Ruggero Maria Santilli

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

Curriculum Vitae

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Last revision May 26, 2003

STRUCTURE MODEL OF NUCLEI AS HADRONIC BOUND STATES OF ISOPROTONS AND ISOELECTRONS, AND THE NEW CONTROLLED HADRONIC FUSION.

**1. INSUFFICIENCIES OF THE STRUCTURE MODEL OF NUCLEI AS QUANTUM MECHANICAL BOUND STATES OF PROTONS AND NEUTRONS.**

There is no doubt that the structure model of nuclei as quantum mechanical bound states of protons and neutrons (jointly called nucleons) has permitted simply historical advances. In particular, its **approximate** validity is beyond doubt, as proven by the fact that, for instance, nuclear reactors built on such a model do indeed work.

Nevertheless, the assumption of the current quantum mechanical structure model of nucl;ei as being of final character is sheer scientific religion, rather than a scientific truth, particularly when proffered by nuclear physicists, because it is well known that physics is a discipline that will never admit "final theories." The true scientific issue addressed here is, therefore, that of identifying the **limitations** of the current quantum model of nuclei, and searching for plausible more adequate structure models.

Along the latter lines, the first aspect to be admitted in order to avoid scientific religions is that quantum mechanics itself, while being exactly valid for the structure of the hydrogen atom, it is only approximately valid for the nuclear structure. This is so because quantum mechanics represented "all" experimental data of the structure of the hydrogen atom in an "exact" and "invariant" way. By comparison, quantum mechanics has failed to provide the same exact and invariant representation of "all" nuclear data, as outlined below (see also Section III.4).
Of course, exact fits have indeed been reached via the introduction of *ad hoc* parameters of unknown origin, then claiming exact validity of quantum mechanics, while in reality these parameters are a direct representation of the **deviations** of the basic axioms of quantum mechanics from experimental data.

Independently from these insufficiencies, **quantum mechanics CANNOT be exactly valid for nuclear physics because its basic spacetime symmetries, the Galilei and Poincare' symmetries, are not exactly valid since "nuclei do not admit nuclei"** (see Figure III.11 and Figure 5 below). In fact, the Galilei and Poincare' symmetries are exactly valid only for **Keplerian systems,** namely, for systems admitting the heaviest constituent at the center with the other constituents orbiting around. By comparison, nuclei are aggregates of particles in contact with each others without any Keplerian center and without any Keplerian orbit at all. Once the fundamental spacetime symmetries of quantum mechanics are seen as being approximately valid in nuclear physics, so must be quantum mechanics itself.

Besides the above insufficiencies of the basic discipline, **nuclear models based on neutrons cannot be of final character because neutrons are composite and unstable particles decaying into protons and electrons (plus the hypothetical antineutrino).** Even for the simplest possible nucleus, the deuteron, about one century of research based on quantum mechanics has left the following basic problems unsolved:

*FUNDAMENTAL PROBLEMS ON THE DEUTERON LEFT UNSOLVED BY QUANTUM MECHANICS AFTER ONE CENTURY OF RESEARCH:*

1) ** Quantum mechanics has been unable to represent the stability of the deuteron.** This is evidently due to the natural instability of the deuteron. The unsolved problem is due to the absence in the technical literature of quantitative numerical proofs that, when bonded to a proton, the neutron cannot decay, as an evident condition for stability. Except for philosophical-political statements, the stability of the deuteron has been left fundamentally unexplained by quantum mechanics to this day (see Figure 1 for more details).

2) ** Quantum mechanics has been unable to represent the spin 1 of the ground state of the deuteron.** The basic axioms of quantum mechanics require that the most stable bound state of two particles with the same spin is that with SPIN ZERO. No such state has been detected in the deuteron. Therefore, following one century of research, quantum mechanics has been unable to represent the spin 1 of the ground state of the deuteron except, again, for political-nonscientific views (see Figure 2 for more details).

3) ** Quantum mechanics has been unable to reach an exact representation of the magnetic moment of the deuteron.** After about one century of research, nonrelativistic quantum mechanics misses 0.022 Bohr units corresponding to 2.6% of the experimental value. Relativistic corrections reduce the error down to about 1% but under highly questionable theoretical assumptions, such as the use for ground state of a mixture of different energy level that are assumed to exist without any emission or absorption of quanta as requested by quantum mechanics. Embarrassing deviations occur for the magnetic moments of heavier nuclei (see Figure 3 for more details).

