V. APPLICATION OF HADRONIC MECHANICS TO PARTICLE PHYSICS
Prepared by the IBR staff from Sect. 3.15 of Refs. [I-1] and [V-3c]

V.1: VALIDITY OF RELATIVISTIC QUANTUM MECHANICS FOR THE ATOMIC STRUCTURE AND ITS EXPECTED LACK OF EXACT VALIDITY FOR THE HYPERDENSE HADRONIC STRUCTURE According to rather numerous historical, conceptual, phenomenological and experimental evidence, relativistic quantum mechanics and its foundations, including the Minkowskian geometry, they Poincare' symmetry and the special relativity, are EXACTLY VALID for the atomic structure, but they CANNOT be exactly valid for the hadronic structure [V-1,V-3]. The clear understanding is that their APPROXIMATE validity is beyond scientific doubts.

On historical grounds it is appropriate to recall Enrico Fermi who, in p. 111 of his lectures notes in Nuclear Physics (Univ. of Chicago Press, 1950), when dealing with the regions of space inside pions and nuclei, stated ³... there are some doubts as to whether the usual concepts of geometry hold for such small region of space². Fermi¹s scientific caution has been confirmed by numerous evidence outlined below.

On historical grounds we should also recall Lorentz who, as indicated earlier, was the first to admit that his own symmetry is not valid in our atmosphere due to the local variation of the speed of electromagnetic waves. The review of numerous other authoritative historical doubts is omitted for brevity.

On conceptual-epistemological grounds, we have also recalled in Sect. 1.9 the shortcomings of the special relativity for other interior conditions, such as the violation of the relativistic law of addition of speeds within homogeneous and isotropic media such as water, with greater inconsistencies occurring within media that are inhomogeneous (e.g., because of the local variation of the density) and anisotropic (e.g., because spinning, thus creating a preferred direction in the media, the underlying space remaining fully homogeneous and isotropic).

If the Minkowski geometry, the Poincare' and the special relativity are already inapplicable (and not violated) within media of very low density such as our atmosphere, the belief that they may be "exactly" valid within the hyperdense media inside hadrons is not expected to resist the test of time.

The phenomenological evidence supporting the above view is considerable. In fact, ALL phenomenological calculations (see Refs. [V-4] and literature quoted therein) done on the geometry of the interior of hadrons without preconceived assumptions on quark or other models, have systematically indicated deviations from the Minkowski metric.

As an example, via the use of conventional gauge theories in the Higgs sector, Nielsen and Picek [V-4h] have shown that the metric inside pions and kaons has the non-Minkowskian structure

(5.1a) m* = Diag. [ (1 -3a), (1 - 3a) , (1 - 3a) , - (1 - a) ],

(5.1b) For pions a = -3.79x10^{-3}; for kaons a = +0.61x10^{-3},

where the quantity a was called the "Lorentz's asymmetry parameter". All remaining phenomenological studies of Refs. [V-4] indicate similar deviations and are omitted for brevity.

The above historical, conceptual and phenomenological evidence is then completed by a number of direct experimental verifications. The main argument of the initiator of the studies considered below, the late D. I. Bloch'intsev of the JINR in Dubna, Russia, is the following. The exact validity of the Minkowskian geometry, the Poincare' symmetry and the special relativity for a hadron in a particle accelerator is beyond scientific doubts (in fact, under these conditions the hadron can be considered as being point-like, thus admitting conventional topologies and geometries). The question asked by Bloch'intsev was how departures from these established theories in the ³interior² problem can manifest themselves in the ³exterior² of hadrons under the condition of conventional center-of-mass trajectories. The answer first provided by Bloch'intsev is: in departures from the Minkowskian behavior of the meanlives

(5.2) t = t_o/[1 - (v/c)^2)]^{1/2},

of unstable hadrons with speed v where t-o is the meanlife at rest.

The latter behavior was first measured by Aronson et al. at Fermilab in 1983 [V-5] and showed DEVIATIONS for kaons in the range 30-100 GeV. The same experiment was then repeated at Fermilab in 1987 by Grossman et al [V-6] in the DIFFERENT energy range of 100 to 350 GeV and showed apparent confirmation of the Minkowskian behavior.

However, Grossman and his colleagues used a rather questionable theoretical assumption in their data elaboration. In fact, they elaborated the data in a frame in which there is no PC violation, namely a frame in which by assumption there cannot be any deviation from the Minkowskian behavior, as known in the literature (see, e.g., Kim [V-4c]). As a result, measures [V-6] are highly unsettled at this writing, and should be repeated without theoretical assumptions in the data elaboration, as advocated by the experimentalist Arestov [V-7] of the IHEP in Protvino, Russia, and others, or they should be re-elaborated in a physical frame with PC violation.

All other direct experimental information on the structure of hadrons, that WITHOUT theoretical assumption on quark or other models in the data elaborations, confirm clear departures from the Minkowskian geometry, provided that physical evidence is identified and admitted.

We here mention only the case of the Bose-Einstein correction at very high [V-8] and very low [V-9] energies. These experiments essentially study the annihilation of the proton-antiproton pair into the so-called ³fireball², that rapidly decays into a variety of unstable particles whose final product is a set of correlated mesons. It is well known that no correlation is possible for a local-differential theory that can only admit point-like particles.

In addition to that, current models of the two-point correlation function (see, e.g., the review [V-10]) achieve consistency by throwing in free parameters of unknown physical origin, such as the so-called "caoticity". The first evidence that must be identified and admitted, is that these parameters are evidence of DEVIATIONS from relativistic quantum mechanics in the interior of the fireball [V-3b], much along the a-parameter by Nielsen and Picek.

The latter point is proved beyond reasonable doubts by the fact that a quantitative representation of the correlation requires OFF DIAGONAL ELEMENTS in the expectation values, that are known to be absent in conventional quantum mechanics. The occurrence appears to be clear cut and without possibilities to ³adjust things² [V-3a]:
1) All quantum mechanical observables are diagonal, A = Diag (A-kk), k = 1, 2, ....
2) The expectation values of observables provide the values in each state |k>.
3) There are no ³mixed terms², that is, terms mixing the state i with the state j,

(5.3) <A> = Sum_k <k|A_{kk}|k>.

As a result, the very STRUCTURE of relativistic quantum mechanics CANNOT provide an EXACT representation of the Bose-Einstein correlation (the communication to the IBR main office of any possibility to bypass the above problem would be appreciated, with the evident exclusion of the APPROXIMATE representations where things can be easily adjusted). As a result, the caoticity parameter is a measure of deviations from the axiom of expectation values of relativistic quantum mechanics.

In view of these and other reasons, the currently available experiments on the Bose-Einstein's correlation, when seeded in a real scientific environment, will likely be regarded by future historians as the first direct confirmation of the historical legacy on the nonlocality of the structure of hadrons and the strong interactions at large [V-3b].

By no means the above outline exhaust all reasons for the lack of exact applicability of relativistic hadronic mechanics in the hadronic structure. An additional set of reasons warranting a mention originate from the the "ether" (also called "substractum") that is needed not only for the propagation of electromagnetic waves, but also for the very existence of elementary particles as excitation precisely of the ether (see Sect. X on some of the open problems in this new field).

It is evident that the existence of the ether as a universal physical medium implies the existence of a privileged reference system that, in turn, requires an evident re-inspection of the special relativity. This study has been conducted by H. E. Wilhelm and others (see Ref. [V-30] and large literature quoted therein). We regret the inability to outline the latter studies to prevent a prohibitive length. Nevertheless, it appears that, thanks to their isotopic and therefore universal character of the methods, the results of this section can be re-formulated in Wilhelm's studies with an absolute frame without a change of the numerical results.

In conclusion, the historical, conceptual, epistemological, phenomenological and experimental evidence on the lack of exact validity of relativistic quantum mechanics for the hadronic structure are rather serious indeed and, as such, they should not be lightly dismissed in any serious scientific environment.

V.2: VALIDITY OF THE SU(3)-COLOR CLASSIFICATION OF HADRONS AND PROBLEMATIC ASPECTS OF QUARK MODELS OF HADRONIC STRUCTURE By keeping in mind the numerous predictions of new hadrons and their historical experimental verifications, the SU(3)-color ³classification² of hadron into family can be safely assumed as being of final character.

On the contrary, the complementary quark theory on the ³structure² of each individual element of a given SU(3) family is one of the most controversial and unsettled theories of the second half of this century in view of a rather large number of basic problems whose solution cannot be realistically expected without a structural revision of the theory [V-3].

In this nontechnical presentation we can evidently outline only some of the problematic aspects of quark theories on the hadronic structure, and refer the interested visitor to the specialized literature for additional shortcomings. In particular, we shall first focus the attention on the historical, conceptual and technical impossibility that one single theory really achieves both the ³classification² and the ³structure² of hadrons. We shall then outline the main shortcomings of the quark models of structure, and close with the indication of the impossibility for quarks to be elementary.

To begin with a historical perspective, we should recall that the nuclear, atomic and molecular phenomenologies required TWO different yet compatible models, one for the CLASSIFICATION into families and a different, yet compatible model for the STRUCTURE of each individual element of a given family.

For instance, it is inconceivable that, say, the Mendeleev model for the classification of atoms into families provides also the structure of each individual atom of a given family. Yet, this is precisely what it is done in contemporary hadron physics, i.e., the same model of classification of hadrons is used also for the structure, contrary to the above historical teaching.

Moreover, the transition from the Mendeleev classification of atoms into families to the structure of each individual element of a given family, required the construction of a NEW MECHANICS, quantum mechanics.

The view submitted in Refs. [I-1,V-1]] is that the same occurrence should be expected also for hadrons, namely, quantum mechanics can be safely assumed as being exact for the classification of hadrons (exterior problem), while a novel mechanics should be expected for the different problem of the hadronic structure (interior problem).

The above expectation is due to rather profound conceptual, analytic, algebraic, topological and other differences existing between the classification and the structure of hadrons. In their classification, hadrons can be effectively approximated as being point-like; the underlying topology and geometry can therefore be local-differential; interactions among points can only be of at-a-distance, potential-Hamiltonian; and the exact validity of quantum mechanics is then consequential.

The problem of the hadronic structure is fundamentally different than that of classification. Hadrons are not ideal spheres with points in them, and are instead some of the densest objects measured by mankind in laboratory until now, being composed by extended wavepackets in condition of total mutual penetration one inside all others. This results in composite states that are dramatically different than those for which quantum mechanics was built, the atomic structure.

It is thought in undergraduate courses of quantum mechanics that the minimal size of the wavepackets of a massive particle is 1 fm. Thus, the size of the wavepackets of all hadronic constituents is essentially the same as that of the hadron as a whole. These experimentally established physical conditions lead to the historical legacy by Bloch'intsev, Fermi, and others on the ultimate nonlocality of the strong interactions. In any case, the idea that a linear, local-differential and potential-Hamiltonian theory like quantum mechanics can be exactly valid within the hyperdense media in the interior of hadrons, has no scientific credibility. The type of generalized mechanics that is applicable in the interior of hadrons is evidently open to scientific debates, but not its need.

