state of an isoproton and an isoelectron, first achieved by R. M. Santilli in Ref. (214).

In this section we shall review the exact nonrelativistic representation of the rest energy, meanlife and charge radius of the neutron. The exact and invariant nonrelativistic representation of the other characteristics of the neutron, as well as their relativistic extension, will be outlined in the next sections. The visitor should be aware that, due to the current insufficiency of the html format for mathematical symbols, this presentation is merely a nontechnical review. A serious knowledge of the topic can only be acquired by studying the original paper (214) reproduced in pdf format at the end of this section.

The basic model is the familiar Schroedinger's equation for the structure of the **hydrogen atom,**

(3.1a) H x |e> = [(-h^{2}/2m)D_{r}D_{r} - e^{2}/r] x |e> = E x |e>,

(3.1b) p x |e> = - i x h x D_{r} |e>,

(3.1c) m = m_{e} x m_{p} / (m_{e} + m_{p}) = m_{e},

where; h represents h-bar; |e> represents the conventional Hilbert state of the hydrogen atom; D_{r} represents partial derivative with respect to r; D_{r}D_{r} represents the usual Laplacian; and the last expression holds in first approximation since the proton mass m_{p} is about 2,000 times bigger than the electron mass m_{e}.

The method for the construction of the hadronic structure equation of the neutron according to Rutherford has been developed in Part IV, Section 1, and consists in subjecting the above equation and the entire related mathematics to the nonunitary transform (IV.1.5a), i.e.,

(3.2) I^ = U x U^{+} = 1/T > 0,

with realization (IV.1.11) and (IV.1.12) adapted to the problem at hand, i.e.,

(3.3) I^ = exp[(|e> / |e^>) x (e^_{up}|x|p^_{down})] =

= exp{- [r x e^{- r / R} / (1 - e^{- r / R})] x
(e^^{-}_{up}|x|p^^{+}_{down})},

where: |e^> represents the isostate of the isoelectron when a constituent of the neutron; |e^^{-}_{up}> represents the same isostate with spin up; |p^^{+}_{down}> represents the isostate of the isoprotons (also when a constituent of the neutron) with spin down; the up/down coupling is requested by the hadronic law for which triplet couplings at short distance are highly repulsive; and R represents the charge radius of the neutron.

For clarify, let us indicate the difference between isounit (1.3) and (3.30 above. The former represents a **two body** interaction and this explains the reason for the presence of two sets of characteristics n-quantities, one per each particle. For the case of isounit (3.3) we have instead a **one body** case, namely, the isoelectron inside the isoproton considered external and unperturbed, as it will be appear clearer in the relativistic treatment of Section 6 via the isotopies of the dirac equation (that DOES NOT represent a two-body particles, but rather one electron in the electromagnetic field of the proton considered as external, the two-body extension of Dirac's equation being still unknown to this day).

p>
As one can see, the above isounit verifies the general condition

(3.4) Lim I^_{r>>1F} = I.

Therefore, quantum mechanics and the conventional hydrogen atom are recovered identically whenever the wave-overlapping is no longer appreciable, i.e., (e^^{-}_{up}|x|p^^{+}_{down} = 0.

At this point, the ENTIRE mathematical treatment of the hydrogen atom must be subjected to nonunitary transform (3.2) to avoid a senseless mixture of quantum and hadronic mechanics with consequential loss of invariance, and the activation of the theorem II.2.1 on the catastrophic inconsistencies of noninvariant theories. The procedure implies the lifting of numbers n into isonumbers n^ = nxI^, fields R, C and Q into isofields R^, C^ and Q^, spaces S(r,m,R) with coordinates r an d metric m over R into isospaces S^(r^,m^,R^)., etc. (see Parts I and II for brevity). Most important is the lifting of differentials and derivatives into the isodifferential form (14)

(3.4) dr = d^r = I^ x dr, D^/D^r = T x D/Dr = T x D_{r}, etc.

The lifting of Eqs. (3.1) under nonunitary transform (3.2) yields the expressions along lines already studied in Part I, Ii and IV

(3.5a) U x H x |e> = (UxHxU^{+}) x (UxU^{+})^{-1} x (Ux|e>) = H^ x T x |e^> = H^*|e^> =

= [(-h^{2}/2m)D^_{r}D^_{r} - (e^{2}/r)xI^] x T x |e^> = E x |e^>,

(3.5b) p^ x T x |e> = - i x h x D^_{r} |e^>,

(3.5c) m = m_{e} x m_{p} / (m_{e} + m_{p}) = m_{e}.

As a result, **when formulated on isospaces over isofields, the hadronic structure equation of the neutron coincides with the quantum structure equation of the hydrogen atoms by conception and construction.** This is a rather general law of hadronic mechanics that is particularly useful for the practical construction of concrete applications.

The numerical solution must be searched in the **projection of the isoequation in our spacetime.** This is done via the explicit form of the iso-Laplacian (IV.1.9) that we shall write for the neutron

(3.6a) [- (h^{2}/2m) x D^_{r} D^_{r} - e^{2}/r] |e^> =

= [ - (h^{2}/m_{e^}) x D_{r} D_{r} - e^{2}/r - (h^{2}xI^xK/2m_{e}) x (D_{r} I^)] x |e^>,

(3.6b) m_{e^} = m_{e} x |I^^{2}|,

where K is the eigenvalue of the linear momentums and |I^^{2}| is average value within the sphere representing the neutron that are good approximations for the model at hand since the only stable hadronic orbit (such as that for Rutherford's electron *inside* the proton) is the circle, as illustrated in Part IV for the case of mesons (since elliptical orbits would imply evident high instabilities that are also evidently absent for the orbits of an electron in vacuum *around* the proton).

.
The replacement in Eq. (3.6) of the isounit (3.3) then yields the Hulten potential that "absorbs" the Coulomb potential as in Eqs. (IV.1.15)-(IV.1.19). In this way we obtain the equivalent of Eqs. (IV.1.22), namely, the following **nonrelativistic structure equation of the neutron according to Rutherford projected in our spacetime,** first achieved in Eqs. (2.19), page 521, Ref. (214),,

(3.7a) n = (e^^{-}_{up}, p^^{+}_{down})_{hm},

(3.7b) [- (h^{2}/2m_{e^}) x D_{r} D_{r} - V x e^{- r / R} / (1 - e^{- r / R}) ]] x |e^> = E x |e^>,

(3.7c) E_{n} = E_{p} + E_{e^,Tot} - | E | = 938 MeV,

(3.7d) t_{n}^{-1} =
4 x p x l^{2} x | e^(0)|^{2} x a x E_{e^,Tot} / h = 10^{3} sec^{-1},

(3.7e) R_{n} 10^{-13 } cm,

where l and h represents l-slash and h-bar, respectively.

The above equations were solved in Ref. (214), and reduced to the algebraic equations

(3.8a) k_{1}x[1 - (k_{2} - 1)^{2}] = ExR/2xc,

(3.8b) (k_{2} - 1)^{3}/k_{1} = 9x10^{6}xR/4xpxcxt,

with numerical solutions

(3.9a) k_{1} = 2.6,

(3.9b) k_{2} = 1 + 0.0.81x10^{-8}.

that should be compared to the corresponding values for the p^{o}, Eqs. (IV.1.28).

In particular, the indicated numerical values imply the **suppression of the quantum spectrum of energy of the hydrogen atom down to one energy level only, that of the neutron.** This is another general feature of hadronic mechanics predicted since the original proposal (38) because all excited states of hadronic mechanics imply distances bigger than 1 F, with consequential limit (3.4) under which *all* excited states of model (3.7a) are those of the hydrogen atom.

The latter feature is technically represented by the fact that the Hulten potential appearing in Eq. (3.7a) is known to admit only * a finite number of energy levels,*

(3.10) E = (1/4xR^{2}xm_{e^})x(m_{e^}xVxR^{2}/n - n),n = 1, 2, 3, ... m,

that only admit the energy level n = 1, since k_{2} is slightly bigger than 1. In fact, for n = 2, 3, 4, ... the indicial equation does not admit real solution and Schroedinger's equation becomes inconsistent.

As we shall see, the reduction of the neutron to a bound state of a proton and an electron has far reaching implications for all of science, e.g., because nuclei can now be reduced to isoprotons and isoelectrons. The reduction also has far reaching industrial implications, e.g., because the isoelectron can be stimulated to exit the neutron, thus permitting the utilization of the inextinguishable clean energy inside the neutron as outlined later on in this Part V.

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**4. NONRELATIVISTIC, EXACT AND INVARIANT REPRESENTATION OF THE NEUTRON SPIN VIA HADRONIC MECHANICS**

The conceptual interpretation of the spin 1/2 of the neutron as first achieved in Ref. (214) is quite simple. As indicated earlier, a general law of hadronic mechanics is that *only the singlet coupling of spinning particles at mutual distances of the order of their size is stable, while triplet couplings are highly unstable.* This law was illustrated in Part IV with the coupling of gears that is stable in singlet only (antiparallel rotations), while in triplet (parallel rotation) the coupling of gears implies large repulsive forces or the breaking of the gears themselves (see Figure IV.2).

Consider the initiation of Rutherford's compression of the electron within the proton in singlet coupling, as illustrated in Figure 2 below. It is evident that, **as soon as the penetration begins, the electron is trapped inside the much heavier and spinning proton, thus resulting in a constrained orbital motion.** This is due to the fact indicated earlier that the proton is 1,836 times heavier than the electron, as a result of which the proton can be assumed in first approximation as remaining un-mutated in its intrinsic angular momentum, while contributions from mutations can at best be of second order.

Under the geometry of Rutherford's compression, it is then evident that ** the electron is constrained to have an orbital angular momentum equal to the proton spin, namely an angular momentum with the value 1/2, yet opposite to the electron spin. Therefore, the spin of the neutron coincides with that of the proton.**

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It should be stressed that **the above interpretation of the neutron spin is prohibited by quantum mechanics because angular momenta can only have integer eigenvalues.** This is due to the fact that, half-odd-integer angular momenta imply the breakdown of the unitarity of the theory, with consequential host of problems, including the loss of causality and probability laws (Theorem II.2.1 of catastrophic inconsistencies).

However, integer angular momenta were solely established for **particles moving in empty space.** Their supine acceptance as being also valid for a particle orbiting within a hyperdense medium without a serious scrutiny is a purely political posture deprived of scientific value. Also, constrained systems are well known in classical and quantum mechanics to imply anomalous eigenvalues. Finally, hadronic mechanics was constructed precisely for the regaining of unitarity on isospaces over isofields (Parts I and II). Therefore, half-off-integer angular momenta, while prohibited for quantum mechanics, are quite natural for the covering hadronic mechanics.

The exact and invariant representation of the spin 1/2 of the neutron for hadronic model (1.5) was first achieved by R. M. Santilli in Ref. (214) of 1990, which paper also provides the resolution of related consistency problems.
Quantitative and invariant studies of the problem here considered evidently require a 2x2-dimensional nonunitary-isounitary lifting of the conventional SU(2)-spin symmetry. It is characterized by the following isounit, isotopic element and isocommutation rules

(4.1a) I^ = Diag. (g_{1}^{-1}, g_{2}^{-1}), T = Diag. (g_{1}, g_{2}),

(4.1b) [J^_{i}, J^_{j}]* = J^_{i}xTxJ^_{j} - J^_{j}xTxJ^_{i} = i x e_{ijk}
xJ^_{k},

(4.1c) (J^^{2^})*|s^> = Mx(M + 1)|s^>,

(4.1d) (J^_{3})*|s^> = N x |s^>,

(4.1e) g_{1} = g_{2} = g,

where M and N will be identified shortly, and condition (4.1e) is needed to assure isounimodularity. A realization of the above isotopy is given by

(4.2a) J^_{1} = Offdiagonal(g^{-1/2}, g^{-1/2}),

(4.2b) J^_{2} = Offdiagonal (-ixg^{-1/2}, ixg^{-1/2}),

(4.2c) J^_{3} = g/2xDiag (g^{-1/2}, -g^{-1/2}),

with isoeigenvalues

(4.3a) (J^^{2})*|s^> = (PxS)x(PxS + 1)x|s^>,

(4.3b) J^_{3}*|s^> = ħ (PxS)x|s^>,

(4.3c) S = 1/2, P = Det I^ = g^{2},

with corresponding liftings for three- and higher-dimensional cases (that require isounits of corresponding dimensions) here omitted for brevity.

