**NUCLEAR STRUCTURE AND **

**FORCE**

**( Revolution in nuclear structure and force by reviving the well-established laws of electromagnetism)**

** By prof. LEFTERIS KALIAMBOS ( Λευτέρης Καλιαμπός ) T.E. Institute of Larissa Greece. Kaliamboslef@Yahoo.gr **

**This article was announced to many universities around the world (December, 2012 ).**

**After my paper “Impact of Maxwell's ...dipolic particles" **

**(Olympia 1993) which invalidates Maxwell's fields and Einstein's relativity, I worked for 9 years in order to formulate a large number of integral equations which reveal the nuclear force and the nuclear structure based on the application of the well-established electromagnetic laws. However when I presented my paper "Nuclear structure is governed by the fundamental laws of electromagnetism" at the 12th Symosium of the Hellenic nuclear physics society (N.C.S.R. "Demokritos", 2002), some elderly physicists influenced by the various theories of relativity and of the Standard Model abandoned the auditorium. Nevertheless after the publication of the paper in Ind. J. Th. Phys. (2003) today many physicists try to understand the new ideas about my discovery of the nuclear structure and force based on natural laws. Note that after the abandonment of electromagnetic laws due to the assumed uncharged neutron (1932) Heisenberg tried to interpret the nuclear structure and force by introducing fallacious exchange forces, which led to false nuclear theories and models. So one can see in “Nuclear structure-WIKIPEDIA” a number of wrong models which cannot lead to the nuclear structure. Also in “Nuclear force-WIKIPEDIA” we see the two contradicting theories of Yukawa (1935) and Gell-Mann (1973) with fallacious force carriers and strange color forces. It is of interest to notice that the paper contains a large number of difficult integral equations and figures which revealed the structure of nuclei. Under this condition and for understanding my discovery of the nuclear structure I present here the diagrams of four nuclei. I present also theAbstract, the Introduction and the Conclusions of the published paper. ( See in User Kaliambos the original published paper alog with the papers "Impact of Maxwell's...dipolic particles" and the "Spin-spin interactions of electrons and also of nucleons create atomic molecular end nuclear structures").**

**Nuclear structure is governed by the fundamental**

**laws of electromagnetism**

( Published in Ind. J. Th. Phys. Vol. 51 No. 1. 2003)

** **( In order to be understandable it was modified by using only the Abstract, the Introduction and the Conclusions)

* ***L. Kaliambos T. E. Institute of Larissa Greece**

**AFTER MY WORK OF 9 YEARS ( FROM 1993 TO 2002 ) I PRESENTED AT THE 12th SYMPOSIUM OF THE HELLENIC NUCLEAR PHYSICS SOCIETY A LARGE NOMBER OF INTEGRAL EQUATIONS BASED ON FUNDAMENTAL ELECTROMAGNETIC LAWS WHICH REVEAL THE NUCLEAR STRUCTURE AND FORCE .**

**Abstract**

Contradicting interpretations of the nuclear force as given by two contrasted approaches like the meson theory and the quantum chromodynamics, are overcome here by reviving the basic electromagnetic laws which are applicable on the existing charged subconstituents in nucleons. On this basis, considerable charge distributions in nucleons as multiples of 2e/3 and -e/3 are determined after a careful analysis of the magnetic moments and the results of the deep inelastic scattering. Basic equations derived from the distributed charges of oriented spins of nucleons give strong and short ranged forces leading exactly to the binding energies of deuteron and other nuclei.

According to these interactions, p-p and n-n systems repel and only the p-n bonds form rectangles and closely packed parallelepipeds providing an excellent description of nuclear properties. In this dynamics such contrary forces create structures of saturation and of finite number of nucleons. They also invalidate the charge independence hypothesis and differ widely from the central potential and the effects of the Pauli principle of the electronic configurations responsible for the development of two different models like the Fermi gas and nuclear shell. There are two kinds of p-n bonds, which imply anisotropy, leading often to elongated shapes of vibrational and rotational

modes of excitation, while the surface tension contributes to the creation of non elongated shapes with stable arrangements. Finally, for A>40 a type of shell structure provides new rules for understanding the structure of magic nuclei for N>Z and the increasing ratio N/Z with A.

