This article was announced to many universities around the world (Dec. 2010).
By Prof. L. Kaliambos T. E. Institute of Larissa - Greece
New ideas on : Maxwell’s waves, Einstein’s fields, photons, Einstein’s relativity, Einstein’s mass-energy equivalence, electrons, Pauli’s principle, two-electron orbitals, covalent bonds, protons and neutrons, nuclear forces, nuclear structure.
Writing in Google Scholar "Kaliambos" one can see my paper "Impact Of Maxwell's...dipolic particles" presented at the international conference " Frontiers of fundamental physics" (Olympia, 1993) which invalidates Maxwell's fields and Einstein's relativity. After the experiment of French and Tessman (1963) who showed the fallacy of Maxwell's fields I presented my dipolic photons of mass which invalidate Einstein's massless quanta of fields. Thus Einstein explained incorrectly the photoelectric effect which led to his invalid relativity. In fact the asorption of the dipolic photons contributes not only to the increase of the electron energy but also to the increase of the electron mass in accordance with the Kaufmann experiment (1902).
In Google Scholar one can see also my paper " Nuclear structure is governed by the fundamental laws of electromagnetism" presented at the 12th symposium of the Hellenic nuclear physics society (NCSR "Demokritos", 2002) . We discovered 9 extra chared quarks in protons and 12 ones in neutrons existing among 288 quarks in nucleos. They interact with electric and magnetic forces to reveal the nuclear structure and binding. You can see also my additional published paper " Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures" (See in "User Kaliambos " the above published papers with a large number of integral equations which revealed the invalidity of relativity and fields, and the structure of nuclei and of atoms).
It is indeed unfortunate that the most new ideas in science at the frontiers that have eventually changed our view of the world, faced a great difficulty in being accepted by the scientific majority. A critical attitude is clearly required of every scientist. But what is require is to be equally critical to the established ideas as to the new. In fundamental physics some important theories like Maxwell’s waves, Einstein’s relativity, quantum waves, molecular bonds, nuclear forces etc. use several postulations, while the above new ideas are based on the well-established laws of electromagnetism. Nevertheless there is a great difficulty for the scientific majority to accept these new ideas, although they are based on fundamental laws, because professors and researchers use the same hypotheses for many years. The confrontation between different lines of research has accompanied science from its birth. Galileo’s scientific ideas were heretical, not only with respect to the dominant religious and political powers of his times, but with respect to the academic establishment of the universities as well: Well- known is the example of the astronomy professor, who refused to look in the telescope. In our century the existence of such attitude within modern science has been observed by the best epistemologists. The confrontation between points of view goes on, but a strange mutation seems to reduce its effects, since ideas on frontiers of physics find difficulties in being accepted by the majority, no matter how well formulated and important they could be. While the ruling of the majorities is a fundamental feature of every democracy, it certainly does not apply to science, where the great steps forward have always been made by isolated individuals like Maxwell, Einstein, Bohr, Sroedinger etc. This dogmatic hardening risks today to make the scientific majority hard and impenetrable to a critical understanding of the foundations of contemporary new scientific ideas based on natural laws.
INVALIDITY OF MAXWELL’S SELF PROPAGATING FIELDSEdit
In the history of science it is surprising that the double-slit experiment of Young (1800), which showed the wave nature of light led to the abandonment of Newton’s famous corpuscular theory. The same surprising occurred also when Faraday (1846) observed the electromagnetic properties of light and the German physicist Weber showed, that the ratio of proportionality factors of electric and magnetic forces of the laws of Coulomb and Ampere is equal to the square of the speed of light c. Under such conditions, in order to interpret the wave nature of light, Maxwell (1865) introduced his postulation of energy transmission through an Aristotelian elastic ether by self propagating electric and magnetic field components (Ey and Bz), which should lead to his wave equations, if Ey/Bz = c.
Early fundamental experiments on electricity and magnetism led to the electric force Fe of the Coulomb Law (1785) and to the magnetic force Fm of the Ampere law (1820). In both cases the force is a simple action at a distance as a fundamental characteristic of nature between charges or between charges in motion. Thus, natural laws involved no mention of an electric field E or a magnetic field B.
