Predicting the Binding Energies of the 1 s Nuclides with High Precision , Based on Baryons which Are Yang-Mills Magnetic Monopoles

In an earlier paper, the author employed the thesis that baryons are Yang-Mills magnetic monopoles and that proton and neutron binding energies are determined based on their up and down current quark masses to predict a relationship among the electron and up and down quark masses within experimental errors and to obtain a very accurate relationship for nuclear binding energies generally and for the binding of Fe in particular. The free proton and neutron were understood to each contain intrinsic binding energies which confine their quarks, wherein some or most (never all) of this energy is released for binding when they are fused into composite nuclides. The purpose of this paper is to further advance this thesis by seeing whether it can explain the specific empirical binding energies of the light 1s nuclides, namely, H, H, He and He, with high precision. As the method to achieve this, we show how these 1s binding energies are in fact the components of inner and outer tensor products of Yang-Mills matrices which are implicit in the expressions for these intrinsic binding energies. The result is that the binding energies for the He, He and H nucleons are respectively, independently, explained to less than four parts in one million, four parts in 100,000, and seven parts in one million, all in AMU. Further, we are able to exactly relate the neutron minus proton mass difference to a function of the up and down current quark masses, which in turn enables us to explain the H binding energy most precisely of all, to just over 8 parts in ten million. These energies have never before been theoretically explained with such accuracy, which leads to the conclusion that the underlying thesis provides the strongest theoretical explanation to date of what baryons are, and of how protons and neutrons confine their quarks and bind together into composite nuclides. As is also reviewed in Section 9, these results may lay the foundation for more easily catalyzing nuclear fusion energy release.


Introduction: Summary Review of the Thesis that Baryons Are Yang-Mills Magnetic Monopoles with Binding Energies Based on Their Current Quark Masses
In an earlier paper [1], the author developed the thesis that magnetic monopole densities which come into existence in a non-Abelian Yang-Mills gauge theory of non-commuting vector gauge boson fiel G ds  are synonymous with baryon densities.That is, baryons, including the protons and neutrons which form the vast preponderance of matter in the universe, are Yang-Mills magnetic monopoles.Conversely, magnetic monopoles, long pursued since the time of Maxwell, have always been hiding in plain sight, in Yang-Mills incarnation, as baryons, and especially, as protons and neutrons.
Maxwell's equations themselves provide the theoretical foundation for this thesis, because if one starts with the classical electric charge and magnetic monopole field equations (respectively, (2.1) and (2.2) of [1]):    and combines the magnetic charge Equation (1.2) with a Yang-Mills (non-Abelian) field strength tensor  is an N × N ma- which, like G F trix for a simple gauge group SU(N) ((2.3) of [1] one immediately comes upon the non-vanishing magnetic monopole ((2.4) of [1]): The question then becomes whether such magnetic monopoles (1.4) actually do exist in the material universe, and if so, in what form.The thesis developed in [1] is not only that these magnetic monopoles do exist, but that they permeate the material universe in the form of baryons, especially as the protons and neutrons observed everywhere and anywhere that matter exists.
Of course, t'Hooft [2] and Polyakov [3] realized several decades ago that non-Abelian gauge theories lead to non-vanishing magnetic monopoles.But their monopoles have very high energies which make them not suitable for being baryons such as protons and neutrons.Following t'Hooft, the author in [1] does make use of the t'Hooft monopole Lagrangian from (2.1) of [2] to calculate the energies of these magnetic monopoles (1.4).But whereas t'Hooft introduces an ansatz about the radial behavior of the gauge bosons  , the author instead makes use of a Gaussian ansatz borrowed from Equation (14) of Ohanian's [4] for the radial behavior of fermions.Moreover, the fermions for which this ansatz is employed enter on the very solid foundation of taking the inverse G I J     of Maxell's charge Equation (1.1) (essentially calculating the configuration space inverse ), and then combining this with the relationship J      0 J  that emerges from satisfying the charge conservation (continuity) equation    in Dirac theory.Specifically, it was found that in the low-perturbation limit, magnetic monopoles (1.4) can be re-expressed as a three-fermion system ((3.12) of [1]): Above,   i ; 1,2,3 i   are three distinct Dirac spinor wavefunctions which emerge following three distinct substitutions of G I -which captures the inverse of Maxwell's charge Equation (1.1) combined with Dirac theory-into the (1.4) magnetic monopole which utilizes the Yang-Mills field strength (1.3) in combination with Maxwell's magnetic monopole Equation (1.2).The detailed derivation of (1.5) from (1.4) also makes use of Sections 6.2, 6.14 and 5.5 of [5] pertaining to Compton scattering and the fermion completeness relation, and carefully accounts for mass degrees of freedom as between fermions and bosons.The quoted denominators    and "quasi commutators" in the above make use of a   compact notation developed and explained in Section 3 of [1], see specifically (3.9) and (3.10) therein.
Then, via Fermi-Dirac Exclusion, the author employed the QCD color group SU (3) C to require that each of the three   i  be SU (3) C vectors in distinct quantum color eigenstates R, G, B, which then leads in (5.5) of [1] to a magnetic monopole: This is similar to (1.5) but for the emergence of the trace.Associating each color with the spacetime index in the related   operator, i.e., , R G and    , and keeping in mind that Tr P  R G B is antisymmetric in all spacetime indexes, we express this antisymmetry with wedge products as         P . So the natural antisymmetry of a magnetic monopole  leads straight to the required antisymmetric color singlet for a baryon.Indeed, in hindsight, this antisymmetry together with three vector indexes to accommodate three vector current densities and the three additive terms in the  of (1.2) should have been a tip-off that magnetic monopoles would naturally make good baryons.Further, upon integration over a closed surface via Gauss'/Stokes' theorem, magnetic monopole (1.6) is shown to emit and absorb color singlets with the symmetric color wavefunction RR  GG BB  logical stability of these magnetic monopoles was estab-expected of a meson.And, in Section 1 of [1], it was shown how magnetic monopoles naturally contain their gauge fields in non-Abelian gauge theory via the differential forms relationship dd = 0 for precisely the same reasons rooted in spacetime geometry that magnetic monopoles do not exist at all in Abelian gauge theory.Thus, QCD itself deductively emerges from the thesis that baryons are Yang-Mills magnetic monopoles, and we began to associate monopole (1.6) with a baryon.
It was then shown in Sections 6 through 8 of [1] that these SU (3) monopoles may be made topologically stable by symmetry breaking from larger SU(4) gauge groups which yield the baryon and electric charge quantum numbers of a proton and neutron.Specifically, the topo-lished in Sections 6 and 8 of [1] based on Cheng and Li [6] at 472-473 and Weinberg [7] at 442.The proton and neutron are developed as particular types of magnetic monopole in Section 7 of [1] making use of SU(4) gauge groups for baryon minus lepton number B L  based on Volovok's [8], Section 12.2.2.The spon s symmetry breaking of these SU(4) gauge groups is then fashioned on Georgi-Glashow's SU (5) GUT model [9] reviewed in detail in Section 8 of [1].
By then employing the earlier-r taneou eferenced "Gaussian ansatz" from Ohanian's [4], namely ((9.9) of [1]): for the radial behavior of the fermion wavefunctions, of [1], the author us ner together with the t'Hooft monopole Lagrangian from (2.1) of [2] (see (9.2) of [1]) it became possible to analytically calculate the energies of these Yang-Mills magnetic monopoles (1.6) following their development into topologically stable protons and neutrons.Specifically, in Sections 11 and 12 ed the pure gauge field terms gauge L of the t'Hooft monopole Lagrangian to specify the e gy of the Yang-Mills magnetic monopoles, exclusive of the vacuum  , via (11.7) of [1]: We then made use in (1.8) of field strength tensors for protons and neutrons developed via Gauss'/Stokes' theorem from (1.6) in (11.3) and (11.4) of [1], respectively: (1.9) where  and d  are Dirac wavefunctions for up and uar de ectron mass is     down q ks, to duce three relationships which yielded remarkable concurrence with empirical data.First, we found in (11.22) of [1] that the el related to up and down quark masses according to: results as a natural consedimen quence of the three-sional integration (1.8) when the Gaussian ansatz for fermions is specified as in (1.7), and where the wavelengths in (1.7) are taken to be related to the quark masses via the de Broglie relation mc    .a Second nd third, we found in (12.12) and (12.13) of [1] that if one postulates the current mass of the up quark to be equal to the deuteron ( 2 H nucleus) binding energy based on 1) empirical concurrence within experimental errors and 2) regarding nucleons to be resonant cavities with binding energies determined in relation to their up and down current quark masses, then the proton and neutron each possess respective intrinsic, latent binding energies B (i.e., energies intrinsically available for nuclear binding): 9.812358 MeV So for a nucleus with an equal number of protons and neutrons, the average binding energy per nucleon is predicted to be 8.726519 MeV.Not only does this explain why a typical nucleus beyond the very lightest (which we shall be studying in detail here) has a binding energy in exactly this vicinity (see Figure 1 below), but when this is applied to 56 Fe with 26 protons and 30 neutronswhich has the distinction of using a higher percentage of this available binding energy than any other nuclide-we see that the latent available binding energy is predicted to be ((12.14) of [1]):  56 Fe nucleus, with a small 0.1570907% balance reserved for confining quarks within each nucleon.This means while quarks are very much freer in the nucleons of 56 Fe than in free nucleons (which also appears to explain the "first EMC effect" [10]), their confinement is never fully overcome.Confinement bends but never breaks.Quarks step back from the brink of becoming de-confined in 56 Fe as one moves to even heavier nuclides, and remain confined no matter what the nuclide.Iron-56 thus sits at the theoretical crossroads of fission, fusion and confinement.
This thesis that protons and neutrons are vities which emit and absorb energies that directly manifest their current quark masses will be central to the   evelopment of this paper.The foregoing (1.12) through ummation: with a non-Abelian Yang-Mills fie d (1.14) provide strong preliminary confirmation of this thesis, as well as of the underlying thesis that baryons are Yang-Mills magnetic monopoles.In this paper, we shall show how the observed binding energies of the 1s nuclides, namely of 2 H, 3 H, 3 He and 4 He, as well as the observed neutron minus proton mass difference, provide further compelling confirmation of the thesis that baryons are Yang-Mills magnetic monopoles which bind at energies which directly reflect the current quark masses they contain.
In ing non-Abelian gauge fields (1.3), taken together with Dirac theory and Fermi-Dirac Exclusion, are the governing equations of nuclear physics, insofar as nuclear physics centers around the study of protons and neutrons and how they bind and interact, and given that we were able to show in [1] that protons and neutrons are particular types of Yang-Mills magnetic monopoles.This theory is thus extremely conservative, based on combining together unquestionable foundational physics principles.
In essence, the purpose of this paper is to further develop the results from [1] into a theory of nuclear bindin hich we confirm by predicting the binding energies of the 1s nuclides as well as the neutron minus proton mass difference with very high precision, each on the order of parts per million.