4) ** Quantum mechanics has been unable to identify the physical origin of the attractive force binding together the proton and the neutron in the deuteron.** Since the neutron is neutral, there is no known electrostatic origin of the attractive force needed for the existence of the deuteron. As a matter of fact, the only Coulomb force for the proton-neutron system is that of the magnetic moments, which force is REPULSIVE for the case of spin 1 with parallel spin. Therefore, a "strong" force was conjectures and its existence was subsequently proved to be true. Nevertheless, the physical origin of such strong force has remained unidentified following one century of research via quantum mechanics. Particularly mysterious remain the "exchange forces," namely, forces originating from the exchange of protons and neutrons.

5) ** Quantum mechanics has also been unable to treat the deuteron space parity in a way consistent with the rest of the theory.** The experimental value of the space parity of the deuteron is positive for the ground state, because the angular momentum L is null. However, in the dream of achieving compatibility of the deuteron phenomenology with quantum mechanics, nuclear physicists assume for the calculation of the magnetic moment that the ground state is a mixture of the lowest state with L = 0 with other states in which the angular momentum is not null, thus implying an embarrassing incompatibility of these calculations with the positive parity of the ground state.

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In conclusion, after about one century of research, quantum mechanics has left unresolved fundamental problems even for the case of the smallest possible nucleus, the deuteron, with progressively increasing unresolved problems for heavier nuclei. Following these insufficiencies, any additional belief on the final character of quantum mechanics in nuclear physics is a sheer political posture in disrespect of the societal need to search for a more adequate mechanics.

Not only the basic discipline of current nuclear models, quantum mechanics, is is not exactly valid in nuclear physics, but the very assumption of neutrons as nuclear constituents is approximately valid since neutrons are composite particles. Therefore, the main objective of this Part VI is the identification of stable, massive physical constituents of nuclei and their theoretical treatment that admits in first approximation the proton-neutron model, while permitting deeper advances.

The replacement of protons and neutrons with the hypothetical quark is mathematically significant, with the clarification that **quarks cannot be physical particles** because, as stresses several times in this web site, **quarks are purely mathematical representations of a purely mathematical symmetry realized in a purely mathematical internal unitary space without any possible formulation in our spacetime (because of the O'Raferartaigh's theorem).**

Consequently, ** quark masses are purely mathematical parameters and cannot be physical inertial masses.** As also stressed several times in this web site, on true scientific grounds without politics or religions, inertial masses can only be defined as the eigenvalues of the second order Casimir invariant of the Poincare' symmetry. But the Poincare' symmetry is notoriously inapplicable for the representation of quarks because they cannot exist in our spacetime. Therefore, quark "masses" cannot have inertia.

I conclusion, quarks can indeed be considered as replacements of protons and neutrons, with the understanding that **matter made up of quarks cannot have any weight,** since the assumption that quarks can experience gravitational attraction while not being definable in our spacetime would be the ultimate climax of scientific politics or religion.

**2. EXACT AND INVARIANT REPRESENTATION OF ALL CHARACTERISTICS OF THE DEUTERON AS A THREE-BODY HADRONIC BOUND STATE OF TWO ISOPROTONS AND ONE ISOELECTRON.**

**2.1: Conceptual foundations.**

The resolution of the historical objections against Rutherford's conception of the neutron as a bound state of a proton and an electron obeying the covering hadronic mechanics (Part V) implies a profound revision of the entire nuclear physics, beginning with the deuteron that now results in being a THREE-BODY bound state of two isoprotons and one isoelectron, and we shall write,

(2.1) d = (p^_{1},e^,p^_{2})_{hm},

where the "hat" denotes isoparticles, namely particles verifying the laws of the isotopic branch of hadronic mechanics (Parts I, II, IV, V). The meaning of the name "deuteron" as a two-body system is then relegated to historical value.

Irrespective of the resolution of the objections against Rutherford's conception of the neutron, a three-body structure provides the ONLY known consistent representation of ALL characteristics of the deuteron, first achieved by R. M. Santilli in Ref. (58) of 1998 and as reviewed below.

It should be recalled that the first hypothesis on structure (2.1) dates back to Rutherford's time when all nuclei were conceived to be bound states of protons and electrons. Nevertheless, as equally well known, this nuclear model had to be abandoned because of too many inconsistencies.
Santilli's priority is that of having achieved the first numerical, invariant and axiomatically correct resolution of all historical objections, such as those for stability, spin, binding energy, magnetic moments, etc.

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In the atomic structure, protons and electrons are at very large mutual distances compared to the size of their wavepackets, while in the deuteron structure the constituents are under a necessary condition of mutual wave-overlapping with consequential nonlinear, nonlocal and nonpotential effects. The belief that the mechanics holding for the former conditions must necessarily be exact also for the dramatically different latter conditions is pure academic politics deprived of scientific value. The only open issue is the selection of a generalization of quantum mechanics suitable for the invariant treatment of the latter conditions while admitting the former in first approximation.