However to simplify the reasoning required as in Gauss’ flux theorem and in the laws of induction and Biot-Savart, there were introduced the fields E and B. For example when two charges Q and q move at a velocity υ along parallel lines at a distance r, one may write E = Fe/q and B = Fm/qυ.
The law of induction was introduced by Faraday (1832), who discovered that whenever the current in a circuit is changing, a force appears in a loop placed close to the circuit. It gives a work W = F2πr where r is the radius of the loop. The same work he observed also when the current in the circuit was constant and the loop was moved toward the circuit with a velocity υ. That is, it was observed that the induction law is consistent with the law of magnetic force Fm giving a work W. In both cases since a changing magnetic field increases at a rate dB/dt, Faraday found that W/q = (dB/dt)A, where W/q is the work per unit charge called electromotive force, emf, and A is the area surrounded by the loop. Moreover since F = Fm.
One could write also W/q = (Fm/q) 2πr = (dB/dt) A .
However Maxwell thought that Fm/q is an electric field E though the force is magnetic produced by a moving loop and a current. Thus, he introduced the false idea in his theory that a rate of changing magnetic field dB/dt, produces an electric field E given by the simple false equation E2πr = (dB/dt)A.
Then, in order to find a symmetrical situation, he postulated that the changing electric field in a capacitor should be similar to a real current, called displacement current Id, able to produce a magnetic field, which he never observed experimentally. That is, in the process of unifying electromagnetic theory, Maxwell proposed the incorrect concept of “self propagating fields” by saying that a varying magnetic field gives rise to an electric field, and a varying electric field gives rise to a magnetic field.Of course, under such adjustable hypotheses Maxwell was able to formulate E/B = c by comparing the false electric field E of the induction law in a loop with the wrong displacement current Id in a capacitor, able to give the above desired result, which led to his famous wave equations.
Note that if one uses the basic laws of electromagnetism in a system of a capacitor and an inductor, he will get in the system the correct ratio E/B = c by equating the stored electric energy density of the capacitor with the stored magnetic energy density of the inductor. However the magnetic energy Um of an inductor implies that a changing magnetic field cannot produce electric field E in it, but only a magnetic force Fm. Also in the capacitor the changing electric field cannot produce magnetic field B in it, but only an electric force Fe giving the electric energy Ue. Of course this fact is consistent with the important experiment of French and Tessman, who showed in 1963 experimentally that Maxwell's hypothesis of displacement current Id involves misconceptions (Am. J. Phys. 31,201, 1963) .
Under such a situation the “self propagating fields” led to serious problems and did much to retard the progress of fundamental physics. Especially after the experiment of Hertz (1886) who produced such radiation of fields, all physicists believed that it was a striking confirmation and one of the best outstanding achievements of Maxwell’s theory. In fact, after Einstein’s photons (1905), Hertz produced a radiation of spinning dipolic particles or spinning dipolic photons, which produce at the speed of light c localized time-varying electromagnetic fields. See in Google dipolic photons introduced by L. Kaliambos in 1993. http://adsabs.harvard.edu/abs/1984ffp..conf..415K
After the establishment of Maxwell’s “self propagating fields” the original fundamental ideas of natural laws of force were changed drastically , because it was believed that the field is a property of space, which propagates at the speed of light, although E was defined as a force per unit charge under the fundamental interaction between charges. Thus, the appearance of forces involved in the basic laws as a result of the action at a distance between charges or currents were regarded as caused by assumed “strange fields”, which may exist in free space without charges or currents.
When Max Planck (1900) had shown that light consists of discrete quanta of energy E = hν, where h is his constant and ν is the frequency of light, it was surprising that he doubted the validity of his quantum theory under the great influence of Maxwell’s continuous “self propagating fields”.