**Introduction**

It is indeed unfortunate that the successful discovery of the uncharged neutron [1] along with the enormous strength and very short range of the nuclear force led to the abandonment of the natural electromagnetic laws in favor of qualitative approaches for the study of the nuclear structure, although these laws govern the atomic and molecular interactions. Actually, both the proton and the neutron have fairly large magnetic moments which imply considerable charge distributions, able to create the nuclear structure by giving strong p-n bonds and repelling forces of identical nucleons under quantitative measurements of short ranged dipole-dipole interactions. Nevertheless, after the failure of Heisenberg’s theory [2] and without detailed knowledge about the charged substructure of nucleons, Yukawa’s meson theory [3] seemed to be valid under the discovery of several mesons [4]. However, many attempts to fit them into a consistent scheme of nuclear forces did not succeed in reproducing quantitatively the known nuclear phenomena. Another serious problem had to do with the p-p scattering at high energies which is quite different from the p-n scattering, showing that the hypothesis of the charge independence [5] cannot be applied to the scattering data. Moreover, such purely attractive forces of p-n, p-p and n-n systems cannot lead to the saturation [6] and the decay of light nuclei.

Thus, in the absence of a realistic force the most important structure models like the liquid drop [7], the Fermi gas [8], the nuclear shell [9], and the collective model [10], lead to complications. H.Ohanian emphasizes that such models are caricatures of the real world [11]. On the other hand, the analysis of the deuteron, alone, based on a square- well potential did not give the desired information about the p-n force [12]. The same difficulties will be observed, also, in the theory of nuclear matter [13].

Of course the aspect of the well-known quantum chromodynamics that the nuclear force is due to the residual strong interaction between the hypothetical color-charged constituents of nucleons [14] cannot provide any framework for quantitative measurements. Moreover, the quark picture [15] could not explain the same phenomena that are treated by the predominant meson theory. Under these conflicting intellectual creations and, starting with the simplest nuclear structure, a satisfactory framework for the quantitative predictions of the simple p-n systems is formulated by reviving the basic electromagnetic laws which are applicable on the existing charge distributions in nucleons of a well described spin in quantum mechanics.

In deducing the equations of a realistic inter-nucleon force, detailed knowledge about the interacting charge distributions in nucleons is derived from the g-factors in connection with the results of the deep inelastic scattering. Note that the experimental values of the g-factors of the proton [16] and neutron [17] indicated charge distributions in nucleons confirmed by bombarding them with high-energy electrons [14]. Moreover a systematic analysis of the experimental data gives fractional charges as -5e/3 and 8e/3 or 8e/3 and -8e/3 distributed in the centers and along the peripheries of p and n respectively. It is surprising that they have a quark structure since they are proportionally greater than those charges of (uud) and (udd) schemes of the simple quark model.

Electromagnetic fields due to such distributed charges favor a coupling of the simple p-n system along the radial direction with S=1 because in this area the motional emf is weaker than that in the direction of the spin axis. Furthermore, quantitative measurements of electromagnetic forces at the shortest separation 2r_{p } for the observed value r_{p} = 0.813 ± 0.008 fm of the proton radius [18] give a p-n bond, whose the binding energy equals the experimental value B(^{2}H)= -2.2246 MeV [5].

The simple p-p and n-n systems operate also in radial direction but they give spins of S=0 with repulsive forces. Similarly the electron-electron system operates in radial direction giving S=0 but at a separation r <578.5 fm appears a special attraction able to explain the Pauli principle (bonding state of S=0 in covalent bonds, etc) and the so-called indistinguishability.

