**The nontechnical presentation below was written in 1999. As of today (January 2003) the best technical presentation on hadronic mechanics and chemistry is available in the monograph
R. M. Santilli,
**

** An 83 pages memoir on the foundations of hadronic mechanics and chemistry can be printed out from the pdf file
<R. M. Santilli
ISO-, GENO-, HYPER-MECHANICS FOR MATTER, THEIR ISODUALS,
FOR ANTIMATTER, AND THEIR NOVEL APPLICATIONS IN PHYSICS, CHEMISTRY AND BIOLOGY,>
in press at the **

**
Additional technical presentations are available in **

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

OF HADRONIC MECHANICS, SUPERCONDUCTIVITY AND CHEMISTRY

**Original content uploaded February 15, 1997. First revisions
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**VI. APPLICATIONS OF HADRONIC MECHANICS TO NUCLEAR PHYSICS**

Prepared by the IBR staff also from Sect. 3.15 of Ref. [I-1]

The understanding is that RQM does indeed provide an excellent "approximation" of nuclear data. However, even though evidently small, the expected deviations have a fundamental role for possible basic advances in nuclear as well as other branches of physics.

The first illustration of the reasons why RQM "cannot" be "exact" for the nuclear structure is its failure to reach an EXACT representation of the total magnetic moment of FEW BODIES nuclei, despite attempts for over three-quarter-of-a-century and the use of large public sums. To minimize ascientific trends, we should insist on the "exact" representation, because an "approximate" representation is out of questions, as mentioned earlier. We should also insist in the exact representation of "few-body nuclei", such as the deuteron, tritium etc., because for many-body nuclei there are several free parameters that allow "to adjust things".

For instance, in standard units, the experimental value of the magnetic moment of the deuteron is given by the well known expression µ-exp = 0.857 while quantum mechanics yields the value µ-theor = 0.880 that is 2.6 % off in "excess" of the experimental value. All possible corrections via RQM by using all allowed states still remain with about 1 % off, as recently confirmed by extensive investigations conducted by Burov and his group at the JINR in Dubna, Russia (see [VI-1a] for a classic account and [VI-b] for a contemporary study).

The problem does not appear to be solvable via quark models because the quark orbits are very small and, under their polarization, can yield corrections of the order of 10-to-minus five, contrary to the 1% corrections needed to represent physical reality.

Rather then preserving old knowledge, in this Web Page we are interested in seeking "new" basic knowledge that has been lacking for decades in nuclear physics, as well known, despite large investments of public funds.

The most plausible explanation of the inability by RQM to achieve an exact representation of nuclear magnetic moments was formulated by the Founding Fathers of nuclear physics in the late 1940's [VI-1a]. Recall that nucleons are not point-like, but have extended charge distributions with the radius of about 1 fm. Since perfectly rigid bodies do not exist in nature, the above ³historical hypothesis ³ (as hereon referred to) assumes that such distributions can be deformed under sufficient external forces. But the deformation of a charged and spinning sphere implies a necessary alteration of its intrinsic magnetic moment. In turn, the latter permits the exact representation of total nuclear magnetic moments as shown in Refs. [VI-2].

The lack of exact character of RQM in nuclear physics can also be seen in a number of independent ways, a compelling one being that based on symmetries. Computer visualization of the Poincare' symmetry P(3.1) indicates its capability to represent Keplerian systems, i.e., systems with the heaviest constituent in the center, as occurring in the atomic structure. By comparison, nuclei do not have nuclei and, therefore, the Poincare' symmetry must be broken to represent structures without the Keplerian center.

In turn, as shown in Ref. [VI-2], the latter breaking is fully in line with the deviations from P(3.1) required by a quantitative treatment of the historical hypothesis on the nuclear magnetic moment. In fact, according to the conventional Poincare¹ symmetry, the intrinsic magnetic moments of nucleons are perennial and immutable.

No other scientifically credible alternative is known at this writing. The Poincare' symmetry and RQM can only represent protons and neutrons as points that, having no dimension, cannot be deformed. Theories in second quantization do indeed introduce form-factors. However, these form-factors are well known to represent only "perfectly spherical" and "perfectly rigid" charge distributions as a necessary condition not to violate a pillar of RQM in any quantization, the rotational symmetry.

If physics is the pursue of physical evidence, rather than personal beliefs, serious scholars should admit that the notion to be treated quantitative here, nucleons as extended, nonspherical and deformable charge distributions, is simply beyond any realistic capabilities of RQM.