NEW IDEAS ON EINSTEIN’S VIEWS FOR MAXWELL’S FIELDS Edit
Although Einstein revived Newton’s corpuscular theory and explained the photoelectric effect (1905) with Planck’s quanta, he also defended Maxwell’s continuous fields and described them as the most profound and the fruitful fields that physics has experienced since the time of Newton.
In his book “The evolution of physics” Einstein emphasizes that Maxwell’s equations describe the structure of continuous fields as real quantities without charges or currents. He says that the two equations ( derived from the false E of the induction law and the wrong displacement current) are the fundamental laws of Maxwell. He also emphasizes the reality of them by saying that the free space is responsible for transferring the continuous fields, which are more important than charges and currents, though in the basic laws of Coulomb and Ampere the prevailing charges or currents are responsible for the force which appears as a fundamental characteristic of nature. According to natural laws without charges or currents the forces of the action at a distance or the related fields cannot exist.
Of course, if such strange fields without charges were real, one could say also that the gravitational field on the earth would leave the earth for travelling away alone without the earth.It is ironic that in 1921 when Einstein was awarded the Nobel prize for his discrete quanta, he acknowledged that he did not know the cause of the discrete energy transfers (photons), which were contradictory to Maxwell’s continuous “self propagating fields”.
In 1954 Einstein wrote to his friend Michael Besso expressing his frustration for quanta under the accepted fields which should exist without charges or currents. He wrote: All these fifty years of conscious brooding have brought me no nearer to the answer to the question what are light quanta. So, that confusion between Maxwell’s fields and the quanta of Planck remained in baffling conflict.
THE NATURE OF PHOTONS.
According to the Charge Conservation photons of spin h/2π move at c as spinning dipolic photons able to give local time-varying Ey/Bz = c.Under the troublesome hypothesis of “self-propagating fields”, based on wrong postulations and the false ideas that the fields may exist without the fundamental charges, it was used Einstein’s photon by L. Kaliambos (1993) which interacts with an electron under the applications of electromagnetic laws and leads directly to relativistic dynamics.
Moreover it was developed the model of dipolic particles or dipolic photons in which photons of spin h/2π behave like spinning dipoles having the spin axis z always perpendicular to the velocity of light c.
This model is based on the experiment of Faraday, who observed in 1846 that the magnetic field B changes the plane of polarization of light, since B exerts a torque on a moving dipole.Here the Charge Conservation implies also that photon is a spinning dipolic particle since γ rays give the charges of electron and positron.( Pair Production, 1932). According to the laws of Coulomb and Biot-Savart the charges of a spinning dipolic photon give local time-varying fields with the ratio E/B = c. Here E is in y direction and B is in z direction. A very simple mathematical analysis is described in <a rel="nofollow" class="external free" href="http://newideasinphysics.blogspot.com">http://newideasinphysics.blogspot.com</a>
The dipole oscillates at c because the repulsive magnetic force under the fundamental action at a distance between the unlike charges becomes equal to the attractive electric force when the dipole axis α = 2r is perpendicular to the speed of light c and when it moves at υ = c. At high frequency its average r becomes very small, because it has a constant angular momentum h/2π like a spinning dancer. The time-varying E/B = c of a photon are always in phase with each other, while Maxwell's theory predicts out-of-phase components near the Ac source propagated through an elastic ether.
When the dipolic photon moves in dielectrics the field E due to two charges is reduced because of the polarization of the dielectric material. Hence, this reduction of E leads to c' < c. In this case we have E'/B = c' and an index of refraction n = c/c' since on a boundary the one charge moves at c' while at the same moment the second one moves at c. Moreover the crowding of photons in pinholes leads to complete waves of Young, which cannot be explained by Maxwell's theory. Conclusions: Under the basic errors of Maxwell's postulations one looks that Faraday’s experiment in 1846 leads to the conclusion that photons move at c as spinning dipolic photons of an energy E = hν and solve the photon-wave dilemma of two different theories, since nature works in only one way.