Some of the problematic aspects of contemporary quark models are the following [I-1]:

1) Inability by current theories to achieve a rigorous confinement of quarks. This shortcoming should be sufficient, alone, for structural revisions of the theory. Note that the lack of confinement is deeply linked to the studies herein reported, because the problem is due to the assumption of the same mechanics for both the exterior problem in vacuum and the interior structural problem, with consequential finite transition probabilities for free quarks originating from Heisenberg"s uncertainties.

As we shall see shortly, the assumption instead of hadronic mechanics for the interior problem (read: a generalized Hilbert space) and the conventional mechanics for the exterior problem (read: a conventional Hilbert space) do indeed imply a rigorous confinement. In fact, being interconnected by a suitable nonunitary transform, the two Hilbert space are incoherent.

2) Inability to formulate gravity for matter composed of quarks. Gravity can be solely formulated in our space-time, while quarks can be solely formulated in mathematical unitary spaces, without any possible interconnection (in view of the O'Rafearthaigh theorem, short of supersymmetric versions that are physically unsettled at this writing). At any rate, the original and primary physical meaning of SU(3) theories is that of classification of hadrons into family. It is then evident that no gravity can be defined for a "classification". This occurrence, alone, should also be grounds for structural revisions of current quark theories.

As treated in detail in the original proposal to build hadronic mechanics, this problem is due to the use mentioned earlier of one single theory for both the classification of hadrons into families and the structure of each individual member of a given family, that failed to succeed in the preceding nuclear, atomic and molecular problems.

3) Inability to introduce quark masses as physical masses unambiguously defined in our space-time. A necessary well known condition for a mass to be physical, that is, to exist in our space-time, is that of being the eigenvalue of the second-order Casimir invariant of the Poincare' symmetry. But quarks are not admitted as representations of the Poincare' symmetry in view of their fractional charges and other anomalous properties. Quark masses cannot therefore be introduced as eigenvalues of said Poincare's Casimir. As a result, on strict scientific grounds, quark "masses" have the sole meaning of being parameters in mathematical unitary spaces, rather than physical masses in our space-time. As such, quark masses cannot possibly originate gravity in any known consistent way.

The lack of admission of quarks by the special relativity as physical particles in our space-time is another shortcoming that, alone, is also sufficient to warrant structural revisions of current theories, because of the evident conflict in assuming mathematical structures in unitary spaces as physical constituents of hadrons in our space-time.

4) Inability for quarks to be the "elementary" constituents of hadrons. This occurrence was first pointed out by Santilli [V-1] back in 1981 and forgotten by everybody thereafter, although the view is now rather widely accepted due to the current impasse suffered by conventional quark theories.

As also pointed out in [V-1] and forgotten for over a decade, it should be noted that the assumption of quarks as composite appears to be the only line of research capable of reconciling the two different problems, the established SU(3)-color theory for the classification of hadrons into family, and a new theory for the structure of each individual hadron of a given unitary multiplet. In turn, this is the only known way permitting the definition of gravity, not for quarks in their unitary spaces, by for their physical constituents in real space-time.

5) Quark theories are unable to represent the historical legacy on the nonlocality of the structure of hadrons and of the strong interactions at large. As it is well known, current unitary theories, QCD and all that are strictly local theories. Such a mathematical structure can be safely assumed to be exactly valid for the problem of classification of hadrons into families, thus confirming the validity of the SU(3) classification. However, the same local structure cannot be expected to be of "final" character for the different problem of the structure of hadrons. At any rate, a linear, local and potential theory of structure of the hyperdense hadrons is not expected to resist the test of time.

In the final analysis, the belief according to QCD that one single quantity, a Lagrangian or a hamiltonian, can represent the hadronic structure and, consequently, most of the physical reality, is contrary to the very teaching by Lagrange outlined at the beginning of this Web Page (Sect. I.1).

V-3. SELECTION OF RELATIVISTIC HADRONIC MECHANICS FOR THE HADRONIC STRUCTURE In order to attempt a resolution of the impasse outlined in the preceding sections, in this Web Page we propose the use of relativistic hadronic mechanics [I-1] for novel, more appropriate studies in the structure of hadrons.

Needless to say, the problem of the hadronic structure is so complex that will likely require investigations well into the next century. Without any claim of completeness, in this section we shall outline the reason for the selection of relativistic hadronic mechanics and the impossibility to use other alternatives, such as the conventional deformations. We shall then indicate the primary objective of the selection, the identification of the hadronic constituents with ordinary massive particles although in a mutated state.

In subsequent sections we shall outline: the available experimental verifications of relativistic hadronic mechanics; its main implications for the hadronic structure; the achievement of a consistent theory of quarks as composite states of elementary ordinary constituents; the identification of the hadronic constituents with true, physical, elementary, massive particles freely produced in the spontaneous decays; the problem of compatibility of the new model of hadronic structure with the established SU(3) model of classification. Once the real physical constituents are permitted to be produced free, novel technological applications are predictable as it was the case for the preceding nuclear, atomic and molecular structures. These possibilities will be outlined in Sect. V-9 with more details in Sect. VI on nuclear physics.

The selection of relativistic hadronic mechanics for new studies on the hadronic structure appears to be compelling and without viable alternatives known at this writing (early 1997). To begin, ALL other alternative theories, such as the q-deformations, k-deformations, quantum groups and all that are afflicted by problematic aspects of physical character so serious (Sect. I-3) to prevent any serious application to the hadronic structure at this writing. By comparison, relativistic hadronic mechanics bypasses all these inconsistencies [I-1].

Moreover, even ignoring the above aspect, ALL alternative theories can be easily proved to be against experimental evidence. In fact, to exit from the c;lass of equivalence of quantum mechanics, q-deformations, k-deformations, quantum groups and all that imply DEVIATIONS FROM QUANTUM LAWS, such as deviations from Heisenberg¹s uncertainties, deviation from Pauli¹s principle, etc. and such deviations are transparently disproved by all available experimental evidence, e.g., for a hadron in a particle accelerator. By comparison, hadronic mechanics has been constructed in such a way to recover identically all conventional physical laws for the center-of-mass trajectories, yet admitting a generalized internal structure (see Sect.s I-8 and I-9 and Ref. [I-1]).

Hadronic mechanics was constructed in such a way to be applicable in the interior of hadrons for the primary purpose of identifying their elementary constituents with ordinary, physical, massive, particles generally produced in the spontaneous decays with the lowest mode (see Sect. V-4 below). Jointly, the identification must be compatible with the SU(3) model of hadronic classification.

It is at this point that the nonlinear, nonlocal and nonunitary structure of hadronic mechanics and its new mathematics emerge in their full light, by therefore justifying a posteriory the scientific journey reviewed in these Web Pages.

To begin, the contact interactions due to the deep mutual penetration of the wavepackets of the hadronic constituents are, by conception and realization, of nonpotential and, thus, nonhamiltonian type (i.e., they violate the integrability conditions for the existence of a Hamiltonian, the so-called conditions of variational selfadjointness [V-2]). As a result, the hadronic structure is expected to have NONUNITARY contributions as a necessary condition for the very admission of contact interactions. This is the reason why Santilli proposed ab initio the construction of hadronic mechanics as a nonunitary image of quantum mechanics (see Hadronic J. vol. I, p. 574, 1978 and Refs. [V-3]).

Once the nonunitary structure of the applicable mechanics is admitted, hadronic mechanics emerges as the ONLY consistent discipline known at this time. In fact, as reviewed in these Web Pages, hadronic mechanics is the only known mechanics that achieves axiomatic consistency under a nonunitary structure (the communication of different views to the IBR main office at <ibr@gte.net would be appreciated).

The uniqueness of hadronic mechanics can also be seen in these introductory lines from the fact that other approaches, such as q- and k-deformations, quantum groups, etc, imply an image of SU(3) that is no longer locally isomorphic to the original symmetry. In turn, this prevents ab initio the compatibility between the structure models of hadrons and the established SU(3) classification. By comparison, Santilli's isotopies guarantee by conception the isomorphism between the isoSU*(3) and the conventional SU(3) symmetry, thus possessing ab initio solid grounds for the indicated compatibility between the models of structure and classification.

Recall from the introductory comments that nonunitary images of Heisenberg's equations referred to a field of ordinary numbers are physically inconsistent. Axiomatic consistency therefore demands the systematic implementation of the nonunitary map to the totality of the mathematical structure of quantum mechanics, beginning from the number theory. This renders mandatory the use of the new mathematics outlined in the preceding Web Page 18. Again, the communication to the IBR main office at <ibr@gte.net of other mathematics applicable to the hadronic structure with equal effectiveness and consistency, would be appreciated.

When passing to the problem of the identification of the hadronic constituents with physical, ordinary, massive particles, the need for hadronic mechanics becomes compelling. It is well known that the reduction of hadrons to composite systems of massive particles produced in their spontaneous decays is impossible for quantum mechanics, that is, under the assumption of a linear, local and unitary theory. The view repeatedly expressed by Santilli through the years [I-1,V-1,V-3] is that the lack of resolution until now of the problem of the true, elementary constituents of hadrons is due precisely to the assumption of quantum mechanics as the applicable discipline.

On the contrary, hadronic mechanics does indeed permit a mathematically and physically consistent identification of the hadronic constituents with physical particles, as outlined below in this section. The main technical reason is that nonunitary interactions imply novel renormalizations of physical characteristics of particles substantially outside any possibility of the conventional renormalizations due to Lagrangians or Hamiltonians. Bound states at short distances (only) that are inconceivable for quantum mechanics become readily consistent for the covering hadronic mechanics. In short, ordinary, elementary, massive particles cannot be interpreted as hadronic constituents under the validity of quantum mechanics, but they can indeed be constituents for hadronic mechanics.

V-4. EXPERIMENTAL VERIFICATIONS OF RELATIVISTIC HADRONIC MECHANICS IN PARTICLE PHYSICS We now outline the existing experimental verifications of relativistic hadronic mechanics independent from its application to the hadronic structure.

A physical reality admitted since Lorentz's time and today established (see [V-3a]) is that MATTER ALTERS THE GEOMETRY OF EMPTY SPACE. The fundamental issue of the problem herein considered is therefore the identification of a covering geometry that is effectively and consistently applicable in the interior of hadrons.

The only answer known at this time for a variety of reasons is the geometry underlying relativistic hadronic mechanics: Santilli's isominkowskian geometry (first introduced in Ref. [V-11]), as outlined in Sect. 1 (see [V-3a] for a comprehensive presentation). We are here referring to a geometry characterized by the joint:

A) lifting of the Minkowski metric m into the form m* = Txm, where T is a 4x4, real-valued and positive-definite matrix with an otherwise unrestricted functional dependence and m = Diag. (1, 1, 1, -1) is the conventional Minkowski metric, as well as

B) the lifting of the original unit of the Minkowski space I = Diag. (1, 1, 1, 1) into the INVERSE of the lifting of the metric, E = 1/T,

and consequential reconstruction of number, differential calculus, topology, etc., in such a way to admit E, rather than I, as the left and right unit.

To begin the indication of the reasons for the above preference, the isominkowskian geometry is "directly universal", that is, it admits as particular cases in the isometric m* = T(t, x, dx/dt, )xm all infinitely possible generalizations of the Minkowski metric m (universality), directly in the frame of the experimenter (direct universality). The isominkowskian geometry therefore applies even when not desired. As an example, it is easy to see that the generalized metric (27) by Nielsen and Picek is a simple particular case of Santilli's isometric m*.