It is evident that the above isotopic SU^(2)-spin symmetry characterizes the following **mutations of spin S and angular momenta L for an electron within the hyperdense medium inside the proton,**, first achieved in Ref. (214)

(4.4a) S = 1/2 => S^ = P x S = P/2, P = g^{2};

(4.4b) L = 1 => L^ = Q x L = Q,

where Q is the equivalent of P in the three-dimensional isotopy of SU(2) for the case of the angular momentum. Note that *hadronic mechanics remains isounitary for all the above infinitely possible eigenvalues of spin and angular momenta, thus including fractional values of angular momenta as a particular case of a much broader class.*

The **spin of the neutron** is given by the sum of the isotopic realizations of the intrinsic and orbital angular momentum of the isoproton and isoelectron with isoeigenvalues

(4.5a) S^_{n}^{2^}*|e^> = S^_{n}*S^_{n}*|e^> = (S_{p} + PxS_{e} + QxL_{e})x(S_{p} + PxS_{e} + QxL_{e} + 1)x|s*> = (3/4) x |e^>,

(4.5b) S^_{n,3}*|e^> = (S_{p} + PxS_{e} + QxL_{e}) x |e^ = ħ(1/2)x|e^>,

(4.5c) J^_{e^,Tot,3}*|s*> = (S_{n} + PxS_{e} + QxL_{e})x|s*> = 0,

(4.4d) S_{n} = S_{p} = 1/2, S_{e} = 1/2, L_{e} = 1,

Since the proton is about two thousand times heavier than the electron, it can be considered at rest in first approximation, thus having conventional (quantum) spin 1/2 as indicated in Figure 2. Also, as indicated earlier, the electron can only have a stable coupling with the proton in singlet. Therefore, the electron has spin -1/2 in the configuration of Figure 2. It then follows that the only possible solution is that indicated earlier, for which the spin of the neutron coincides with that of the proton, and the isoelectron has null total angular momentum.

The invariant isounitary representation of the spin of Rutherford's neutron via the isotopies of SU(2)-spin is then characterized by the values

(4.6a) PxS + QxL = P/2 + Q = 0, Q = - P/2,

(4.6b) P = 1, Q = -1/2,

as derived conceptually before, namely, the spin of the electron is not mutated, while only the orbital angular momentum is mutated from the value L = 1 to L^ = 1/2.

It should be noted that *in a more realistic model all angular momenta of the isoelectron and of the isoproton are mutated, thus implying eigenvalues that are neither integer or half-off-integer* (see later on Section 6).

Note also the NECESSITY of the isotopies for the achievement of an exact and invariant representation of the spin of Rutherford's neutron. Note finally the **direct universality** of the above isotopies of SU(2)-spin, in the sense that any other nonunitary realization is equivalent to the preceding one.

The nonrelativistic, exact and invariant representation of the magnetic moment of the neutron (-1.913 m_{N}) from those of the proton and of the electron was also achieved for the first time by R. M. Santilli in Ref. (214) of 1990.

Recall from the preceding sections that: the spin of the neutron coincides with that of the proton; the electron's spin is antiparallel to that of the proton; and the orbital angular momentum of the electron is parallel to that of the proton spin, yet the magnetic moment it creates is antiparallel due to the negative charge of the electron. Recall also that the intrinsic magnetic moment of the electron when isolated in vacuum is much bigger than that of both the proton and the neutron because 1 m_{B} = 1,836.151 m_{N}.

The magnetic moment of Rutherford's neutron is characterized by **three** contributions, the magnetic moment of the proton, that of the electron, and that caused by the orbital motion of the electron. Note that for quantum mechanics the third contribution is completely missing because all particles are considered as points, in which case the electron cannot rotate *inside* the proton. As we shall see later on in this Part V, *the inability by quantum mechanics to treat the orbital motion of the electron inside the proton was the very origin of the conjecture of the neutrinos. *

With reference to the orientation of Figure 2, and by keeping in mind that a change of the sign of the charge implies a reversal of the sign of the magnetic moment, the derivation of Ref. (214) is based on the identity

(5.1) m_{n} =
m_{p^} + m_{e^,Intrinsic} - m_{e^,Orbital} = -1.9123 m_{N},

Since the spin of the proton and of the electron can be assumed to be conventional in first approximation, we can assume that the magnetic moments of the proton and of the isoelectron are conventional, i.e.,

(6.2a) m_{p^} = m_{p} = + 2.793 mu_{N},

(5.2b) m_{e^} = m_{e} = - 1.001 m_{B} = 1,837.987 m_{N},

(5.2c) m_{p^} + m_{e^} = 1,835 m_{N}.

It is then evident that *the anomalous magnetic moment of the neutron originates from the magnetic moment of the orbital motion of the isoelectron inside the proton, namely, a contribution that has been ignored since Rutherford's time until treated in Ref. (214).*

It is easy to see that the desired **exact and invariant representation of the anomalous magnetic moment of the neutron** is characterized by the following numerical values

(5.3a) m_{e^,Orbital} = +1.004 m_{B},

(5.3b) m_{e^,Total} = 3x10^{-3} m_{B},

(5.3c) m_{n} = -1.9123 m_{N},

and this complete our nonrelativistic review. Note that the small value (5.3b) 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, as clarified in the next section).

The most important treatment of the structure of the neutron according to Rutherford, today known as Rutherford-Santilli neutron, is the relativistic treatment first achieved in Ref. (30) of 1996 via **relativistic hadronic mechanics,** that includes the **isotopies of the Minkowski spacetime, of the Poincare' symmetry and of special relativity** (see Refs. (15,29,55) for more recent accounts and the references of memoir (226) for comprehensive quotations).

The main objective of the study is to show that **the isotopies of Dirac's equation permit an exact and invariant representation of the electron when compressed within the hyperdense medium inside the proton.** In this way one single set of abstract axioms, those originally conceived by Dirac, represents the structure of the hydrogen atom when realized with the simplest possible unit I, and the structure of the neutron when realized with the more general isounit I^.

Let M(q,m,R) be the conventional Minkowski spacetime with local coordinates q = (q^{k}) = (r, t), k = 1, 2, 3, 4, metric m = Diag. (1, 1, 1, -1) and invariant

(6.1) q^{2} = (q^{i}xm_{ij}xq^{j}) x I e R

on the field R of real numbers. The **Minkowski-Santilli isospace** M^(q^,m^,R^), first introduced in Ref. (26) of 1983, is characterized by the isospacetime coordinates q^ = (r^, t^) = qxI^, isometric m^xI^ = (Txm)xI^ (namely, a matrix whose elements are isonumbers) and isoinvariant

(6.2) q^^{2}^ = q^^{i}*(m^)_{ij}xI^)*q^^{j} =
[q^{i}x(Txm)_{ij}xq^{j}]xI^ e
R^,

defined on the isofield R^ of isoreal numbers, all isotopic structures having the same 4x4-dimensional, nowhere singular, positive-definite isounit and isotopic element

(6.3a) I^ = Diag. (g_{11}^{-1}, g_{22}^{-1}, g_{33}^{-1}, g_{44}^{-1}) =
Diag (n_{1}^{2}, n_{2}^{2}, n_{3}^{2}, n_{4}^{2}) = 1/T > 0,

(6.3b) T = Diag. (g_{11}, g_{22}, g_{33}, g_{44}) =
Diag (n_{1}^{-2}, n_{2}^{-2}, n_{3}^{-2}, n_{4}^{-2}) > 0.

where the quantities g_{kk} and n_{k}, beside being sufficiently smooth and positive-definite, have an unrestricted functional dependence and are called **characteristic quantity of the iso-Minkowski space.**

By using the isodifferential calculus, the **isotopic line element** on M^ is given by

(6.4) d^q^^{2}^ = (d^r^_{1}^{2}^ + d^r^_{2}^{2}^ +
d^r^_{3}^{2}^ - c_{o}xd^t^^{2}^)xI^ = (g_{11}xdr_{1}^{2} + g_{22}xdr_{2}^{2} +
+ g_{33}xdr_{3}^{2} - c_{o}xg_{44}xd^t^{2})xI^.

The gravitational implications have been discussed in Section II.4 in which the isometric g_{kk} coincides with a Riemannian metric, although it represents in general interior gravitational metrics characterized by the Riemannian metric multiplies by characteristic quantities representing interior conditions.

This presentation is devoted to the structure of the neutron. Therefore, we shall restrict the g_{kk} quantities to represent physical characteristics of the proton. Nevertheless, for a deeper study, the visitor should always keep in mind the hidden gravitational implications.

It is easy to see that the isotopy M => M^ permits **a direct geometrization of the locally varying speed of electromagnetic waves when propagating within physical media,** c_{o} => c = c_{o}/n_{4}, where n_{4} is the familiar **index of refraction. ** Therefore, n_{4} represents a **geometrization of the density** of the medium inside the proton that is normalized to 1 for the case of the vacuum.

The space components n_{1}^{-2}, n_{2}^{-2}, n_{3}^{-2} represent the **actual, extended, nonspherical and deformable shape **of the particle considered, also normalized to 1 for the case of the perfect and rigid sphere. The **space inhomogeneity** of the physical medium considered is represented by the locally varying character of the n's. The **spacetime anosotropy** of the medium for the case of cylindrical symmetry along the third axis is represented by the difference between n_{3} and n_{4}.

The simplest possible form of the **Dirac-Santilli isoequation** on M^ over R^ is given by (30)

(6.5a) [g^^{k}*(p^_{k} - ixe^*A^_{k}) - ixm^]*|e^> =
[g'^{k} x (p^_{k} - i x e x A_{k} x I^) - i x m x I^] x T x |e^> = 0,

(6.5b) g^^{k} = g'^{k} x I^ =
n_{k}^{-1}xg^{k}xI^, k = 1, 2, 3,
g^^{4} =g'^{4} x I^ =
n_{4}^{-1}xg^{4}xI^,

(6.5c) e^ = exI^, A^ = AxI^, m^ = mxI^,

where the g^s are the **isogamma matrices** and the gs are the conventional Dirac gamma matrices. Note that the above realization is the simplest possible in the sense that the isotopy solely occurs in spacetime without any isotopy of the SU(2) spin, that is not necessary for a first relativistic study of Rutherford-Santilli. For the most general possible form of the Dirac-Santilli isoequation one may consult monograph (55) and various contributions quoted therein.

The **orbital isosymmetry** O^(3) of the isoelectron is characterized by

(6.6a) L^_{1} = (r^_{2})*(p^_{3}),
L^_{2} = (r^_{3})*(p^_{1}),
L^_{3} = (r^_{1})*(p^_{2}),

(6.6b) [L^_{1}, L^_{2}]* = n_{3}^{2}xL^_{3},
[L^_{2}, L^_{3}]* = n_{1}^{2}xL^_{1},
[L^_{3}, L^_{1}]* = n_{2}^{2}xL^_{2},

(6.6c) (L^)^{2}^*|e^> = (n_{1}^{2}xn_{2}^{2} +
n_{2}^{2}xn_{3}^{2} + n_{3}^{2}xn_{1}^{2})x|e^>,

(6.6d) (L^_{3})*|e^> = ħ n_{1}xn_{2})x|e^>,

where [A, B]* = A*B - B*A = AxTxB - BxTxA is the isocommutator. Note that the isogroup O^(3) is locally isomorphic to the conventional O(3) group (because the n's are positive-definite). In this way, the isotopies reconstruct the exact rotational symmetry for all possible signature-preserving deformations of the sphere, as already indicated in Section II.4.

Recall that the conventional Dirac equation describes an electron moving in vacuum under the *external* electromagnetic field of the proton (that is, Dirac's equation IS NOT a two-body equation), in which case the angular momentum is *paleways*conserved. The iso-Dirac equation has been conceived and worked out to describe the motion of the same electron, this time within a physical medium, in which case the angular momentum must be generally nonconserved to avoid the belief of the perpetual motion within a physical environment (see below for the case of the neutron). Nevertheless, for the specific case of the electron compressed inside the proton and ensuring circular orbits, the angular momentum is mutated but indeed conserved.