Other compelling arguments are of dynamical nature. RQM was constructed for the
characterization of action-at-a-distance, potential interactions among
point-particles, as occurring in the atomic structure. By comparison, nucleons
in a nuclear structure are in an average state of mutual penetration of about
10-to-minus-3 parts of their charge distribution [VI-3]. But hadrons are some of the
densest objects measured in laboratory until now. Their mutual penetration therefore
implies a (generally small) component of the nuclear force that is [V-3]:

1) of contact type i.e., with zero-range, thus requiring new interactions without
particle exchanges;

2) nonlinear in the wavefunctions and, possibly, their derivatives, thus requiring
a theory with an exact superposition principle under said nonlinearity;

3) nonlocal, e.g., of integral-type over the volume of overlapping, thus requiring
a new topology, as necessary to represent consistently interactions over
extended regions;

4) nonpotential, in the sense of violating the conditions to be derivable from a
potential or a Hamiltonian (the conditions of variational selfadjointness of
Ref.s [V-2]), thus requiring new dynamical equations; and

5) of consequential nonunitary type, as a necessary condition under nonhamiltonian
interactions.

It is evident that the above realistic physical characteristics of the nuclear force are beyond any scientific possibility of quantitative treatment via RQM.

For comprehensive studies on the impossibility for RQM to be exact in nuclear physics, the visitor may inspect monographs [V-3].

**VI.2. ISOTOPIC BRANCH OF RELATIVISTIC HADRONIC MECHANICS
FOR NUCLEAR PHYSICS.** One of the primary reasons why Santilli
[V-1a] conceived and proposed the construction of hadronic mechanics is to represent
protons and neutrons as extended, nonspherical and deformable charge distributions
under linear and nonlinear, local and nonlocal and potential as well as nonpotential
interactions.

As reviewed in Sect. 1.9, relativistic hadronic mechanics (RHM) represents conventional action-at-a-distance interactions via the Hamiltonian H = T + V and represents all non-Hamiltonian characteristics and effects via a generalization of the basic unit of the positive and diagonal type

(6.1) E = Diag. (n_1^2, n_2^2, n_3^2, n_3^2, n_4^2)xG(t, r, dr/dt, psi, D(psi)/Dr,..) = 1/T,

where: the semiaxes of an extended and nonspherical charge distributions (in this case a spheroidal ellipsoid) are represented by the space nk-squared under the following volume-preserving condition and cylindrical symmetry along the spin-axis

(6.2) (n_1^2) x (n_2^2) x (n_3^2) = 1, n_1 = n_2;

the deformability of the above spheroidal ellipsoids is represented via the variable character of the nk's, e.g., because of their dependence on the intensity of an external field; the density of the medium in which nucleons move is represented by n4 with value 1 representing the density of empty space; and all nonlinear, nonlocal-integral and nonpotential-nonunitary interactions are represented by the factor G.

The diagonal and positive-definite character of the isounit should be stressed in nuclear physics because it assures the preservation of conventional physical laws, such as Heisenberg¹s uncertainties, Pauli¹s exclusion principle, etc. (Sect. I.8 [I-1]). On the contrary, other more general realizations may imply departures from these laws that may be of interest in other fields (e.g., in the core of stars), but not in nuclear physics. On a comparative basis, RQM can only represent nucleons as perfectly spherical and perfectly rigid charge distributions in SECOND QUANTIZATION, while the methods underlying RHM, the isotopies, permit the representation of extended, nonspherical and deformable shapes via isounit (6.1) beginning at the NEWTONIAN LEVEL. The representation then persists at all subsequent levels, including that in FIRST QUANTIZATION (Sect. I).

The selection of the unit over other possibilities appears to be compelling and without any physically viable alternative known at this time. In fact, the selection of the unit for the representation of nonhamiltonian effects permits the preservation of all original axioms and physical laws of RQM and, for this reason, RHM is an "axiom-preserving isotopic completion" of RQM (Sect. 1). As a result, the axiomatic consistency of the treatment is assured ab initio.

Other alternatives, such as q-deformations, k-deformations, quantum groups, nonlinear theories, and others, are afflicted by rather serious problems of physical consistency outlined in Sect. I.3.

The axiom-preserving isotopies of nuclear models can today be constructed in a way so simple to appear trivial, via the step-by-step implementation of the nonunitary transform

(6.3) UxUÝ = E = 1/T /not= 1,

to the TOTALITY of the aspects of a conventional nuclear model. Any exception to the latter rule, such as lifting of the equations of motion, but preservation of the Hilbert space and field of RQM, implies a number of inconsistencies that generally remain undetected by nonexperts in the field [M-I-1,I-1].