Structured O Paper
In deriving the empirically-accurate binding energy relanships (1 which, when carefully considered, requires us to amend the Lagrangian in (1.8) in a slight but important way.This amendment, developed in Section 3, will reveal that the latent binding energies (1.12) and (1.13) actually employ the inner and outer tensor products of two 3 × 3 SU(3) matrices, one for protons, and one for neutrons.These matrices, and their inner and outer products, will be critical to the methodological development thereafter.
In section 4 we lay the foundation for being able to derive the binding energies of the 1s nuclides using the ea or the 4 He alpha bi parts in one million A ss excess rather th how these can be combined to ex-pr not only the accuracy of the re ical, because the po e results for 3 H, 3 He and 4 H y in Figure 11, in rlier-discussed postulate that the mass of the up quark is equal to the deuteron ( 2 H nucleus) binding energy, and the thesis extrapolated from this that the binding energies of nuclides generally are direct functions of the current quark masses which their nucleons contain.Specifically, in (4.9) through (4.11) infra, we develop two tensor outer products and their components which will be critical ingredients for expressing 1s binding energies as functions of up and down current quark masses.
Section 5 shows how this binding energy thesis leads directly to a theoretical expression f nding energy which matches empirical data to less than 3 parts in 1 million AMU.Exploring the meaning of this result, we see that this binding energy together with that of the 2 H deuteron are actually components of a (3 × 3) × (3 × 3) fourth rank Yang Mills tensor of which the 2 H and 4 He binding energies merely two samples.Thus, we are motivated to think about binding energies generally as components of Yang-Mills tensors.So the method for characterizing binding energies is one of trying to match up empirical binding energies with various expressions which emerge from, or are components of, these Yang-Mills tensors.In Section 6, we similarly obtain a theoretical expression for 3 He helion binding to just under 4 parts in 100,000 AMU as well as its characterization in terms of these Yang-Mills tensors.
Developing a similar expression for the 3 H triton to what ends up being just over three MU turns out to be less straightforward than for any of 2 H, 3 He and 4 He, and requires us to work with mass excess rather than binding energy.However, a bonus is that in the process, we are also motivated to derive an expression for the neutron minus proton mass difference accurate to just over 7 parts in ten million AMU.To maintain clarity and focus on the underlying research ideas, these results are summarized in Section 7, while their detailed derivation is presented in the Appendix.
Section 8 aggregates the results of Sections 5 through 7, and couches them all in terms of ma an binding energy.In this form, it becomes more straightforward to study nuclear fusion processes involving these 1s nuclides.
Section 9 makes use of the mass excess results from Section 8, and shows ess the approximately 26.73 MeV of energy known to be released during the solar fusion cycle entirely in terms of the up, down and electron fermion masses.This highlights sults for 2 H, 3 H, 3 He and 4 He binding energies and the neutron minus proton mass difference, but it establishes the approach one would use to do the same for other types of nuclear fusion, and for fission reactions.And, it vividly confirms the thesis that fusion and fission and binding energies are directly based on the masses of the quarks which are contained in protons and neutrons, regarded as resonant cavities.
But perhaps the most important consequence of the development in Section 9 is technolog ssibility is developed via this "resonant cavity" analysis that by bathing a store of hydrogen in gamma radiation at certain specified, discrete frequencies which are also defined functions of the up and down quark masses, one can catalyze nuclear fusion and perhaps develop more effective ways to practically exploit the promise of nuclear fusion energy release.
In Section 10, we take a closer look at experimental errors that still do reside in th e binding and the neutron minus proton mass difference, generally at parts per 10 5 , 10 6 or 10 7 AMU.We explain why the original postulate identifying the up quark mass exactly with the 2 H deuteron binding energy should be modified into the substitute postulate that the theoretical neutron minus proton mass difference is an exact relationship, and why the equality of the up quark mass and the deuteron binding energy is simply a very close approximation (to just over 8 parts in ten million) rather than an exact relationship.We then are required to adjust (recalibrate) all of the prior numeric mass and energy calculations accordingly, by about parts per million.As a by-product, the up and down quark masses become known with the same degree of experimental precision as the electron rest mass and the neutron minus proton mass difference, to ten decimal places in AMU.
Section 11 concludes by summarizing and consolidateing these results, laying out most compactl fra, how the thesis that baryons are Yang-Mills magnetic monopoles which fuse at binding energies reflective of their current quark masses can be used to predict the binding energies of the 4 He alpha to less than four parts in one million, of the 3 He helion to less than four parts in 100,000, and of the 3 H triton to less than seven parts in one million, all in AMU.And of special import, by exactly relating the neutron minus proton mass difference to a function of the up and down quark masses, we are enabled to predict the binding energy for the 2 H deuteron most precisely of all, to just over 8 parts in ten million.
What renders this work novel is 1) that the 1s light in (1.8), because of suppression of the Yang-Mills matrix indexes, nuclide binding energies and the neutron minus proton actually has an ambiguous mathematical meaning, and can be either an ordinary (inner product) matrix multiplication, or a tensor (outer) product.The outer product is the most general bilinear operation that can be performed on mass difference do not appear to have ever before been theoretically explained with such accuracy; 2) the degree to which this accuracy confirms that baryons are Yang-Mills magnetic monopoles with binding energies which are components of a Yang-Mills tensor and which are directly related to current quark masses contained in these baryons; 3) the finding that nuclear physics appears to be grounded in unquestionable conservative physics principles, governed by simply combining Maxwell's two classical equations into one equation using Yang-Mills gauge fields in view of Dirac theory and Fermi-Dirac Exclusion for fermions; and 4) the prospect of perhaps improving nuclear fusion technology by applying suitably-chosen resonances of gamma radiation for catalysis.