THE NATURE OF SPINNING ELECTRONS Edit
Unfortunately, when Thomson ( 1897 ) announced the existence of the electron as an elementary particle and a basic component of all atoms, the scientific majority did not accept that experimental discovery, because it was believed that atoms are the smallest elements in nature like the atoms of Democritus. Thomson determined the charge-to-mass ratio (-e/m) of electrons that constituted the cathode rays. When Millikan in 1909 measured the charge -e in the famous oil drop experiment, it was found than the mass of electron is 1836.1 times smaller than the mass of a proton.
In 1923 De Broglie proposed the wave nature of electrons, which was greeted with almost universal skepticism, even derision. But successfully that concept led to quantum mechanics, by using the same relation c = hν/p which leads to relativistic dynamics. Then, under the rules of wave mechanics Pauli suggested his qualitative Exclusion Principle for the behavior of two interacting electrons. Moreover, Uhlenbeck and Goudsmit (1925) on the basis of various experimental data, made a bold suggestion that the electron in addition to its orbital angular momentum about the nucleus rotates like a spinning particle. They called this new intrinsic angular momentum “spin”, which has always the half value of the photon spin S = h/2π and takes two values
S = +0.5 (h/2π) and S = -0.5( h/2π), which are completely unacceptable in classical physics.
It is even more puzzling to note that if the electron is considered as a small disk of a radius r < 1 fm, it may then be shown that the tangential linear velocity υ at the periphery 2πr will be much greater than the speed of light c. Indeed, for an electron rotating as a very small spinning disk one is able to write
S = 0.5(mυr) = 0.5(h/2π) where m is the electron mass and h is the Planck constant. Since the radius of electron is less than one fermi, by using the experimental values of m and h one gets υ > c. Because of all these conceptual difficulties this suggestion met opposition from many physicists, including also Pauli, who was already famous for his exclusion principle. The pressure was so great that Uhlenbeck and Goudsmit wanted to withdraw the paper they had submitted, but it was too late to do so, becauser the paper was sent for publication.
Today no one doubts the electron spin S = 0.5(h/2π) because all particles called fermions like the proton and neutron have the same spin of electron. Under this condition a careful analysis by L. Kaliambos (2006 and 2008) of the electron magnetic moment μ led to the conclusion that the electron is a spinning disk having its charge –e along the periphery. (See in Google non dipolic electrons). It is well-known that μ = 0.5(-e)υr
when –e is along the periphery. On the other hand for an electron spinning as a disk one writes S = 0.5(mυr). Since the experiments showed that μ/S = -1.00116(e/m) one leads to the conclusion that electron rotates like a spinning disk having its charge -e along the periphery. The puzzle of the peripheral velocity (υ>c) could be solved by assuming that the spin cannot be related to the relativistic mass of electron, since in the relation hν/m = ΔΕ/Δm matter-light equivalence the electron spin cannot be affected by the absorptions of dipolic photons. That is, the peripheral velocity (υ>c) must be an intrinsic characteristic of the electron spin. Whereas the electron with a relativistic mass, under the absorptions of dipolic photons increases its mass and its velocity, but according to the relations of relativity it cannot move as fast as the speed of light c.
Moreover a system of two electrons cannot operate along the spin axis. That is, it cannot operate like a pair of two front wheels or back wheels of a car, because along the spin axis z appears a very strong attractive magnetic force (much more stronger than the electric repulsion at very short separation), which produces enormous electromotive force of the induction law able to give very great currents in antiparallel directions to the spin. So they operate always in radial direction with opposite spin. According to a detailed analysis of L. Kaliambos (2003) between the electrons appears an electromagnetic force Fem with a repulsive electric force Fe of long range and an attractive magnetic force Fm of short range, which becomes stronger than the electric one at short separations. Note that the parallel spin (like the wheels of a bike) gives both electric and magnetic forces of great repulsions.
QUANTITATIVE EXPLANATION OF PAULI’S PRINCIPLEEdit
At the beginning of 1925 in addition to the three known quantum numbers (n,l,m) of the stationary states, Pauli had proposed that a fourth quantum number with two values was needed to give the electron a complete description. But although Uhlenbeck and Goudsmit in the same year discovered the electron spin for explaning Pauli’s the two values, Pauli strongly doubted the correctness of the spin because of its mechanical character and the enormous peripheral velocity (υ>c).