Since the nonlinear, nonlocal and nonpotential internal effects are of contact type, they are purely short-range. As such, they are not visible in the outside. This implies that, when inspected from the outside, all said effects are averaged into constants that essentially isorenormalize the characteristic quantities nk and n4. A total isounit of a nuclear structure currently under study then has the form

(6.4) E{tot} = E_1 x E_2 x . . . x E_N, Ek = Diag. (n_1^2, n_2^2, n_3^2, n_4^2)_k.

By recalling that protons and neutrons have approximately the same size, shape and mass, all nucleons of a nuclear structure can be assumed in first approximation to have the same isounit, i.e., E_1=E_2=E_3= ... = E_N = E.

The latter approximation has been proved to be sufficient for the exact-numerical representation of the total magnetic moment of few-body nuclei, as outlined below. However, the same approximation is expected to be insufficient for other aspects of nuclear physics, e.g., the representation of the dynamical differences between, say, nucleons on a complete shell in the core of a nucleus and those in the exterior of an incomplete shell. in which case nucleons should be differentiated via their respective isounits.

A simpler representation that has considerable practical value is the following

(6.5) E_{tot} = {E_1 x E_2 x . . . x E_N}xn_4, E_k = Diag. (n_1^2, n_2^2, n_3^2)_k,

namely, it is characterized by the assumption of a unique isonormalized characteristic quantity n4 for the entire nucleus and the use of different space isounit for different nucleons.

The latter representation is important to disprove the belief held throughout this century that photons, gluons and other massless particles are exchanged "inside a nucleus² necessarily at the speed of light ³in vacuum² c, or that photons emitted by and measured from the outside of a nucleus with a given frequency have been necessarily emitted within the nucleus with that frequencies, and others mere personal beliefs (Sect. V-2). It is known today that these assumptions cannot be verified within "any" physical medium, whether a hadron, a nucleus or a star. In RHM, the maximal causal speed within a nucleus is C = c/n4 and NOT c. The frequency of photons is then shifted accordingly , thus requiring the use of Santilli's isospecial relativity [V-3,V-12] (see Sects. I.6 and V.4 for a rudimentary outline).

RHM today possesses numerous direct verifications in nuclear physics., some of that are outlined below. With the above main lines and a technical knowledge of the new mechanics, any interested researcher can study the isotopic completion of any given nuclear model.

**VI.3. PROBLEMATIC ASPECTS OF DISSIPATIVE NUCLEAR MODELS.** The comments
of the preceding section have been specifically intended for nuclear structures
considered as closed-isolated from the rest of the universe. As such, they
should be treated via the isotopic branch of RHM (Sect. 1.5 and 1.6).

A separate class of nuclear topics is given by current treatments of "dissipative nuclear processes", where dissipation can be due to a variety of occurrences, e.g., scattering of a particle on a nucleus considered as external, in which case the energy of the particle is not evidently conserved.

The visitor should be aware that contemporary treatments of dissipative nuclear
processes are afflicted by rather serious problems of physical consistency that
include:

a) Lack of physically acceptable observables because of either the lack of
Hermiticity of the quantities to be observed, or lack of
conservation of the Hermiticity under the time evolution of the theory when
it exists initially.

2) Lack of physically acceptable numerical predictions because of their
lack of
uniqueness and invariance under dissipative time evolutions, as one can see
from the variety of inequivalent dissipative models existing in the literature,
all with noninvariant special functions;

3) Clear violation of Einstein's axioms of the special relativity;

and other shortcomings much similar to those outlined in Sect. I.3 (see Ref. [I-1]).

The above occurrences suggest caution before accepting the numerical predictions of contemporary dissipative nuclear models, and establish the need for a structural revision of their treatment.

**VI.4. GENOTOPIC AND HYPERSTRUCTURAL BRANCHES OF RELATIVISTIC HADRONIC MECHANICS
FOR NUCLEAR PHYSICS.** Santilli [V-Ia] conceived and suggested the construction
of hadronic mechanics for the general case of NONHERMITEAN generalized units he
called "genounits",

(6.6) E^{>} = 1/S and {<}^E = 1/R = (E>)Ý, R = SÝ,

generally given by nowhere singular, real-valued and nonsymmetric matrices, with genotopic dynamical equations (9),

(6.7a) idA/dt = (A, H) = A<H - H>A = AxRxH - HxSxA,

(6.7b) idH/dt = (H, H) = Hx(R - S)xH /not= 0,

under which the Hamiltonian is "necessarily" nonconserved.