The Lagrangian of Nuclear Binding Energies
, while the inner product represents a contraction of the outer product which reduces the Yang-Mills rank by 2. When carefully considered, this provides an opportunity for developing a nuclear Lagrangian based on the t'Hooft's original development [2]  F F  down to rank two.In the sixth, final term, we the final terms in (3.1), (3.2)): here, in the final terms, we use . This highlights the st notational ambiguity in (1.8) as well as the difference ter  and inner matr ircum-between the ou ix products.Now, in general, the trace of a product of two square matrices is not the product of traces.The only c ance in which "trace of a product" equals "product of traces" is when one forms a tensor outer product using: and y a linear combination of both inner and outer products.And because (1.12) and (1.13) predict binding energies per nucleon in the range of 8.7 MeV and yield an extremely clo to 56 F energies, nature herself appears to be telling us that we need to combine inner and outer products in this way in order to match up with empirical data.This, in turn, gives us important feedback for how to construct our Lagran-(1.12)and To see this most vividly, we start with (11.8) and (11.9) from [1]: ment in Section 11 and (12.12) and (12.13) of [1], we can produce Equations (1.12) and (1.13) for the empiri-cally-accurate latent binding energies of neutron using linear combinations of inner and outer Yang-Mills matrix products, respectively, as follows:


Using these in (3.1) and (3.2) following the developre a proton and These now provide matrix expressions for intrinsic, latent binding energies of the proton and neutron, con- acted down to scalar energy numbers which specify th ing nuclear binding energies in general.
Contrasting (3.6) and (3.7) with (3.1) and (3.2), we see that in order to match up with the empirical data, the tent binding ener tr ese binding energies and match the empirical data very well.And it is from these, that we learn how to amend the Lagrangian in (1.8) to lay a foundation for consider-general form of a Lagrangian for the la gy of a nucleon, rather than (1.8), needs to be: Using this, we now start to amend the t'Hooft Lagrangian (9.2) of [1], reproduced below: to rewrite (3.9) in the Yang-Mills matrix form: (3.10) with (9.4) of [1] also written in compacted matrix form: the pure gauge Lagrangian term, because we know from (3.6) and (3.7) that this yields latent binding energies those empirically observed in nuclear physics.Thus, we in the pure ga y the latent nu ng energies, that ake (3.8).Based on this, we reconstruct the t'Hooft Lagrangian so uge terms specif clear bindi is, we choose to m very much in accord with take (3.10), introduce a factor of   in front of all the ordinary matrix products, subtract off a term AA BB F F  , introduce similarly-contracted te ywhere else, and so fashion the Lagrangian: It is readily seen ure gauge terms This simply restates th in Sections 11 and 12 of [1] in more form t ties formal eoretical expressions based on a Lagrangian   e results found al terms.But, i th and an energy very practical formula for deriving real, numeric, empirically-accurate ergies.A goo ample is (1.14) for B , the latent binding energy of B) via (3.13), but also the observed binding energi the 3 H triton, 3   2 0 B for the 3 He helion, an tantly given that it is a fundamental building block of the larger nuclei and many decay process, 4 B for the 4  Fe.
On the foregoing basis, we now show how to derive not only the latent, available binding energies (designnated es (which will be designated throughout as 0 B with a "0" subscript) for several basic light nuclides.Specifically, we now lay the foundation for deriving 3   1 0 B for 2 0 alpha, all extremely closely to the empirical da

Foundation for Deriving Observed Binding Energies of the 1s Nuclides
Our goal is to derive the observed, empirical binding energies for all nuclides with 2; 2 Z N   on a totally theoretical basis.We thereby embark on the unde d most imporset forth at the end of [1], to understand in de collections of Yang-Mills magnetic monopolesole collections we now understand to be when the monopoles are protons and neutrons-organize and structure themselves.