The consequence of the Pauli principle here is that two electrons of opposite spin tend to be at the same position (pairing of two electrons), while the electrons of the same spin (parallel spin) are kept apart. This fact was explained qualitatively by Heisenberg (1926) who assumed that between the electrons there is an “exchange interaction” under a property of spins called “exchange symmetry”.
Because of the qualitative descriptions of the spinning electrons (exchange symmetry) neither was able to provide satisfactory equations for explaining the pairing of two electrons and the energies in the ground states of heliumlike atoms etc. Under these difficulties detailed calculations of two electrons of opposite spin ( S=0 ) lead to an electromagnetic force Fem = Fe – Fm. The two electrons of mass m at a separation r = 3h/4πmc = 578.8 fm give
Fe = Fm. That is at r < 578.8 fm the attractive Fm becomes stronger than Fe (L. Kaliambos 2006).
As a result the electromagnetic force Fem becomes an attractive force which leads to vibrations of two electrons under an electromotive force. So at r < 578.8 fm the two electrons behave like one particle and produce a vibration energy Ev in the system which leads to the indistinguishability. Also note that calculations for two electrons with parallel spin lead to Fem = Fe + Fm.
WAVE FUNCTION AND ENERGY OF TWO-ELECTRON ORBITALSEdit
It is surprising that Einstein who favored crucial contributions to Quantum Theory at the beginning did not accept as final the probabilistic form of the Quantum Mechanics. He defented his views with subtle arguments and summed them up in the aphorism “God does not play dice”.
In fact, both theories of Special Relativity and Quantum Mechanics have the same origin. Writing again the applications of electromagnetic laws on the interaction of a dipolic photon with an electron we get the equation E/B = c = hν/p, which leads to relativistic dynamics.Now if one writes c = λν and p = mυ where m is the electron mass and υ is its velocity he gets the electron wave length λ = h/p of the De Broglie relation which led to the quantum mechanichs since nature is inherently symmetric. That is, applications of fundamental electromagnetic laws on interactions of dipolic photons with electrons lead not only to the relativistic mass of particles but also to the wave nature of them discribed in the famous Shroedinger equation.
It is well-known that the Bohr model and the Shroedinger equation of the one-electron in the hydrogen atom gave a very accurate explanation of the hydrogen spectrum. But when it came to helium with two electrons it collapsed. Hisenberg and other physicists developed theories for modification of Bohr’s model but they did not succed in reproducing quntitatively the known phenomena. By using complicated wave functions the ground state energy of helium did not give the experimental binding energy Ε = –79 eV.
After these difficulties L. Kaliambos in 2006 observed that the two electrons of opposite spin at very short separations behave like one particle with a charge -2e. So according to Bohr’s model the system of the two-electron particle and the nucleus of charge +2e has a ground state energy Eo = -108.8 eV. Also at the short distance r < 578.8 fm a motional electromotive force creates an energy of vibrations of two electrons confined between two potential barriers. After a careful analysis of ground state energies of many heliumlike atoms the vibration energy Ev measured in eV is given by the empirical formula Ev = 16.95Z – 4.1 where Z is the number of protons. Ιn this case of helium (Z = 2) we have Ev = 29.8 eV which leads to the experimental value E = Eo + Ev = -108.8 +29.8 = -79 eV. That is, the ground state energy Ε of a system with a two-electron orbital is given if we add the vibration energy Ev in the energy Eo of the Bohr model by using the same wave function of the one-electron particle.
Moreover no third electron can approach this electron-electron system, since the antiparallel spin gives B = 0. Therefore in the helium atom with two electrons of opposite spin orientation which give such a great binding energy, this fact accounts for the chemical inertness (noble gas). Also for the hydrogen with a two-electron orbital one applies the same wave function as that of the one-electron, by writing the energy
E = Eo + (16.95Z – 4.1) = -27.2 + 12.85 = - 14.35 eV. This energy gives also the experimental electron affinity of hydrogen which is equal to 0.75 eV. On the other hand under the rules of quantum mechanics the third electron in Li must occupy the 2s state able to be removed and attached to the single electron with S = 0 of a non-metal atom for making an ionic bond.