The **spin isosymmetry** SU^(2) is given by

(6.7a) J^_{1} = (g^_{2})*(g^_{3})/2,
J^_{2} = (g^_{3})*(g^_{1})/2,
J^_{3} = (g^_{1})*(g^_{2})/2,

(6.7b) [J^_{1}, J^_{2}]* = n_{3}^{-2}xJ^_{3},
[J^_{2}, J^_{3}]* = n_{1}^{-2}xJ^_{1}, [J^_{3}, J^_{1}]* = n_{2}^{-2}xJ^_{2},

(6.7c) J^^{2}^*|e^> = (1/4)x(n_{1}^{-2}xn_{2}^{-2} +
n_{2}^{-2}xn_{3}^{-2} + n_{3}^{-2}xn_{1}^{-2})x|e^>,

(6.7d) J^_{3}*|e^> = ħ (1/2)(n_{1}^{-1}xn_{2}^{-1})x|e^>.

Note again that SU^(2) is locally isomorphic to the conventional SU(2) because the n's are positive-definite. Nevertheless, the eigenvalues of the spin are not generally constant to represent the electron when in the core of a collapsing star, or other extreme internal conditions under which the preservation of the quantum value 1/2 is a pure nonscientific-political belief (see, again, below for the case of the neutron). Again, for the specific case here considered, the electron is constrained within the proton structure. The conservation of the angular momentum of the much heavier proton then implies that the spin of the isoelectron is indeed mutated, but constant.

The **isospinorial covering of the Poincare'-Santilli isosymmetry** P^(3.1) = SL^(2.c)xT^(4) is then characterized by the generators

(6.8) P^(3.1): J^_{k}, k = 1, 2, 3, W^_{k} = (g^_{k})*(g^_{4})/2, k = 1, 2, 3, p^_{i}, i = 1, 2, 3, 4.

The symmetry is, however, *eleven-dimensional* due to the new isotopic invariance of the line elements m^' => m' = m/k, I^ => I^' = I^ x k (see Section II.4 for details).
The isocommutation rules are given by Eqs. (II.4.21), and are here omitted for brevity. It is an instructive exercise to work them again via the above isogenerators and isocommutators and prove that P^(3.1) is locally isomorphic to P(3.1).

The **isoelectron** e^ characterized by the iso-Dirac equation is an irreducible isorepresentation of the Poincare'-Santilli isosymmetry P^(3.1). The above realization then illustrates the ** relativistic mutation (isorenormalization) of the orbital momentum and spin of the electron,** already obtained in the preceding sections via nonrelativistic methods.

We finally have the **isotopies of the magnetic and electric dipole moments,** whose derivation has been worked out in Ref. (30,55) as a simple isotopy of the conventional derivation, resulting in the isolaws valid for the case of an axial symmetry along the third axis

(6.9) m^ = m x n_{4} / n_{3}, e^ = e xn_{4} / n_{3}.

The above laws provide a technical representation of the well known semiclassical property that the deformation of a charged and spinning sphere necessary implies an alteration of its magnetic moment. In particular, we have a decrease (increase) of the magnetic moment when we have a prolate (oblate) deformation or when we decrease (increase) the angular momentum.

It is easy to see that the above formalism permits a relativistic, exact and invariant representation of ALL characteristics of the Rutherford-Santilli neutron. To begin, the neutron is assumed to be isolated from the rest of the universe, thus being a quantum state with spin 1/2. Since the proton is much heavier than the electron, we also assume for simplicity that the proton is un-mutated, thus remaining a quantum state with spin 1/2. Under these assumptions, the sole mutations occur for the isoelectron.

Therefore, Ref. (30) used the iso-Dirac equation for the isorenormalization of the rest energy, spin, angular momentum and orbital magnetic moment of the electron.

Recall that the quantity n_{4} represents the density of the medium inside the proton. Its numerical value has been computed via the fit to a number of experiments, such as the Bose-Einstein correlation reviewed in Section III.3, the anomalous behavior of the meanlife of unstable particles with speed in Section II.2, astrophysical consideration in Section III.7, and other experimental fits. All these fits essentially give the following numerical value (III,3.16d) independetly from the problem of the structure of the neutron,

(6.10) n_{4} = 0.605, n_{4}^{2} = 0.366.

It is easy to see that the above value permits a **relativistic, exact and invariant representation of the neutron rest energy,** as well as a resolution of the Historical Difficulty # I of Section 2. In fact, under the above value we have the following **rest energy of the isoelectron**

(6.11) m_{e^} = m_{e} x c_{o}^{2} / n_{4}^{2} = 1.396 MeV,

under which we have a **negative binding energy**, i.e.,

(6.12a) m_{n} = m_{p} + m_{e^} + BE,

(6.12b) BE = - 0.104 MeV.

while for conventional quantum mechanics the representation of the mass of the neutron would require the anathema of a "positive binding energy."

It should be remembered that value (6.10) represents the density of the proton-antiproton fireball in the Bose-Einstein correlation, which density is evidently bigger than that of the proton. Under the assumption of a null potential energy (due to the fact that all assumed forces are of contact nonpotential type), we expect a **null binding energy.** with value of the proton density

(6.13a) n_{4} = 0.629, n_{4}^{2} = 0.396,

(6.13b) m_{n} = m_{p} + m_{e^}, BE = 0.

As we shall see in the next section,. the latter value has a direct industrial significance because, irrespective of whether with or without a binding energy, the **total energy of the isoelectron** is given by

(6.14) m_{e^} = 1.292 MeV = m_{n} - m_{p},

due to the assumed lack of mutation of the proton.

The resolution of Historical Difficulty # 1 of Section 2 has far reaching implications. In fact, it implies that **the propagation of light inside the proton occurs at a speed that is BIGGER than that in vacuum,**

(6.15) c = c_{o} / n_{4} = 1.590 x c_{o}.

This is the first fundamental, necessary consequence of Rutherford's conception of the neutron out of a considerable number of far reaching implications throughout all of science identified only in minimal part later on. Is easy to prove that without the mutation of the speed of light within hadrons, no other mutation is possible, and Rutherford's conception of the neutron becomes inconsistent.

Next, the **relativistic, exact and invariant representation of the spin of the neutron** via the iso-Dirac equation was also achieved first in Ref. (30). Recall that, under the assumption that the proton is un-mutated due to its size, the representation of the spin of the neutron requires that the total angular momentum of the isoelectron is null, namely, that its mutated spin is identical in absolute value, yet opposite to the mutated angular momentum. This condition is readily verified by the identities

(6.16a) L^^{2}^*|e^> = (n_{1}^{2}xn_{2}^{2} +
n_{2}^{2}xn_{3}^{2} + n_{3}^{2}xn_{1}^{2})x|e^> =

= J^^{2}^*|e^> = (1/4)x(n_{1}^{-2}xn_{2}^{-2} +
n_{2}^{-2}xn_{3}^{-2} + n_{3}^{-2}xn_{1}^{-2})x|e^>,

(6.16b) L^_{3}*|e^> = - n_{1}xn_{2})x|e^> =

= J^_{3}*|e^> = ħ (1/2)(n_{1}^{-1}xn_{2}^{-1})x|e^>,

with algebraic solution

(6.17a) n_{1}^{2} = n_{2}^{2} = n_{3}^{2} = 1 / 2^{1/2}

(6.17b) L^^{2^} = S^^{2^} = 3/2,

(6.17c) |L^_{3}| = |S_{3}| = 1 / 2^{1/2}.

Note not only the mutated values of the third components, but also those of the magnitudes of conventional angular momenta. Note also that the relationship between the mutated values of the third components and those for the magnetudes are NOT conventional, as apparently necessary for the constrained conditions of Rutherford's electron trapped inside the proton.
Note also the **exact and invariant** character of the solution, since it is based on the isotopies of the rotational and spin symmetries.

We now remain with the **relativistic, exact and invariant representation of the anomalous magnetic moment of the neutron** that was also achieved in Ref. (30) for the first time. Recall that the the total magnetic moment of model (1.5) requires three contributions,

(6.18) m_{n} =
m_{p^} + m_{e^,Intrinsic} - m_{e^,Orbital} = -1.9123 m_{N},

Recall also that the intrinsic magnetic moment of the isoelectron is mutated into the expression

(6.19) m_{e^,Intrinsic} = m_{e} x n_{4} / n_{3},

where now both characteristic quantities n_{4} and n_{3} are known, resulting in the **intrinsic magnetic moment of the isoelectron**

(6.20) m_{e^,Intrinsic} = 0.8545 x m_{e},

The desired representation of the anomalous magnetic moment of the neutron is then given by the following **orbital magnetic moment of the isoelectron**

(6.21) m_{e^,Orbital} = 0.8521 x
m_{e^,Intrinsic}.

Note the **decrease** of the intrinsic magnetic moment of the electron that is fully in line with the decrease of the third spin component from 1/2 to 1/2^{1/2}. Note also that the above values are different than those in Eqs. (5.2) and (5.3) because in the nonrelativistic treatment of the latter case we assumed in first approximation that the spin, and, consequently, the intrinsic magnetic moment of the electron are not mutated. Ref. (30) pointed out that at a relativistic level a mutation of both spin and magnetic moment does indeed occur. Such a result could be predicted by the underlying symmetry, the Poincare'-Santilli isosymmetry, for which the mutation of one intrinsic characteristic of a particle generally implies that of all others.

This completes our review of the relativistic, exact and invariant representation of ALL characteristics of the neutron as a bound state of one proton and one electron obeying the laws of hadronic mechanics.

**7. COMPATIBILITY OF THE RUTHERFORD-SANTILLI NEUTRON STRUCTURE WITH SU(3) CLASSIFICATIONS**

Once the fundamental reduction of the neutron to a consistent bound state of one proton and one electron has been achieved, the reduction of all remaining baryons to protons and electrons (and their antiparticles) is readily permitted by hadronic mechanics. In fact, a mere repetition of the formalism of the preceding sections yields the following **structure models of the remaining unstable baryons with physical constituents,** here presented in the order of increase of their mass

(7.1a) L(1115 MeV) = (p^,p^)_{hm} = (n^,p^{o^})_{hm},

(7.1b) S^{+}(1189 MeV) = (L^,e^{+})_{hm},

(7.1c) S^{o}(1192 MeV) = (L^,e^^{+}, e^^{-})_{hm},

(7.1d) S^{-}(1197 MeV) = (L^,e^^{-})_{hm},

(7.1e) X^{o}(1314 MeV) = (L^,p^{o})_{hm},

(7.1f) X^{-}(1321 MeV) = (L^,p^{-})_{hm},

(7.1f) W^{-}(1672 MeV) = (L^,K^{-})_{hm},

(7.1g) etc.

It is an instructive exercise for the interested reader to prove that the hadronic structure model of the preceding sections permits an exact and invariant representation of ALL characteristics of the particle considered. It is equally instructive to prove that in each case we have the suppression of the atomic spectrum of energy down to one energy level only, that of the particles considered via the characteristic solution k_{1} of increasing (positive) values bigger than 1 and k_{2} more and more closer, but bigger than 1, as in values (IV.1.28) and (3.9), thus ensuring the suppression of the atomic spectrum down to only one level.

Note the equivalence of models with different isotopic constituents, such as in case (7.1a). This is due to the equivalence of different isoparticles when having similar mutations, provided that their rest energy is similar (otherwise there is the need to increase the number of constituents).

In continuing the model to heavier baryons a number of additional rather complex events occur, such as pair creation *inside* hadrons. Quantitative studies of these events require the prior development of **hadronic field theory** that has not been constructed to date. As such, these aspects are deferred to the specialized technical literature.

The compatibility of the above hadronic structure model of baryons with SU(3) classifications is elementary, as first pointed out in Ref. (31) and it is achieved via the construction, for instance, of the eight-fold hyperunit

(7.2) I^_{8} = (I^_{p}, I^_{n},
I^_{L},
I^_{S+},
I^_{So},
I^_{S-},
I^_{Xo},
I^_{X-})

and then the construction of the hypersymmetry SU^(3) characterized by the above hyperunit (see Ref.s (47,57,226)). The isomorphism between such a hypersymmetry and the conventional SU(3) symmetry (ensured by the positive-definite character of all isounits) confirms the achievement of the desired equivalence under new intriguing degrees of freedom that can be used to resolve remaining problems, such as that of the spin.