The empirical nuclear weights (masses A
Z M ) of the 1s nuclides are set forth below in Figure 2 (again, A = Z + N).Because we wish to do very precise calculations, and because nuclide masses are known much more precisely in u (atomic mass units, AMU) than in MeV due to the "relatively poorly known electronic charge" [11], we shall work in AMU.When helpful for illustration, we shall convert over to MeV via 1u = 931.494061(21)MeV/c 2 , but only after a calculation is complete.The data for these nuclides (and the electron mass below) is from [11] and/or [12], and is generally known to ten-digit precision in AMU with experimental errors at the eleventh and twelfth digits.For other nuclides not listed at these sources, we make use of a very helpful online compilation of atomic weights and isotopes at [13].Vertical columns list isotopes, horizontal rows list isotones, and diagonal lines link isobars of like-A.The nuclides with border frames are stable nuclides.The mass of the neutron is and the mass of the proton is The observed binding energies B 0 are readily calculated from the above via using the proton and neutron masses , a e 3 below nd are summarized in Figur nding energies will be denoted energies denoted simply already show (12.9) of [1] (again, the observed bi throughout as 0 B with a "0" subscript, while latent, theoretically-available binding B will omit this subscript).Now let's get down to business.We ed in and discussed in the introduction here, that by identifying the mass of the up quark with the deuteron binding energy via the postulate that 224566 MeV , we not only can establish very precise masses for the up and down quarks but also can explain the confluence of confinement and fission and fusion at 56 Fe in a very profound way, wherein 99.8429093% of the available binding energy goes into binding the 56 Fe nucleus and only the remaining 0.1570907% is unused for nucleon binding and so instead confines quarks.And, we extrapolated this to the thesis to be further confirmed here, that nucleons in general are resonant cavities fusing at energies reflective of their current quark masses.
So we now write this postulate identifying (defining) the up quark mass u with the observed deuteron binding energy , in notations to be employed here, in AMU, as: In AMU, the electron mass, which we shall also need, is: . (4.2)  We then use (1.11) (see also (12.10) of [1]) with (4.1) and (4.2) to obtain the down quark mass: 3) It will also be helpful in the discussion following to use: see, e.g., (1.12) and (1.13) in which this first arises.
We then use the foregoing in (1.12) and (1.13) to calculate the latent, available binding energy of the proton and neutron, designated B without the "0" subscript: for any nuclide of given Z, N. For the nuclides in Figures 2 and 3, this theoretically-available, latent binding energy B, is predicted to be: see Figure 4.
Taking the ratio of the empirical values in Figure 3 over the theoretical values in Figure 4 and expre these as percentages then yields: see Figure 5.
So we see, for example, that the 4 He alpha nucleus uses about 81.06% of its total available latent binding sus released for nuclear binding dependent on the particular nuclide in question.
As a point of comparison, we return to 56 Fe which has the highest percentage of used-to-available binding energy of any nuclide.Its nuclear weight 2% lar e proton, neutrons will in general find it easier to bind into a he by a factor of 28.42%.Simply put: neutrons available binding energy to the table than protons and so ar 1 284225880325 .  The above ratio explains the long-observed phenomenon why heavier nuclides tend to have a greater number of neutrons than protons: For heavier nuclides, because the neutrons carry an energy available for binding which is about 28. 4 ger than that of th (4.8) avy nucleus bring more e more welcome at the table.The nuclides running from 31 Ga to 48 Cd tend to have stable isotopes with neutron-to-proton number ratios (N/Z) roughly in the range of (4.8).Additionally, and likely for the same reason, this is the range in which, beginning with 41 Nb and 42 Mo, and as the N/Z ratio grows even larger than (4.8), one begins to see nuclides which become theoretically unstable with regard to spontaneous fission., and one for the neutron, N ABCD E , according to: From the above, one can readily obtain the eighteen non-zero diagonal outer product components (nine for the proton and nine for th This is why (4.1), (4.3) and (4.4) will be of interest in the development following.With the "toolkit" (4.9) to (4.11) we now have all ingredients needed to closely deduce the empirical binding energies in Figure 3 on totally theoretical grounds.We start with the alpha, 4 He.ers, th examine theoretical reasons why this may ma .If in fact this numerical coincidence is not just a coincidence but has real physical meaning, this would mean the empirical binding energy 4   2 0 B of the alpha is predicted to be (4.7) for 4  2 B , 2 m u d m , that is:

Prediction of the
where we calculate using , is extremely small, with these two values, as noted just above for the reserved energy, differing from one another less than 3 parts in 1 .1)to ng energy to theo retical reasons why In [1], a key postulate was to identify the mass of the down quark with the deuteron binding ener here in which we again reviewed that iden yond the numerical concurrence, a theoretical explana- gy, see (4.1) tification.Betion is that in some fashion the nucleons are resonant cavities, so the energies they release (or reserve) during fusion will be very closely tied to the masses/wavelengths of the contents of these cavities.But, of course, these "cavities" contain up quarks and down quarks, and their masses are given in (4.1) and (4.3) together with the u d m m construct in (4.4), and so these will specify preferred "harmonics" to determine the precise energies which these cavities resonantly release for nuclear binding, or hold in reserve for quark confinement.
We also see that components of the outer products     . tually the 11 22 componen outer product ABCD E , in linear combination with traces of ABCD E .

That is, this binding energy is a component of a Yang-Mills tensor!
This is reminiscent, for example, of the Maxwell Ten- This totally theoretical Yang-Mills tensor expression yields the alpha binding energy to 2.26 parts per million.
In this form, ( 53) tells us that the alpha binding energy is ac , which provides a suitable analogy.The on-diagonal components of the Maxwell tensor contain both a component term and a trace term just like (5.3).For example, for the 00 term 00 0 0 3).The off-diagonal components of the Maxwell tensor, however, do not include a trace term.For example, for the 01 term in Maxwell, if we consider , the Minkowski metric   filters out the trace.This latter, off-diagonal an   alogy allows us to represent (4.1) for the deuteron as a tensor component without a trace term, for example, as (see (4.11)):