DETAILED EXPLANATION OF COVALENT BONDSEdit
The same two-electron orbitals we observe also in molecules. In the molecule of hydrogen the binding energy is weaker than that of the helium atom (-79 eV), since the system of two electrons wich behaves like one particle attracts less the two separated protons. On the other hand the system of two protons at a separation of 0.074 nm gives a repulsive energy in the proton-proton system which is weaker than the Coulomb repulsion since the two protons operate with opposite spin (S=0) where an attractive Fm appears between the two protons.(bonding state). Detailed calculations of two protons with opposite spin ( L. Kaliambos 2003) showed that because of the opposite spin they exert an electomagnetic force Fem = Fe – Fm where Fe is always stronger than Fm. That is, Fem is always a repulsive force but weaker than Fe. Note that in the antibonding state the two protons operate with parallel spin where both electric and magnetic forces exert a great repulsion. Fem = Fe + Fm.
Of course in the hydrogen molecule ion the vibration energy Ev disappears as in the case of the helium ion, where the one electron attracts the nucleus of +2e. But in this case the binding energy is weaker than that of the helium ion, because of the separated protons. Here the proton-proton repulsion is given also by Fem = Fe – Fm ( bonding state of opposite spin of the p-p system).
THE NATURE OF SPINNING PROTONS AND NEUTRONS Edit
Fast moving protons were first observed by Thomson in 1905 among the “positive rays” produced by the electric discharge in gas containing hydrogen at low pressures. Proton is a fundamental building block of matter with a mass 1836.1 times that of the electron. All atoms of the lightest isotope of hydrogen have a nucleus that is a single proton. Also at those years of limited knowledge the simple experiments showed that proton has a positive charge +e equal in magnitude to that of the electron.
After the discovery of neutron by Chadwick in 1932 it was found that it has zero charge and mass 838.65 times the mass of the electron. It was also found that all nuclei are composed of assemblies of protons and neutrons. Unfortunately that successful discovery of the uncharged neutron along with the several experiments which showed 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 proton-neutron interaction, although these laws govern the atomic and molecular interactions.
So in the absence of detailed knowledge on the nature of spinning nucleons (protons and neutrons) Heisenberg, who proposed in 1926 the idea of an exchange interaction between the electrons, in 1932 he introduced another idea of “exchange force” produced by the exchange of “force carriers”. Starting with the hydrogen molecule ion, he postulated that in general the nuclear attractive force between protons is due to the exchange of a hypothetical electron between the two protons of antiparallel spin (bonding state of S=0), under the qualitative exclusion principle of Pauli, since he did not know the magnetic attraction Fm between two protons of opposite spin.
Of course such a postulation did much to retard the progress of nuclear physics, because in 1935 Yukawa using the same ideas of Heisenberg proposed another nuclear force based not on natural laws but on the exchange of some hypothetical “force carriers” called mesons.In 1957 there were determined the factors g = 2.793 of proton and
g = -1.913 of neutron giving the magnetic moments which imply charge distributions as +e = (-q + Q) for proton and
(+Q' -Q') = 0 for neutron, confirmed by bombarding them with very energetic electrons.
In 1964 Gell-Mann and Zueig in their model of uud quarks for proton and udd quarks for neutron proposed that d quark has –q = -e/3 and 2u quarks have +Q = +4e/3 giving a charge distribution for proton +e = -e/3 +4e/3, while for neutron the udd scheme gives (+2e/3 -2e/3) = 0. Note that recent estimates made by researchers on muonic hydrogen put the proton radius r at about 0.84 fm. However at the shortest separation 2r = 1.68 fm of the simple proton-neutron system they cannot give the observed binding energy E = -2.2246 MeV of deuteron.