The above assumptions imply in a natural way TWO units and related products, one representing motion forward in time > and one motion backward in time <, thus yielding a natural axiomatization of irreversibility.

A first important aspect is that the genotopic branch of RHM, when formulated on the appropriate genomathematics (Web Page 18 and Sect. 1 of this Page), is as axiomatically consistent as RQM, thus resolving all shortcomings of conventional treatments of dissipative nuclear processes.

The best way to see this occurrence is by learning that, when treated in genospaces over genofields, the Hamiltonian is indeed conserved, dH/dt = 0 (see Web Page 18). Its nonconservation (6.7b) occurs only in the projection of the theory in the mathematics of RQM.

To understand the consistency of the theory, the interested researcher is suggested to verify that, when defined in the appropriate genohilbert spaces over genofields, the Hamiltonian H is HERMITEAN and thus OBSERVABLE at the initial time, and that such Hermiticity is preserved under the time evolution of the theory (when treated with the correct mathematics).

The visitor should meditate a moment on the fact that this is one of the few (if not the only) theory of dissipative nuclear processes in which the NONCONSERVED Hamiltonian is HERMITEAN and therefore OBSERVABLE. The Hamiltonians of current dissipative nuclear models are generally NONHERMITEAN and, therefore, NON-OBSERVABLE.

Similar occurrences hold also for other aspects, including the preservation of Einstein's axioms by the genotopic branch of RHM, for which we have to refer the interested visitor to the technical literature.

The construction of the genotopic branch of RHM in the needed explicit form is as simple as that of the isotopic branch. In fact, the forward and backward genounits are characterized by TWO different nonunitary transforms of the conventional unit of RQM,

(6.8) E^{>} = AxIxBÝ, {<}^E = BxIxAÝ, AxAÝ /not= I, BxBÝ /not= I.

The application of the above two nonunitary transforms, one for motion forward in time and the other for motion backward, to the totality of the aspects of conventional (conservative) nuclear models assures its generalization into an axiomatically consistent dissipative extension.

Note that the genotopic branch of RHM also originates at the purely classical level via the Historical Hamilton¹s equations, those WITH external terms), and then persists under genoquantization.

The visitor of this section should finally be aware of the additional multivalued hyperstructural branch of RHM [M-I-1,I-1] in which the genounits E> and <E are given by an ordered ³set² of nonhermitean elements, with consequential multivalued mathematics. To have an idea of the generalize character, we note that the multiplication ³2x2² yield 4 in RQM, while it yields a ³set of values² for RHM in multivalued realization (see Web Page 18).

The latter branch is under study for applications in biology (see Web Page 20) and it has not yet been applied to nuclear physics to our best knowledge. Nevertheless, its emergence in nuclear physics appears to be unavoidable due to the necessary multi-value character of the generalized unit of a nuclear structure, Eq. (6.4).

**VI.5. FIRST EXACT REPRESENTATION OF NUCLEAR MAGNETIC MOMENTS. **One of
the first applications and experimental verification of RHM in nuclear
physics is the
exact-numerical representation of total nuclear magnetic moments that, as indicated
earlier, is still lacking with RQM. The representation was first achieved in Ref.
[V-4] under a joint mutation of intrinsic magnetic moments as well as of angular
momentum and spin of nucleons. The more recent papers [V-2] achieve, apparently for
the first time, an exact representation of nuclear magnetic moments under a mutation
of intrinsic magnetic moments but conventional values of angular momentum and spin.

The fundamental assumption is the the historical hypothesis mentioned in Sect.VI-1, that is, the characterization of the nuclear constituents as extended and nonspherical charge distribution that experience a deformation when members of a nuclear structure. In turn, the deformation of these charge distributions imply a necessary alteration (called ³mutation²) of the intrinsic magnetic moments of protons and neutrons when member OF a nuclear structure. The latter mutation is then responsible for the deviation of the total nuclear magnetic moments from conventional quantum values (Schmidt's limits).

The above representation is merely done by characterizing nucleons via his isounit (6.1). The request that such new unit be the fundamental invariant, then mandates the unique and only use of RHM, with no known exception. In turn, this implies the use of the formalism of RHM, including isofields, isospaces, isoalgebras, isosymmetries, etc., all characterized by the common isounit (6.1) or (6.4), thus justifying a posteriory the mathematical research of Web Page 18.