In this web site we assume the exact validity of quantum mechanics for the structure of the hydrogen atom and the validity of the covering hadronic mechanics for quantitative studies on the structure of the deuteron, not only because hadronic mechanics permits the only known invariant and consistent treatment of said nonunitary effects, but also because it achieves the only known exact and invariant representation of "all" characteristics of the neutron as a bound state of one proton and one electron.

The main mechanism is that, in the transition from motion in vacuum at large mutual distances (hydrogen atom), to motion in the condition of deep overlapping of their wavepackets (deuteron), particles experience an alteration of their intrinsic characteristics, called mutation (38), or isorenormalization (namely, renormalization originating from the generalization of the unit rather than from potential interactions (58)).

As a result, when members of the deuteron structure, protons and electrons are not ordinary particles as known in the standard literature (that is, irreducible representations of the Poincare' group), and are instead **isoprotons and isoelectrons** (that is, irreducible isorepresentations of the Poincare'-Santilli isogroup (29)). In turn, as shown below, the latter mutations resolve all problematic aspects identified above.

**2.2: Deuteron Stability.**

As indicated earlier, the lack of a quantitative representation of the stability of the deuteron when composed by the stable problem and the unstable neutron has been one of the fundamental problems left unsolved by quantum mechanics in about one century of research.

By comparison, protons and electrons are stable. Therefore, structure model (2.1) resolves the problem of the stability of the deuteron in a simple, direct, and final way.

The only remaining aspect to be shown below is that the potential and contact forces in pair-wise singlet couplings are so "strong" when mediated by the isoelectron, to overcome Coulomb repulsion among the protons and form a permanent bound state, as already established for the valence bond and Cooper pairs of identical electrons (Part III).

As shown below in Section 2.7, the stability of the deuteron results to originate from the so-called "exchange forces."

**2.3: Deuteron Size.**

Experimental data have established that the proton has a charge radius of the order of R_{p} = 0.8x10^{-13} cm = 0.8 fm, or diameter D_{p} = 1.6 fm, that can be well assumed as the size of its wavepacket for the purpose of this analysis. The corresponding value of the wavepacket of the electron is assumed to be of the order of R_{e} = 0.5 fm as that providing appreciable nonlocal effects, or D_{e} = 1 fm, namely

(2.2a) R_{p} = 0.8x10^{-13} cm = 0.8 fm, D_{p} = 1.6 fm,

(2.2b) R_{e} = 0.5 fm, D_{e} = 1 fm.

Numerous values of the charge radius of the deuteron can be found in the literature, such as the value D_{d} = 4.31 fm. However, such a value is derived via theoretical elaborations based on a number of quantum mechanical assumptions. These assumptions are unacceptable for a treatment via hadronic mechanics.

After consultations with nuclear physicists, we have been unable to locate in the literature any actual experimentally measured value of the size of the deuteron without said theoretical manipulations (the indication of such un-manipulated experimental value would be appreciated, if available).

For these reasons, we assume the value of the charge radius of the deuteron derived by the known formula that is experimentally verified for a large variety of nuclei, and yields the value for the deuteron

(2.3a) R_{nucleus} = 1.12xA^{1/3} fm,

(2.3b) R_{d} = 1.41 fm, D_{d} = 2.82 fm.

By recalling that D_{p} = 1.6 fm, the two isoprotons of model (2.1) are in conditions of mutual penetration of their hyperdense structure in the remarkable amount of 0.38 fm. In turn, these conditions imply that the electron is totally immersed within the proton structure, in full compatibility with the neutron structure (Part V), yielding the configuration of Figure 4.

**2.4: Deuteron Charge. **

At a first glance, model (2.1) trivially represents the deuteron positive charge +e. The structure of the deuterium *atom* is then treated by *quantum* (and not hadronic) mechanics (because all nonunitary effects are null at atomic distances).

Nevertheless, a quantitative representation of the charge of the deuteron is not trivial at a deeper inspection. This is due to the fact that hadronic mechanics generally implies the mutation of *all* characteristics of particles, thus including the mutation Q^ of conventional charges Q, and we shall write

(2.4) Q^_{p1} = a x e, Q^_{e} = b x e, Q^_{p2} = c x e,

where a, b, c are non-null positive parameters, and e is the conventional elementary charge. These mutations are necessary for consistency beginning with the reconstruction of the exact isospin symmetry in nuclear physics (58).

However, these mutations are only internal, under the condition of recovering the conventional total charge +e for the system as a whole, precisely as it was the case for the reconstruction of the exact isospin symmetry.