Note the achievement of a full, rigorously proved quark confinement, thus resolving a vexing problem of the hadron physics of the 20-th century. In fact, quarks emerge as purely mathematical representations of the purely mathematical hypersymmetry SU^(8) on a purely mathematical multi-valued hyperspace that cannot even minutely defined in our spacetime. Identically null probability of tunnel effect of such mathematical quarks into our physical spacetime is then evident to all. Note also the necessity of having different isounits for different baryons, since different hadrons have different density. For additional aspects we refer the interested reader to the specialized literature.

**8. PHYSICAL LAWS PREDICTED BY HADRONIC MECHANICS FOR NEW HADRONIC ENERGIES OF CLASS I**

The studies outlined in the preceding parts can be summarized via the following physical laws (58):

** Law V.8.1: Nonunitary effects produce isorenormalizations of intrinsic characteristics of particles.** The intrinsic characteristics of particles are mutated by short range nonunitary effects due to deep overlappings of the wavepackets at distances of 1 Fermi or less, resulting in novel isorenormalizations
for the rest energy, meanlife, magnetic and electric dipoles, etc., characterized by the Poincare~-Santilli isosymmetry, or its realization via the Dirac-Santilli isoequation. As a result, hadronic constituents are not ordinary particles, but isoparticles.

**
Law V.8.2: Only singlet hadronic bound states are stable at mutual distances of one Fermi or less. **According to quantum mechanics, bound states at large mutual distances can occur for particles in both singlet and triplet couplings (spin antiparallel and parallel, respectively), as it is the case for the structure of the hydrogen, helium, etc. According to hadronic mechanics, stable bound states at distances of 1 Fermi or less can occur only for singlet couplings. Triplet couplings are highly unstable, as illustrated by the gear model of Figure IV.2, because they imply a drag force experienced by the rotation of one particle within and against that of the other.

** Law V.8.3: Atomic spectra are suppressed by hadronic bound states down to only one admissible energy level per each pair of isoconstituents. **Quantum mechanical bound states admit an infinite number of energy levels, as it is typically the case for the hydrogen atom, the positronium, etc. By comparison, bound states according to hadronic mechanics admit only one energy level, that of the hadron considered, because all excitations imply the increase of mutual distances beyond 1 Fermi, with consequential recovering of the infinite quantum spectra since at those distances hadronic mechanics recovers quantum mechanics identically.

**
Law V.8.4: The size of hadronic bound states remains essentially constant with the increase of the mass, as a consequence of which the range of strong interactions coincides with the range of applicability of hadronic mechanics.** Quantum mechanical bound states, such as nuclei or atoms, increase their size with mass, while the size of hadronic bound states of particles at distances of 1 Fermi or less (the hadrons) remains essentially the same with the increase in the mass, thus confirming their origin as due to total mutual penetration of the wavepackets. Since all isounits assume the conventional value I at mutual distances sufficiently bigger than 1 Fermi, the range of applicability of hadronic mechanics is that of the strong interactions, and this explains the origin for the name "hadronic mechanics."

**
Law V.5.6: The interaction between isoparticles in singlet couplings is strongly attractive irrespective of whether the Coulomb interactions are attractive or repulsive, thus setting the foundations for the precedingly unexplained charge independence of nuclear forces.** The forces described by hadronic mechanics due to deep overlapping of wavepackets are so strongly attractive as to create a bound state irrespective of whether the Coulomb force is attractive or repulsive. This law is established also in nuclear physics under the name of charge independence of the nuclear forces, as well as in in the Cooper pair in superconductivity and in the valence bond (559).

** Law V.8.6: The synthesis of unstable hadrons "requires" energy because their total energy is bigger than the sum of the rest energies of the constituents. **Quantum mechanical bound states can only occur when the total energy is smaller than the sum of the energies of the constituents with negative binding energies resulting in a mass defect]. For hadronic mechanics, bound states can occur for total energies much bigger than those of the constituents, because of the isorenormalization of the rest energy of the constituents, constraints due to motion within a physical media and other effects completely absent in quantum mechanics.

**
Law V.8.7: The stimulated decay of unstable hadrons such a the neutron "releases" a new form of energy called HADRONIC ENERGY OF CLASS I** (58). Contrary to the preceding law, the spontaneous or simulated *decay* of unstable hadrons into ordinary particles *releases* energy, as one can see in the decay of the neutron and other hadrons. As we shall see in the subsequent sections, the new energies of Class I can be produced via resonating and other effects, that are capable of expelling one or more constituents. The new energies of Class I then consist in capturing the energy released in said decays.

Hadronic energies of **Class II** are of nuclear character (Part VI) and those of **Class III** are of molecular character (Part VII, where the word "hadronic" stands to denote the fact that the energies ARE NOT predicted by quantum mechanics, but are instead predicted and quantitatively treated by the covering hadronic mechanics. Equivalently, the word "hadronic" stands to illustrate the fact that the new energies are based on mechanisms dependent on contact nonpotential effect that, as such, are beyond any dream of treatment via quantum mechanics.

As we shall see, the above physical laws are important to maximize the efficiency of the new energies here considered. Researchers in the field are, however, warned not to extend blindly all the above subnuclear laws to the nuclear level because of significant differences between the hadronic and nuclear levels treated in Part VI.

Nevertheless, some of the above physical laws will persist in the transition to nuclei, most notably the charge independence of nuclear forces, that is dynamically explained for the first time by hadronic mechanics.

**9. DON BORGHI'S EXPERIMENT ON THE SYNTHESIS OF THE NEUTRON FROM PROTONS AND ELECTRONS**

Another far reaching implication of Rutherford's conception of the neutron is the prediction that the neutron can be synthesized from protons and electrons in laboratory without the extremely high pressures in the core of stars. In turn, the possibility to synthesize the neutron implies the capability to utilize the inextinguishable clean energy contained in its interior in view of Hadronic Law V.8.7.

Clear experimental evidence on the capability of synthesizing the neutron in laboratory has existed since the birth of nuclear physics, and it is given by the well known process of **electron capture (EC),** in which an unstable nucleus achieves stability by capturing one of the peripheral electrons. It is evident that this electron is absorbed by one of the peripheral protons that is consequently turned into the neutron at ordinary conditions here on Earth without the pressure in the core of a star.

While the EC process is indeed admitted by all scientists and quoted in all treatises in nuclear physics, rather oddly, the related evidence that the neutron can indeed be synthesized at ordinary conditions here on Earth is dismissed by members of organized interests on quantum mechanics evidently because it implies the capability of achieving stimulated nuclear transmutations also at ordinary conditions on Earth.

Moreover, a widespread belief in the physics of the 20-th century was that fusion requires very high energies and temperatures. This belief originated from the attempts to reach the **controlled hot fusion.** However, as we shall see in the Part VI, the controlled hot fusion failed precisely because of the excessive energies and temperature that caused uncontrollable instabilities at the initiation of the fusion process.

Hadronic mechanics characterizes a basically new method for the fusion of particles (as well as of nuclei) called **controlled hadronic fusion.** It can be essentially defined as *a fusion occurring at the threshold energies needed for conservation laws, via geometries verifying all hadronic laws identified earlier, plus an external "trigger" suitable to bring the constituents at mutual distances sufficient to activate attractive hadronic forces.*

The problem of the synthesis of the neutron then essentially consists in bringing polarized protons and electrons with mutual energy of 0.78 MeV (needed to reach the neutron rest energy) at mutual distances of 1 Fermi in singlet coupling, at which value the strongly attractive Hulten force takes over and the neutron is synthesized.

With respect to Figure 3 below, we see that protons and electrons experience the *attractive* Coulomb force due to opposite charges, as well as the *repulsive* Coulomb force due to parallel magnetic moments when in singlet spin coupling. Even though the resulting force is unknown to the author, it is expected to be repulsive due to the extremely high value of the magnetic moment of the electron when compared to that of then proton. Under such assumption, under the availability of the indicated relative energy of 0.78 Mev, and under polarizations permitting singlet spin couplings, the "trigger" is essentially given by means to overcome said repulsive total Coulomb force and bring the particles to distances of 1 Fermi. As we shall see, there are a number of geometries and embodiments that can indeed achieve and optimize these conditions, thus confirming the prediction that the neutron can indeed be synthesized in our laboratory from protons and electrons.

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The experimental verification of the synthesis of the neutron from protons and electrons was first conducted by C. Borghi, C. Giori and A. Dall'Olio in the 1970s at the CEN Laboratories in Recife, Brazil, and published only later in 1993 (123) (in the prestigious Russian Journal of Nuclear Physics) due to the notorious opposition by journals of physical societies against basic novelty.

This experiment is today known as **Don Borghi's experiment** from the leader of the team, the late Italian priest-physicist C. Borghi, formerly from the Department of Physics of the University of Milan, Italy, who spent his research life in the study of Rutherford's legacy.

Needless to say, Don Borghi's experiment is in need of independent verifications, either in its original form, or in one of several alternative possibilities presented in Section 13. Nevertheless, Don Borghi's experiment constitutes the first historical verification of Rutherfordıs conception of the neutron, and is remarkable because of its simplicity.

In essence, the experimenters created in the interior of a cylindrical metal chamber (called *klystron*) a gas of ionized hydrogen gas (free protons and electrons) originating from the electrolytical separation of water, and kept the gas mostly ionized via an electric discharge. Since protons and electrons are charged, they could not escape from the metal chamber.

All around the exterior of the klystron the experimenters put a variety of fissionable and non-fissionable material, and, after periods of time ranging from days to weeks, they detected transmutations in said exterior material that can only be caused by a flux of neutrons. In the absence of any other source, said neutron flux can only originate from the synthesis of neutrons from protons and electrons in the interior of the klystron. Since the neutrons are neutral, once created inside the klystron, they can escape to the outside, and cause the detected nuclear transmutations.

It is evident that, if confirmed, Don Borghi's experiment establishes Rutherford's conception of the neutron, as well as its treatment via hadronic mechanics, the only known mechanics that achieves an *exact* and *invariant* representation of *ALL* characteristics of the neutron.

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A few comments are now in order. It is evident that the number of neutrons that can be synthesized by the unpolarized random gas of protons and electrons inside the klystron is extremely small as compared to the flux of neutrons measured by the experimentalists in the outside. Therefore, at a first superficial analysis, the results of Don Borghi's experiment appear to be untrue.

However, at a deeper analysis, calculations done by the author have indicated that **in Don Borghi's experiment the neutrons are synthesized by the electric arc used to maintain the ionization of the hydrogen gas.** In fact, a DC electric arc polarizes protons and electrons with their magnetic moments parallel because tangent to the line of force (see Figure 6 below), thus achieving the desired polarization of parallel magnetic moments and, consequently, antiparallel spins. Moreover, DC electric arcs have the additional effect of compressing said magnetic polarities toward their symmetry axis, thus being ideally suited to realize the needed "trigger."

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This author has conducted a a search through the literature related to paper (123),
and found no reference to the electric arc as the source of the neutron synthesis. A confirmation or denial of this point would be appreciated by Italian colleagues (since most of the literature is in Italian). If the crucial role of the arc did indeed escape the experimentalists, and such role is confirmed (as suggested in the proposed experiments of Section 13), Don Borghi and his collaborators achieved the historical first synthesis of the neutron by chance.

**10. INDUSTRIAL UTILIZATION OF THE INEXTINGUISHABLE CLEAN ENERGY INSIDE THE NEUTRON**

Another far reaching consequence of Rutherford's conception of the neutron is the possibility of stimulating its decay, thus permitting the utilization of the inextinguishable clean energy contained in its interior that is under industrial development by **Betavoltain Industries, Inc., Michael McDonnough, President, **

http://www.betavoltaic.com.

It is evident that the *utilization of said energy is possible if and only if the electron is a physical constituent of the neutron,* irrespective of whether in a conventional or mutated form. In fact, only in this case the electron can be stimulated to exist the neutron, thus stimulating its decay. In the event the conjectural quarks were indeed physical constituents of the neutron, no possibility whatever exist to utilize the energy in its interior, as we shall see.

The energy under consideration is ** inextinguishable** because of the existence of a selected number of nuclei available on Earth in unlimited quantities (to be identified below) that are predicted to admit said stimulated decay of the neutron.

The energy contained in the interior of the neutron is **clean** because, as we shall see in detail below, it does not release harmful radiations and does not leave harmful waste.