The fundamental structure of the treatment is the Poincare'-Santilli isosymmetry P*(3.1) in its spinorial form [V-11g] also characterized by the same isounit that, in turn, characterizes an axiom-preserving generalization of the conventional Dirac's equation in which angular momentum and spin remain unchanged, but the intrinsic magnetic moment µ is mutated into the form

(6.9) µ* = µ x n_4/n_3.

Explicit calculations done in Ref.s [VI-2] then yield the numerical values for the deuteron

(6.9a) µ*^{Theor} = [g_p + g_n ] x n_4 x n_3 = µ^{Exp} = 0.857 ,

(6.9b) n_4^2 = 1.000, n_3^2 = 1.054, n_1^2 = n_2^2 = [ 1/n_3^2 ]^{1/2} = 0.974.

under the assumptions that the proton and the neutron have the same shape, mass and density.

As one can see, µExp is exactly represented by merely assuming that the charge distribution of the nucleons in the deuteron experiences a deformation of shape of about 1/2 %. Note that the mutation is of prolate character that implies a decrease of the (absolute value of the) intrinsic magnetic moment of nucleons as needed (because the representation by RQM is in excess).

Note also that the representation is of geometric character; it is independent from any assumed nucleon constituent; and it identifies the polarization of the constituent orbits that is needed for their compliance with physical reality. Corrections due to the value n4 =/ 1 and other aspects (e.g. the difference in densities between protons and neutrons) are of 2-nd or higher order and will not be considered in this first study. The application of the model to the exact representation of the total magnetic moment of tritium, helium and other nuclei is straightforward.

Note that, the mutation of the charge distribution of the nucleons is not a universal constant, because it depends on the local conditions, thus being generally different for different nuclei. This illustrates the need of having infinitely possible different isounits (6.1) as well as the inconsistency of any theory seeking a sort of ³universal deformation²of nucleons for all nuclear structures.

A criticism is that, since the n-parameters are too many, they can adjust anything. Such a criticism has no scientific value because the quantities nµ are not "parameters", but specific physical characteristics of nucleons. In fact, the space nk's characterize the actual shape of the charge distribution of the nucleons while n4 characterizes the density of the medium in which nucleons move. For the deuteron we have a 1/2% prolate deformation, while the density of the medium is close to that of the vacuum because of the relatively large mutual distance (for nuclear standards), with the understanding that different values hold for other nuclei.

At any rate, if the shape and density of nucleons are ³parameters², one must also consider as ³parameters² other characteristics, such as mass, spin, charge., etc., that is notoriously not the case.

Another criticism is that the model should derive the result within the context of quark theories. This criticism too has no scientific value because of the plethora of physical problematic aspects of quarks conjectures outlined in Sect. V-2. At any rate, the impossibility for quark conjectures on the hadronic structure to achieve an exact representation of the total magnetic moment of the deuteron is known among experts, as indicated earlier, because of the very small character of the orbits and correspondingly insufficient corrections under their polarization.

In reality, the appropriate scientific attitude is that quark theories should be modified in such a way to achieve an exact-numerical representation of the experimental value of the magnetic moment of the deuteron and other few-body nuclei.Such a possibility does indeed exist for the isoquark theory of Sect. V, and its study is recommended to interested researchers.

**VI.6. RECONSTRUCTION OF THE EXACT SU(2)-ISOSPIN SYMMETRY IN NUCLEAR
PHYSICS. ** As indicated earlier, Santilli¹s isotopies of Lie¹s theory
can be interpreted as methods for the exact reconstruction in isospace
over isofields of space-time and internal symmetries when believed to
be conventionally broken.

This capability has been illustrated in Sect. V for the reconstruction of the exact Lorentz symmetry for Nielsen-Picek ³Lorentz asymmetric metric², for the reconstruction of the exact Poincare¹ symmetry for the nonlocal and nonhamiltonian origin of the Bose-Einstein correlation, and other cases.

The reconstruction of the exact SU(2)-isospin symmetry in nuclear physics under electroweak interactions was proved in Ref. [V-11d]. The mechanism is so simple to appear trivial and consists in embedding all symmetry breaking terms in the isounit. It then follows that protons and neutrons have ³equal mass in isospace over isofields², thus possessing an exact isospin symmetry, while recovering conventional, physical values of mass under the isoeigenvalue or isoexpectation values.

The reconstruction OF the exact parity under weak interactions is proved in monograph [V-3b]. The reconstruction of the exact SU(3) symmetry has not been studied until now.