Technically, the preservation of the conventional total charge +e under mutations (2.4) is established by the fact that the total charge operator of the Poincare'-Santilli isosymmetry coincides with that of the conventional Poincare~ symmetry. We can therefore write the subsidiary constraint

(2.5) Q_{d} = +e, a + b + c = 1.

In different terms, the conventional value of the total charge of the deuteron can be claimed to be +e only at large mutual distances, while at the structural level the situation is dramatically more complex. Its quantitative treatment requires hadronic field theory that has not been developed to date. Therefore, the problem of the local value of the charge inside the deuteron is deferred to future technical studies.

**2.5: Deuteron Spin.**

As recalled in Section 1, quantum mechanics predicts that the most stable state between two particles with the same spin is the singlet, for which the total spin is zero, thus predicting that the ground state of the deuteron should have spin zero, contrary to the experimental value of spin 1.

When hadronic mechanics is used, the exact and invariant representation of the spin 1 of model (2.1) is achieved in a way similar to that of the Rutherford-Santilli neutron (Part V). It is easy to see that the electron is trapped inside one of the two protons, thus being constrained to have an angular momentum equal to the spin of the proton itself. In this case, with reference to Figure 4, the total angular momentum of the isoelectron is null (as for the Rutherford-Santilli neutron). By recalling that the ground state has null angular momentum,** the total angular momentum of the deuteron is given by the sum of the spin 1/2 of the two isoprotons.**

Again, fractional angular momenta are anathema for quantum mechanics (namely, when angular momenta are defined on a conventional Hilbert space over the conventional field of complex numbers), because they violate the crucial condition of unitarity, with consequential violation of causality, probability laws, and other basic physical axioms.

For hadronic mechanics, the isotopic lifting S^ and L^ of the spin S and angular momentum L of the electron when immersed within a hyperdense hadronic medium are characterized by Eqs. (V.4.3) and (V.4.4), i.e.,

(2.6a) (S^^{2})*|s^> = (PxS)x(PxS + 1)x|s^>,

(2.6b) S^_{3}*|s^> = ± (PxS)x|s^>,

(2.6a) (L^^{2})*|l^> = (QxL)x(QxL + 1)x|l^>,

(2.6c) Q^_{3}*|l^> = ± (QxL)x|l^>,

(2.6d) S = 1/2, L = 0, 1, 2, ...

where P and Q are arbitrary (non-null) positive parameters. Recall that the above isotopy of SU(2)-spin was introduced (28,33) to prevent the believe of the perpetual motion that is inherent when the applicability of quantum mechanics is extended in the core of a star. In fact, quantum mechanics predicts that an electron moves in the core of a star with an angular momentum that is conserved in exactly the same manner as when the same electron orbits around proton in vacuum, thus exiting the boundaries of science and ethics, since an electron in the core of a star can only have a **locally varying** angular momentum and spin as represented by Eqs. (2.6).

Unitarity for angular momenta different than 0, 1, 2, ... is reconstructed on iso-Hilbert spaces with the isoinner products of the type

(2.7) ( l^ | x T x | l^) x I^, T = Q, I^ = 1/Q,

in which case causality, probability and all other physical laws are recovered.

For the case of Rutherford's electron and for the isoelectron in the deuteron, we have the **constraint** that the orbital angular momentum must be equal but opposite to that of the spin,

(2.8) S^_{e^} = P x (1/2) = - L^_{e^} = Q, Q = - P/2, J^_{e^,Tot} = 0.

The exact and invariant representation of the spin 1 of the ground state of the deuteron then follows according to the rule

(2.9) J_{d} = S_{p1} + S_{p2} = 1.

Note that there is no violation of Pauli's exclusion principle since that principle only applies to "identical" particles and does not apply to protons and neutrons, as well known (more explicitly, one of the two protons of Eq. (2.9) is in actuality the neutron since it has embedded in its interior the isoelectron).

Note also the crucial importance for model (2.1) that **the SU(2)-spin symmetry is broken under EXTERNAL strong interactions,** as stated beginning with the title of the original proposal to build hadronic mechanics (38). Note finally the **reconstruction of the exact SU(2)-spin symmetry at the isotopic level,** since SU^(2) is isomorphic to SU(2) (see Parts II and V).

A fully equivalent classical example is that of Jupiter that admits in its interior vortices with varying angular momenta, yet its total angular momentum is fully conserved (see of monograph (51) for a technical treatment of the classical case).