The hypothesis of the **stimulated decay of the neutron** was first submitted by R. M. Santilli in Ref. (215) of 1994). Recall that *the neutron is naturally unstable* with a meanlives ranging from nanoseconds to perfect stability depending on the nucleus in which the neutron is embedded, with well known decay

(10.1) n => p^{+} + e^{-} + antineutrino.

In view of this natural instability, the hypothesis submitted in Ref. (215) is then that *there must exist mechanisms (called "triggers") capable of stimulating its decay*

(10.2) Trigger + n => p^{+} + e^{-} + antineutrino.

The new structure model of nuclei permitted by hadronic mechanics has identified a number of triggers for the above stimulated decay. In this section we review the original proposal (215) of **stimulating the decay of the neutron via a photon g^ with the resonating frequence 1.292 MeV that is equal to the isorenormalized rest energy of the isoelectron,** Eq. (6.14) (an alternative testable value is 0.511 MeV, namely, the rest energy of an electron in vacuum),

(10.3) g^ + n => p^{+} + e^{-} + antineutrino.

Since the stimulated beta decays under consideration below release several MeV of energy, the positive energy output of the process here considered is out of question.

Quantum mechanics predicts that reaction (10.3) does indeed exist, but has a very low cross section for all photon energies, thus having no practical value. However, this is a pure "experimental belief" because the reaction has been solely measured at very few energies of the photon, and certainly not for 1.292 MeV. From this limited information, it is then generally concluded that the result holds for all energies.

The isoscattering theory of hadronic mechanics (that, for brevity, has not reviewed in this web site; see Chapter XII of monographs (55)) recovers the very low value of the cross section of reaction (10.3) for all energies of the photon *except for a resonating peak at the sharp value of 1.294 MeV,* in which case stimulated decay (10.3) has indeed a practical value (a smaller peak is also predicted for photons with 0.511 MeV).

The case is similar to the discovery in the 1960s of the W particle at CERN. A group of physicists predicted a very flat cross section and no new particle. Other physicists looked for novelty, predicted a resonating peak, found it, and got the Nobel prize.

The HADRONIC ENERGY OF CLASS I (international patents pending) here considered is given by the stimulated decay of the neutron when members of suitably selected nuclei called **hadronic fuel,** with large energy release, no secondary radiations other than electrons (that can be easily trapped and the hypothetical innocuous neutrinos), as well as leaving no harmful waste, and we shall write

(10.4) g^ + N(A, Z) => N'(100, Z+1) + b^{-},

where A is the total number of nucleons and Z is the number of protons.

Ref. (215) conducted a comprehensive study of nuclei to ascertain those admitting stimulated decay (10.3). It turned out that most nuclei *do not* admit reaction (10.3) because of the violation of one or another conservation law. Nevertheless, a specific class of nuclei verifying all conditions to be hadronic fuel do indeed exist, thus offering a serious possibility for the industrial realization of the new Hadronic Energy of Class I.

A first example of admitted **Stimulated Beta Transmutation** (SBT) is given by (215):

(10.5a) g^ + Z(70, 30) => Ga(70, 31) + b^{-}

(10.5b) Ga(70, 31) => Ge(70, 32) + b^{-}.

where the first reaction is stimulated and the second is spontaneous because Ga(70, 31) is naturally unstable and decays spontaneously also via beta decay

Note that the original element Z(70, 30) is a *light natural stable element* and so is the final element Ge(70, 32). This illustrates the lack of harmful waste. The lack of harmful radiation is evidence since electrons can be trapped with a thin metal shield.

Another example of hadronic fuel is the Mo(100,42) that also admits a first stimulated decay followed by a spontaneous beta decay

(10.6a) g^ + Mo(100, 42) => Tc(100,43) + b^{-},

(10.6b) Tc(100, 43) => Ru(100, 44) + b^{-}.

Again, the initial and final isotopes are light, natural, and stable elements. The intermediate isotope Tc(100, 43) is unstable, and beta-decays in 18 seconds into Ru(100, 44); one photon produces two electrons; the first electrons are predicted to have a maximum energy of 5.2 MeV, while the second electrons have tabulated energy ranging from 2.22 MeV to 3.38 MeV. Therefore, double reaction (10.6) can release a total energy of at least 5.5 MeV, thus being definitely esoenergetic.

Another class of hadronic fuel is given by the so-called **mirror nuclei** verifying all necessary conservation laws and other conditions, such as the isotope C(13,7) that admits the stimulated beta transmutation (215)

(10.7) g^ + C(13, 7) => N(13, 7) + b^{-}.

.

For additional selections of hadronic fuels we refer the interested visitors to paper (215).

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It is evident that the above stimulated beta decays constitute a possible realization of the Hadronic Energy of Class I. This energy is actually **two-folds,** the first being given by the kinetic energy carried by the emitted electrons that can be trapped with a shield and converted into usable heat via a heat exchanger, the second being of electric character. In fact, a bar of Mo(100, 42) subjected to process (10.6) will acquire a positive charge due to the release of the electrons. The latter can be trapped with a metal shield,, therefore resulting in the **production of a difference of potential between the Mo(100, 42) bar and the metal shield, with ensuing production of a DC electric current of subnuclear (rather than nuclear) origin.**

Note again that the above hadronic energy is clean because it does not release any harmful radiation, and does not leave any harmful waste. Note also that the energy can be fully controlled via the control of the flux of the incident excitation photons.
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http://www.betavoltaic.com.

The energy is called Hadronic Energy of Class I because based on hadronic mechanics and originating in the structure of the neutron, (Class II being nuclear and Class III molecular). The embodiment consists of a rod of pure, light, natural, stable isotope admitting process (10.4), such as Mo(100,42) that is invested by a coherent beam of photons with the excitation energy of 1.292 MeV, under which some of the peripheral neutrons of the Mo(100, 42) are stimulated to decay, by creating Tc(100,43) that is unstable and beta decays into the light, natural, stable isotope Ru(100, 44). The embodiment is predicted to produce at least 3 MeV energy per process (10.6). This implies the production of millions of Joules per minutes for an efficiency of one process per 10,000,000,000 nuclei per minute. This energy is fully controllable because it can be initiated, increased or decreased and halted via the control of the flux of the incident excitation photons. Note that

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Another intriguing possibility is the use of the stimulated decay of the neutron to **synthesize rare isotope.** As an illustration from Ref. (215), the extremely rare isotope Be(6, 4) can be apparently synthesized from the more readily available isotope Li(6, 3) via the hadronic (and not quantum) process

,p>
(10.8) g^ + Li(6, 3) => Be(6,4) + b^{-}.

Note that, unlike the preceding cases, the atomic mass of the resulting isotope, 6.019 a.m.u., is bigger than that of the original isotope, 6.015 a.m.u. Therefore, the above reaction * requires* (rather than releases) energy. Therefore, reactions of types (10.8) are intended to synthesize new isotopes, and not for the production of energy.

Needless to say, the above Hadronic Energy of Class I requires considerable additional studies. Nevertheless, it is appropriate to recall the view expressed by a member of the Rockefeller family at the end of the 19-th century, according to which fossil oil was at best expected to "light-up lamps in public streets" due to the predicted enormous costs for: drilling deep holes into the crust of Earth; pumping the oil out into containers; transporting the oil to a refinery; refining the oil; storing the final fuel; and finally delivering it to the user. Contrary to these gloomy predictions of the 19-th century, fossil oil resulted to be one of the most successful industrial programs of the 20-th century. I hope that this episode suggests cautions before venturing similar claims for hadronic and other new energies.

**11. TSAGAS' EXPERIMENTAL VERIFICATION OF THE STIMULATED DECAY OF THE NEUTRON**

The experimental verification of stimulated nuclear transmutation (10.4) has been initiated by N. Tsagas and his group (124) at the Nuclear Engineering Department of the University of Thrace, Xanthi, Greece, with preliminary, yet positive results.

The test was conducted in the following way: 1) using a disk of Eu-152 as the source of photons with 1.3 MeV energy; 2) placing said disk next to a disk of natural Molybdenum as target; and 3) measuring the background without any source, the emission with the Europa source alone, and the emission with the joint disks of Europa and natural Molybdenum.

Electrons originating from the Compton scattering of photons with peripheral atomic electrons can at most have 1 MeV energy, as well known. Therefore, the detection of electrons with energy over 2 MeV establishes their nuclear origin.

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Since the Europa source does not emit electrons, and the Molybdenum is stable, the only possible origin of electrons is due to the stimulated decay of neutrons inside the Molybdenum disk. In fact, as recalled earlier, the first reaction (10.6a) emits electrons with minimal energy of 2.8 MeV, while the second reaction emits electrons with energy ranging from 2.22 MeV to 3.38 MeV.

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It should be indicated that Tsagass test (124) is limited by the fact that it used ordinary Molybdenum, that contains the isotope Mo-100 only in 0.6%. The possibilities of reaction (10.7) are then rather limited because it is easy to prove that none of the other isotopes of natural Molybdenum allow the stimulated decay of the neutron. Despite the above insufficiency, the results are encouraging and deserve further tests.

**12. RECYCLING OF RADIOACTIVE NUCLEAR WASTE VIA STIMULATED BETA DECAYS**

There is little doubt that the highly radioactive nuclear waste accumulating in our nuclear power plants is one of the biggest unsolved problems of contemporary society.

In the U.S. alone we have over 80,000 tons of radioactive waste currently stored at nuclear power plants. We have, therefore, surpassed the limits for safe storage in the pools of nuclear power plants. Europe has an even bigger tonnage of nuclear waste, and an unknown amount exists in other countries, all waiting for a serious addressing and a successful resolution. The yearly world production of about 15,000 tons of additional waste then sets the premises for a truly serious environmental problem of potentially historic proportions.

As it is well known, the official position by the U.S., European and other governments has been that of transporting the highly radioactive nuclear waste to a dumping area. This "solution" has met with predictable resistance from environmental groups and residents near the proposed dumping grounds. In fact, the transportation of the nuclear waste must occur on public streets, with evident dangers nobody can credibly deny. Assuming that local residents will permit the transit of such dangerous a material and in such a large amount, additional potentially catastrophic dangers exist in the intended storage of the nuclear waste, because it cannot be credibly predicted to be viable for tens of thousands of years. This scenario has led to the current lack in the U. S. as well as abroad of a credible solution for the disposal of the highly radioactive nuclear waste.

After studying the problem for several years, it is the author's opinion that contemporary scientific and industrial knowledge permits the **recycling of highly radioactive nuclear waste via its stimulated decay within an environment capable of absorbing the debris, such as the water of nuclear pools.** In fact, the nuclei of this waste are *naturally unstable.* As such, they must admit some form of stimulated decay.

Moreover, the above mentioned recycling can be achieved via relatively light equipment in the sense of having such size to be usable by nuclear power corporations in their own plant. Therefore, the above new recycling would avoid completely the transportation of the highly radioactive waste throughout public streets, and its storage.

Finally, the new means for recycling nuclear waste are expected to create a new industry, that for the development, production and sale of the new equipment, that is expected to be needed by nuclear power plants all over the world.

Since the nuclei here considered are very large and naturally unstable, they are expected to admit a variety of means to stimulate their decay (rather than wait for their natural decay). Some of them are of Class II, namely, of nuclear character, that is, acting on the waste nuclei as a whole. These means will be considered in Part VI. In this section e consider means of Class I, namely, based on process occurring in the interior of the nuclear constituents.

The possible recycling nuclear waste via the stimulated decay of the neutron was proposed by R. M. Santilli in Ref. (121). It consists of exposing the radioactive nuclear waste to an intense and coherent beam of photons with the needed resonating frequency, that can be obtained from a synchrotron of a few meters in diameter, thus resulting in equipment that can be transported to and used by the nuclear power plants.

Under a certain intensity and other conditions [that cannot be disclose here, various peripheral neutrons of the nuclei are predicted to decay simultaneously, thus creating an instantaneous excess of protons, under which the stimulated decay is consequential, due to the extreme instability of these large nuclei.

On merely indicative grounds, consider the isotope U(238-92) of the waste released by nuclear power plants, that has the very long life of 4.51 x 10^{9} years with the known harmful fission with the emission of alpha particles and other debris. The use of the technology under consideration would imply the primary artificial transmutation (121)

(11.1) g^ + U(238, 92) => No(238. 93) +
b^{-},

where Np(238, 93) is also an unstable isotope, but with meanlife of 2.1 days and spontaneous beta decay with 1.29 MeV.