.4) r binding energies as compone
So we now start to think about individual observed nuclea nts of a fourth rank Yang Mills tensor of which (5.3) and (5.4) are merely two samples.Thus, as we proceed to examine many different nuclides, we will want to see what patterns may be discerned for how each nuclide fits into this tensor.
Physically, the alpha parti otons two neutrons, in terms of q nd quarks enter (5.3)One other physical observation is also very noteworthy, and to facilitate this discussion we include the wellknown "per-nucleon" binding graph as Figure 1 above.One perplexing mystery of nuclear physics is why there large "chasm" between bindi ies for the 2 H, 3 H and 3 He nuclides, and the biding energy of the 4 He nuclide which we have now predicted to within parts ontrasting (5.3) for 4 He with (5.4) for 2 H, we see that for the l teron, we "start at the bottom" with 1   1 0 B 0  for 1 H (the free proton), an n "add" 2 B 0  rth of energy .But as we learned in Section 12 of [1] and have reiterated here, any time we do not use some of the latent energy for nuclear binding, that unused energy remains behind in reserve to confine the quarks in a type of nuclear see-saw.
So what we learn is that for the alpha particle, a total of is held in reserve to confine the quarks, while the majority balance is released to bind the nucleons to one another.In contrast, for the deuteron, a total of .u   is released for inter-nucleon binding while the majority balance is held in reserve to confine the quarks.Now to the point: for some nuclides (e.g. the deuteron) the question is: how much energy is released from quark confinement to bind nucleons?This is a "bottom to top" nuclide.For uclides (e.g., the alpha) the question is: how gy is reserved out of the theoretical maximum available, to confine quarks.This is a "top to bottom" nuclide.For top to bottom nuclides, there is a scalar ls tensors.For bottom to other n much ener trace in the Yang-Mil top nuclides or analogy, one may suppose that somewhere there is not.Using the Maxwell tens there is a Kronecker delta A B  and/or AB CD  which filters out the trace from "off-diagonal" terms and leaves the trace intact for "ondiagonal" terms.In this way, the "bottom to top" nuclides are "off-diagonal" tensor components and the "top to bottom" nuclides are "on diagonal" components.In either case, however, the "resonance" for nuclear binding is established by the components of the N ABCD E , which are , m m in some combination and/or integer multiple.And, as regards Figure 1 above, the chasm between the lighter nuclides and 4 He is explained on the basis that each of 2 H, 3 H and 3 He are "bottom to top" "o 4 ff-diagonal" nuclides, while He, which happens to fill the 1s shells, is the lightest "top to bottom" "on-diagonal" nuclide. 2 H, 3 H and 3 He start at the bottom of the nuclear see-saw and move up; 4 He starts at the top of the see-saw and moves down.
To amplify this point, in Figure 7 below we peek ahead at some heavier nuclides, namely, 3 Li and 4 Be.Using a nuclear shell model similar to that used for electron structure, all nucleons in the 4 He alpha are in 1s shells.The two protons are spin up and down each with 1s, as ar the two ne trons.As soon as we add one more nucleon, by Exclusion, we must jump up to the 2s shell, which admits four more nucleons and can reach up to 8 4 Be before we must make an incursion into the 2p shell.
We note immediately from the above-which has been noticed by others before-that the binding energy 8 Be is almost twice as large as that of the alpha particle, to just under one part in ten thousand AMU.Specifically: This is part of why 8 Be is unstable and invariably decays almost immediately into two alpha particles ( 9 Be is the stable Be isotope).But e u of particular interest here, is to thre subtract off the alpha 4   2 0 B 0 030376586499 .u  from each of the Li and Be isotopes, and compare them side by side with the non-zero binding energies from H and He.The result of this exercise is in Figure 8  B rn from the other three nuclides in the 1s square.This means that three of the four nuclides in the 2s square start f-diagonal" just as in 1s, and the fourth, 8 Be, starts "on diagonal" "at the top."But, in the 2s square, the "bottom" is th pa  0376586499 .
u.So the filled 1s shell provides a " below the 2s shell; a non-ze minimum ennderpinning binding in the 2 e. least from the 1s and 2s e nuclides of 4   2 0Predicted B 0.030379212155u  for the alpha in (5.1), in contrast to 4   2 0 B 0.030376586499u  from the empirical data, is an exact match in AMU through the fifth decimal place, but is still not within experimental errors.Specifically, the alpha mass listed in [12] and shown in Figure 2 is 4.001506179125(62)u, which is accurate to ten decimal places in AMU.Similarly, the proton mass 1.007276466812(90)u and the neutron mass 1.00866491600(43)u used to calculate 4   2 0 B are accurate to ten and nine decimal places respectively in AMU.So the match between 4   2 0Predicted

B
and the empirical B to under 3 parts per million is still not within the experimental errors beyond five decimal places, because this energy is known to at least nine decimal places in AMU.Consequently, (5.1) must be regarded as a very close, but still approximate relationship for the observed alpha binding energy.Additionally, because (5.1) is based on (4.1), wherein the mass of the up quark is identified with which is the deuteron binding energy, the question must be considered whether this identification (4.1), while very close, is also still approximate.
Specifically, it is possible to make (5.1) for the alpha into an exact relationship, within experimental errors, if we reduce the up quark mass by exactly ε = 0.000000351251415u (in the seventh decimal place), such that: And it apth full shells are "diagonal" tensor components and all others are off diagonal.The see-saw for 2s is elevated so its bottom is at the top of the 1s see-saw.
It is also important to note that as we consider much heavier nuclides-and 56 Fe is the best example-even more of the energy that binds quarks together is released from all the nucleons.For 56 Fe, calculating from the discussion prior to (4.8), the unused U binding energy cond by all 56 nucleons totals only 0.00082662u.But in Figure 6 we saw that 0.00709663u of the 4 He binding energy is unused.Much of this, therefore, is clearly used by the time one arrives at 56 Fe.So, almost all the binding energy that is reserved for quark confinement for lighter nuclides becomes released to bind together heavier nuclides, with peak utilization at 56 Fe.That is, by the time an 56 Fe nuclide has been fused together, much of the binding energy previously reserved in the 1s and 2s shells to confine quarks has been released, and this contributes to overall binding for the heavier nuclides.One may thus think of the unused binding energy in lighter nuclides as a "reservoir" of energy that will be called upon for binding together heavier nuclides.For nuclides heavier than 56 Fe, the used-to-available percentage, cf. Figure 1, tacks downwards again, and more energy is channeled back into quark confinement and less into nuclear binding.So while quark confinement is "bent" to the limit at 56 Fe, with almost all latent binding energies see-sawed into nucleon binding rather than quark confinement, quark confinement can never be "broken." Finally, before turning to 3 He in the next section, let us comment briefly on experimental errors.The prediction relationship if we make (4.1) for the up quark into an approximate relationship, or vice versa, but not both.So, should we do this?
A further clue is provided by (5.5), whereby the empirical 8   4 0 B B 2  is a close but not exact rat al place n can ge near gard (4.1) identifying the up quark mass with the deuteron binding energy to be an exact relationship, and to regard (5.1) for the alpha to be an approximate relationship that still requires some tiny correction in the sixth decimal place.Similarly, as we develop other relationships which, in light of experimental errors, are also close but still approximate, we shall take the view that these relationships too, especially given (5.5), will require higher order corrections.Thus, for the moment, we leave (4.1) intact as In section 10, however, we shall show why (4.1) is not an exact relationship but is only approximate to about 8 parts per ten million AMU.But this will be due not to the closeness of the predicted-versus-observed energies for the alpha particle, but due to our being able to develop a theoretical expression for the difference , but still approximate relationship.This close io is not a comparison between a theoretical prediction and empirical observation; it is a comparison between two empirical data points.So this seems to suggest, as one adds more nucleons to a system and makes empirical predictions such as (5.1) based on the up and down quark masses, that higher order corrections (at the sixth decim in AMU for alpha and the fifth decimal place in AMU for 8   4 0 B ) will still be needed.So because two-body systems such as the deutero nerally be modeled ly-exactly, and because a deuteron will suffer less from "large A = Z + N corrections" than any other nuclide, it makes sense absent evidence to the contrary to re an exact relationship.actually M n M p  between the observed masses of the free utron and t ne he free proton to better than one part per million AMU.