Under such contrary forces, as in ionic crystals, a close packing of nucleons tends to increase the binding energy B(Z,N) by bringing the unlike nucleons (p-n bonds) closer together with oriented spins which form rectangles and closely packed parallelepipeds, whereas the p-p and n-n systems of repulsion favor a stable structure ,when they are arranged at greater distances (diagonals) with non oriented spins.

According to the electromagnetic laws, two deuterons are coupled along the spin axis with S=0 (the motional emf is negligible) involving stronger p-n bonds in axial direction than those in radial one. They form ^{4}He with S=0 which is a two-dimensional rectangle with a coordination number of 2. Despite this small number, ^{4}He is extremely stable since the identical nucleons exert weak repulsions as a result of the non oriented spins and the greater separations (diagonals). Two-dimensional shapes are formed, also, in other light nuclei. However they have B(Z,N)/A smaller than that of ^{4}He due to repulsive forces of additional oriented p-p and n-n systems. On the other hand, the lightest nuclei ^{3}H and ^{3}He have some disorder introduced by a missing nucleon, while in other nuclei, additional neutrons outside closely packed systems make single p-n bonds of weak binding energy often leading to the decay, in contrast to the stable single bond of ^{2}H which has not any p-p or n-n repulsion.

Also in ^{2}H there is not any orbital (spatial) motion and in the absence of a motion due to ħ any application of the uncertainty relation or the Schrodinger equation for estimating a repulsive kinetic energy leads to complications.

Dramatically, at the beginning of the three-dimensional structure there is a great difficulty for two rectangles to form a simple parallelepiped belonging to the extremely unstable ^{8}Be; this is due to the parallel spin of identical nucleons, repelling with electric and magnetic forces along the diagonals of the squares, so as to reduce significantly the weak radial p-n bonds in a symmetrical shape with a coordination number of 3.

Fortunately, for the structure of the heavier α particle nuclei, for A = 12, 16, 20 and 24, proper combinations of rectangles form symmetrical shapes (parallelepipeds) with an increasing coordination number from 3 to 4 or 5 in inner rectangles or squares. This dynamic situation, which implies decrease of the so-called surface tension [7], is able to overcome the repulsions of the oriented p-p and n-n systems to make stable arrangements. Such contrary forces invalidate the charge independence and charge symmetry, as well as the models of the orbital shell and the Fermi gas. Unlike the electronic binding energy per electron, which increases as Z^{3/4}, they lead to the saturation properties and to unstable nuclei.

The two kinds of p-n bonds, which imply anisotropy, often lead to elongated shapes of vibrational and rotational modes of excitation described in terms of quanta. High symmetry together with the values of spins [19] and the known binding energies of nuclei [20] are the basic tools for understanding the structure of stable light nuclei, when Z=N, since for a fixed A any change from Z=N to N>Z or N<Z reduces the number of p-n bonds.

As the nuclei become heavier suitable geometric shapes like tetragonal or orthorhombic systems (cores) are surrounded by outer p-n composite bonds (non single bonds) by increasing the coordination number to the maximum number of 6. This situation implies a significant decrease of the surface tension leading to non elongated shapes with a minimum nuclear surface area. Other polyhedra, as well as spherical or ellipsoidal shapes, are unacceptable because of the oriented spins. Under such a dynamics the outer p-n bonds appear with equal number of p and n and behave like the unfilled shells because they form « empty» positions as many as possible between two or three protons able to receive extra neutrons, which make extra p-n composite bonds in order to overcome the repulsive energies of the dominant long ranged p-p repulsions. In magic nuclei for N>Z, such shells are occupied completely. So, this sort of “shell structure” is responsible for the increasing N/Z with A. The known ratio N/Z along with the symmetry allow us to reveal the structure of magic nuclei and other stable nuclei for odd Z when N>Z.

If there are sufficient additional nucleons outside the shape of a magic nucleus, the anisotropy leads to an elongation along the spin axis. In general, a compromise between the surface effect and the anisotropy determines the various shapes of massive nuclei. Such shapes of closely packed nucleons confirm the observable very short distance between nucleons which is comparable to the nuclear size.

