_{1}

After one century of nuclear physics, its underlying fundamental laws remain a puzzle. Rutherford scattering is well known to be electric at low kinetic energy. Nobody noticed that the Rutherford scattering formula works also at high kinetic energy, needing only to replace the repulsive electric -2 exponent by the also repulsive magnetic -6 exponent. A proton attracts a not so neutral neutron as amber attracts dust. The nucleons have magnetic moments that interact as magnets, equilibrating statically the electric attraction between a proton and a not so neutral neutron. In this paper, the electromagnetic potential energies of the deuteron 2H and the α particle 4He have been calculated statically, using only electromagnetic fundamental laws and constants. Nuclear scattering and binding energy are both electromagnetic.

Two millenaries ago, Thales discovered the electrical properties of amber (

The neutron, discovered in 1931 by Chadwick, seeming to be uncharged, the electromagnetic hypothesis of the nuclear interaction was abandoned. The magnetic moments of the proton and of the deuteron were discovered in 1932 by Stern [

In nuclear physics, electric (except so-called Coulomb force) and magnetic interactions between nucleons are still considered to be negligible, although: “The positive charge attracts negative charges to the side closer to itself and leaves positive charges on the surface of the far side. The attraction by the negative charges exceeds the repulsion from the positive charges, there is a net attraction” [

The electrostatic attraction in the deuteron between a proton and a not so neutral neutron is equilibrated statically by the repulsion between the opposite magnetic moments of the proton and of the neutron. The magnetic interaction between nucleons is attractive or repulsive depending on the position and orientation of their magnetic moments. First theoretical results have been obtained for hydrogen and helium isotopes [

The sum of the electric and magnetic potential energies between electromagnetic particles is the fundamental combination of Coulomb electric and Poisson magnetic potentials [

The first term is the sum of the electrostatic interaction potential energy between electric charges

The electrostatic potential energy per nucleon

According to the general formula (1) the total magnetic potential energy of the deuteron is:

The magnetic moments of the proton and of the neutron in the deuteron are known to be collinear and opposite, (

Adding the attractive electrostatic Equation (3) and the repulsive magnetic Equation (5), the electromagnetic potential formula (1) becomes, per nucleon, with A = 2 of the deuteron ^{2}H:

or, numerically (see Appendix):

There is one variable

The single neutron-neutron and proton-proton bonds, being small in comparison with the 4 neutron-proton bonds, have been neglected provisionally. The electric interactions between protons are surely repulsive. The electric interaction between neutrons is probably weak. The magnetic interactions between neutrons and between protons are assumed to be repulsive. The structure of ^{4}He is shown on

We shall calculate the ^{4}He binding energy per nucleon from the deuteron ^{2}H potential energy, which is, as seen before (Equation (6)):

A neutron-proton ^{4}He bond is one total attractive ^{2}H deuteron bond, thus −2.2 MeV equilibrated by the product of 2 magnetic interactions, inclined by 60˚, thus dividing the repulsive magnetic potential binding energy twice by 2 thus by 4. The magnetic moments of the proton and the neutron, being perpendicular (

or, numerically (see Appendix):

The graphical solution (

The binding energies of the deuteron and of the α particle have been calculated by applying only fundamental electromagnetic laws and constants with the experimentally proved properties of the nucleons and the nuclei. The binding energy error is about a few percent for the deuteron and almost 10 percent for the α particle, due to the neglect of the neutron-neutron and proton-proton interactions. The only adjusted parameter a is used to obtain the single horizontal inflection point characterizing the binding energy of a nucleus. Not to be confused with fits.

The agreement between experimental results and the electromagnetically calculated Rutherford nuclear scattering (normal and not so “anomalous”) and nuclear binding energy proves the electromagnetic nature of the nuclear interaction. No need of hypothetical strong force and quarks.

Thanks to persons at Dubna for their interest to my electromagnetic theory of the nuclear energy. The first question was about scattering. I said I don’t know. Now I know: The anomalous Rutherford scattering is magnetic. The second question was: “The strong force doesn’t exist?” and a third one about orbiting nucleons [

Schaeffer, B. (2016) Electromagnetic Theory of the Nuclear In- teraction. World Journal of Nuclear Science and Technology, 6, 199-205. http://dx.doi.org/10.4236/wjnst.2016.64021

・ Light velocity:

・ Fundamental Electric charge

・ Electric constant

・ Magnetic constant

・ Proton mass:

・ Proton magnetic moment

・ Neutron magnetic moment

・ Proton-neutron magnetic moments combined