Prediction of the Helion Nuclide Binding
Energy to 4 Parts in 100,000 Now, we turn to the 3  2 He nucleus, also referred to as the helion.In contrast with the alpha and the deuteron already examined which are integer-spin bosons, this nucleon is a half-integer spin fermion.Knowing as pointed out after (5.4) that we will "start at the bottom" of the see-saw for this nuclide, and knowing that our toolkit for constructing binding energy predictions is , , m m m m , it turns out after some trial and error exercises strictly with these energies that we can make a fairl ose prediction by setting:

 
The empirical energy from Figure 3, in comparison, is 3 2 0 B 0.008285602824u  , so that: While not quite as close as (5.2) for the alpha particle, this is still a very clos 0 008323342076 0 008285 .u .u tch to just under 4 parts in 10 n ABBA , then referring to (4.9), we find that:   e ma 0,000 AMU.But does this make sense in light of the outer products (4.9), (4.10)?
If we wish to write (6.1) in the manner of (5.3) a d (5.4) in terms of the components of an outer tensor product (AA index summation) of one of the matrices in (4.9), times a u m taken from the 33 (or possibly 22) diagonal component of the other matrix in (4.9).The use in (6.3) of P E from (4.9) rather than of N E from (4.10), draws from the fact that we need the AA trace to be 2

So the expression
, and not 2 as would otherwise occur if we used (4.10).S here, the empirical data clearly causes us to use P E om the from the neutron matrix in (4.10).We also note that physically, 3 He has one more proton than neutron.This is a third data point in the Yang-Mills tensor for nuclear binding.

Prediction of the Triton Nuclide Binding
Energy to 3 Parts in One Million, and the Neutron minus Proton Mass Difference to o fr proton matrix in (4.9) rather than N E

Parts in Ten Million
Now we turn to the 3 1 H triton nuclide, which as shown in Figure 3, has a binding energy 3   1 0 B 0 009105585412 .u  , and as discussed following (5.4), is a "bottom to top" nuclide.As with the alpha and the helion, we use the energies from components of the outer products ABCD E , see again (4.9) to (4.11).However, following careful trial and error consideration of all possible combinations, there is no readily-apparent combination of , , , which is the observed 3 1 H binding energy.But all is not lost, and much more is found: When studying nuclear data, there are two interrelated ways to formulate that data.First, is to look at binding energies as we have done so far.Second, is to look at mass excess.The latter form ach that enables us to match up the empirical binding data for the triton to the ulation, mass excess, is very helpful when studying nuclear fusion and fission processes, and as we shall now see, it is this appro , , , 2π that we have ployed already successfully em for the deuteron, alpha, and helion.As a tremendous bonus, we will be able to derive a strictly theoretical expression for the observed, empirical difference: between the free, unbound neutron mass . u and the free, unbound proton mass , see Figure 2. The derivation of the 3 He binding energy and the neutron minus proton mass difference is somewhat involved, and so is detailed in the Appendix.But the results a follows: For the neutron minus proton mass differen (A15), also using (1.11), we obtain: g energy in (A17), we use th 0.001389166099u  which differs from the empirical (7.1) by a mere 0.000000716911u , or just over seven parts per ten million!And for the 3 He bindin as in (5.3), (5.4) and (6.3), may be written as: As earlier noted following (5.4), there will be some flexibility in these tensor component assignments until we develop a wider swathe of binding energ

Mass Excess Pred
the "1s square" and start to discern the wider patterns.

With the foregoing, we have now reached our goal o ducing precise theoretical expressions for all of the 1s ding energies, solely as a function of elementary feron masses. In the process, w like-expression for th eutron-proton mass difference!
From here, after consolidatin our binding energy results and expressing them as mass excess in Section 8, we examine the solar fusion cycle in Section 9, including possible technological implications of these resu ts for catalyzing nuclear fusion.In Section 10 we again focus on experimental errors as we did at the end of Section 5, and explain why (7.2) should be taken as an exa retical relationship with the quark masses and bi then slightly recalibrated.

ictions
Let us now aggregate some of the results so far, as well as those in the Appendix.First of all, let us draw on (A4), and use (A14) and the neutron minus proton mass difference (7.2) to rewrite (A4) as: Specifically, we have refashioned (A4) to include one proton mass and two neutron masses, because the 3  1 H triton nuclide in fact contains one proton and two neutrons.Thus,   over the mass they possess when fused into a triton, expressed equal in Similarly for heliu via a negative number as a fusion mass loss.This is magnitude and opposite in sign to binding energy (7.3).
m nuclei, first we use (A5) to write: We then place 3  2 M on the left and use (6.1) to write: is the fusion mass loss for the helion, also equal and opposite to binding energy (6.1).
Next, we again use (A5) to write: Combining this with (5.1) then yields: The fusion mass loss for the alpha-much larger than for the other nuclides we have examined-is given by the lengthie 13 SciRes.
r terms after M p M n  .Agai equa ha binding energy with terms consolidated above.via (A5), it is easy to n, this is in (5.1), l and opposite to the alp Finally, from (4.1), deduce for the deuteron, that: to of this relationship is as follows:

Energy
The mass equivalent yield alpha particles plus protons, which protons then are available to repeat the cycle starting at (9.1): V, which is also a well-known energy from solar fusion studies.
g. [14]), the reaction he two 3 He which 8003u Now, as is well known (see, e. (9.4) must occur twice to produce t 2 are input to (9.7), and the reaction (9.1) must occur twice to produce the two 2  1 H which are in turn input to (9.4).So pulling this all together from (9.1), (9.4) The above shows at least two things.First, the total energy of approximately 26.73 MeV leased during solar fusion is expresse ed!This portends the ability to do the same for other types of fusion and fission, once the analysis of this paper is exnded to larger nuclides Z > 2, N > 2.
ons as resonant cavities w more practical, because (9.8) tells us the precise that go into releasing the total 26.73 MeV of energy in the above.In particular, if one wanted to create an artificial "sun in a box," one would be inclined to amass a store of hydrogen, and subject that hydrogen store to g h In the above, we have explicitly sho fre ap h.So, what do we learn?If the nucleons are regarded as resonant cavities and the ener pend on the masses of their current quarks as is made ve and harmonics highlighted in (9.9) and (9.10 for harmonic fusion is to subject a hydroge high-fre proximate of with the v ill catalyze fusion by perhaps reducing the amount of heat that is required.In present-day approaches, fusion reactions are trigge heat generated from a fission reaction, and would be to reduce or eliminate this need for such high as, but not limited to, Compton backscattering and any other methods which are known at present or may become known in the future for producing gamma radiation, it would also be necessary to provide substantial shielding against the health effects of such radiation.The highest energy/smallest wavelength component, 6  29 44MeV 6 69F d m . .known to be red entirely in terms of a theoretical combination of the up and down (and optionally electron) masses, with nothing else add te Secondly, because the results throughout this paper seem to validate modeling nucle ith energies released or retained based on the masses of their quark contents, this tells us how to catalyze "resonant fusion" which may make fusion technology resonances amma radiation at or near the specified discrete ener- gies that appear in (9.8), so as to facilitate resonant cavity vibrations at or near the energies required for fusion to occur.Specifically, one would bathe the ydrogen store with gamma radiation at one or more of the following energies/frequencies in combination, some without, and some with, the Gaussian   wn each basic quency/energy which pears in the second, third or fourth lines of (9.8) as well as harmonics that appear in (9.8).Also, one should consider frequencies based on the electron mass and its wavelengt gies at which they fuse dery evident by (9.8), and given the particular energies ), the idea n store to quency gamma radiation at least one the frequencies (9.9), (9.10), iew that these harmonic oscillations w red using one goal heat and especially the need for any fissile trigger.That is, we at least posit the possibility-subject of course to laboratory testing to confirm feasibility-that applying the harmonics (9.9), (9.10) to a hydrogen store can catalyze fusion better than known methods, with less heat and ideally little or no fission trigger required.
Of course, these energies in (9.9), (9.10) are very high, and aside from the need to produce this radiation via known methods such   , is e energetic and would be very difficult to shield (and to produce), but this resonance arises from (9.8) which is for the final Not only is this easiest to produce because its energy is the lowest of all the harmonics in (9.9) and (9.10), but it is the easiest to shield and the least harmful to humans.
Certainly, a safe, reliable and effective method and associated hardware for producing energy via fusing protons into deuterons via reac (9.1), and perhaps tion nd deuterons into lions as in one of the ha onics (9.9), (9.10) into a hydrogen store perhaps in combination with other known fusion methods, while insufficient to create the "artificial sun" modeled above if one foregoes the further fusing protons a he (9.4), by introducing at least rm final alpha production in (9.7), would nonetheless represent a welcome, practical addition to sources of energy available for all forms of peaceful human endeavor.