** Conclusions**

The distributed fractional charges in the spinning nucleons deduced from the o bservable magnetic moments, in connection with the deep inelastic scattering, explain not only the spin S=1 of the simplest structure of ^{2}H, but also give exactly the radial p-n force, since the quantitative measurements, performed in carefully controlled experimentation, lead to the impressive agreement of the calculations with the experimental value B(^{2}H)= - 2.2246 MeV.Such fractional charges which are proportionally greater than the fundamental charges of 2e/3 and -e/3 satisfy the conservation of charge in the beta-decay of n, while the charges of (uud) and (udd) schemes lead to complications. On the other hand , the repulsive energy of the non oriented p-p system in ^{4}He, as calculated by applying the fundamental Coulomb law, is not only in excellent agreement with the p-p repulsion deduced from the observable binding energies of the simplest mirror nuclei, but also it fits into a consistent scheme of binding and repulsive energies in ^{4}He. According to the electromagnetic laws the negligible motional emf in the coupling of two deuterons is responsible for the strong p-n bonds with S=0 along the spin axis. This situation seems to justify the Heisenberg concept of isotopic spin while the simple p-n bonds have always S=1 in radial direction of weak binding energy. Of course the radial energy of -2.2246 MeV and the strong axial energy of -12.4 MeV imply a great anisotropy which explains the rapidly increase of the binding energy from the odd-odd nucleus ^{2}H, to the even-even nucleus ^{4}He, while the asymmetric shape of ^{3}He (odd A) gives an intermediate energy. Also the odd-odd nuclei as ^{6}Li, ^{10}B and ^{14}N are not closely packed in contrast to the α particle nuclei. While the shapes of odd A nuclei as ^{19}F and ^{23}Na are not of high symmetry. These simple examples explain very well the pairing term in the mass formula [32] used for predictions of stability against β decay for numbers of an isobaric family.

Such structures show also that the Pauli principle of the electronic configurations is inapplicable in nuclei, since the p-p and n-n systems repel and often are not oriented. For this reason, no bound state is observed for the simple p-p and n-n systems and only in neutron stars the long ranged gravitational energy can hold the repelling neutrons together. Moreover, such repelling forces are responsible for the saturation and the decay of nuclei.

In contrast to the shell model here the symmetrical shape of ^{ 4}He contains non-oriented spins of like nucleons for very stable arrangements, while most of light nuclei contain additional oriented spins of like nucleons reducing the total binding energy. This peculiarity explains the magic number of 2 and the non smooth curve of B(Z,N)/A for light nuclei. From the structure of ^{4}He, it became clear that only the geometry of positions and the orientation of spins of p-n bonds are responsible for holding back the protons. Consequently, the two concepts of charge symmetry and charge independence did much to retard the progress of nuclear physics. Unfortunately the known p-p repulsion seemed to become an attractive force at very short separations, and so far, in vain, nuclear physics aims at the exploration of new natural laws or an unification of different field theories.

Accounting for the so-called asymmetry term , a good example is the structure of ^{6}He, in which the imbalance of p and n allows the formation of single p-n bonds of weak binding energy outside the stable rectangle. However, in other light nuclei (and often in massive nuclei) one observes excess neutrons giving stable arrangements, as in the cases of ^{9}Be and ^{19}F, since the additional neutrons make composite p-n bonds connecting two protons for stable arrangements. This fact invalidates the Fermi gas model.