Second, the isominkowskian geometry is the only one known that is axiom-preserving (as the visitor will recall, this is due precisely to the dual liftings m into m* = Txm and I into E = 1/T that render mandatory the use of the generalized mathematics of Web Page 18).

The isominkowskian geometry permits the rather remarkable preservation of the Poincare' symmetry and the special relativity, and only express them in their most general possible form, a framework generally referred to as Santilli's isospecial relativity (see the forthcoming monograph [V-12]).

Therefore, the space and time symmetries of the isometric m* = Txm, when computed with respect to the isounit E = 1/T, results to be isomorphic to the conventional symmetries of m. Because of this occurrence, Santilli's isotopies are also known as being methods for the reconstruction of exact space-time and internal symmetries when believed to be conventionally broken.

As an illustration, Nielsen and Picek [V-4h] assumed that generalized metric (27) implies the breaking of the Lorentz symmetry, as indicated earlier. Santilli [V-11] showed however that the Lorentz symmetry does indeed remain exact for metric (27), evidently when computed with respect to the new unit E = 1/T. The same reconstruction of the exact character of the symmetry has been shown for the SU(2)-isospin symmetry under weak and electromagnetic interactions, parity under weak interactions, the Poincare' symmetry under nonlocal interactions (see below), and other cases [V-3].

Other available geometries, such as the so-called "deformed geometries", are no longer isomorphic to the original geometry. As such, they create the sizable problems of identifying coverings of Einstein's axioms, proving their axiomatic consistency and, after all that, establishing them experimentally. At any rate, the latter geometry are afflicted by the rather serious physical shortcomings outlined in Sect. I.3/

We assume the reader is familiar with the technical distinction between "isogeometries" and "deformed geometries". The former are "isotopic" in the sense of being "axiom-preserving", are "universal" in the sense of admitting all infinitely possible generalizations of the original metric m* = Txm, and are computed on generalized numbers with unit E = 1/T. The latter are not isotopic, thus being "axiom-violating", admit a limited class of deformed metrics and, by central assumption, are defined over a field of conventional numbers, that is, with the conventional unit I.

Irrespective of its universality and effectiveness, the validity of Santilli's isominkowskian geometry within hadronic media has been established by a variety of rather convincing fits of experimental evidence. First, the validity has been proved by Cardone et al [V-13] via a remarkable fit with the time behavior law of the isospecial relativity, here formulated from line element (25) [11]

(5.4) t* = t/[1 - [(v_k/n_k)/(c/n_4)^2)]^{1/2}

for both experimental data [V-5,V-6]. In fact, the new geometry has permitted a fit, not only of the Minkowskian anomalies alone as measured by Aronson et al [V-5], but also of the joint anomalous behavior between 30-100 GeV and conventional behavior between 100 and 350 GeV, resulting in the numerical values [V-5,V-6]

(5.5a) 1/n_k^2 = 0.9023 +/- 0.0004,

(5.5b) 1/n_4^2 = 1.003 +/- 0.0021.

Independently from this direct experimental verification, the isominkowskian geometry has been additionally verified with the Bose-Einstein correlation via the two-mesons isocorrelation function [14]

(5.6) C = 1 + (K^2/3)x{Sum_{µ = 1,2,3,4} m*_{µµ} x exp[-qx(n+µ)^2]},

where q is the momentum transfer, m*-µµ are the components of the isometric, and K-squared = Sum k=1,2,3 (1/n-k)-square. It should be recalled that the above expression was derived via the application of relativistic hadronic mechanics without any approximation other than the assumption of the longitudinal momentum transfer being null, as experimentally established. In particular, relation (30) has no unknown parameters thrown in to "adjust things". In fact, the space component n-k represents the semiaxes of the fireball, while the forth component n-4 is a measure of the density of the fireball, all expressed in a scale invariant form.

Expression (5.6) was fit to the UA1 experimental data on q by Cardone and Mignani [V-15]. The main result of these studies are the following:

1) The fit of available data from CERN is indeed remarkable;

2) the fit is done from first axiomatic principles without any ad hoc parameters;

3) the fit provides a direct representation of the actual, very elongated ellipsoidical shape of the proton-antiproton fireball as well as of its density via the values [V-15]

(5.7a) 1/n_1 = 0.267 +/- 0.064, 1/n_2 = 0.437 +/- 0.035, 1/n_3 = 1.661 +/- 0.013,

(5.7b) 1/n_4 = 1.653 +/- 0.015

4) the isominkowsian geometry predicts the upper value 1.67 for the two-point correlation function that is experimentally verified [V-14]; and, last but not least,

5) the isominkowskian geometry reconstructs the exact Poincare' symmetry in the interior of the fireball under nonlinear, nonlocal and nonunitary internal effects.

A number of additional, equally remarkable, direct and indirect experimental verifications also exist for the validity of Santilli's isominkowskian geometry, isopoincare' symmetry and isospecial relativity in the interior of hadrons that cannot be reviewed here for brevity [V-12].

V-5. MAIN IMPLICATIONS OF RELATIVISTIC HADRONIC MECHANICS FOR THE HADRONIC STRUCTURE. Researchers interested in the studies herein suggested should be aware that the ISOMINKOWSKIAN GEOMETRY PREDICTS MAXIMAL CAUSAL SPEEDS IN THE INTERIOR OF HADRONS GENERALLY GREATER THAN THE SPEED OF LIGHT IN VACUUM, as first predicted by Santilli IN 1982 [V-4f] and first confirmed also in 1982 by De Sabbata and Gasperini [V-4g] via phenomenological calculations based on gauge theories.

The main idea of Ref. [V-4f] is that the speed of light in vacuum c is certainly a barrier UNDER ACTION-At-A DISTANCE INTERACTIONS, as it is the case for a hadron in a particle accelerator. The main hypothesis submitted in Ref. [V-4f] is that STRONG INTERACTIONS CAN ACCELERATE PARTICLES TO ARBITRARY SPEEDS BEYOND c under the sole condition that they have a contact nonpotential component. In fact, the acceleration under the latter component is basically different than that under potential forces.

These initial studies were confirmed by the subsequent geometrical research [V-3]. In fact, as recalled in Sect. I, the isopoincare' symmetry P*(3.1) is the invariance for arbitrary causal speeds C = c/n4, without any restriction on n4 other than that of being nowhere null, thus admitting in a natural way speeds bigger than c.

The latter geometric studies are in turn confirmed by all available experimental data. As an example, phenomenological data (5.1) by Nielsen and Picek imply a causal speed in the interior of kaons bigger than c

(5.8) C_{kaons} = c/n_4 = c/(1 - a) = 1.003xc.

Quite remarkably, the use of independent fit (5.5) also for kaons yields exactly the same numerical result

(5.9) C_{kaons} = c/n_4 = 1.003xc.

The same result is then expected for all remaining (heavier) hadrons due to their bigger density. As an illustration, the use of fit (5.7) for the different case of the proton-antiproton fireball yields the maximal causal speed [V-12]

(5.10) C{p-anti p fireball} = 1.653xc.

The same results are confirmed by all other direct experimental data available at this writing [V-12].

It should be stressed that, by no means, hadronic constituents traveling faster than the speed of light in vacuum are necessarily "tachyons". In fact, they are ordinary particles with ordinary, real, positive mass. The change is in the maximal causal speed. In fact, the only meaning of tachyons in isominkowskian spaces is that of particles traveling faster than the maximal causal speed C = c/n4, and not faster than c (these particles are called "isotachyons" [V-12]).

Another aspect researchers should be aware of is that, by no means, the constant speed in vacuum c is replaced by another "universal constant" C inside hadrons. All hadrons have approximately the same charge radius (of about 1 fm), but they have all different masses. As a result, hadrons have all different densities that increase with mass. The term n4-squared in the fourth component of the isominkowskian metric m* geometrizes precisely that density (the density of the vacuum being normalized to 1). This implies that the maximal causal speed in the interior of hadrons cannot possibly be a new constant and actually varies from hadron to hadron because it varies with its density.

Another foundational aspect researchers should keep in mind is the misleading conception, due to protracted use for decades, that photons and gluons inside hadrons propagate in vacuum with speed c. In the physical reality, photons and gluons propagate within the hyperdense medium composed by the wavepackets of all constituents. As a result, they propagate within a physical medium and CANNOT propagate with the speed c.

The latter occurrence has a number of implications, the first being the isoshift of the frequencies f* predicted by Santilli's isospecial relativity, e.g., for the case of null aberration [V-11,V-12]

(5.11) f* = f_o x {1 - [(v/n_s)/(c/n_4)]^2}^{1/2

where v is the speed of the observer with respect to the source, n_s is the space average of the n-k, f-o is the frequency for v = 0, and f is the conventional Doppler form for ns = n4 = 1. When f* is bigger than f we have an "isoblue shift", and when f* is smaller than f we have an "isoredshift".

The above occurrence has the rather intriguing implication that the exterior measure of a given frequency of a photon emitted by a hadron, by no means, implies that the same photon is emitted in the interior with the same frequency. Remarkably, this important expectation is independently confirmed by the nonpotential-nonunitary scattering theory for the interior of hadrons (see Sect. VII) and, as such, it should be taken seriously.

The isospecial relativity predicts that [V-3b,V-12]:
1) The photon is isoredshifted, that is, it gives energy to the hadronic medium, when the "isotopic factor" n4/ns is bigger than 1;
2) the photon has no isotopic shift (but may have a conventional Doppler's shift) for n4/ns = 1; and
3) the photon is isoblueshifted, namely, it receives energy from the hadronic medium, when n_4/n_s is smaller than one.

Jointly with a maximal causal speed systematically greater than c, all experimental data considered above imply an isoblueshift for the interior of hadrons, namely, photons are emitted at a frequency lower than than predicted by conventional theories, absorbs energy from the hadronic medium, and exit the hadron at a higher frequency.

In essence, we have in first approximation f* = f-o[1 - (v/c)x(n4/ns)/2 +..]. When the term n4/ns is smaller than one, the value of f* becomes closer to 1, thus experiencing an increase of the frequency (isoblushift).In fact, for data (5.8) we have an isoblue shift with isotopic factor

(5.12) n_4/n_s = 0.99;

for data (5.9) we have the similar isoblue shift with factor

(5.13) n_4/n_s = 0.95;

and for data (5.10) referred to a much higher density we have an isoblue shift characterized by the factor

(5.14) n_4/n_s = 0.273.

The above isotopic shift has predictable applications in astrophysics, e.g., for the origin of cosmological redshift, and is therefore considered in Sect. VII. An important implication for the structure of hadrons is that the rest energies currently assumed for quarks may eventually need revisions due precisely to the above isorenormalization. In fact, the principle of equivalence of the isospecial relativity is [V-3,V-12]

(5.15) E = m x C^2 = m x (c/n_4)^2.

From the preceding values of n4 one can therefore see that the rest energies of quarks are expected to be higher than currently assumed values when isorenormalized by contact nonunitary effects due to their immersion within a hyperdense medium. Note the impossibility to avoid the isorenormalization of quark rest energies under the sole use of the contact effects due to total mutual penetration of the wavepackets. In fact, these contact effect are nonhamiltonian, thus, nonunitary. The isorenormalization is then unavoidable.