Recalibration of Masses and Binding Energies via an Exact Relation the Neutron minus Proton Mass Difference
At the end of Section 5, we briefly commented on experimental errors.As between the alpha particle and the deuteron, we determined it was more sensible to associate the binding energy of the deuteron precisely with the mass of the up quark, thus making the theoretically-predicted alpha binding energy a close but not exact match to its empirically observed value, rather than vice versa.But the prediction in (7.2) for the neutron minus proton mass difference to just over 7 parts in ten million is a very different matter.This is even more precise by half an order of magnitude than the alpha mass pred and given the fundamental nature of the relationship for which is central to beta-decay, we now argue why (7.2) should be taken as an exact relationship with all other relationships recalibrated accordingly, so that now the up quark mass will still be very close to the deuteron binding energy, but will no longer be exactly equal to this energy.
First of all, as just noted, the

   
M n M p  mass difference is the most precisely predicted relationship of all the relationships developed above, to under one part per million AMU.Second, we have seen that all the other nuclear binding energies we have predicted are close ap a preciselykn a basic sense, the deutero proximations, but not exact, and would expect that this inexactitude will grow larger as we consider even heavier nuclides, see, for example, 8 Be as discussed in Figures 7  and 8. So, rhetorically speaking, why should the deuteron be so "special," as opposed to any other nuclide, such that it gets to have an "exact" relation to some combination of elementary fermion masses while all the other nuclides do not?Yes, the deuteron should come closest to the theoretical prediction (namely the up mass) of all nuclides, because it is the smallest composite nuclide.Closer than all other nuclides, but still not exact.After all, even the A = 2 deuteron should suffer from "large A = Z + N" effects even if only to the very slightest degree of parts per ten million.Surely it should suffer these effects more than the A = 1 proton or neutron.
Third, if this is so, then we gain a new footing to be able to consider how the larger nuclides differ from the theoretical ideal, because even for this simplest A = 2 deuteron nuclide, we will already have own deviation of the empirical data from the theoreticcal prediction, which we may perhaps be able to extrapolate to larger nuclides for which this deviation cer-tainly becomes enhanced.That is, the deviations between predicted and empirical binding data for all nuclides becomes itself a new data set to be studied and hopefully explained, thus perhaps providing a foundation to theoreti-cally eliminate even this remaining deviation.
Fourth, in n, which is one proton fused to one neutron, has a mass which is a measure of "neutron plus proton," while

   
M n M p  to be exact relationship, with the chips falling where they may for all other relatio act relationship which drives all others, is: nships, including the deuteron binding energy.Now, the deuteron binding energy is relegated to the same "approximate" status as that of all other compound polynuclides, and only the proton and neutron as distinct mono-nuclides get to enjoy "exact" status.
Let us therefore do exactly that.Specifically, for the reasons given above, we now abandon our original pos- tulate that the up quark mass is exactly equal to the deuteron binding energy, and in its place we substitute the postulate that (7.2) is an exact relationship, period.That is, we now define, by substitute postulate, that the ex Then, we modify all the other relationships accord-ingly.
The simplest way make this adjustment is to modify the original postulate (4.1) to read: and to then substitute this into (10.1)with ε taken as very small but unknown.This is most easily solvable numerically, and it turns out that 0 000000830773 ε .u   , which is just over 8 parts in ten million u.That is, sub-0 000000830773 .u stituting ε   the following critical mass/energies into (10.2),then using (1.11) to derive the down quark mass, then substituting all of that into (10.1),will make (10.1)exact through all twelve decimal places (noting that experimental errors are in the last two places).
As a consequence,  Additionally, this will slightly alter the binding energies that were predicted earlier.The new results are as follows (contrast (5.1), (6.1) and (7.3) respectively):

B
to be equal to the mass of the up quark, but because the mass of the up quark has now been slightly changed because of our substitute postulate, the observed energy, which is 2 1 0 B  .002388170100u, will no longer be exactly equal to the predicted energy (10.11).Rather, we will now have M n M p  difference in (10.1).As a bonus, the up and down quark masses now become known cision in AMU, with experimental errors in the 11th and 12th digits, which is inherited from the precision with which the electron, proton and neutron masses are known.
One other point is very much worth noting.With an entirely theoretical, exact expression now developed for the neutron min s difference via (10.1),we start to target the full, dressed proton and neutron masses themselves.Specifically, it would be extremely desirable to be able to specify the proton and neutron masses as a function of the elementary up, down, and electron fermion masses, as we have here with binding energies.Fundamentally, by elementary algebraic p to ten-digit pre us proton mas rinciples, takin rst time, we now have an exact theoretical expression for the difference between these masses.But we still lack an independent expression related to their sum.
Every effort should now be undertaken to fi relationship related to the sum of these masses.In all likelihood, that relationship, which must inherently explain the natural ratio just shy of 1840 between the m of about 420 and 190 involving the up and down m those terms which involve the vacuum g each of the proton and neutron masses as an unknown, we can deduce these masses if we have can find two independent equations, one of which contains an exact expression related to the sum of these masses, and the other which contains an exact expression related to the difference of these masses.Equation (10.1) achieves the first half of this objective: for the fi nd another asses of the nucleons and the electron, and/or similar ratios asses, will need to emerge from an examination of the amended t'Hooft Lagrangian terms in (3.10) which we have not yet explored, particularly  .While analyzing olve differences.Wha bers for result referenced for The mass loss (negative m Section 8 which was very amining the solar fusion cycle negative (positive) of what is s just considered the binding energies and mass excess and nuclear reactions as we have done here is a very valuable exercise, the inherent limitation is that all of these analyses inv t is needed to obtain the "second" of the desired two independent equations, are sums, not differences (Note: the author lays the GUT foundation for, and then tackles this very problem, in two separate papers published in this same special issue of JMP).