The above features belong to the new class of bound states permitted by the isotopies and known under the name of **closed non-Hamiltonian (or variationally nonselfadjoint) systems**. These systems are "closed" in the sense of being isolated from the rest of the universe, thus verifying conventional total conservation laws and are given by aggregates of constituents at small mutual distances, as occurring for Jupiter at the classical level or for nuclei at the particle level. Despite the total conservation laws, the systems admit in their interior nonpotential (variationally nonselfadjoint) forces under which we have the internal breaking of conventional spacetime symmetries as a necessary condition to avoid the presence of the Keplerian center.

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The universal spacetime symmetries of closed non-Hamiltonian systems are given by the Galilei-Santilli (52,53) and Poincare'-Santilli (54,55) isosymmetries whose generators coincides with those of the conventional symmetries, thus assuring the total conservation laws, while the isotopic generalization of the unit and product assures the existence of internal nonpotential forces and the absence of the Keplerian center.

Conventional closed Hamiltonian systems (such as the planetary or atomic systems considered as isolated from the rest of the universe) require the exact validity of the SU(2) symmetry for both the system as a whole as well as the individual constituents, thus achieving a total conserved angular momentum as a sum of individually conserved ones, as well known.

For the case of the more general closed non-Hamiltonian systems (such as Jupiter, a hadron, a nucleus or a star considered as isolated from the rest of the universe), we have the conservation of the total angular momentum, while the angular momentum of the constituents are generally nonconserved. We merely have internal exchanges of angular momenta in such a way that these nonconservation compensate each other, resulting in a conserved total value, as clearly established for the case of Jupiter in a form visible with our eyes through a telescope.

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**2.6: Deuteron Magnetic Moment. **

Recall the the first exact and invariant representation of the magnetic moment of the deuteron was reached in Section III.4 under the conventional proton-neutron interpretation while the proton and the neutron are isoparticles.

We review here the second, exact and invariant representation of the magnetic moment of the deuteron according to model (2.1). Let us recall the following experimental magnetic moments for the deuteron and its constituents

(2.10a) m_{d} = 0.8754 e x h / M_{p} x c,
m_{p} = 2.792782 e x h / 2 x M_{p} x c;

(2.10b) m_{e} = 1 e x h / 2 x M_{e} x c = (e x h / 2 x M_{p} x c) x (m_{p} / M_{e} = (938.272 / 0.511) x e x h / 2 x M_{p} = 1.836 x 10^{3} x e x h / 2 x M_{p} x c,

where h stands for h-bar.

Recall also that the deuteron is in its ground state with null angular momentum in which case there is no orbital contribution to the total magnetic moment from the two protons. By keeping in mind the structure of the deuteron as per Figure 4, the **exact and invariant representation of the total magnetic moment of the deuteron** is then given by

(2.11a) m_{d} = 2 x m_{p} + m_{tot,e} = 2 x 2,792 e x h / 2 x M_{p} x c + m_{tot,e^} = 0.8754 e x h / M_{p} x c,

(2.11b) m_{tot,e^} = 0.8754 e x h / 2 x M_{p} x c - 5.584 e x h / 2 x M_{p} x c = - 4.709 e x h / 2 x 2 x M_{p} x c =
- 4.709 e x h / 2 x M_{e} x c x (M_{e} / M_{p}) = - 8.621 x 10^{-4} x e x h / 2 x M_{e} = m_{e^,orb} - m_{e^,spin} ,

namely, the missing contribution is provided by the total magnetic moment of the isoelectron. In particular, the latter numerical value is given by the difference between the orbital and the intrinsic magnetic moment that is very small (per electron's standard) since the total angular momentum of the isoelectron is indeed small. Also note the correct value of the sign because the isoelectron has the orbital motion in the direction of the proton spin. But the charge has changed in sign. Therefore, the direction of the orbital magnetic moment of the isoelectron is opposite that of the proton, ac correctly represented in Eqs. (2.11). Note finally that the small value of the total magnetic moment of the isoelectron for the case of the deuteron is close to the corresponding value for the Rutherford-Santilli neutron, Eqs. (V.5.3).

**2.7: Deuteron Force. **

As indicated in Section 1, the assumption that the deuteron is a bound state of a proton and a neutron permits no identification of the physical origin of the nuclear force. Quantum mechanics merely provides numerous mathematical descriptions of the attractive force via a plethora of potentials, although none of them admits a clear physical explanation of the strong attraction between protons and neutrons. Also, due to the inability to achieve a satisfactory representation of nuclear phenomena, nuclear physicists have kept adding potential and potentials throughout the past century, by still failing to achieve a satisfactory theory. Besides, doubts have existed since the beginning of the 20-th century that not necessarily all nuclear forces must admit a potential.

A primary objective of any generalization of quantum mechanics for nuclear physics is the truncation of this century old failed process of keep adding new and new potentials in the nuclear force, and search instead for fundamentally different notions and representations, a task for which hadronic mechanics has no known equals.