Still another foundational aspect that needs addressing in these introductory lines to prevent possible misrepresentations, is the INAPPLICABILITY WITHIN HYPERDENSE HADRONS OF THE CONVENTIONAL NOTION OF PARTICLE IN FAVOR OF SANTILLI'S NOTION OF ISOPARTICLE.

As it is well known, a conventional particle is a unitary irreducible representation of the conventional Poincare' symmetry P(3.1). As such, it crucially depends on said symmetry for its applicability. The historical, conceptual, phenomenological and experimental evidence considered in this section indicating deviations from the Minkowskian geometry inside hadrons imply the inapplicability of the conventional symmetry P(3.1) with consequential inapplicability of the conventional notion of particle inside hadrons.

The impossibility to avoid this additional occurrence should also be kept in mind under the sole presence of internal, contact, nonunitary effects, without any known possibility of maintaining the conventional notion of particle known at this writing./

It should be stressed that we are not referring to a mathematical occurrence, but to an alteration of the INTRINSIC characteristics of particles called "mutation" [V-3] (in order to distinguish them from the "deformation" of the current literature) that are unavoidable under nonunitary transforms. In different terms, the assumption for the studies herein considered that a hadronic constituent has conventional charge, conventional parity, conventional spin, etc., has no meaning of any type, whether direct, indirect or implied. In reality, the first fundamental problem suggested for study below is precisely the identification of the mutations of these conventional characteristics of particles when immersed in the hyperdense media inside hadrons.

The reader with some technical knowledge of relativistic hadronic mechanics knows that these deviations are solely applicable for the individual constituents, because all characteristics and physical laws of the center-of-mass of hadrons are conventional.

Stated in different words, before the problem on the "identification of the hadronic constituents" can be addressed on real scientific grounds, one must first identify the notion of particle constituent that is applicable within the hyperdense hadronic medium on grounds of available evidence

PROPOSED RESEARCH V-5-1: STUDY THE NOTION OF HADRONIC CONSTITUENT AS AN ISOPARTICLE, THAT IS, AS ISOUNITARY IRREDUCIBLE REPRESENTATION OF THE POINCARE'-SANTILLI ISOSYMMETRY P*(3.1) OF CLASS I (POSITIVE-DEFINITE ISOUNITS), IN BOTH DIAGONAL AND NONDIAGONAL REALIZATIONS [V-16]. Recall from the mathematical Web Page 18 that, when computed in isominkowski space over the isofield of isoreals with the same generalized unit E = 1/T, the representation here suggested for study are expected to COINCIDE with the conventional ones. In fact, the notion of isoparticle coincides at the abstract level with that of particle by conception [V-3]. The research here suggested consists, not only in the formulation in isospace over isofields, but also, and most importantly, in the study of its projection on conventional space-time over a conventional field. In fact, mutations of conventional characteristics are expected only in the latter case. The best illustration is that of the maximal causal speed in isospace that coincides with the value c in vacuum. In fact, in isospace we have the value C = c/n4, but the unit is lifted by the inverse amount E = n4, thus yielding the value c (because the line element has the structure [Length]x[Unit] and not [Length]/[Unit]). The mutation emerges when the value in isospace C = c/n4 is projected in ordinary space, i.e., it is computed with respect to the conventional unit. Essentially the same mutations are expected for all characteristics of the hadronic constituents, including mass, charge, spin, angular momentum, space and charge parity, magnetic moment, etc. In turn, the prior knowledge of general rules on the latter mutations is evidently fundamental for any structure model of hadrons according to hadronic mechanics.

PROPOSED RESEARCH V-5-2: RE-ELABORATE THE MEASURES BY GROSSMAN ET AL [V-6] IN A FRAME IN THAT, BY ASSUMPTION, THERE IS A PC-VIOLATION, AS NECESSARY FOR KAONS; REPEAT THEIR FIT VIA SANTILLI'S ISOMINKOWSKIAN GEOMETRY; AND CONFIRMS OR DENY MAXIMAL CAUSAL SPEEDS OF THE HADRONIC CONSTITUENTS GREATER THAN THE SPEED OF LIGHT IN VACUUM. As indicated earlier, the fit of Ref. [V-13] was done by assuming measures [V-6] in their prima facie value,i.e., of being correct. The latter measure, however, do not have full credibility because they are elaborated in such a way that no anomaly is possible by assumption. In addition to the conduction of new experiments as suggested by Arestov [V-7], the research here suggested is simply that of RE-ELABORATING EXPERIMENTAL DATA ALREADY AVAILABLE AT FERMILAB in a frame with PC violation. The study should establish whether the claim of no anomaly by Grossman et al [V-6] between 100 and 350 GeV is valid or not. Note that the validity of the isominkowskian geometry would persist even in case of results favorable to Ref. [V-6] because fits [V-13] were precautionarily done precisely under that assumption.

PROPOSED RESEARCH V-5-3: FIT THE EXPERIMENTAL DATA [V-9] OF THE BOSE-EINSTEIN CORRELATION AT VERY LOW ENERGIES VIA SANTILLI¹S ISOMINKOWSKIAN GEOMETRY AND CONFIRM OR DENY MAXIMAL CAUSAL SPEEDS FOR THE HADRONIC CONSTITUENTS GREATER THAN THE SPEED OF LIGHT IN VACUUM. As recalled earlier in this section, relativistic hadronic mechanics predicts the unique two-points isocorrelation function (30) under nonlinear, nonlocal and nonunitary internal effects in the proton-antiproton fireball irrespective of the energy of the original particle-antiparticle. The sole available fit of Eq. (30) is that for the UA1 data at very high energy [V-8] done in Ref. [V-15]. It is then important to conduct a fit also for the experimental data [V-9] at low energy. Besides an additional possible verification of the isominkowskian geometry, the fit is important to confirm or deny that maximal causal speeds inside hadrons are bigger than c, as predicted by the fit at high energy. In turn, the latter information has paramount important for applications as indicated by the additional problems below.
TECHNICAL NOTE: The experimental data of Ref. [V-9] have a scale different than that of Ref. [V-8], thus requiring a different, multiplicative normalization factor in in the two-point isofunction (30).

TECHNICAL ASSISTANCE. Contact the IBR main office for referral to experts.

V-6: STUDIES ON THE ISOQUARK THEORY The line of inquiries suggested in Refs. [I-1,V-1, V-3] is essentially the following:
a) Assume the SU(3)-color classification of hadrons as of final character;
b) Submit the quark theory of structure (only) to an isotopic lifting into composite states obeying hadronic mechanics; and
c) Identify the ultimate massive constituents of hadrons under the conditions that: they can be produced free in the spontaneous decays; they achieve compatibility with composite quarks; and they resolve the problematic aspects of conventional quark theories as outlined in the preceding section.

In this section we outline the conceptual foundations of step b). A knowledge of the Lie-Santilli isotheory as outlined in the preceding Web Page 18 is assumed to avoid un-necessary repetitions.

As now familiar from the preceding outlines, the isotopic SU(3) symmetry, here denoted SU*(3), is the image of the conventional symmetry under nonunitary transforms UxUÝ ‚ I. For consistency, such transforms must be applied to the totality of the conventional formulation. As a result, SU*(3) is defined on isohilbert spaces H* over isofield F* with common isounit E = UxUÝ = 1/T and isoproduct A*B = AxTxB, where E and T have the same dimension of the considered representation. The elements of SU*(3) are therefore isounitary transforms on H* over F*

(5.16) U*xTxU*Ý = U*ÝxTxU* = E = 1/T, U = U*x(T^{1/2}).

As now familiar, a main feature of Santilli's isotopies is that of being "axiom preserving". A main property of the isoquark theories is therefore the preservation of the conventional SU(3) structure constants. A main implication is that, under the selection of the appropriate isorepresentation (those characterized by the Klimyk's Rule for diagonal isotopic elements), the quantum numbers characterized by SU(3) and SU*(3) coincides.

As a results, isotopic SU(3) theories are indistinguishable from the conventional SU(3) theories on all possible experimental grounds related to the classification (that is, the prediction of new particles). The selection which of the two theories is the appropriate one is therefore deferred to which theory represents more closely physical reality without unjustified aprioristic assumptions.

Visitors with a minimal technical knowledge of hadronic mechanics should have expected the above result. Hadronic mechanics preserves all conventional quantum mechanical laws for the center-of-mass behavior of a composite system, such as Heisenberg's uncertainties, Pauli's exclusion principle, etc. The preservation of the experimental data on the SU(3) classification is then consequential. The differences between quantum and hadronic mechanics can only be seen in interior conditions, such as in different characterizations of the notion of constituents and their interactions when at sufficiently small mutual distance to activate nonlinear, nonlocal and nonunitary effects.

The primary difference between SU(3) and SU*(3) theories is in the particles they characterize, the ordinary quarks for the former and the isoquarks for the latter, namely, the regular, isounitary representations of SU*(3).

Quarks have linear, local-differential and potential-unitary interactions. Isoquarks have instead been proposed to verify the historical legacy on the nonlocality of the strong interactions due to deep wave-overlappings (irrespective of whether the charges are point-like or not, see Sect. IX on the "nonlocal interactions" of the electrons - with notorious "point-like charge" - of the Cooper pair in superconductivity). In fact, isoquarks have interactions that are linear and nonlinear (in the wavefunctions), local-differential and nonlocal-integral (e.g., integral over the volume of wave overlapping) and potential as well as nonpotential.

The conventional interactions are represented with the conventional Hamiltonian, while the nonlinear, nonlocal and nonpotential interactions are represented with the isounit E that, being the fundamental invariant of the SU*(3) symmetry, has an unrestricted functional dependence, E = E(t, r, psi, dr/dt, dpsi/dr, etc.).

Action-at-a-distance interactions are long range and persist in the outside of hadrons. On the contrary, the nonlinear, nonlocal and nonpotential effects are internal and have no visible effect to the outside except for the isorenormalization of the characteristics of the constituents. This occurrence is expressed by the fact that the isoexpectation value of the quantity E representing these internal effect recovers the conventional unit I of SU(3),

(5.17) (E) = ( |xTxExTx| )/( |xTx| ) = I.

The explicit form of the matrix representation q* of isoquarks can also be constructed via nonunitary transforms of conventional representations, q* = UxqxUÝ. By recalling that E is positive-definite and can be therefore diagonalized, isoquarks possess three additional functional degree of freedom with respect to quarks, that are given by the minimal number of independent positive-definite diagonal elements of E, e.g., A(t, r, psi, ...), B(t, r, psi, ...), C(t, r, psi, ...).

The elements of the matrix representation of quarks are ordinary constant numbers, as well known. On the contrary, the elements of the matrix representations of isoquarks are nonlinear, integro-differential functions A, B, C.

Most importantly, being irreducible unitary representation, quarks are elementary by conception, as also well known. On the contrary, Santilli's notion of isoquark [V-3,V-12] consists a composite structure also by conception, even though the representation remains three-dimensional. This is due to the fact that the fundamental unit I = Diag. (1, 1, 1) of SU(3) is irreducible. On the contrary the isounit E of SU*(3) can be reducible, i.e. it can be the tensorial product of various isounits [V-12]

(5.18) E = E_1 x E_2 x . . . x E_n

By recalling that isoparticles in our space-time are characterized precisely by a generalized unit, the above feature is evidently at the foundation of the capability by the isoquark theory to resolve the shortcomings of the conventional theory [V-12].