Summary and Conclusion
Summarizing our results here, we now have the following theoretical predictions for the binding energies in  ing energy for the 2 H deuteron most precisely of all, to just over 8 parts in ten million.These energies as well as the neutron minus proton mass difference do not appear to have ever before been theo-gies in Figure 9, in AMU, using the recalibrated (10.8) through (10.11), are no ed to be: see Figure 10.These theoretical predictions should be carefully compared to the empirical values in Figure 3. Indeed, subtracting each entry in Figure 3 from en mmarize our results for all of the 1s nuclides in Figure 11.
ows how much each predicted binding energy differs from observed empirical binding energies.As has been reviewe f these predictions is accurate to under four parts in 100,000 AMU ( 3 He has the largest difference).Specifically: we have now used the thesis that baryons are resonant cavity Yang-Mills magnetic monopoles with binding energies reflective of their current quark m tically explained with such accuracy, and each of the foregoing energy predictions is mutually-independent from all the others.So even if any one prediction is thought to be nothing more than coincidence, the odds against five indepe ns on the order of 1 part in 10 5 or better being mere coincidence exceed 10 25 to 1.This is not mere coincidence!This leads to the conclusion that the underlying thesis that baryons generally, and neutrons and protons especially, are re asses to predict the binding energies of the 4 He alpha to under four parts in one million, of the 3 He helion to under four parts in 100,000 and of the 3 H triton to under seven parts in one million.Of special import, we have exactly related the neutron minus proton mass difference-which is central to beta decay-to the up and down quark masses.This in turn enables us via the substitute postulate of Section 10 to predict the bind-ons and loped in [1] and further amplified here, establishes a basis for finally "decoding" the abundance of known data regarding nuclear masses and binding energies, and by

Figure 1 .
Figure 1.The empirical binding energy per nucleon of various nuclides.
simple s ld strength (1.3), Yang Mills magnetic monopole baryons result from simply combining Maxwell's classical electric (1.1) and magnetic (1.2) charge equations together into a single equation, making use of Dirac's continuity, and imposing SU(3) C Exclusion on the fermions of the resulting three-fermion monopole system.No further ingredients or assumptions are required, and all of these ingredients being so-combined in novel fashion are among the undisputed, uncontroversial bedrock foundations of modern physics.The Gaussian ansatz (1.7) enables the energy (1.8) to be analytically calculated, the mass relation (1.11) naturally emerges, and once we further apply the resonant cavity thesis, the resulting ener-binding energies.In even simpler summation: Maxwell's Equations (1.1), (1.2) themselves, Fermi-Dirac gies turn out to match up remarkably well with nuclear combined together into one equation us g w utline of the Contents of Thistio.12) through (1.14) there is an aspect of(1.8) 13) (and also (12.4) and (12.5) of[1] which erroneously applied (3.2), (3.3) rather than (3.1) because of this ambiguity)to match the empirical data.
itself together, with the remaining 18.94% retained to confine the quarks inside each nucleon.The deuteron releases about 12.74% of it latent binding energy for nuclear binding, while the isobars with A = 3 release about 31% of this latent energy for nuclear binding with the balance reserved for quark confinement.The free proton and neutron, of course, retain 100% of this latent energy to bind their quarks and release nothing.So one may think of the latent binding energy as an energy that "see-saws" between confining quarks and binding together nucleons into nuclides, with the exact percentage of latent energy reserved for quark confinement ver-

Figure 5 .
Used-to-available binding energiesNext, we subtract Figure3from Figure4, to obtain the unused (amount of the latent binding energies reserved for and channeled into intra-nucleon quark confinement, rather than released and used for inter-nucleon binding.Of course, for the proton and neutron, all of this energy is unused; it is fully re e quarks.These unu gi inding energy e unused binding e served and channeled into confining sed, reserved-for-confinement ener-th es are: see Figure 6.Finally, to lay the groundwork for predicting the observed binding energies B 0 in Figure 3, let us refer to (3.6) and (3.7), remove the trace, and specify two (3 × 3) × (3 × 3) outer product matrices, one for the proton, P ABCD E in(4.4).In fact, these energies are equal to about 2.26 parts per million!Might this be an indication that the alpha uses all its latent binding energy less 2 u d m m for nuclear binding, wi th the 2 u d m m balance reserved on the other side of e quarks within each of its four the "see saw" to confin First, let's look at the numb en ke sense less nucleons?
prediction of the alpha bindi 3 parts per million.Now, let's discuss the this makes sense.

6 )
That is, we can make (5.1) for the alpha into an exact

Figure 7 .
Figure 7. Empirical binding energies   0 B of selected 1s and 2s nuclides (AMU).A Z 1) in fact has a very natural formulation which utilizes the trace 2 ABBAEas in (5.3), (5.4) and (6.3), may be written as: the mass excess of two free neutrons and one free proton with difference of part per million AMU.The precise, theoretical exactitude now belongs to the    

Fig- ure 3 ,
with isobar lines shown, and with equation num convenience: see Figure9.ass excess) discussed in helpful to the exercise of exin Section 9, is simply the hown in Figure9.Having   M n M p  mass difference, it is useful to also look at the difference between the 3 He isobars, A = 3 in the above.Given that3 He is the stable nuclide and that 3 H undergoes 3 H and   decay into3 He, we may calculate the predicted difference in bind ergies to be:The empirical difference −0.00081998 from the predicted difference by 0.000 helpful to contrast the above to (the n which represents the most elementary 9u 2588 u differs 041719399u.It is egative of) (10.1)  decay of a neutron into a proton.Similar calculations may be carried out as between the isotopes and isotones in FThe numerical values of these theoretica Figure 11 sh

Figure 11 .
Predicted minus observed bindin agnetic charges (nucl has heretofore gone unrecognized in the 140 years since Maxwell first published his Treatise on Electricity and Magnetism.

492.253892 MeV. That
is, precisely 99.8429093% of the available binding energy predicted by this model of nucleons as Yang-Mills magnetic monopoles goes into binding together the

Alpha Nuclide Binding Energy to 3 Parts in One Million, and
The alpha particle is the4He nucleus.It is highly stable, with fully saturated 1s shells for protons and neutrons, and is central to many aspects of nuclear physics including the decay of nuclides into more stable states v so-called alpha decay.In this way, it is a bedrock buil block of nuclear physics.The unused binding energy in Figure6for the alph The table on the left is a "1s square" and the table on the right is a "2s square."But they are both "s-squares."What is of interest is that the remaining e nuclides in the 2s square are not dissimilar in pat-

and a Possible Approach to Catalyzing Fusion Energy Release As
a practical exercise, let us now use all of the foregoing results to theoretically examine the solar fusion cycle.
u m 