In fact, hadronic model (2.1) permits a clear resolution of this additional insufficiency of quantum mechanics via the precise identification of TWO types of nuclear farce, the first derivable from a Coulomb potential and the second of contact type derivable from the isounit.

The constituents in the configuration of Figure 4 have short range pair-wise opposite signs of charges and magnetic moments with long range identical signs of charges and magnetic moments. This configuration implies the following **net attractive Coulomb force in the deuteron**

(2.12) V_{d} = - e^{2} / 0.6 fm + e^{2} / 1.2 fm -
m_{p} x m_{e^} / 0.6 fm + m_{p} x m_{e^} / 1.2 fm.

In addition, the constituents admit an attractive force not derivable from a potential due to the deep penetration of their wavepackets in singlet pair-wise couplings, which force is the same as that of: the two identical electrons in the Cooper and valence pairs (Part III); the structure of mesons (Part IV); the structure of the neutron (Part V); and can be represented via the isounit

(2.13) I^ = Exp {N x [y_{e,down}(r) x d^{3}/y_{e^,down}(r)] x Integral (y^{+}_{p,up}(r) x y_{e^,down}(r) x d^{3})].

where: y_{e^,down}(r) x d^{3} represents the wavefunction of the electron with spin down in the atomic structure; y_{e^,down}(r) x d^{3} represents the wavefunction of the isoelectron with spin down within the proton structure; and y^{+}_{p,up}(r) represents the wavefunction of the proton with spin up.

As the reader may recall from Parts III, IV and V, the projection of the above force in our spacetime (that with trivial unit 1) implies the emergence of a strongly attractive Hulten potential, that behaves at short distances like the Coulomb potential, by therefore "absorbing" the latter and resulting in a single, dominating Hulten well with great simplification of the calculations.

Besides the above potential and contact force, no additional nuclear force is needed for an exact and invariant representation of the remaining characteristics of the deuteron (such as binding and total energies), as shown below.

For instance, the mysterious ** potentials of exchange forces** (in which protons and neutrons interchange themselves) are completely unnecessary and, if used, grossly misleading because the underlying physical effect is of purely **contact type,** thus having no meaningful potential at all. If a potential is granted, as done for one century by nuclear physics, it is like describing the resistive force of a spaceship during re-entry in our atmosphere with a potential, that is a nonscientific, nontechnical nonsense.

It is easy to prove that the isoelectron cannot solely be restricted to exist within one of the two protons, because there exists a 50% isoprobability of moving from the interior of one proton to that of the other proton. Therefore, the existence of the **proton-neutron exchange** is confirmed by model (2.1) and so is the attractive character of the related force.

More particularly, the most probable configuration is for the isoelectron do describe a particular oo-shaped orbit within both protons as illustrated in Figure 6 below. We are here referring to a type of orbit that turned out to be crucial for the new "strong valence bond" of hadronic chemistry that permitted the first exact representation of molecular binding energies (59).

Intriguingly, **the oo-shaped orbit of the isoelectron in the deuteron and related exchange forces provide the final interpretation of the stability of the deuteron,** as one can easily see.

The main point is that **there exists no actual, real physical foundations for the proton-neutron exchange to admit a potential.** In any case, the addition of an "exchange potential" would imply the loss of the exact and invariant representation of the binding, and total energies, since the latter are already represented in full by the Coulomb and contact forces.

Alternatively, we can say that the strongly attractive contact forces for singlet couplings at short distances represented by the isounit incorporates ALL contact interactions, thus eliminating the need for their individual identification. In turn, this feature is crucial for the truncation of the incredible plurality of currently used "nuclear potentials."

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Similarly, **noncentral forces** are eliminated by model (2.1) as particular case of the broader nonlocal forces extended over the entire volume of wave-overlappings. The important point is that, again, noncentral forces generally do not have a potential in classical mechanics and the idea that they could instead acquire a potential in nuclear mechanics can certainly be part of a religion, but not of science

A similar fate holds for the various other mysterious forces adopted in nuclear physics during the twentieth century (Section III.4). They all disappear from the treatment via hadronic mechanics because they have no clear physical origin.

An illustration is that of velocity-dependent forces. They are known to be particular cases of contact nonlocal forces because the latter are precisely approximated via power series in the velocities and other terms.

The occurrence illustrates again the remarkable power of the isounit of unifying a considerable variety of forces assumed to be of potential type in the 20-th century, with a consequential dramatic reduction of the number of physical or otherwise meaningful nuclear forces.

**2.8: Deuteron Binding Energy. **

As it is well known, the binding energy of the deuteron is given by

(2.14) E_{d} = - 2.26 MeV.