The main contributions on the isoquark theory to date are the following. In 1973 Y. Nambu [V-17] constructed a classical theory of triplets characterized by two Hamiltonians H1 and H2. The operator counterpart of Nambu's mechanics for triplets was first identified by A. J. Kalnay [V-18] in 1983 and resulted to possess precisely the general Lie-admissible structure of hadronic mechanics (Sect. 1). In the same year, Kalnay and Santilli [V-19] proved that such an operator mechanics has the structure of the isotopic branch of hadronic mechanics with the iso-Heisenberg law

(5.19a) idA/dt = A*H - H*A = AxTxH - HxTxA,

(5.19b) H = H_1 + H_2, T = 1/H_1 + 1/H_2.

In 1984 R. Mignani [V-20] constructed the isotopies SU*(3) of the SU(3) symmetries and proved their isomorphism. In 1995 Santilli [V-21] introduced the isoquark theory and proved the following:
a) Quark and isoquark theories have the same total quantum numbers and are therefore indistinguishable experimentally in regard to the classification;
b) Isoquarks are strictly confined, that is, they admit an identically null probability of tunnel effects even in the absence of a potential barrier (asymptotic freedom at all energies) because of the structural incoherence between the internal isohilbert space and the external conventional Hilbert space;
c) Isoquark theories have convergent perturbative series. This is another general characteristic of the isotopies whereby a given divergent canonical series A(k) = A(0) + [A, H]xk/1! + . . ., where k is a parameter bigger than one, the same series can always be turned into a convergent form via the isotopies

(5.20) A(k) = A(0) + [A, H]*xk/1! + . . . = A(0) + (AxTxH - HxTxA)xk/1! + ...

under the condition that the magnitude |T| of the isotopic element T is sufficiently smaller than k, e.g., |T| ‰ 1/k-squared.

The Nambu-Kalnay-Santilli mechanics does indeed verify all the above conditions. In fact, the isotopic lifting of SU(3) with isounit E = 1/T, where T is given by Eq. (41b), preserves conventional total quantum numbers; the isohilbert space with isoinner product (psi*|x(1/H1+1/H2)x|psi*) is incoherent with the external Hilbert space and product (psi|x|psi), thus yielding identically null probability of tunnel effects for free isoquarks (but NOT for free quarks); and the magnitude |1/H1 + 1/H2| is smaller than one, thus admitting convergent perturbative expansions.

The main ideas of this subsection are studied in details in Santilli's forthcoming monograph [V-12]. Those are all contributions available on the isoquark theory at this writing.

In summary, the isoquark theory has the following main characteristics:
1) it is indistinguishable experimentally from the conventional theory in regard to the classification of hadrons;
2) preserves conventional physical laws in the center-of-mass trajectory of hadrons;
3) permits a quantitative representation of the numerous evidence on the nonlinearity, nonlocality and nonunitary character of the hadronic structure;
4) permits the isoquarks to be composite, yet preserving the three-dimensional character of their regular representations;
5) possesses an identically null probability of tunnel effects for free isoquarks even in the absence of a potential barrier;
6) admits convergent perturbative series; and
7) offers realistic possibilities of resolving the remaining shortcomings outlined in the preceding section.

Needless to say, the isoquark theory is at its very beginning and so much remains to be done, a feature that is expected to be a reason for interest by researchers in the field.

PROPOSED RESEARCH V-6-1: Construct the step-by-step isotopies of quark theories (in first quantization); prove the preservation of conventional quantum numbers; study the consistency of the isoquark theory with available experimental data for the classification; prove the achievement of an exact confinement of isoquarks with an identically null probability of tunnel effects for free isoquarks even in the absence of a potential barrier; establish the composite character of the isoquarks.

TECHNICAL ASSISTANCE: Contact the ibr staff at ibr@gte.net

V-7. IDENTIFICATION OF HADRONIC CONSTITUENTS WITH PHYSICAL PARTICLES

V-7-A.THE CONSTITUENTS OF THE NEUTRAL PION. All the mathematical and physical knowledge outlined until now is used in this section for the main objective for which it was developed: the identification of the constituents of hadrons with ordinary massive particles produced free in the spontaneous decays, generally those with the lowest mode as tunnel effect of the constituents.

The first application and verification of hadronic mechanics was done in Sect. 5 of the very proposal for its construction [V-1a] via the identification of the constituents of the lightest known hadron, the neutral pion pi-o, according to the following main lines.

The pi-o meson admits the spontaneous decay with the lowest mode into an electron e- and a positron e+. It is well known that the ONLY bound state of these two particles admitted by quantum mechanics is the Positronium = (e-, e+)QM that holds a very large mutual distances as compared to the size of the ¼-o. A quantum mechanical bound state of e- and e+ for the representation of the ¼-o is therefore impossible for numerous reasons [V-1a], such as: the impossibility to reach the charge radius of the pi-o (about 1 fm); the impossibility to represent the rest energy of the pi-o of about 134 MeV (because it would require a "positive binding energy" that is contrary to all tenets of quantum mechanics); the model would not represent the mean life of the pi-o of about 10-to-16 sec; and other shortcomings identified in [V-1a].

In Sect. 5 of Ref. [V-1a] Santilli showed that the use instead of the hadronic mechanics proposed in the preceding sections does indeed resolve all the above shortcomings and permits the representation of ALL the characteristics of the pi-o meson as a novel bound state of one electron and one positrons at short distances, pi-o = (e*-, e*+)HM where * represents mutation.

The first assumption for the achievement of such a representation is that, when in condition of deep mutual penetration of their wavepackets, electrons and positrons are no longer the same as in the positronium, and are instead "mutated" [loc. cit.] into a form called "eleton" (here denoted e*-) and "antieleton" (here denoted e*+). Santilli's structure model of the neutral Pi-0 meson can therefore be written Pi-0 = (e*-, e*+)HM, where a singlet coupling is assumed hereon.

The original proposal [V-1a] also contained the first identification of the isorenormalization of the intrinsic characteristics of the electrons and positrons e -> e*, beginning with the most important isorenormalization of their rest energy that avoids the use of positive binding energy. The model also identified the local approximation of the structure consisting of a particular form of the Hulten potential. This resulted into one single equation of structure for the ¼-o that represents the ¼-o rest energy, charge radius, meanlife, charge, spin, magnetic moment, and all other characteristics.

It should be noted that these results are the same as those for the hydrogen atom where one single equation, the Schroedinger's equation for the Coulomb interactions, represents the totality of the characteristics of the atom considered. It should equally be noted that the same results, representation of the totality of the physical characteristics via one single equation of structure, have never been achieved by quark theories.

The following difference in emphasis should finally be noted. The objective of quark theories is that of linking the ¼-o with other mesons, an objective that is indeed correct for the CLASSIFICATION of mesons into family defined in the mathematical unitary space, essentially as done by Mendeleev for the atoms.

On the contrary, the objective of Santilli¹s model pi-o = (e*-, e*+)HM is that of studying the STRUCTURE of the selected hadron as ONE INDIVIDUAL MEMBER of a given SU(3) family, by carefully avoiding even the mention at this time of the remaining mesons, in essentially the same way as Bohr considered the structure of the hydrogen atom as one, single, individual element of a Mendeleev family, without any mention in the STRUCTURE problem of the other atom of the Mendeleev CLASSIFICATION.

The scientific price to pay for the different view of doing jointly the classification and the structure is the inability to define gravity for any type of matter composed of quarks, have no confinement of the hypothetical quarks, etc.

Today Santilli¹s model pi-o = (e*-, e*+)HM can be confirmed via the advanced occurred since 1978, as well as via direct experiments proposed in Sect. XI. First of all, the notion of eletons e*- and antieletons e*+ can be rigorously constructed via the isounitary irreducible representations of the Poincare'-Santilli isosymmetry P*(3.1) with respect to the isounit \

(5.21) E = Mx(Dig. (n_1^2, n_2^2, n_3^2, n_4^2)xexp{NxVol. of wave overl.}

where the space nk represent the size (charge distribution), n4 represents the density of the hadronic state, and M and N are suitable nonlinear functions. The ¼-o is then conceived a "compressed positronium" down to 1 fm mutual distances [V-1a], that can be quantitatively represented via the isotopic lifting

(5.22) Positronium = (e^-, e^+)QM ---) pi^o = (e*^-, e*^+)HM

characterized by a step-by-step nonunitary transform UxUÝ =/ I of the positronium's equation as described in Sect. 1, under the condition

(5.23) UxUÝ = E.

In fact, under the above transform the conventional Schroedinger's equation for the Coulomb problem is transformed into the iso-Schroedinger's equation for the ¼-o

(5.24a) Hx|psi) = Ex|psi) ---) H*xTx|psi*) = E*x|psi*),

(5.24b) |psi*) = Ux|psi), H* = UxHxUÝ, T = 1/UxUÝ.

The selection of isounit (43) then permits the recovering in first approximation of Santilli's original model [V-1a] identically, including its "spectrum suppression", that is, the suppression of the infinite spectrum of the hydrogen atom into one single possible energy level, that of the pi-o (see [V-23] for details).

In summary, we can state today that, thanks to the advent of hadronic mechanics, an electron and a positron admit the typical infinite spectrum at large mutual distances (read: for ignorable nonlocal effects) characterizing the positronium, plus one and only one additional bound state at mutual distances of the order 1 fm (read: under appreciable nonlocal interactions due to wave overlapping) characterizing the neutral ¼-o meson [V-1a].

The model pi-o = (e*-, e*+)HM represents all characteristics of the ¼-o, including the decay with the lowest mode representing an iso-tunnel effect of the constituents and, as such, it is already confirmed by experimental evidence, and certainly cannot be dismissed on grounds of unsettled quark conjectures on the hadronic structure.

Rather remarkably, the basic principles of Santilli's model pi-o = (e*-, e*+)HM have resulted to be applicable also to the two identical electrons of the Cooper pair in superconductivity. In fact, it is known today that the attractive character of the nonlocal interactions due to mutual overlapping of the wavepackets of electrons in singlet couplings is so strong to hold also for identical electrons, i.e., it produces a bound state at short distances even under repulsive Coulomb interactions (charge independence of strong force).

V-7-B. THE CONSTITUENTS OF THE NEUTRON. The neutron n was conceived by Rutherford in 1920 as a "compressed hydrogen atom" in the core of stars, that is, as an electron compressed all the way inside the proton under the high pressures available in the core of stars.

Rutherford's hypothesis on the "existence" of the neutron was confirmed 12 years later by Chadwick. However, Rutherford's "conception" of the neutron as a bound state of a proton and an electron at small distances, n = (p+, e-), was rejected by Pauli, Heisenberg, Schroedinger and other founders of quantum mechanics on various grounds, such as:

1) Rutherford's model n = (p+, e-) does not permit the representation of the spin 1/2 of the neutron (because both the proton and the electron have spin 1/2);

2) The same model does not permit the representation of the total energy of the neutron because its rest energy is "bigger" than the sum of the rest energies of the constituents, contrary to the "mass defect" of nuclear physics (experts in the field would know that, in the case considered, the indicial equation of Schroedinger's representation no longer admits real solutions and the bound state loses the conventional physical meaning with a real total energy, see [V-1a] for details);

3) Rutherford's model n = (p+, e-) does not permit the representation of other characteristics of the neutron, such as its magnetic moment, mean life, and others.