A double stimulated transmutations yields

(11.2) 2g^ + U(238, 92) => Pu(238, 94) + 2b^{-},

where Pu(238, 94) has the meanlife of 86 days during which it can be left under suitable shields.

Possible tertiary artificial transmutations would yield Am(238, 95) that is unstable with meanlife of 1.9 hours, spontaneous electron capture back to Pu(238,94) and emission of 2.3 MeV. The atomic weight of the initial element U(238, 92) is 238.050 amu and that of the final element Pu(238, 94) is the smaller value 238.049 amu, thus implying the possible release of usable energy in the stimulated decay.

The advantage of the above stimulated transmutations is then evident. A sufficiently intense bombardment of photons of the indicated excitation frequency is expected to transmute the highly radioactive element U(238, 92) with the very long meanlife of 109 years into the element Pu(238, 94) with the reduced meanlife of the order of days.

The reader should be aware that the above recycling requires complementary means to weaken the nuclear force via new effects, as well as the complementary use of other methods such as the deformation of nuclei via very strong electric fields.

Numerous additional methods to stimulate the decay of nuclear waste have been proposed. Some of them are presented in the web site

http://www.recyclingnuclearwaste.com

Numerous *basic*experiments are possible to obtains the knowledge necessary for further scientific and industrial advances in new energies of Class I, such as:

**Proposed experiment 1: Repeat Don Borghi's test on the synthesis of the neutron (123) via a polarized electron beam on a beryllium target saturated with polarized hydrogen.** The test can be conducted in a number of way, such as: 1) saturating a beryllium mass at low temperature with hydrogen, in which case the hydrogen nuclei (protons) can be considered to be essentially at rest; 2) hitting said mass with a beam of electrons with the needed threshold energy of 0.78 MeV; and 3) use magnetic fields for the opposite polarization of the spins of the protons and of the electrons. The detection of neutrons emitted by the Beryllium would provide a final confirmation of the laboratory synthesis of the neutron from protons and electrons at low temperature.

**Proposed experiment 2: Repeat Don Borghi's experiment on the synthesis of the neutron via the use of a DC arc submerged within a hydrogen gas.** The text can be conducted via the use of 50 Kwh DC electric arc in between tungsten electrodes submerged within a hydrogen gas at high pressure, say, 10,000 psi. The arc decomposes the H atoms into protons and electrons and properly polarizes them as needed for their synthesis (Figure 5). Finally, the arc compresses the polarized protons and electrons toward its axis, thus having the necessary pre-requisites for the synthesis of the neutron.

** Proposed experiment 3: Repeat Tsagas test on the stimulated decay of the neutron (124). ** This test should be first repeated via the use of the pure isotope Mo(100, 42). Then it should be conducted for the other hadronic fuels identified in Section 10.

**Proposed experiment 4: Test the recycling of radioactive nuclear waste via the stimulated decay of their peripheral neutrons.**The stimulated decay of the neutron can also be tested with radioactive nuclei, such as U(238, 92) that has a meanlife of 4.51z10^{9} years with the decay into alpha particles and other debris. Its transmutation via stimulated neutron decay would yield Np(238, 93), that is also highly radioactive, yet possesses the reduced meanlife to 2.1 days.

**Proposed experiment 5: Test the synthesis and stimulated decay of other hadrons.** Besides the neutron, another excellent test is the synthesis of the p^{o} from an electron and a positron with the needed threshold relative energy, and again polarizations yielding a single coupling. One of the resonating frequencies of the p^{o} is 86.5 MeV. By hitting the p^{o} with photons of said frequency, the meson should decay into an electron a positron and a photon. A similar stimulated decay should exist for all other unstable hadrons. Another candidate is the synthesis of L(1115 MeV) via a proton and a p or a neutron and a p^{o^}.

**14. LACK OF NEED OF THE NEUTRINO HYPOTHESIS FOR EXTENDED HADRONS**

There is little doubt that, on real scientific grounds (those outside outside academic politics), neutrinos constitute the biggest controversy of the 20-th century for numerous reasons, such as the lack of clear experimental evidence of neutrinos via scattering processes. Supporters of the neutrino hypothesis argue that this is due to the lack of charge as well as of (appreciable?) mass. However, the belief that the flux of about 10^{23} solar neutrinos per cm^{2} could pass throughout the entire Earth without any collision has no credibility at all, thus casting serious shadows on the existence of the neutrinos themselves.

Other reasons to doubt the existence of the neutrinos are due to the essential failure of the Gran Sasso laboratory in Italy, as well as other laboratories, to achieve unequivocal detections of neutrinos in significant numbers despite huge investment over a protracted period of time. Subsequently, there have been a number of alleged detections of neutrinos. However, inspection of the detectors reveals the presence of radioactive elements some of which emit precisely the excitation frequency for the stimulated neutron decay.

As a result, the advent of hadronic mechanics has rendered the controversy even more complex, because hadronic mechanics identifies numerous plausible alternative interpretations of current claims on the detection of neutrinos all without any need of the neutrino hypothesis at all.

The controversy has raged also on theoretical grounds because after the impossibility to achieve consistent theories with the original hypothesis of the neutrinos, theoreticians were forced to introduce the so-called "neutrino oscillations." However, such an approach cannot be possibly a solution of the controversy because it replaces an essentially undetectable particle with an even more remote and undetected conjecture. At any rate, neutrino oscillations remain themselves highly controversial (even tough fashionable within circles of organized academic interests not interested real science).

On historical grounds, the conjecture was **necessary** under the point-like approximation of hadrons, as illustrated in Figure 10 below. However, it is easy to see that **the neutrino hypothesis is not needed at all when hadrons are represented as extended while continuing to verify all known conservation laws.**

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Another far reaching consequence of Rutherford's conception of the neutron is the lack of need for the neutrino hypothesis, as pointed out recently by R. M. Santilli (255). In fact, the attentive reader will have noted that in the achievement of the exact and invariant representation of all characteristics of the neutron of Sections 3-6 there is no need whatever to hypothesize the existence of the neutrino, and we shall write

(14.1) p^{-} => n.

The physical reasons is the property well known in classical mechanics according to which **kinetic energy can be converted into angular momenta,** as it occurs in various nonconservative processes, such as the capture of a ball in linear motion by a circular guide, that is essentially the event of the capture of the electron by the proton during the synthesis of the neutron (Figure 10).

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Vice versa, in the spontaneous or stimulated decay of the neutron there is also no need at all to conjecture the existence of the neutrino for the complementary physical property according to which **angular motion can be transformed into linear motion,** as it is the case of the "sling shot" (a stone held with a rope in rotational motion and then released, thus propelling the stone at large distances), which process is essentially that occurring in the neutron decay. We shall, therefore, write the complementary process

(10.2) n => p^{-}.

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Another origin of the controversy is that the neutron synthesis and its spontaneous decay have been treated in the 20-th century via quantum mechanics and underlying fundamental spacetime symmetries, the Galilei and Poincare' symmetries, and related conservation laws for the total linear momentum and, separately, for the total angular momentum. In turn, this assumption mandates again the hypothesis of the neutrino to fix things since the Galilei and Poincare' symmetries do not allow transition of linear into angular mo,mentum, and bice-verse, as well known.

However, the Galilei and Poincare' symmetry SOLELY apply for KEPLERIAN SYSTEMS, that is, systems with the heaviest constituent in the center and the other constituents ORBITING IN VACUUM around the Keplerian center. The beliefe that symmetries manifestly valid for the atomic structure are also valid for the electron orbiting INSIDE the proton is purely political nonscientific.

The real scientific issue is the identification of the MODIFICATIONS of the Galilei and Poincare' symmetries to represent said interior conditions of the electron. It is easy to see that the first modification is given by the isotopies since they are the only known method for the invariant treatment of nonlocal and non-Hamiltonian contact interactions. Moreover, the neutron structure requires the use of **isotopic symmetries with subsidiary constraints,** the latter implying precisely the transition from linear to angular momentum and vice-versa, without any need to hypothesize a large number of hypothetical neutrinos all essentially undetectable. The study of the iso-Galilei and iso-Poincare' symmetries with subsidiary constraints is excessively technical to be outlined here, and its study has to be deferred to the technical literature.

This completes the illustration of the author's view that neutrinos, like quarks, are dark episodes in the history of physics, because they have been conjectured on highly debatable grounds, they have been kept for over half a century via academic power rather than physical reality, and have prevented truly basic advances with far reaching implications, including the jeopardizing or otherwise obstructing the scientific and industrial development of new clean energies and fuels.

On historical grounds, it should be indicated that studies on Rutherfordıs conception of the neutron as a bound state of a proton and an electron were never halted, despite historical objections raised by Pauli, Fermi, Heisenberg;s and other founders of quantum mechanics (reviewed in the next section). This occurred not only because of the beauty and simplicity of Rutherfordıs conception, but also because other models (such as the quark model) imply the literal *disappearance* of proton and electrons at the time of the synthesis of the neutron, which disappearance is contrary to any rational thinking, since protons and electrons are permanently stable particles that cannot simply disappear just because a distinguished scientist says so on grounds of academic allegiances.

To avoid an excessive bibliography, a comprehensive presentation of these studies can be found in Conference Proceedings (91). However, in this authorıs view, none of these studies truly resolved the historical objections against Rutherfordıs conception of the neutron. Also, none of them achieved a numerically exact representation of ALL characteristic of the neutron. Above all, none of them achieved a truly invariance of the numerical results, due to the fact that the underlying mathematics was ultimately that of quantum mechanics. These are the reasons why the author could not possibly use ANY of these studies.

The only exact and invariant representation of all characteristic of the neutron known to the author is that achieved in Ref. (214) at the nonrelativistic level and in Ref. (30) at the relativistic level. The nonrelativistic solution was reached by R. M. Santilli in the 1980ıs immediately following the achievement of consistent isotopies of the SU(2)-spin symmetry (see, e.g., Ref. (11) of 1985), due to their truly crucial role for the problem here considered.

The publication of the nonrelativistic solution, so crucial for the utilization of the clean new energy contained in the neutron, was delayed for years for the following reason. As it is well known, a general rule of science is that advances honoring a known preceding scientist must be submitted in the journal of original publication. Rutherford published his hypothesis on the structure of the neutron in the *Proceedings of the Royal Society,* Vol. A97, page 394, 1920. Therefore, it was this authorıs duty to submit the resolution of the historical objections against such a basic hypothesis in the same journal.

Unfortunately, officers and editors of the British Royal Society resulted to be extremely repulsive and repugnant toward the authorıs sincere effort to honor their most famous fellow, and continued to reject the authorıs submissions with ³refereeıs reports² that were pure nontechnical-nonscientific-nonsense, their only transparent meaning being that of passing the boundary of science to protect organized interests on quantum mechanics.

Most educational for the reader was the repulsive and repugnant behavior by officers and editors of the British Royal Society ultimately against the honoring of their most illustrious fellow *in their full, repeated and documented awareness that the resolution of the historical objections against Rutherfordıs conception of the neutron implies new inextinguishable and clean energies,* that are the ultimate motivation for all these studies as reviewed in this Part V, thus raising evident problems of scientific ethics and accountability by the British Royal Society via-a-vis clear societal; needs, let alone the suppression of scientific democracy for qualified inquiries at the benefit of equivocal personal gains.

After wasting several years without any scientific input of any type, paper (214) was published in the *Hadronic Journal* of which the author is the editor in chief, so as at least have a record of the results.

The relativistic resolution of the historical objections against Rutherfordıs conception of the neutron had a dramatically better scientific reception by Russian colleagues, at *Moscow State University,* at the *Joint Institute for Nuclear Research* in Dubna, and at other Russian Institutions. In fact, paper (30) was written while the author was a visiting professor at the JINR in the summer of 1993, and was initially released as an official communication of the JINR, number E4-93-352. The author would like to take this opportunity to express his most sincere and deepest appreciation to all Russian colleagues. Following its initial appearance as a communication in Russia, the publication of the paper encountered truly extreme, at times hysterical objections by the editors of the journals of the American, Italian, British, Swedish and other physical societies. The paper was eventually published with no problem in China (see Ref. (30)). The author would like to take this opportunity to thanks also all Chinese colleagues for their respect and support of true scientific democracy for qualified inquiries.