Hadronic mechanics permits the identification of the physical origin of such a numerical value, thus providing another experimental verification of the theory.

Recall from the main lines of hadronic mechanics (Parts I and II) that the binding energy is necessarily and solely characterized by forces derivable from a potential. In fact, the contact forces due to mutual wave-overlapping have no potential energy at all.

The binding energy of the deuteron is, therefore, exclusively due to the potential component of the deuteron binding force, Eq. (2.12). Moreover, the reader is encouraged to verify that for the conventional values of charges and magnetic moments, potential (2.12) has a numerical value close to 2.26 MeV. More accurate results are reached via the isorenormalization of the charge and magnetic moments, that are ignored here for simplicity.

**2.9: Deuteron Total Energy. **

Hadronic mechanics also permits the exact and invariant representation of the total energy of the deuteron, that, as such, becomes another verification of model (2.1).

Recall the following conversion of one atomic mass unit to MeV

(2.15) 1 amu = 941.49432 MeV.

In these units we have the known values

(2.16) M_{p} = 938.256 MeV/c^{2} = 1.00727663 amu,
M_{e} = 0.511 MeV/c^{2} = 5.48597?10-4 amu.

The mass of a nucleus with A nucleons and Z protons without the peripheral atomic electrons is characterized by the known expression

(2.17) M_{nucleus} = M_{amu} - Z x M_{e} + 15.73 x Z^{-3} x 10^{-6} MeV,

that yields the well-known mass of the deuteron

(2.18) M_{d} = 2.0135 amu = 1,875.563 MeV.

The iso-Schrodinger equation for model (2.1) can be easily reduced to that of the neutron, Eq. (V.3.7), under the assumption that the isoelectron spends 50% of the time within one proton and 50% within the other, thus reducing model (2.1) in first approximation to a two-body system of two identical particles p^ each with un-isorenormalized mass M_{p^} = 937.782 MeV, the main differences being given by different numerical values for the energy, meanlife and charge radius. We shall then write the **structure equation of the deuteron in a first two-body approximation**

(2.19a) d = (p^_{up}, p^_{down})_{hm},

(2.19b) [- (h^{2}/2xM_{p^}) x D_{r} D_{r} - V x e^{- r / R} / (1 - e^{- r / R}) ]] x |p^> = E x |p^>,

(2.19c) E_{d} = 2x E_{p^} - | E | = 1,875 MeV,

(2.19d) t_{d}^{-1} =
4 x p x l^{2} x | p^(0)|^{2} x a x E_{p^,Tot} / h = infinity,

(2.19e) R_{d} = 1.41 x 10^{-13 } cm,

It is easy to see that Eqs. (2.19) admit a consistent solution reducible to the algebraic expressions as for the case of Rutherford-Santilli neutron

(2.20a) k_{2} = 1, k_{1} = 2.5.

In this model, the deuteron binding energy is identically null,

(2.21) E = - V x (k_{2} - 1)^{2} / 4 x k_{2} = 0

because all potential forces have been "absorbed" by the nonlocal forces and k_{2} has now reached the limit value of 1 (while being close but bigger than 1 in the preceding models).

A more accurate description is obtained via the restricted three-body configuration of Figure 4 that, as such, also admits an exact solution. In this case, one can repeat the procedure used for the Rutherford-Santilli neutron consisting, in this case, of a nonunitary transform of the conventional restricted three-body Schroedinger equation for two protons and one electron as per Figure 4 with conventional Hamiltonian H = T + V_{Coul}, where V_{Coul} is expression (2.12). The nonunitary transforms then produces an additional strong Hulten potential that can, again, "absorb" the Coulomb potential resulting in a readily solvable structure equation of the deuteron as a three-body system. This more accurate approach is not outlined here because of the current limitations in the html format.

**2.10: Deuteron Electric Dipole Moment and Parity.**

The electric dipole moment of the deuteron is identically null. Its representation via hadronic mechanics then follows because isotopies cannot alter null values.

The positive parity of the deuteron is trivially represented by hadronic mechanics via the expression

(2.22) Isoparity = (-1)^{L^},

and the restriction of the unperturbed deuteron to its ground state for which L^ = L = 0.

By comparison, the reader should be aware of another misrepresentation existing in the nuclear literature consisting of the fact that, on the one hand, the parity of the deuteron is positive (L = 0), while on the other hand, in order to attempt a recombination of deuteron magnetic moments with quantum mechanics, the unperturbed deuteron is assumed as being a mixture of different levels, some of which have non-null values of L, thus implying the impossibility of a positive parity.