The above criticisms assume historical implications if one note that they signaled the abandonment of structure models with physical ordinary constituents in favor of unitary symmetries. In fact, the SU(2)-isospin symmetry emerged from the rejected of Rutherford's model that was then followed by the SU(3) symmetry.

However, the historical objections by Pauli, Heisenberg, Schroedinger and others against Rutherford's conception of the structure of the neutron have one FUNDAMENTAL FLAW: They all assumed the tacit belief that the discipline effective for the structure of atoms, quantum mechanics, was also applicable in the same effective way to the different physical conditions of the structure of the neutron.

In reality, the above belief literally implies the assumption of a "tiny atom inside the proton", evidently because the atomic structure is the only one predicted by quantum mechanics, or that "the electron freely orbits within the hyperdense medium inside the proton", because these are the only conditions described by quantum mechanics, and other transparently unsound consequences.

In short, the historical objections against Rutherford's conception of the neutron have never been final on true scientific grounds. Because of this occurrence, studies on Rutherford's conception of the neutron were never halted through this century (see the literature identified in Ref, [V-12]).

After achieving in 1978 [V-1a] the structure model of the pi-o with physical constituents, Santilli conducted most of the subsequent mathematical and physical studies for the achievement of a structure model of the neutron exactly along Rutherford's original conception, although realized via hadronic mechanics, n = (p*+, e*-)HM, where p* and e* represent mutation of the conventional quantum particles under short-range nonlinear, nonlocal and nonunitary effects due to the total penetration of the electron's wavepacket within the hyperdense proton structure.

The primary obstacle was the achievement of a consistent representation of the spin 1/2 of the neutron from two constituents, the proton and the electron, each having spin 1/2. For this reason Santilli conducted the first studies on the nonlinear, nonlocal and nonunitary isotopies of: the rotational symmetry O(3) [V-11c]; the SU(2)-spin symmetry [V-11d]; the Lorentz symmetry L(3.1) [V-11a]; the Poincare' symmetry P(3.1) = L(3.1)xT(3.1)[V-11f]; its spinorial covering SL(2.C)xT(3.1) [V-11g]; their operator realization via the isotopies of Wigner's theorem on symmetries [V-11b]; their isorepresentation [V-3,V-12], their isodualities [loc. cit.], resulting in a body of knowledge today known as the Poincare'-Santilli isosymmetry (see [V-16] and references quoted therein).

A main objective was to achieve the mutation of the TOTAL angular momentum of the electron, from the conventional value in vacuum J = 1/2 + m, m = 0, 1, 2, ..., to the only admissible value J = 0 within the hyperdense medium inside the proton.

A first solution was presented in paper [V-24] of 1990; the first detailed study of the structure model n = (p*+, e*-)HM appeared in Communication [V-25] of 1993 of the JINR in Russia, that was then published in Ref. [4.11g].

As it is often the case for fundamental physical advances, when seen in retrospect, the solution of the spin problem is so simple to appear trivial. At the initiation of Rutherford's compression the only possible penetration of the electron within the proton is in singlet coupling. As one can see even classically via ordinary gears, triplet couplings at short distances are repulsive [V-1a].

But the proton is about 2,000 times heavier than the electron. As such, the electron is dragged by the proton into its intrinsic spin. The coupling p-e then has the constraint that THE ORBITAL MOMENTUM OF THE ELECTRON WITHIN THE PROTON MUST COINCIDE WITH ITS SPIN, thus resulting in the desired null value of the total angular momentum of the electron, J = 0. The spin of the neutron in the Rutherford-Santilli model n = (p*+, e*-)HM coincides with that of the proton.

Needless to say, ³half-odd-integer values of the angular momentum² are strictly forbidden in quantum mechanics. The knowledge of the reason implies the solution. In fact, said values are forbidden because they violate the unitary character of the angular momentum theory. But hadronic mechanics is structurally nonunitary (actually isounitary). Thus, the nonunitary values of angular momentum that are forbidden for quantum mechanics become routinely acceptable for hadronic mechanics.

The exact-numerical representation of all physical characteristics of the neutron then follows, again, via one single structure equation, as it was the case for the ¼-o. In fact, in Ref. [V-11g] one can see the representation via an isotopic Dirac equations of the following characteristics of the neutron: rest energy, spin, charge radius, mean life, anomalous magnetic moment, charge, space and charge parity, etc., as well as a representation of the spontaneous decay of the neutron into a proton, an electron and an antineutrino, the latter being realized via the decay of the eleton e*,

(5.25a) n = (p*^+, e*^-)HM --> (p^+ + e^- + anti-v,

(5.25b) e*^- --> e^- + anti-v.

Note that the constituents of the neutron were in our space-time before Rutherford's compression, and they evidently remain in our space time after the compression. As a result, the Rutherford-Santilli structure model of the neutron does indeed permit a fully consistent representation of the gravity of the neutron. By comparison, one should keep in mind that, when quarks are assumed as the constituents of the neutron, no characterization of its gravity is possible, besides having all the additional shortcomings indicated earlier.

Intriguingly, a research conducted by A. Kalnay of IVIC, Venezuela, in the mid 1980's revealed that the first mutation of the total angular momentum of the electron, from the conventional value J = 1/2 + m, to an integer value J = m, m = 0, 1, 2, 3, ... was achieved by Dirac in two of his last papers on a generalization of his celebrated equation which resulted to have an essential isotopic structure, that is, an equation with the essential structure of hadronic mechanics (see Refs. [V-3,V-12] for details and references).

In particular, "Dirac's generalization of Dirac's equations" has precisely the isotopic structure used by Santilli [V-11g] for the characterization of the eleton e*. In order words, the conventional Dirac equation represents one electron under EXTERNAL LONG-RANGE ELECTROMAGNETIC INTERACTIONS, e.g., the electron of the hydrogen atom under the field of the proton considered as external (recall that a two-body formulation of Dirac's equation does not exist, thus confirming the OPEN character of the equation).

The Dirac-Santilli isoequations represents the same electron, this time under the additional presence of EXTERNAL SHORT-RANGE NONUNITARY INTERACTIONS, that is, the equation represents the mutated electron e*- under conventional plus nonlinear, nonlocal and nonpotential interactions due to total immersion within the hyperdense proton, that remains external. Conventional interactions are represented via the conventional minimal coupling rule, while the contact interactions are represented via the isounit E = 1/T and generalized product A*B = AxTxB. The nontriviality of the generalization can be illustrated by the fact that, e.g., the diagonal elements of T enter into the definition of the new gamma matrices (see [V-12] for details).

We regret the inability of present the new equation in this Web Page due to insufficiencies in the available mathematical symbols.

The difference between the current view on weak interactions and the Rutherford-Santilli model should be indicated. According to current views, the synthesis of protons and electrons is indeed possible according to the familiar reaction

(5.26) p^+ + e^- --> n + v

The same reaction evidently persists for the isotopic lifting

(5.27) Hydrogen atom = (p^+, e^-)QM --> n = (p*^+, e*^-)HM + anti-v,

with one difference of paramount importance, particularly for possible practical applications of hadron physics considered later on. For the current theory of weak interactions, the electron "disappears" in process (48), while for isotopy (49) the electron persists, and only experiences a mutation of its characteristics due to the different environment.

It should be indicated that, besides representing all characteristics of the neutron, the Rutherford-Santilli model has also received a direct experimental verification by don Borghi et al. [V-26], according to which the synthesis of protons and electrons into neutrons can apparently occur also in ordinary conditions on Earth under the threshold energy of 0.80 MeV of the electron (this experiment is suggested for a new conduction in Sect. XI).

In conclusion, the Rutherford-Santilli structure model of the neutron with physical constituents, n = (p*+, e*-)HM, is sufficiently verified on direct theoretical and experimental grounds and cannot be dismissed via unverified quark conjectures.

The "spectrum suppressing" character of the new model is particular importance for its consistency, as well as for the problem of structure of other hadrons. In fact, under any possible excitation, the constituents of the structure n = (p*+, e*-)HM exit the range of the strong interactions (1 fm), by therefore acquiring the infinite spectrum of the conventional hydrogen atom. This point is important to clarify that the possible search within hadronic mechanics of a sort of new spectrum inclusive of the neutron and its resonances is fundamental flawed in its conception, let alone in its technical realization.

As it was the case for the pi-o, the neutron is a single, unique, individual bound state under nonlinear, nonlocal and nonunitary effects whose range is that of the strong interactions that, in turn, coincides with the effective width of the Hulten well [V-1a,V-22,V-11g]. Under any excitation, distances increase beyond 1 fm, that is, beyond the applicability of hadronic mechanics. The excited states are therefore purely quantum mechanical, that is, of long range electromagnetic character.

As we shall see later on in this Web Page, the model also predicts one of the apparently first practical applications of hadron physics (other than those of nuclear character), given by an apparent new source of subnuclear energy. This provides further reasons to warrant additional studies on the Rutherford-Santilli structure model of the neutron.

V-4-C. THE CONSTITUENTS OF THE REMAINING HADRONS. Once the basic structure model of the pi-o and of the neutron with ordinary massive particles as physical constituents have been worked out, the construction of similar structure models for the remaining UNSTABLE particles is straightforward.

In fact, for the muons and for the remaining mesons we have structure models of the type [V-12]

(5.28a) muon^{+/-} = (e*^-, e^{+/-}, e*^+)HM

(5.28b) pions+{+/-} = (pi^o*, e*^{+/-})HM,

(5.28c) eta = (µ*^+, µ*^-)HM,

(50d) Neutral Kaon = (pi*^+, pi*^-)HM,

and so on, with corresponding models for baryons

(5.29a) Gamma = (n*, pi^o*)HM,

(5.29b) Signa^{+/-} = (n*, pi*^{+/-}),

and so on, where * denotes mutation and lack of * denote conventional particle. In each case the model represents ALL characteristics of the particle considered and its decays via one single equation of structure that, in each case, admits only ONE energy level, that of the particle considered.

It should be noted that the above "bootstrap-type" models HAVE receiveD a rather remarkable confirmations by independent studies by Gareev [V-27] in which unstable hadrons are interpreted as simple resonances of the particles produced in the decays. In fact, hadronic mechanics provides the underlying discipline for a quantitative representation of Gareev resonance model. Additional related studies are those by A. O. E. Animalu and C. N. Animalu [V-28].

A comparison between the new model of hadronic structure and the conventional quark model (also of structure) is in order:

1) The former model predicts that the hadronic constituents can be released free and it is verified with the spontaneous decays with the lowest mode, while the latter model implies a finite probability of free quarks that is contrary to experimental evidence;

2) The former model uses conventional, massive, physical particles as constituents defined in our space-time and, therefore, permits a fully consistent definition of gravity for hadrons, while the latter model permits no consistent definition of gravity, thus being against experimental evidence;

3) The former model represents the totality of the physical characteristics of hadrons, thus being again verifies by physical reality, while the latter model does not (e.g., quark theories do not reproduce correctly the single charge radius for all hadrons, the various magnetic moments, and other data).