*******************************************

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Following the publication of both the nonrelativistic and relativistic solution, the author circulated papers (214,30) rather widely among particle and nuclear physicists asking for technical comments he could not get from editors of seemingly professional journals. Unfortunately, a number of physicists who received these copies as well as the authorıs numerous joining letters, plagiarized the authorıs work by publishing a number of papers without any quotation at all of Refs. (214,30), yet copying most passages and formulae identically even in the symbols. These works subsequent to Refs. (214,30) are not reviewed here because, in a seemingly frantic anxiety of achieving novelty on a solution rigorously proved to be directly universal, plagiarizing authors made such structural modifications of the original papers to cause horrendous inconsistencies and activations of Theorem II.2.1, besides representing only *some* of the characteristics of the neutron. A number of additional studies that *developed* one aspect or another of papers (214,30) are indeed interesting, and their authors have been asked to prepare a contribution for uploading in Part VIII of this web site.

[1] ** HISTORICAL REFERENCES:**

(1) I. Newton, * Philosophiae Naturalis Principia Mathematica* (1687),
translated and reprinted by Cambridge Univ. Press. (1934).

(2) J. L. Lagrange, * Mechanique Analytique* (1788), reprinted by
Gauthier-Villars, Paris (1888).

(3) W. R. Hamilton, * On a General Method in Dynamics* (1834), reprinted
in {\it Hamilton's Collected Works,} Cambridge Univ. Press (1940).

(4) S. Lie, * Over en Classe Geometriske Transformationer,* English translation by E.
Trell, Algebras Groups and Geometries {\bf 15}, 395 (1998).

(5) A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. {\bf 47}, 777 (1935).

(6) P. A. M. Dirac, * The Principles of Quantum
Mechanics,* Clarendon Press, Oxford, fourth edition (1958).

(7) A. A. Albert, Trans. Amer. Math. Soc. {\bf 64}, 552 (1948).

[2] ** BASIC MATHEMATICAL PAPERS:**

(8) R. M. Santilli, Nuovo Cimento {\bf 51}, 570 (1967).

(9) R. M. Santilli, Suppl. Nuovo Cimento {\bf 6}, 1225 (l968).

(10) R. M. Santilli, Hadronic J. {\bf 3}, 440 (l979).

(11) R. M. Santilli, Hadronic J. {\bf 8}, 25 and 36 (1985).

(12) R. M. Santilli Algebras, Groups and Geometries {\bf 10}, 273 (1993).

(13) R. M. Santilli and T. Vougiouklis, contributed paper in {\it New Frontiers in
Hyperstructures,} T., Vougiouklis, Editor, Hadronic Press, p. 1 (1996).

(14) R. M. Santilli, Rendiconti Circolo Matematico di
Palermo, Supplemento {\bf 42}, 7 (1996).

(15) R. M. Santilli, Intern. J. Modern Phys. D {\bf 7}, 351 (1998).

[3] ** ISODUAL FORMULATIONS:**

(16) R. M. Santilli, Comm. Theor. Phys. {\bf 3}, 153 (1993).

(17) R. M. Santilli, Hadronic J. {\bf 17}, 257 (1994).

(18) R. M. Santilli, Hadronic J. {\bf 17}, 285 (1994).

(19) R. M. Santilli, Communication of the JINR, Dubna, Russia,. No. E2-96-259 (1996).

(20) R. M. Santilli, contributed paper in {\it New Frontiers of Hadronic Mechanics,}
T.L.Gill, ed., Hadronic Press (1996).

(21) R. M. Santilli, Hyperfine Interactions, {\bf 109}, 63 (1997).

(22) R. M. Santilli, Intern. J. Modern Phys. A {\bf 14}, 2205 (1999).

[4] ** ISOTOPIC FORMULATIONS:**

(23) R.M.Santilli: Hadronic J. {\bf 1}, 224 (1978).

(24) R. M. Santilli, Phys. Rev. D {\bf 20}, 555 (1979).

(25) C.Myung and R.M.Santilli, Hadronic J. {\bf 5}, 1277 (1982).

(26) R. M. Santilli, Novo Cimento Lett. {\bf 37}, 545 (1983).

(27) R. M. Santilli, Hadronic J. {\bf 8}, 25 and 36 (1985).

(28) R. M. Santilli, JINR Rapid. Comm. {\bf 6}, 24 (1993).

(29) R. M. Santilli, J.Moscow Phys.Soc. {\bf 3}, 255 (1993).

(30) R. M. Santilli, Communication of the JINR, Dubna, Russia, # E4-93-352, 1993, published in Chinese J.Syst.Ing. \& Electr.{\bf 6}, 177 (1996).

(31) R. M. Santilli, Found. Phys. {\bf 27}, 635 (1997).

(32) R. M. Santilli, Found. Phys. Letters {\bf 10}, 307 (1997).

(33) R. M. Santilli, Acta Appl. Math. {\bf 50}, 177 (1998).

(34) R. M. Santilli, contributed paper to the {\it Proceedings of the International Workshop on
Modern Modified Theories of Gravitation and Cosmology,} E. I. Guendelman, Editor, Hadronic Press, p. 113 (1998).

(35) R. M. Santilli, contributed paper to the {\it Proceedings of the VIII M. Grossmann Meeting
on General Relativity,} Jerusalem, June 1998, World Scientific, p. 473 (1999).

(36) R. M. Santilli, contributed paper in {\it Photons: Old Problems in Light of New Ideas,} V. V.
Dvoeglazov, editor, Nova Science Publishers, pages 421-442 (2000).

(37) R. M. Santilli, Found. Phys. Letters {\32}, 1111 (2002).

[5] ** GENOTOPIC FORMULATIONS:**

(38) R. M. Santilli: Hadronic J. {\bf 1},574 and 1267 (1978).

(39) R. M. Santilli, Hadronic J. {\bf 2}, 1460 (l979) and {\bf 3}, 914 (l980).

(40) R. M. Santilli, Hadronic J. {\bf 4}, 1166 (l981).

(41) R. M. Santilli, Hadronic J. {\bf 5}, 264 (l982).

(42) H. C. Myung and R. M. Santilli, Hadronic J. {\bf 5}, 1367 (l982).

(43) R. M. Santilli, Hadronic J. Suppl. {\bf 1}, 662 (l985).

(44) R. M. Santilli, Found. Phys. {\bf 27}, 1159 (1997).

(45) R. M. Santilli, Modern Phys. Letters {\bf 13}, 327 (1998).

(46) R. M. Santilli, Intern. J. Modern Phys. A {\bf 14}, 3157 (1999).

[6] ** HYPERSTRUCTURAL FORMULATIONS:**

(47) R. M. Santilli, Algebras, Groups and Geometries {\bf 15}, 473 (1998).

[7] ** MONOGRAPHS:**

(48) R. M. Santilli, {\it Foundations of Theoretical Mechanics}, Vol. I,
Springer--Verlag, Heidelberg--New York (1978).

(49) R. M. Santilli, {\it Lie-admissible Approach to the Hadronic Structure,}
Vol.I, Hadronic Press, Palm Harbor, Florida (1978).

(50) R. M. Santilli, {\it Lie-admissible Approach to the Hadronic Structure,} Vol.
II, Hadronic Press, Palm Harbor, Florida (1981).

(51) R. M. Santilli, {\it Foundations of Theoretical Mechanics}, Vol. II,
Springer--Verlag, Heidelberg--New York (1983).

(52) R. M. Santilli, {\it Isotopic Generalizations of Galilei and Einstein Relativities,}
Vol. I, Hadronic Press, Palm Harbor, Florida (1991).

(53) R. M. Santilli, {\it Isotopic Generalizations of Galilei and Einstein Relativities,}
Vol. II, Hadronic Press, Palm Harbor, Florida (1991).

(54) R. M. Santilli, {\it Elements of Hadronic Mechanics},
Vol I, Ukraine Academy of Sciences,
Kiev, Second Edition (1995).

(55) R. M. Santilli, {\it Elements of Hadronic Mechanics},
Vol II, Ukraine Academy of Sciences,
Kiev, Second Edition (1995).

(56) C. R. Illert and R. M. Santilli, {\it Foundations of Theoretical Conchology,}
Hadronic Press, Palm Harbor, Florida (1995).

(57) R. M. Santilli {\it Isotopic, Genotopic and Hyperstructural Methods
in Theoretical Biology}, Ukraine Academy of Sciences, Kiev (1996).

(58) R. M. Santilli, {\it The Physics of New Clean Energies and Fuels According to
Hadronic Mechanics,} Special issue of the Journal of New Energy, 318 pages (1998).

(59) R. M. Santilli, {\it Foundations of Hadronic Chemistry with Applications to New
Clean Energies and Fuels,} Kluwer Academic Publishers, Boston-Dordrecht-London
(2001).

(60) R. M. Santilli, {\it Ethical Probe of Einstein's Followers in the USA: An insider's view,} Alpha Publishing, Newtonville, MA (1984).

(61) R. M. Santilli, {\it Documentation of the Ethical Probe,} Volumes I, II and III, Alpha Publishing, Newtonville, MA (1985).

(62) H. C. Myung, {\it Lie Algebras and Flexible
Lie-Admissible Algebras,} Hadronic Press (1982).

(63) A.K. Aringazin, A. Jannussis, D.F. Lopez, M. Nishioka, and B. Veljanoski,
{\it Santilli's Lie-isotopic Generalization of Galilei's and Einstein's
Relativities,} Kostarakis Publishers, Athens (1991).

(64) D. S. Sourlas and G. T. Tsagas, {\it Mathematical
Foundations of the Lie-Santilli Theory,} Ukraine Academy of Sciences,
Kiev (1993).

(65) J. L\^{o}hmus, E. Paal and L. Sorgsepp, {\it
Nonassociative Algebras in Physics}, Hadronic Press, Palm Harbor, FL,
USA (1994).

(66) J. V. Kadeisvili, {\it Santilli's Isotopies of
Contemporary Algebras, Geometries and Relativities},
Second Edition, Ukraine Academy of Sciences, Kiev , Second Edition (1997).

(67) R. M. Falcon Ganfornina and J. Nunez Valdes, {\it Fondamentos de la Isoteoria de
Lie-Santilli,} (in Spanish) International Academic Press, America-Europe-Asia,
(2001), also available in the pdf file
http://www.i-b-r.org/docs/spanish.pdf

(68) Chun-Xuan Jiang, {\it Foundations of Santilli's Isonumber Theory,}
with Applications to New Cryptograms, Fermat's Theorem and Goldbach's Conjecture,
International Academic Press, America-Europe-Asia
(2002) also available in the pdf file
http://www.i-b-r.org/docs/jiang.pdf

[8] ** CONFERENCE PROCEEDINGS AND REPRINT VOLUMES:**

(69) H. C. Myung and S. Okubo, Editors, {\it Applications of Lie-Admissible Algebras
in Physics,} Volume I, Hadronic Press (1978).

(70) H. C. Myung and S. Okubo, Editors, {\it Applications of Lie-Admissible Algebras
in Physics,} Vol. II, Hadronic Press (1978).

(71) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Second Workshop on
Lie-Admissible Formulations,} Part I, Hadronic J. Vol. 2, no. 6, pp. 1252-2033 (l979).

(72) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Second Workshop on
Lie-Admissible Formulations,}Part II, Hadronic J. Vol. 3, no. 1, pp. 1-725 (l980.

(73) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Third Workshop on
Lie-Admissible Formulations,}Part A, Hadronic J. Vol. 4, issue no. 2, pp. 183-607 (l9881).

(74) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Third Workshop on
Lie-Admissible Formulations,} Part B, Hadronic J. Vo. 4, issue no. 3, pp. 608-1165 (l981).

(75) H. C. Myung and R. M. Santilli, Editor, {\it Proceedings of the Third Workshop on
Lie-Admissible Formulations,} Part C, Hadronic J. Vol. 4, issue no. 4, pp. 1166-1625
(l981).

(76) J. Fronteau, A. Tellez-Arenas and R. M. Santilli, Editor, {\it Proceedings of the First
International Conference on Nonpotential Interactions and their Lie-Admissible
Treatment,} Part A, Hadronic J., Vol. 5, issue no. 2, pp. 245-678 (l982).