**VI.7. RECONSTRUCTION OF THE EXACT ROTATIONAL SYMMETRY FOR DEFORMED-OSCILLATING
NUCLEI. ** Another symmetry that is reconstructed as exact in nuclear
physics is that for the rotational symmetry O(3) for nonspherical or
oscillating nuclei, that was reached in the original proposal [V-11c]
of the isorotational symmetry O*(3).

The geometric origin of the reconstruction is the so-called ³isosphere², that is the perfect sphere in isoeuclidean space over isofields,

(6.10) [(x/n_1)^2 + (y/n_2)^2 + (z/n_3)^2] x E = E.

As one can see, when inspected in the ³conventional² Euclidean space (read: referred to the conventional unit 1), the above equation characterizes a spheroidal ellipsoid. However, in isoeuclidean space (read: referred to the isounit E) the above equation characterizes the perfect sphere because, jointly with the deformation of the semiaxes 1-k -> 1/nk-sq, there is the ³inverse² mutation of the related units 1k -> nk-sq, thus preserving the original perfect spheridicity (because the invariant is [Length]-sqx[Unit]-sq).

It is evident that in the above isosphere the nk¹s are not necessarily constant. The rotational symmetry is therefore reconstructed as exact also for variable, e.g., oscillating, shapes of nuclei. In turn, the occurrence has a number of intriguing applications, such as a novel representation of nuclear fission worked out by T. Gill [VI-5] as a decomposition of the unit, under the exact rotational symmetry. A number of other applications are under study.

**VI.8. NOVEL STUDIES ON NUCLEAR FORCES ** One of the most important
implications of RHM in nuclear physics is a re-inspection of the studies
conducted on nuclear forces during this century.

As it is well known, nuclear forces have been represented until now by adding new and new potentials to the Hamiltonian that have nowadays reached a considerable number. RHM implies the termination of this approach because it is contrary to the historical teaching by Lagrange and Hamilton on the impossibility for one single quantity to represent interior systems, as recalled in the first lines of this Web Page.

The novel scientific process initiated by RHM for nuclear forces is the identification of the terms that are truly of action-at-a-distance character, thus admitting a correct representation via a potential, and the identification of other terms that are of contact, zero-range nature or characterize other physical conditions for which a potential energy has no physical meaning. The latter terms should be represented with anything EXCEPT the Hamiltonian, otherwise it would be like granting potential energy to resistive forces experienced by bodies moving within physical media. RHM represents the latter effects via the generalization of the unit for geometric and axiomatic reasons discussed earlier.

Needless to say, any basic advance in the nuclear force implies corresponding advances in virtually all aspects of nuclear physics, including advances in the various models of nuclear structure, nuclear reactions, etc..

**VI.8. NOVEL STUDIES ON NUCLEAR CONSTITUENTS ** One of the most intriguing
implications of RHM in nuclear physics is a basically novel perspective on
the nuclear constituents.

As it is well known, the first conception of the nuclear structure was that of a bound state of protons and electrons. Such conception had to be abandoned because of numerous well known insufficiencies for much of the same reason that lead to the abandonment of Rutherford¹s conception of the structure of the neutron as a bound state of a proton and an electron (Sect. V-5).

What is lesser known is that these insufficiencies were all based on RQM, that is, on the (generally tacit) assumption that the nuclear structure can be ³entirely² represented via only one quantity, the Hamiltonian, under the sole presence of local-differential, action-at-a-distance, potential interactions.

The possibility that the nuclear structure has small, contact, nonlocal-integral, and nonpotential internal effects evidently implies a revision of the very foundations of the issue of nuclear constituents. In fact, the scientifically correct problem is the identification of the nuclear constituents under conventional, Hamiltonian forces, plus generally small NONUNITARY contributions.

A primary objective for the very construction of RHM was to show that, under the latter conditions, the neutron can indeed admit the proton and the electron as physical constituent, although in a mutated state characterized by the Poincare¹-Santilli isosymmetry P*(3.1) [V-11g].

The visitor is then suggested to meditate a moment on these results. They literally imply that the nuclear structure is indeed reducible to a generalized bound state of protons and electrons, with far reaching implications at all levels of nuclear physics. We here mention, for instance, the prediction of the subnuclear ³hadronic energy² (Sect. V-9 and Proposed Research Problems VI-3 and VI-4) that simply cannot be predicted by the RQM and related conventional conception on the nuclear structure.

As another illustration of the implications we mention the possibility that the deuteron has THREE constituents (two protons and one isoelectron), as the apparently only known possibility to explain the ³absence² in the deuteron of the lowest state with null spin (the absence of the singlet coupling of proton and neutron), that is one of the most intriguing and fundamental open problems of nuclear physics.