In 1973 Gell-Mann and Fritzsch in their theory of Quantum Chromodynamics replaced the fundamental charge of natural laws by a color charge which may give a color force between quarks or nucleons produced by gluons which have never been observed. Of course they developed that theory since they believed that the e of quarks is not responsible for the interactions between the quarks. That is, we see again Heisenberg's and Yukawa's qualitative description of an exchange force and so far physicists in vain look for a new natural law for finding the quantitative forces between nucleons. In fact, at very short separations of 0.001 fm, since the quarks are fermions the charges e of quarks are spinning with a spin S = 0.5(h/2π) and behave like electrons with attractive magnetic forces much more stronger than the electric repulsions. So the quarks as spinning point charges at very short distances may give a very strong attractive Fem = Fe -Fm much more stronger than the nuclear force.
Under these difficulties it was analysed the factors g = 2.793 for proton and the g = -1.913 for neutron ( L. Kaliambos 2002), which give for proton +e = (-5e/3, +8e/3) and for neutron (+8e/3, -8e/3) = 0 distributed at the centers and along the peripheries respectively. It is of interest to note that for a uniform +Q in proton one is able to get +Q = +16e/3. However it cannot occur, since for protons many experiments showed that the uncharged mass amounts to 93% of the total mass. In a simple discussion, the picture of the proton of mass m could be as a rather oblate spheroid with a radius r = 0.84 fm associated with its spin S = 0.5(h/2π) and the magnetic moment μ.To examine the experimental relation μ/S = g(e/m) = 2.793(e/m) one may find that g < 2.793, when the charges in proton Q = 4e/3 and –q = -e/3 of the quark model are distributed uniformly. Even in the extreme case in which Q = 4e/3 is along the periphery and
–q = -e/3 is limited at the center the distribution gives again g < 2.793. These puzzles are resolved under a reasonable assumption that Q = 8e/3 along the periphery and –q = -5e/3 at the center. Note that the limitation of –q at the center is supported by the deep inelastic scattering experiments, since the deflections suffered by the electrons indicated the presence of a point like charged region in the deep interior of the proton. The contribution of Q = 8e/3 to the magnetic moment μ as a circular current with a peripheral velocity υ is: μ = (Q/2)υr.
Whereas the spin S is given by S = tmυr where 0.5> t >0.4 which characterizes the shape of proton between a disk (S=0.5mυr) and a sphere (S=0.4mυr). Now if t = 0.47742 ( oblate spheroid) we get the experimental value g = 2.793. The charge Q = 8e/3 along the periphery, which is twice greater than the charge 4e/3 of the quark model, can be justified also by the fact that the moment of proton is about twice greater than that given by the simple quark model of the uud scheme. Note that using the same method for neuton we get the distribution Q’ = 8e/3 at the center and
–Q’ = -8e/3 along the periphery.
THE ATTRACTIVE NUCLEAR FORCE IS DUE TO ( p-n ) INTERACTIONEdit
After the failure of Heisenberg’s “exchange force” and without detailed knowledge about the charged substructure of proton (p) and neutron (n), Yukawa’s meson theory seemed to be valid under the discovery of several mesons. 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 general hypothesis of the “charge independence” cannot be applied to the scattering data. Also, the general ideas of all physisists that there exist purely attractive forces of p-n, p-p and n-n systems cannot lead to the saturation and the decay of light nuclei.
Thus, in the absence of a realistic force the most important structure models like the liquid drop, the Fermi gas, the nuclear shell, and the collective model, lead to complications. Ohanian emphasizes that such models are caricatures of the real world. 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.Of course the aspect of the quantum chromodynamics that the nuclear force is due to the residual strong interaction between the hypothetical color-charged constituents of nucleons, cannot provide any framework for quantitative measurements. Moreover, the quark picture, 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 was formulated by L. Kaliambos (2002) 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 fact the so-called strong interaction is due to a dipolic force of p-n systems since both proton and neutron behave like dipolic particles because of the charge distributions. . Strong interactions 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 with a large number of detailed calculations of electromagnetic forces at the shortest separation 2r = 1.68 fm give a p-n bond, whose the binding energy equals the experimental value E = -2.2246 MeV. Here the dipolic force F(p-n) is
given by F(p-n) = -Fe(- 5e/3,8e/3) – Fe(8e/3-8e/3) – Fm(8e/3-8e/3) +Fe(-5e/3,-8e/3) +Fe(8e/3,8e/3).