By recalling that physics is a quantitative science based on physical evidence, rather than the pursuit of personal beliefs, the serious researcher can decide for himself/herself which of the two models of structure of hadrons is preferable on grounds of current knowledge.

PROPOSED RESEARCH V-7-I: Repeat all calculations of Santilli's nonrelativistic model pi-o = (e*-, e*+)HM of Sect. 5, Ref. [V-1a] and verify: the representation of all characteristics of the pi-o; the 1 fm width of the Hulten well; and the suppression of the atomic spectrum into one energy level only. Re-derive the same model via nonunitary transform of type (43).

PROPOSED RESEARCH V-7-2: Construct a relativistic version of the model pi-o = (e*+, e*-)HM via the Dirac-Santilli isoequations of Ref. [V-11g], and verify the preservation of all results achieved at the nonrelativistic level. Prove that the model is a nonunitary image of the relativistic treatment of the positronium.

PROPOSED RESEARCH V-7-3: Repeat all calculations of the Rutherford-Santilli model n = (p*+, e*-)HM of Ref. [V-11g] and verify the representation of all characteristics of the neutron. Prove that the model is a nonunitary image of the model of the hydrogen atom and identify the transform.

PROPOSED RESEARCH V-7-4: Work out in details all models (5.28) and (5.29).

PROPOSED RESEARCH V-7-5: Reformulate all preceding models via "Dirac's generalization of Dirac's equation" [V-29], and show that the emerging structure only have two space-time dimension (HINT: in his instinctive brilliance, Dirac selected one of the most complex forms of isotopies of his own equation, that with an isominkowskian metric m* = Txm, m = Diag. (1, 1, 1, -1) in which T is entirely off-diagonal and such that the only surviving components in the isotopic invariant (Xt)xm*xX, X = {X1, X2, X3, X4} are in two dimension, see Ch. 10, Ref. [V-3b]).

TECHNICAL ASSISTANCE. Contact the IBR main office at ibr@gte.net for referral to experts.

V.8: STUDIES ON THE COMPATIBILITY OF THE NEW STRUCTURE MODEL OF HADRONS WITH THE SU(3) CLASSIFICATION. These studies are at their initiation. We here merely mention that, according to Santilli's notion of isoparticle, each constituent of the hadrons has its own distinctive isounit E. In fact, all constituents are different in the models reviewed above and, even assuming that they are the same, they require different isounits when referred to different densities in different hadrons.

As a result, the axiomatically most important characterization of the new structure model of hadrons reviewed earlier is given by their total isounits E-tot which are given by

(5.30a) E_{tot-pi^o} = E(e*^-) x E(e*^+)

(5.30b) E_{tot-pions} = E(pi^o*) x E(e*^{+/-}),

(5.30c) E_{tot-kaon} = E(pi*) x E(pi*),

and so on. The important point is that all mesons are reducible to TWO isoparticles.

Compatibility with TWO isoquarks (as needed for mesons) is then expected to be consequential and merely given by the isotopic of quarks and antiquarks with a FAMILY of isounits, yielding the multivalued hyperstructures of Web Page 18.

TECHNICAL ASSISTANCE. Researchers interested in advances in the latter lines of inquiries are suggested to contact the Institute for Basic Research at the main office at ibr@gte.net.

V-9: APPLICATIONS PREDICTED BY THE NEW MODEL OF HADRONIC STRUCTURE. As it is well known, quark models on the hadronic structure have no known practical application of any type, not even remote, and none is foreseeable on scientific grounds. On the contrary the new model of hadronic structure predicts indeed novel technological applications.

The main reason for the above disparity is that quark models have been conceived to have the hadronic constituents perennially confined, while the new structure model has been conceived for the specific purpose to permit the constituents of (unstable) hadrons to be produced free. In fact, a great majority of the technological and practical applications of the nuclear, atomic and molecular structures are due precisely to the fact that the constituents can be produced free.

The most important predictions of novel applications by relativistic hadronic mechanics originate from the resolution of the objections against Rutherford¹s historical conception that the electron is an actual, real, physical constituent of the neutron, although in a mutated form e* verifying the Poincare-Santilli isosymmetry P*(3.1), as outlined in the preceding section V-7-B and studied in details in Ref. [V-11g].

In fact, the above resolution has permitted [V-31] the prediction that THE NEUTRON CAN BE SYNTHESIZED IN LABORATORY, the prediction that THE NEUTRON CAN BE ARTIFICIALLY STIMULATED TO DECAY, that is essentiality the ³inverse² of the preceding process, and other predictions. In turn, each of these predictions, if experimentally confirmed, has a number of technological applications, including new means for the production of neutrons for industrial and other uses, a new source of energy of ³subnuclear² type called ³hadronic energy², new means for the recycling nuclear waste, and other applications, some of that are currently under patenting.

V-9.A: THE PREDICTION OF THE SYNTHESIS OF THE NEUTRON FROM PROTONS AND ELECTRONS (ONLY) AND ITS ONGOING EXPERIMENTAL VERIFICATION As it is well known, stars initiate their lives as being solely composed of hydrogen, and end it being composed of all natural elements. As such, stars synthesize the neutron from protons and electrons only, as originally conceived by Rutherford (Sect. V-7.B).

Note that the above fundamental process in nature cannot be studied with quark theories, evidently because one would need the entire ³octet² of baryons that do not exist as yet. This confirms the main distinction between the problem of ³classification² and that of ³structure² of Sect. V-2, and establishes again, the need to STUDY THE STRUCTURE OF THE NEUTRON ALONE AS ONE, SINGLE, INDIVIDUAL ENTITY without any first need of the classification of the family to which the neutron belongs. The latter task is that addressed by the new structure model of hadrons outlined earlier.

#With a clear understanding on the above foundations, relativistic hadronic mechanics predicts that the synthesis of the neutron from protons and electrons only can also be done on our Earthly environment under the availability of the threshold energy of

(5.31) E(e) = 0.80 MeV = E(n) - [E(p) + E(e)],

provided that the coupling p-e is in singlet, in which case the nonlocal-nonunitary effects provide a novel attractive interactions (while triplets couplings under deep mutual penetrations of the wavepackets are highly repulsive).

In essence, the synthesis here considered is indeed described by conventional relativistic quantum mechanics via the familiar weak process

(5.32) p + e -> n + v ,

The point is that, according to conventional theories, the cross section of the above reaction is ³predicted² (because it has not been sufficiently measured) to be very small at all energies, thus being of no practical significance.

Relativistic hadronic mechanics confirms the very low value of the cross section of reaction (5.32) at all energies (See Sect. VIII), but PREDICTS A PEAK IN THE CROSS SECTION AT THE SHARP ENERGY 0.80 MeV FOR ELECTRONS IN SINGLET COUPLINGS ON PROTONS AT REST. The existence of such a peak would evidently bring the synthesis within practical realization on Earth at ordinary temperatures.

The mechanism of the peak is the given by the contact, nonlocal and nonhamiltonian effects of the p-e couplings that, being ³nonunitary², are outside any hope of prediction via conventional quantum mechanics. As it is the case for all resonances, the effects is measurable only the immediate neighborhood of the threshold energy of 0.80 MeV and it is impossible either at smaller energies (evidently because of insufficient energies to create the neutron) or at higher energies.

A preliminary, yet intriguing experimental verification of the above synthesis has been conducted by Don Borghi and his associates [V-32] in Brasil. In essence the experiment consists of a metallic cylinder filled up with ionized hydrogen gas obtained from a conventional electrolytic process and kept (partially) ionized via an electric discharged. Since protons and electrons are charged, they cannot escape the metallic cylinder and are kept inside. Around all the outside of the cylinder, the experimenters put a variety of stable and unstable elements for various periods of times ranging from days to weeks, after which they apparently detected nuclear transmutations due to a neutron flux. In the absence of any other neutron source, the only possible explanation of the experiment, if confirmed, is the interior synthesis of the neutron from protons and electrons, namely, a number of these particles had the needed threshold energy and coupled in the needed singlet state to allow their bound state into the neutron according to the structure of the neutron of Sect. V-5-B. Being neutral, the neutron can then escape the metallic cylinder and produce the measured nuclear transmutations in the outside.

Needless to say, the experiment must be re-run independently a number of times to reach scientific validity and can be re-done in a number of different ways. One of them is that of the Proposed Experiment 5 of Sect. XI.

It should be noted that experiment [V-32] is of manifestly fundamental character on historical grounds, because it could confirm Rutherford¹s legacy on the structure of the neutron, on technological grounds, because it could establish new means of producing neutrons for industrial and other purposes, as well as on theoretical grounds, because it would establish relativistic hadronic mechanics. Moreover, the experiment is of truly low costs, and can be run in any laboratory equipped with neutron detecting devices. It is therefore hoped that the re-run is indeed conducted by interested experimentalists, perhaps jointly with other more expensive and lesser relevant tests.

V-9-B:THE STIMULATED DECAY OF THE NEUTRON AND ITS EXPERIMENTAL VERIFICATION If the neutron can be synthesized in laboratory, then, being the inverse process, its stimulated decay is only a matter of time.

At any rate, the neutron is not an unstable particle with an absolutely rigid and fixed meanlife. In fact, the neutron has a meanlife: of a few seconds to a few minutes when a member of certain nuclei; of 15 minutes when isolated in vacuum; and of days, months and all the way to full stability when a member of other nuclei. In short, clear physical evidence establishes that the meanlife of the neutron depends on the physical conditions of its environment. If the environment can control the meanlife of the neutron, the existence of its stimulated decay becomes out of scientific debates, the open issue being the identification of the most effective means for its decay.

Among a variety of possibilities, Santilli [V-31] has studied the Gamma Stimulated Neutron Decay (GSND), i.e., its decay via the reaction

(5.33) Gamma + n -> p + e + anti-v.

Again, the above reaction is fully admitted by relativistic quantum mechanics, but it is ³predicted² (again, because of lack of sufficient measures) to have a very low cross section at all gamma energies, thus being insignificant for practical uses.

Relativistic hadronic mechanics confirms the low value of the cross section of reaction (5.33) at all energies, with the prediction of a PEAK at gamma energies of [V-11g,V-31]

(5.34) E(Gamma) = 1.294 MeV (3.129x10^{20} Hz)

that, if confirmed, would permit the stimulated decay of the neutron in a form usable for future technological and practical uses.

The experimental verification is under way at this writing by N. Tsagas and his associates in Greece [V-33] and other groups. A typical set up of the experiment essentially requires:

1) A disk of radioactive isotope Eu-152 that releases photons precisely of the needed 1.3 MeV energy;
2) A disk of an isotope admitting the GSND (see Sect. VI for details), such as the isotope Mo(100; 42), and
3) A scintillator or other device capable of measuring the energy of electrons.

the experiment consists in placing the Eu-Mo disks next to each other and measuring the energy of the electron produced as a result of the Eu-Gamma penetrating inside the Mo-disk. If these electrons are of 1 MeV or less, they are due to Compton scattering and are not important for the test. On the contrary, the measure of a few electrons with energies of 2 MeV or more would establish the principle of the GSND. In fact, these electrons could only originate from the nuclear structure. But the Eu-disk does not emit electrons and the Mo(100, 42) is stable. As a result, electrons with energy of 2 MeV or higher could only originate from the stimulated decay of one of the peripheral neutrons in the Mo-nuclei.