. The aspect that must be stressed again to minimize misrepresentations is that Rutherford¹s electron is not the conventional one, and is mutated in its intrinsic characteristics because immersed within hyperdense hadronic matter.

A number of basic studies are under way along the latter lines (some of that are under patenting), that we hope to report in this Web Page in some future upload. At this time we limit ourself to recall that RQM does indeed provide a good approximation of nuclear physics. As a result, the interpretation of nuclear constituents as being protons and neutrons was correct before the advent of RHM, and evidently remains correct after its appearance, provided that it is interpreted for what it is, S A FIRST APPROXIMATION of a rather complex physical reality.

The basically novel studies under way via RHM that reduce nuclei to a collection of protons and mutated electrons essentially constitutes a deeper layer of investigation, beyond the proton-neutron first approximation, according to conceptual lines not that different than those in the transition to quark constituents. By keeping in mind that physics is a discipline that will never admit ³final theories², the next expected layer of study is that based on the medium permitting the very existence of protons and electrons, the Ether (Sect. X).

As a final comment, we mention that the totality of notions presented in this section for nuclei considered as isolated from the rest of the universe can be uniquely and unambiguously derived from Santilli's isopoincare' symmetry P*(3.1) [V-11f,V-11g]. This includes quantitative studies on the nuclear structure as a non-Keplerian systems without the heaviest constituent in the center, the reduction of nuclei to protons and electrons in their mutated isotopic form inclusive of deformed intrinsic magnetic moments, the exact representation of total nuclear magnetic moments, the reconstruction of the exact rotational and isospin symmetries in nuclear physics, the prediction of the new subnuclear hadronic energy, the prediction of new forms of recycling nuclear waste, etc.

**PROPOSED RESEARCH VI-1: **Reinspect all terms of the nuclear force;
identify which term really admits a potential energy and which term does not;
represent the former with the Hamiltonian and the latter with the isounit;
identify the explicit form of the isounit under the latter representation
whose isoeigenvalues equations provide numerical results in agreement with
available experimental evidence.

**PROPOSED RESEARCH VI-2: ** Reinspect nuclear reactions under the
admission of a small nonlinear, nonlocal and nonunitary contribution due t
o mutual penetration of the charge distribution; study separately the case
of singlet and triplet couplings and verify that the former (latter) yield
a novel attractive (repulsive) effect; identify an example of a nuclear
reaction that is prohibited by the linear-local-potential RQM, but it is
indeed admitted by the covering nonlinear-nonlocal-nonunitary RHM; propose
specific experiments for the resolution of the alternative.

**PROPOSED RESEARCH VI-3: ** Assume that photons with the excitation
frequency 1.294 MeV do indeed imply the stimulated decay of the neutron
(Sect. V-9). Compute the flux of such photons that would imply the stimulated decay, say, of 50% of given radioactive nuclear waste, such as Ur-238, due to excess of repulsive Coulomb forces. Identify means for the production of the needed beam of excitation photons, e.g., via synchrotron radiation.

**PROPOSED RESEARCH VI-4: ** Assume that the excitation frequency of
1.294 MeV does indeed imply the stimulated decay of the neutron. Conduct
a systematic studies of all ³stable² isotopes that admit such a decay in
compliance with all conventional conservation and other laws on total
nuclear quantities, such as reaction (5.35) (see [V-31] for various other
possibilities). Compute the positive energy output in each of the admissible
reaction. Study the emerging two forms of ³hadronic energy² [V-31], i.e.: I)
compute the electric current generated as a result of capturing via a metal
shield all electrons generated in these stimulated decays for a given initial
flux of excitation photons ; and II) compute the additional heat produced by
said electrons in the metal shield.

**PROPOSED RESEARCH VI-7: ** Study total nuclear magnetic moments via
Santilli¹s model of the deuteron based on the isopoincare¹ symmetry [VI-2].
Identify the average shape of the charge distribution of nucleons, as well
as the average value of the maximal causal speed within nuclei, C = c/c4,
where c is the speed of light in vacuum.

**PROPOSED RESEARCH VI-8: ** Study total nuclear angular momenta via the
isotopic SU(2)-spin symmetry in its regular isorepresentations [V-11d]. Study
the connection with the isotopic model of magnetic moments. Identify a reaction
that is prohibited by the conventional theory of total angular momentum but
that is otherwise permitted by the isotopic covering of the same theory and
conventional values J = 0, 1/2, 1, ....

**PROPOSED RESEARCH VI-9: ** Reformulate nuclear dissipative processes via
the genotopic branch of hadronic mechanics and compare the results with the
prediction of conventional approaches.