On the other hand, according to this model, ^{8}Be should be one of the most stable nuclides. In fact, it splits into two α particles since the identical nucleons with S=1 reduce significantly the radial p-n bonds. That is, as in the decay of massive nuclei the long ranged p-p repulsion along with the short ranged n-n interaction are responsible also for the instability of light nuclei. Note that the application of the uncertainty relation for estimating a huge nuclear force (much more greater than the simple p-p repulsion) leads to complications. In the heavier α particle nuclides for A=12, 16, 20 and 24, the closely packed parallelepipeds explain the peaks of B(Z,N)/A very well since the packing of these shapes increases the coordination number from 3 to 4 or 5. This fact implies a decrease of the surface tension for stable arrangements. The reasons Z=N and S=0 imply high symmetry with a maximum number of p-n bonds, since for a constant A any change from Z=N to N>Z or N<Z not only reduces the number of p-n bonds but also leads to asymmetric shapes.

In a systematic analysis of the magic numbers 2, 8, 20, 28, 50, 82 and 126 we see that unlike the regular behavior of the electron orbital structure the magic nuclei are only special shapes of very stable arrangements in widely different groups. For example, ^{4}He belongs to the group of a two-dimensional structure, while ^{16}O belongs to the group of parallelepipeds. In the shell structure of the tetragonal system we observe the magic nuclei ^{40}Ca, ^{48}Ca and ^{64}Ni , while the magic nuclei ^{88}Sr and ^{208}Pb belong to another group of orthorhombic systems. As a result the magic nuclei are not related to the noble gases because in the nuclear structure there is not any central potential or any interaction to obey the Pauli principle.

Now, it is easy to understand, why in the shell model the use of the hypothetical harmonic oscillator or the spherical-well potential could not reproduce all the data and why the additional postulation of the strong spin-orbit interaction is accompanied with adjustable parameters for reproducing the available data [ 9 ]. According to these postulations, the total potential has the form V= V_{( r ) }- f_{( r ) }L.S where f_{( r ) }is an arbitrary function of the radial coordinates chosen appropriately to fit the available data. Furthermore the shell model cannot explain how in odd-odd nuclei protons and neutrons should couple.

Here, a type of shell structure which differs fundamentally from the orbital shells in atoms, favors stable structures after increasing the ratio N/Z with increasing A. This is due to the increasing surface area, able to receive a considerable number of outer p-n bonds for making blank positions as many as possible. More excess neutrons than those of blank positions lead to single bonds (saturated bonds). Therefore, the stability region cannot depart significantly from the line Z=N in the Segre plot [19].

The elongation along the spin axis, involving a number of nuclei between the magic nuclei, is explained here by the strong p-n bonds leading to a great anisotropy. However, as the elongation increases very much, a considerable surface tension energy favors the increase of the lattice points with the maximum coordination number of 6 by constructing non elongated shapes withcompleted shells belonging to heavier magic nuclei. Under extreme conditions, this anisotropy leads to super elongated formations exhibiting large quadrupole moments. In general, a dynamic interplay between the surface effect and the anisotropy contributes to the creation of various types of nuclear shapes.

This real explanation, based on the electromagnetic interaction of nucleons, is very different from the collective model [10 ], which presents a great dilemma by using fundamentally different concepts from the nuclear shell and the liquid drop model. Actually, the p-n bonds of oriented spins in the nuclear structure cannot be related to the isotropic material of a liquid drop structure, which gives always spherical shapes neglecting the spins of nucleons. Nevertheless, after the compound nucleus model and our first understanding of the dynamics of nuclear fission it is emphasized that the p-n bonds along with the repulsions of p-p and n-n arrangements have some affinities with the liqui drop structure due to the polar covalent bonds of H_{2}O including H^{+}-O^{- - }bonds and repulsions of H^{+}-H^{+} and O^{- -}- O^{-}

^{ }In fact, a nucleus is divided into components relating to the intrinsic motion of the nucleons, described in the quantum mechanics, and to vibration and rotation of the nucleus as a whole. On this basis, the α- decay can be explained by assuming a dynamic equilibrium at the surface where the nucleons of ^{4}He receive an impulse which will raise the kinetic energy enough to break the weak radial bonds. Whereas in the β^{-} decay the single p-n bonds of a weak binding energy become very stable rectangles as in the case of the radioactive ^{14}C which becomes a stable ^{14}N.

** **

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