(77) J. Fronteau, A. Tellez-Arenas and R. M. Santilli, Editor, {\it Proceedings of the First
International Conference on Nonpotential Interactions and their Lie-Admissible
Treatment,} Part B, Hadronic J. Vol. 5, issue no. 3, pp. 679-1193 (l982).

(78) J. Fronteau, A. Tellez-Arenas and R. M. Santilli, Editor, {\it Proceedings of the First
International Conference on Nonpotential Interactions and their Lie-Admissible
Treatment,} Part C, Hadronic J. Vol. 5, issue no. 4, pp. 1194-1626 (l982).

(79) J. Fronteau, A. Tellez-Arenas and R. M. Santilli, Editor, {\it Proceedings of the First
International Conference on Nonpotential Interactions and their Lie-Admissible
Treatment,} Part D, Hadronic J. Vol. 5, issue no. 5, pp. 1627-1948 (l982).

(80) J.Fronteau, R.Mignani, H.C.Myung and R. M. Santilli, Editors, {\it Proceedings of the
First Workshop on Hadronic Mechanics,} Hadronic J. Vol. 6, issue no. 6, pp. 1400-1989
(l983).

(81) A. Shoeber, Editor, {\it Irreversibility and Nonpotentiality in Statistical Mechanics,}
Hadronic Press (1984).

(82) H. C. Myung, Editor, {\it Mathematical Studies in Lie-Admissible Algebras,} Volume I,
Hadronic Press (1984).

(83) H. C. Myung, Editor, {\it Mathematical Studies in Lie-Admissible Algebras,} Volume II,
Hadronic Press (1984).

(84) H. C. Myung and R. M. Santilli, Editor, {\it Applications of Lie-Admissible Algebras
in Physics,} Vol. III, Hadronic Press (1984).

(85) J.Fronteau, R.Mignani and H.C.Myung, Editors, {\it Proceedings of the Second Workshop on
Hadronic Mechanics,} Volume I Hadronic J. Vol. 7, issue no. 5, pp. 911-1258 (l984).

(86) J.Fronteau, R.Mignani and H.C.Myung, Editors, {\it Proceedings of the Second Workshop on
Hadronic Mechanics,} Volume II, Hadronic J. Vol. 7, issue no. 6, pp. 1259-1759 (l984).

(87) D.M.Norris et al, {\it Tomber's Bibliography and Index in Nonassociative
Algebras,} Hadronic Press, Palm Harbor, FL (1984).

(88) H. C. Myung, Editor, {\it Mathematical Studies in Lie-Admissible Algebras,} Volume III,
Hadronic Press (1986).

(89) A.D.Jannussis, R.Mignani, M. Mijatovic, H. C.Myung B. Popov and A. Tellez Arenas,
Editors, {\it Fourth Workshop on Hadronic Mechanics and Nonpotential Interactions,}
Nova Science, New York (l990).

(90) H. M. Srivastava and Th. M. Rassias, Editors, {\it Analysis Geometry and Groups:
A Riemann Legacy Volume,} Hadronic Press (1993).

(91) F. Selleri, Editor, {\it Fundamental Questions in Quantum Physics and Relativity,}
Hadronic Press (1993).

(92) J. V. Kadeisvili, Editor, {\it The Mathematical Legacy of Hanno Rund}, Hadronic Press
(1994).

(93) M. Barone and F. Selleri Editors, {\it Frontiers of Fundamental Physics,} Plenum, New
York, (1994).

(94) M. Barone and F. Selleri, Editors, {\it Advances in Fundamental Physics,} Hadronic Press
(1995).

(95) Gr. Tsagas, Editor, {\it New Frontiers in Algebras, Groups and Geometries
,} Hadronic Press (1996).

(96) T. Vougiouklis, Editor, {\it New Frontiers in Hyperstructures,}
Hadronic Press, (1996).

(97) T. L. Gill, Editor, {\it New Frontiers in Hadronic Mechanics,} Hadronic Press (1996).

(98) T. L. Gill, Editor, {\it New Frontiers in Relativities,} Hadronic Press (1996).

(99) T. L. Gill, Editor, {\it New Frontiers in Physics,}, Volume I, Hadronic Press (1996).

(100) T. L. Gill, Editor, {\it New Frontiers in Physics,}, Volume II, Hadronic Press (1996).

(101) C. A. Dreismann, Editor, {\it New Frontiers in Theoretical Biology,} Hadronic Press
(1996).

(102) G. A., Sardanashvily, Editor,{\it New Frontiers in Gravitation,} Hadronic Press (1996).

(103) M. Holzscheiter, Editor, {\it Proceedings of the
International Workshop on Antimatter Gravity,} Sepino, Molise, Italy,
May 1996, Hyperfine Interactions, Vol. {\bf 109} (1997).

(104) T. Gill, K. Liu and E. Trell, Editors, {\it Fundamental Open Problems in Science at the
end of the Millennium,}} Volume I, Hadronic Press (1999).

(105) T. Gill, K. Liu and E. Trell, Editors, {\it Fundamental Open Problems in Science at the
end of the Millennium,}} Volume II, Hadronic Press (1999).

(106) T. Gill, K. Liu and E. Trell, Editors, {\it Fundamental Open Problems in Science at the
end of the Millennium,}} Volume III, Hadronic Press (1999).

(107) V. V. Dvoeglazov, Editor {\it Photon: Old Problems in Light of New Ideas,} Nova Science
(2000).

(108) M. C. Duffy and M. Wegener, Editors, {\it Recent Advances in Relativity Theory} Vol. I,
Hadronic Press (2000).

(109) M. C. Duffy and M. Wegener, Editors, {\it Recent Advances in Relativity Theory} Vol. I,
Hadronic Press (2000).

[9] ** EXPERIMENTAL VERIFICATIONS:**

(110) F. Cardone, R. Mignani and R. M. Santilli, J. Phys. G: Nucl. Part. Phys.
{\bf 18}, L61 (1992).

(111) F. Cardone, R. Mignani and R. M. Santilli, J. Phys. G: Nucl. Part. Phys. {\bf 18}, L141
(1992).

(112) R. M. Santilli, Hadronic J. {\bf 15}, Part I: 1-50 and Part II: 77134 (l992).

(113) Cardone and R. Mignani, JETP {\bf 88}, 435 (1995).

(114) R. M. Santilli, Intern. J. of Phys. {\bf 4}, 1 (1998).

(115) R. M. Santilli Communications in Math. and Theor. Phys. {\bf 2}, 1 (1999).

(116) A. O. E. Animalu and R. M. Santilli, Intern. J. Quantum Chem. {\bf 26},175 (1995).

(117) R. M. Santilli, contributed paper to {\it Frontiers of Fundamental Physics,} M. Barone and
F. Selleri, Editors Plenum, New York, pp 4158 (1994).

(118) R. Mignani, Physics Essays {\bf 5}, 531 (1992).

(119) R. M. Santilli, Comm. Theor. Phys. {\bf 4}, 123 (1995).

(120) Yu. Arestov, V. Solovianov and R. M. Santilli, Found. Phys. Letters {\bf 11}, 483 (1998).

(121) R. M. Santilli, contributed paper in the {\it Proceedings of the International Symposium on
Large Scale Collective Motion of Atomic Nuclei,} G. Giardina, G. Fazio and M. Lattuada,
Editors, World Scientific, Singapore, p. 549 (1997).

(122) J.Ellis, N.E. Mavromatos and D.V.Napoulos in {\sl Proceedings of the
Erice Summer School, 31st Course: From Superstrings to the Origin of Space--Time},
World Sientific (1996).

(123) C. Borghi, C. Giori and A. Dall'OIlio Russian J. Nucl. Phys. {\bf 56}, 147 (1993).

(124) N. F. Tsagas, A. Mystakidis, G. Bakos, and L. Seftelis, Hadronic J. {\bf 19}, 87 (1996).

(125) R. M. Santilli and D., D. Shillady, Intern. J. Hydrogen Energy {\bf 24}, 943 (1999).

(126) R. M. Santilli and D., D. Shillady, Intern. J. Hydrogen Energy {\bf 25}, 173 (2000).

(127) R. M. Santilli, Hadronic J. {\bf 21}, pages 789-894 (1998).

(128) M.G. Kucherenko and A.K. Aringazin, Hadronic J. {\bf 21}, 895 (1998).

(129) M.G. Kucherenko and A.K. Aringazin, Hadronic Journal {\bf 23}, 59 (2000).

(130) R.M. Santilli and A.K. Aringazin, "Structure and Combustion of
Magnegases", e-print http://arxiv.org/abs/physics/0112066, to be published.

,
[10] ** MATHEMATICS PAPERS:**

(131) S. Okubo, Hadronic J. {\bf 5}, 1564 (1982).

(132) J. V. Kadeisvili, Algebras, Groups and Geometries {\bf 9}, 283 and 319 (1992).

(133) J. V. Kadeisvili, N. Kamiya, and R. M. Santilli, Hadronic J. {\bf 16}, 168 (1993).

(134) J. V. Kadeisvili, Algebras, Groups and Geometries {\bf 9}, 283 (1992).

(135) J. V. Kadeisvili, Algebras, Groups and Geometries {\bf 9}, 319 (1992).

(136) J. V. Kadeisvili, contributed paper in the {\it Proceedings of the
International Workshop on Symmetry Methods in Physics,} G. Pogosyan et al., Editors,
JINR, Dubna, Russia (1994).

(137) J. V. Kadeisvili, Math. Methods in Appl. Sci. {\bf 19} 1349 (1996).

(138) J. V. Kadeisvili, Algebras, Groups and Geometries, {\bf 15}, 497 (1998).

(139) G. T. Tsagas and D. S. Sourlas, Algebras, Groups and Geometries {\bf 12}, 1 (1995).

(140) G. T. Tsagas and D. S. Sourlas, Algebras, Groups and geometries {\bf 12}, 67 (1995).

(141) G. T. Tsagas, Algebras, Groups and geometries {\bf 13}, 129 (1996).

(142) G. T. Tsagas, Algebras, Groups and geometries {\bf 13}, 149 (1996).

(143) E. Trell, Isotopic Proof and Reproof of Fermatıs Last Theorem Verifying Bealıs
Conjecture. Algebras Groups and Geometries {\bf 15}, 299-318 (1998).

(144) A.K. Aringazin and D.A. Kirukhin,, Algebras, Groups and
Geometries {\bf 12}, 255 (1995).

(145) A.K. Aringazin, A. Jannussis, D.F. Lopez, M. Nishioka, and B. Veljanoski, Algebras, Groups and Geometries {\bf 7}, 211 (1990).

(146) A.K. Aringazin, A. Jannussis, D.F. Lopez, M.
Nishioka, and B. Veljanoski, Algebras, Groups and
Geometries {\bf 8}, 77 (1991).

(147) D. L. Rapoport, Algebras, Groups and Geometries, {\bf 8}, 1 (1991).

(148) D. L. Rapoport, contributed paper in the{\it
Proceedings of the Fifth International Workshop on
Hadronic Mechanics,} H.C. Myung, Edfitor, Nova Science Publisher (1990).

(149) D. L. Rapoport, Algebras, Groups and Geometries {\bf 8}, 1 (1991).

(150) C.-X. Jiang, Algebras, Groups and Geometries {\bf 15}, 509 (1998).

(151) D. B. Lin, Hadronic J. {\bf 11}, 81 (1988).

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(155) S. Vacaru, Algebras, Groups and Geometries {\bf 14}, 225 (1997) (155).

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(176) A. O. Animalu and R. M. Santilli, contributed paper in {\it Hadronic
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(200) A.K. Aringazin, D.A.Kirukhin, and R.M. Santilli, Had-ronic J. {\bf 18}, 257 (1995).

(201) T. L. Gill, Hadronic J. {\bf 9}, 77 (1986).

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(225) R. M. Santilli, Found. Phys. {\bf 11}, 383 (l981).

(226) R. M. Santilli, "Iso-m geno-, hyper-mechanifor matter and their isoduals for antimatter," in press at *Journal of Dynamical Systems and Geometric Theories,* also available in pdf format.

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(248) H. Arp, * Quasars Redshifts and Controversies,* Interstellar media, Berkeley, 1987.

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