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**REFERENCES OF SECT. VI: **

[VI-1] J. M. Blatt and V. F. Weiskopf, Theoretical Nuclear Physics, Wiley & Sons (1964) [VI-1a]; S. G. Bondarenko, et al., JINR Communication E4-95-440 [1995], Dubna, Russia [VI-1b]

[VI-2] R. M. Santilli, in Proceedings of the International Symposium On Large Scale Collective Motion of Atomic Nuclei, G. Giardina, G. Fazio and M. Lattuada, Editors, World Scientific, Singapore (in press); R.M. Santilli, Use of relativistic hadronic mechanics for the exact representation of total nuclear magnetic moments and the prediction of new recycling of nuclear waste, Preprint IBR-TH-97-S-039, submitted for publication.

[VI-3] C. N. Ktorides, H. C. Myung and R. M. Santilli, Phys. Rev. D 22, 892 (1980)

[VI-3] R. M. Santilli, in Deuteron 1993, V. K. Lukianov, Editor, JINR, Dubna, Russia (1994)

[VI-5] T. L. Gill, in New Frontiers of Hadronic Mechanics, T. L. Gill, Editor, Hadronic Press (1997) [5-6] R. M. Santilli, Intern. J. Phys. Vol. 4, p. 1 (1999) [5-7] R. M. santilli, J. New Energy, Vol. 4, issue no 1, pages 7-314 (1999).

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ADVANCES AND OPEN PROBLEMS IN SCATTERING THEORY

under preparation

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**VIII. PROPOSED NEW EXPERIMENTS
**

Prepared by the IBR staff (see[I-1] for details and references)

**PROPOSED EXPERIMENT 1**:The finalization of the deformability of the intrinsic
magnetic moment of neutrons under sufficiently intense external fields, as
theoretically studied by Eder and preliminarily measured by Rauch via neutron
interferometric techniques. This test is of evidently fundamental relevance
because: it can provide independent verification of the old hypothesis on the
alteration of conventional intrinsic magnetic moments of protons and neutrons
when bound in a nuclear structure, as apparently necessary for a representation
of total nuclear magnetic moments. The proposed measures can also establish the
notion of isoparticle that is at the foundation of the new structure model of
hadrons with physical constituents indicated earlier; it may permit new
technological advances, such as the design of new equipment for the recycling
of nuclear waste by the utilities themselves, thus avoiding their transportation
to and storage in a yet un-identified side; and other advances.

**PROPOSED EXPERIMENT 2**: Measure the difference of the redshift "component"
of the tendency toward the red of sun light at sunset and sunrise. This difference
is visible to the naked eye and it is predicted to have an isotopic origin. The
measures can evidently confirm or deny the validity of Santilli's isominkowskian
geometry within physical media such as our atmosphere, resolve the problem of the
origin of the large difference in redshifts of physically connected quasars and
galaxies, as well as identify the geometry most effective in astrophysics and
cosmology.

**PROPOSED EXPERIMENT 3**: Finalize the direct and indirect measures on
deviations from the Minkowskian geometry inside hadrons, such as the measures on
the behavior of the meanlives of unstable hadrons with energy,the Bose-Einstein
correlation and others. These measures are of such a fundamental character of
rendering conjectural any theory on the structure of hadrons, whether quarks of
isoparticles, prior to their scientific finalization in a form without theoretically
questionable assumption in the data elaborations.

**PROPOSED EXPERIMENT 4**: Measure the total cross section of the reaction of
photons on neutrons decaying into protons, electrons and neutrino to confirm or
deny the prediction by relativistic hadronic mechanics of a peak for photons with
1.294 MeV . This test can confirm or deny the new model of the hadronic structure
with physical constituents in in its most fundamental case, the synthesis of the
neutron from protons and electrons only as occurring in stars at their initiation.
An additional possible test is recommended for the reaction photons + pion-0 into
photons that is predicted to have a peak for photons of 67 MeV.

**PROPOSED EXPERIMENT 5**: Measure the gravity of positrons in horizontal
flight in Earth's field inside a suitably designed, sufficiently long and
shielded vacuum tube, that has been theoretically predicted by the isodual
theory of antimatter to experience antigravity and experimentally studied as
being within technical feasibility. The latter experiment too, if successful,
would have far reaching implications for all of science. As an indication, the
detection of antigravity would establish that contemporary mathematics, let alone
of theoretical physics (that based on the trivial unit +1) is inapplicable for
the treatment of antimatter.

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