Note that the objective here is to verify or deny the PRINCIPLE of the GSND that would be achieved by the measure of A FEW ELECTRONS with the indicated energy (recall that the predictions of new particles by the SU(3) model were first verified by extremely few events......). The problem of the LARGE PRODUCTION of electrons of nuclear origin as needed in practical applications via the maximization of the effect is a SEPARATE PROBLEM requiring separate studies and experiments (Sect. VI).

We should finally note that, in the above experimental set-up, the principle of the GSND could be confirmed in a way beyond any possible or otherwise credible doubt. Under reaction (5.33), the isotope Mo(100,42) can only transform into Te(100, 43) that is unstable and beta-decays into Ru(100, 44),

(5.35) Gamma + Mo(100, 42) -> TE(100, 43) + Beta-minus ->

-> Te(100, 43) + beta-minus -> Ru(100, 44).

The latter isotope is one of the rarest on Earth. The possible confirmation here considered is therefore given by the possible detection of even minute traces of Ru(100, 44) in the originally pure Mo(100, 42) disk after a sufficient running period.

The experiment here considered is also of manifestly fundamental character on historical, applied and theoretical grounds, it is also of quite modest cost, and it can also be conducted in any laboratory equipped with scintillators or other means for measuring the energy of the emitted electrons.. It is therefore hoped that the experiment will indeed be considered by experimentalists, perhaps jointly with other more expensive and lesser relevant tests.

V-9-C: CONCEIVABLE PRACTICAL APPLICATIONS. With the understanding that applications are far ahead in the future and are here considered primarily as motivations for the continuation of the research, we point out that the control of the life of the neutron would have far reaching practical implications.

First, it would imply a new form of ³subnuclear² energy called ³hadronic energy² [V-31]. In fact, reactions of type (5.35) have a transparently positive energy output in full compliance with the principle of conservation of the energy, because the process merely transforms one nucleus, the Mo(100, 42) into another, Ru(100, 44) of SMALLER atomic weight, while releasing the energy difference via the emitted electrons.

The process is called ³subnuclear² because it occurs in the STRUCTURE OF THE NEUTRON, rather than that of nuclei as it is the case for the conventional nuclear energy. The energy is expected to be considerably ³clean², because the only particles produced are the electrons, that can be easily captured by a metallic shield to utilize the energy, and the harmless neutrinos, and it does not imply use or release of radioactive material or waste (because the original element is a light, natural, stable element that is then transformed into another light, natural, stable element). Additional aspects are studied in Sect. VI.

Moreover, the control of the life of the neutron would permit the conception and possible development of new forms of recycling nuclear waste essentially consisting in the bombardment of the nuclear waste via a beam of excitation gammas with 1.294 MeV. Since these nuclei are heavy and naturally unstable, the beam is expected to produce the stimulated decay of some of its peripheral neutrons, thus causing the decay of at least a percentage of them due to instantaneous excess of protons and related increase of Coulomb repulsion.

Additional aspects on the latter application are studied in Sect. VI where the above new means for recycling nuclear waste are complemented with others to maximize efficiency. At this point we only wanted to indicate these applications as a way to warrant further studies.

Once the above possibilities are verified and sufficiently developed, numerous other practical applications of the new model of hadronic structure are possible, such as the production of otherwise very rare isotopes, novel industrial applications in drilling, new medical applications, and others [V-31].

On scientific ground possible new experimental applications are equally intriguing. For instance, the principles of artificial synthesis and stimulated decay of the neutron are evidently applicable to all other (unstable) hadrons. Rather than current means for producing a beam of a given particle, say of kaons, the same beam could be produced via its artificial synthesis from lighter particles along the line of the new structure model of mesons of Sect. V-7-C.

REFERENCES OF SECTION 5 [V.1] R. M. Santilli, Hadronic J. Vol.. 1, p. 574 (1978) [V-1a]; Foundations of Physics Vol. 111, p. 383 (1981) [V-1b]

[V-2] R. M. Santilli, Foundations of Theoretical Mechanics, Vol. I, 1978 [V-2a] and II, 1983 [V-2b], Springer-Verlag, Heidelberg

[V-3] R. M. Santilli, Elements of Hadronic Mechanics, Vols. I [V-3a], II [V-3b] and III [V-3c] (in preparation), Ukraine Academy of Sciences, Kiev, second edition, 1995

[V-4] D. I. Bloch'intsev, Phys. Rev. Lett. Vol. 12, p. 272 (1964) [V-4a]. L. B. Redei, Phys. Rev. Vol. 145, p. 999 (1966) [V-4b]. D. Y. Kim, Hadronic J. Vol. 1, p. 343 (1978) [V-4c]. J. Ellis et al., Nuclear Phys. B Vol. 176, p. 61 (1980) [V-4d]. A. Zee, Phys. Rev. D Vol. 25, p. 1864 (1982) [V-4e]. R. M. Santilli, Lett. Nuovo Cimento Vol. 33, p. 145 (1982) [V-4f]. V. de Sabbata and M. Gasperini, Lett. Nuovo Cimento Vol. 34, p. 337 (1982) [V-4g]. H. B. Nielsen and I. Picek, Nuclear Physics B Vol. 211, p. 269 (1983) [V-4h]. M. Gasperini, Phys. Lett. B Vol. 177, p. 51 (1986) [V-4i].

[V-5] B. H. Aronson et al., Phys. Rev. D Vol. 28, p. 476 and 495 (1983)

[V-6] N. Grossman et al., Phys. Rev. Lett. Vol. 59, p. 18 (1987)

[V-7] Yu. Arestov, Hadronic J. Vol. 19, p. 205 (1996)

[V-8] UA1 Collaboration, Phys. Lett. B Vol. 226, p. 410 (1989)

[V-9] R. Adler et al, Phys. Rev. C Vol. 63, p. 541 (1994)

[V-10] B. Lorstad, Intern. J. Modern Phys. A Vol. 4, p. 2861 (1989)

[V-11] R. M. Santilli, Nuovo Cimento Lett. Vol. 37, p. 545 (1983) [V-11a]; Lett. Nuovo Cimento Vol. 37, p. 509, (1983) [V-11b]; Hadronic J. Vol. 8, pp. 25 and 36 (1985) [V-11c]; JINR Rapid Comm. Vol. 6, p. 24 (1993) [V-11d]; J. Moscow Phys. Soc. Vol. 3, p. 255 (1993) [V-11f]; Chinese J. Syst. Eng. & Electr. Vol. 6, p. 177 (1996) [V-11g]

[V-12] R. M. Santilli, Isorelativity, with Applications to Quantum Gravity, Antigravity and Cosmologies, Balkan Geometry Society, in press
\
[V-13] F. Cardone, R. Mignani and R. M. Santilli, J. Phys. G. Vol. 18, pp.L 61 [V-13a] and L141 [V-13b] (1992)

[V-14] R. M. Santilli, Hadronic J. Vol. 15, p. 1 (1992)

[B-15] F. Cardone and R. Mignani, Preprint Univ. Rome No. 894

[V-16] J. V. Kadeisvili, Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, p. 83 (1996)

[V-17] Y. Nambu, Phys. Rev. D Vol. 7, p. 2405 (1973)

[V-18] A. J. Kalnay, Hadronic J. Vol. 6, p. 1 (1983)

[V-19] A. J. Kalnay and R. M. Santilli, Hadronic J. Vol. 6, p. 1873 (1983)

[V-20] R. Mignani, Lett.. Nuovo Cimento Vol. 39, p. 413 (1984)

[V-21] R. M. Santilli, Comm. Theor. Phys. Vol. 4, p. 123 (1995)

[V-22] A. O. E. Animalu, Hadronic J. Vol. 14, p. 459 (1991) and Vol. 17, p. 349 (1995)

[V-23] A. O. E. Animalu and R. M. Santilli, Intern. J. Quantum Chemistry vol. 29, p. 175 (1995)
[V-24] R. M. Santilli, Hadronic J. Vol. 13, p. 513 [1990)

[V-25] R. M. Santilli, JINR Communication ER4-93-352 (1993)

[V-26] C. Borghi et al. (Russian) J. Nucl. Phys. Vol. 56, p. 147 (1993)

[V-27] F. A. gareev, Hadronic J. Vol. 20 (1997), inn press

[V-28] A. O. E. Animalu and C. Animalu, in New Frontiers of Hadronic Mechanics, Hadronic Press (1996)

[V-29] P. A. M. Dirac, Proc. Roy. Soc A, Vol. 322, p. 435, 1971, and Vol. 328, p. 1 (1972).

[V-30] H. E. Wilhelm, Hadronic J. Vol. 19, p. 1 (1996)

[V-31] R. M. Santilli, Hadronic J. Vol. 17., p. 331 91994)

[V-32] C. Borghi et al., J. Nuclear Physics V. 56, p. 147 (1993)

[V-33] N. Tsagas et al, Hadronic J. Vol. 19, p. 87 (1996)

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RECENT PAPERS APPEARED ON THE RESEARCH PROPOSED IN SECT. V

AN ADVANTAGE IN THE ASYMMETRIC e+/e- COLLIDERS WITH
POLARIZED BEAMS FOR THE VERIFICATION OF MINKOWSKIAN
GEOMETRY INSIDE HADRONS
Yu. Arestov
Institute for High Energy Physics
142284 Protvino, Moscow Region, Russia

ON LOGARITHMIC NONLINEAR SCHROEDINGER'S EQUATION COMPATIBLE
WITH HADRONIC MECHANICS AND ITS CONNECTION WITH OTHER APPROACHES
FOR THE DESCRIPTION OF DISSIPATIVE SYSTEMS
D. Schuch
Institute fur Theoretische Physik
J. W. Goethe Universitat
Robert Mayer Strassse 8-10
D-60054 Frankfurt am Main, Germany
"New Frontiers in Hadronic Mechanics"
T. L. Gill, Editor, Hadronic Press (1996), p. 113

SUPERSYMMETRY AND THE LIE-ISOTOPIC LIFTING OF THE GENERALIZED
DIRAC EQUATION
L. Ntibashirakandi and D. Callebaut
Physics Department, UIA,
University of Antwerp
B-2610 Antwerp, Belgium
"New Frontiers in Hadronic Mechanics"
T. L. Gill, Editor, Hadronic Press (1996), p.131

ANALOGOUS HADRONIC STRUCTURE OF MESONS AND COOPER PAIRS
A. O. E. Animalu and C. Animalu
Department of Physics and Astronomy
University of Nigeria
Nsukka, Nigeria
"New Frontiers in Hadronic Mechanics"
T. L. Gill, Editor, Hadronic Press (1996), p.169

LIE-ADMISSIBLE STRUCTURE OF CALDI'S MODEL
A. Janmnussis
Department of Physics
University of Patras
Patras 26110, Greece
Hadronic J. Vol. 19, p. 535 (1996)

APPLICATION OF HADRONIC MECHANICS TO A NEW SUBNUCLEAR
ENERGY AND NEW RECYCLING OF NUICLEAR WASTE
S. Smith
Institute for Basic Research
P.O.Box 1577
Palm Harbor, FL 34682, U.S.A.
ibr@gte.net
"New Frontiers in Hadronic Mechanics"
T. L. Gill, Editor, Hadronic Press (1996), p.257