In summary, these sections have shown that nonrelativistic hadronic mechanics (in its isotopic branch) permits the exact and invariant representation of ALL the characteristics of the deuteron composed of two protons and one electrons, while jointly resolving all insufficiencies due to quantum mechanics.

See Ref. (114).

**4. THE NEW HADRONIC CONTROLLED FUSION.**

Wait for patents.

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

*FIGURE 10: A view of the $300.000 hadronic reactor built by R. M. Santilli to prove the achievement of an industrially viable controlled hadronic fusion to such an extent of disqualifying the usual political-pseudoscientists who throw judgments with zero knowledge of the topic, let alone before inspecting the machine, under the illusion that such judgments have any value for anybody.*

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

**5. INDUSTRIAL APPLICATIONS.**

[1]

(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) H. 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. Lohmus, 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 Fermat¹s Last Theorem Verifying Beal¹s
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).

(152) R. Aslaner and S. Keles, Algebras, Groups and Geometries {\bf 14}, 211 (1997).

(153) R. Aslander and S. Keles,. Algebras, Groups and Geometries {\bf 15}, 545 (1998).

(154) M. R. Molaei, Algebras, Groups and Geometries {\bf 115}, 563 (1998) (154).

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

(156) N. Kamiya and R. M. Santilli, Algebras, Groups and Geometries {\bf 13}, 283 (1996).

(157) S. Vacaru, Algebras, Groups and Geometries {\bf 14}, 211 (1997).

(158) Y. Ylamed, Hadronic J. {\bf 5}, 1734 (1982).

(159) R. Trostel, Hadronic J. {\bf 5}, 1893 (1982).

[11] **PHYSICS PAPERS:**

(160) J. P. Mills, jr, Hadronic J. {\bf 19}, 1 (1996).

(161) J. Dunning-Davies, Foundations of Physics Letters, {\bf 12}, 593 (1999).

(162) E. Trell, Hadronic Journal Supplement {\bf 12}, 217 (1998).

(163) E. Trell, Algebras Groups and Geometries {\bf 15}, 447-471 (1998).

(164) E. Trell, "Tessellation of
Diophantine Equation Block Universe," contributed paper to {\it Physical
Interpretations of Relativity Theory,} 6-9 September 2002, Imperial College, London.
British Society for the Philosophy of Science, in print, (2002).

(165) J. Fronteau, R. M. Santilli and A. Tellez-Arenas, Hadronic J. {\bf 3}, 130 (l979).

(166) A. O. E. Animalu, Hadronic J.{\bf 7}, 19664 (1982).

(167) A. O. E. Animalu, Hadronic J. {\bf 9}, 61 (1986).

(168) A. O. E. Animalu, Hadronic J. {\bf 10}, 321 (1988).

(169) A. O. E. Animalu, Hadronic J. {\bf 16}, 411 (1993).

(170) A. O. E. Animalu, Hadronic J. {\bf 17}, 349 (1994).

(171) S. Okubo, Hadronic J. {\bf 5}, 1667 (1982).

(172) D.F.Lopez, in {\it
Symmetry Methods in Physics}, A.N.Sissakian, G.S.Pogosyan and X.I.Vinitsky, Editors (
JINR, Dubna, Russia (1994).

(173) D. F. Lopez, {\it Hadronic J.} {\bf 16}, 429 (1993).

(174) A.Jannussis and D.Skaltsas,{\it Ann. Fond. L.de Broglie} {\bf
18},137 (1993).

(175) A. Jannussis, R. Mignani and R. M. Santilli,
{\it Ann.Fonnd. L.de Broglie} {\bf 18}, 371 (1993).

(176) A. O. Animalu and R. M. Santilli, contributed paper in {\it Hadronic
Mechanics and Nonpotential Interactions} M. Mijatovic, Editor,
Nova Science, New York, pp. 19-26 (l990).

(177) M. Gasperini, Hadronic J. {\bf 6}, 935 (1983).

(178) M. Gasperini, Hadronic J. {\bf 6}, 1462 (1983).

(179) R. Mignani, Hadronic J. {\bf 5}, 1120 (1982).

(180) R. Mignani, Lett. Nuovo Cimento {\bf 39}, 413 (1984).

(181) A. Jannussis, Hadronic J. Suppl. {\bf 1}, 576 (1985).

(182) A. Jannussis and R. Mignani, Physica A {\bf 152}, 469 (1988).

(183) A. Jannussis and I.Tsohantis, Hadronic J. {\bf 11}, 1 (1988).

(184) A. Jannussis, M. Miatovic and B. Veljanosky, Physics Essays {\bf 4}, (1991).

(185) A. Jannussis, D. Brodimas and R. Mignani, J. Phys. A: Math. Gen. {\bf 24}, L775 (1991).

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*

*
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