Note that the first term –Fe(-5e/3,8e/3) of these point charges at the centers of nucleons under the application of the simple Coulomb potential at the short separation 2r = 1.68 fm give E = - 3.81 MeV, which is stronger than the binding energy E = - 2.2246 MeV of deuteron.The simple p-p and n-n systems operate also in radial direction but they give spins of S = 0 with repulsive forces since in nucleons the repulsive electric force is always stronger than the magnetic one.
Note that the proton and the neutron can interact also along the spin axis z with a very strong dipolic force, when the two deuterons interact for the formation of helium, because the parallel spin of each deuteron gives B=0. In this case there is not any opposite current to the spins during the formation of helium. However it is a great difficulty for the formation of helium because of the great repulsions of protons. But at a separation r < 2fm the p-n attraction becomes stronger than the p-p repulsion.
NUCLEAR STRUCTURE IS DUE TO p-n BONDS WHEN THEY EXCEED THE p-p AND n-n REPULSIONS SINCE A CLOSE PACKING BRINGS p-n BONDS CLOSER TOGETHEREdit
Although the simple p-n bond does not obey the Pauli principle the most important structure models like the Fermi Gas, the Nuclear Shell and the Collective are based on this principle leading to complications. Under these difficulties there were used the p-n bonds which must exceed the p-p and n-n repulsion.(L.Kaliambos,2002). Here a close packing of nucleons tends to increase the binding energy 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 involving stronger p-n bonds in axial direction than those in radial one. They form helium nucleus with S=0 which is a two-dimensional rectangle with two p-n bonds per nucleon.(See in diagrams). Despite this small number of p-n bonds per nucleon, helium is extremely stable since the identical nucleons exert weak repulsions as a result of the non oriented spins and the greater separations (diagonals). In the first diagram you see the two deuterons D1 and D2 formed along the radial direction with parallel spins of p1-n1 and p2-n2 systems.
For the structure of Helium the two deuterons D1 and D2 of the first diagram are coupled along the spin axis z. Here the p1-n2 and p2-n1 bonds along the spin axis are very strong with oriented spins of S=0. They exceed the weak repulsions of non-oriented spins of the p1-p2 and n1-n2 systems along the diagonals x of the formed rectangle. Therefore a very strong binding energy of -28.29 MeV appears with a total spin S=0 of the p-n bonds. This opposite spin led to the Fermi Gas model, because it was believed that helium has no p-n bonds but p-p and n-n bounds of S=0 according to the Pauli principle, even though the simple p-p and n-n systems cannot exist. Also, the large energy of helium and of other very stable nuclei (magic nuclei) led to the model of the nuclear shell, which cannot be related to the stable electron shells due to the central potential in atoms. Two-dimensional shapes are formed, also, in other light nuclei. However they have binding energy weaker than that of helium due to repulsive forces of additional oriented p-p and n-n systems. On the other hand, some lightest nuclei 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, as in the Carbon-14 in contrast to the stable single bond of deuteron which has not any p-p or n-n repulsion.
Dramatically, at the beginning of the three-dimensional structure there is a great difficulty for two rectangles of Helium-4 to form a simple parallelepiped of the extremely unstable Beryllium-8. 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 three p-n bonds per nucleon.(See in diagram).
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 increasing 4 or 5 p-n bonds per nucleon in inner rectangles or squares.(See the diagram of O-16). This dynamic situation 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.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 and the known binding energies of nuclei 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 number of p-n bonds per nucleon to the maximum number of 6.(See the diagram of Pb-208). 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.
Here you see the diagrams of He-4, Be-8, O-16 and Pb-208 with the centers of p (٠) and extra n (o) while the centers of ordinary neutrons are at the rest cross sections.