## Electromagnetic Nuclear Physics

B. Schaeffer,

retired,

bschaeffer@wanadoo.fr

**Nuclear Scattering is electric at low kinetic energy and magnetic at high kinetic energy.**

The electric and magnetic forces were discovered qualitatively ** 2** millenaries ago by Thales, and quantitatively by Coulomb and Poisson, two centuries ago.

Rutherford discovered the electric scattering with a ** -2 **slope in logarithmic scales. At high kinetic energies, the not so "anomalous" scattering has a slope

**, magnetic,**

*-6***before:**

*never noticed*Generalised Rutherford scattering is **electric** or **magnetic**

at **low** or **high** kinetic energy**.**

**Nuclear Energy is Electromagnetic**

Deuteron **^{2}H** and α particule

**binding energies calculated graphically:**

^{4}HeAssuming that the deuteron **^{2}H** has one proton with one

**charge and one neutron**

*+e***and**

*+e***charges, separated by**

*-e***, adjusted to the single horizontal inflection point. The electric attraction is equilibrated statically by the magnetic repulsion, function of the neutron-proton separation distance**

*2a***and the electric**

*r*_{np}**charges separation.**

*2a***, the binding energies of**

*As by chance***and**

^{2}H

^{4}He**coincide**with their

**horizontal inflection points**.

*References:*

Electric and Magnetic Coulomb Potentials in the Deuteron

ADVANCED ELECTROMAGNETICS,

Vol. 2, No. 1, September 2013, p. 69.

Anomalous Rutherford Scattering Solved Magnetically

World Journal of Nuclear Science and Technology 2016, 6, 96-102

## NUCLEAR PHYSICS IS ELECTROMAGNETIC

It is usually believed that the "strong interaction" is a fundamental force although its fundamental equation has never been discovered, even after one century after the discovery of the electric Rutherford scattering. The best known formula of this mysterious force is that of Yukawa, a combination of an ersatz of Coulomb's law and an exponential:

It is attractive with 2 empirical parameters. The negative sign of the potential is wrong. The problem is that the nuclear physicists know from the electromagnetic interaction only what they call "Coulomb force", repulsive.

The real nuclear interaction is electromagnetic. The electric part was discovered by Rutherford. At high kinetic energy, the magnetic part overcomes the electric part, as shown on the graph below. They reject systematically my papers because they fear to be ridiculous. They ignore that there is also an attractive Coulomb force. The Poisson magnetic interaction is completely ignored: the nuclear interaction is entirely and only electromagnetic.

There are two proofs of the electromagnetic nature of the nuclear interaction: **1 - RUTHERFORD SCATTERING IS ELECTROMAGNETIC**

The Rutherford scattering is well known to be electric. One century ago, Chadwick, the discoverer of the neutron, assumed a strong attractive force. Bieler assumed it to be magnetic, unfortunately also attractive. I assumed it to be also magnetic, but repulsive, as for the electric Rutherford scattering.

Indeed, it needs only to change, in the Rutherford formula, the electric exponent -2 by the magnetic -6. These numbers correspond to the electric, 1/r, and magnetic potentials 1/r³, whose exponents are multiplied by 2, due to scattering surface. One obtains straight lines, with slopes -2, for electric Rutherford scattering, and -6, for the so-called anomalous scattering, discovered to be magnetic:

Attached, the paper rejected by the Royal Society: RSPA_Author_tex

Here is their arguments again my paper:

"In this article the author promotes his view of nuclear forces, which is that the **Strong Force does not exist**. The author's arguments lack credibility being simply classical arguments and fits, there is no fraction of the substance that would be required to seriously challenge one of the pillars of modern physics, i.e. the **Standard Model**" A PILLAR MAY CRUSH...

**IN CONTRAST WITH THE ELECTROMAGNETIC THEORY, THE STANDARD MODEL, HAVING NO FUNDAMENTAL LAWS, IS UNABLE TO CALCULATE THE BINDING ENERGY OF EVEN A SIMPLE BOUND NUCLEUS AS 2H**.

**2 - BINDING ENERGY OF NUCLEI IS ELECTROMAGNETIC**

The binding energies of nuclei can be calculated successfully, without fit, by the bare application of the electromagnetic theory. Indeed, there is an electric attraction between a proton and a not so neutral neutron equilibrated by their magnetic repulsion, both ignored by mainstream nuclear physicists.

This graph shows that the binding energy of atomic nuclei can be calculated electromagnetically.

A published paper shows the electromagnetic calculation of the simplest bound nucleus, the deuteron ²H:

The H and He isotopes have also been calculated electromagnetically:

**3 - STABILITY VALLEY HAS A MAGNETIC SLOPE**

Moreover, this equation has a physical meaning. Indeed, the 0.71 is the ratio between the neutron (-1.913) and proton (+2.793) magnetic dipoles. This is not by chance: as shown in paragraph 2, it is due to the fact that the magnetic moments equilibrate the electric attraction. The magnetic moment of the neutron being smaller than that of a proton, it needs more neutrons than protons to equilibrate the electric force.

Nuclear physicists know only the repulsion between protons, ignoring that there is an attraction between a proton and a neutron, a phenomenon discovered by the Greeks two millenaries ago between amber, elektron, and dust. They call "spin" the magnetic interaction, discovered by Magnès,

## Nuclear models

It is known since one century that nuclear energy is of the order of one million times more concentrated, in the same mass, than chemical energy.The radius of the atomic nucleus is, indeed, of the order of one million times smaller than that of a molecule. This is because the chemical and nuclear binding energies are of the same electric nature : they obey both to the Coulomb's laws, in **1/r** where r is the radius of either a nucleus or a molecule. No need of a mysterious "strong force". According to Einstein, the energy of an object of mass m is **E = mc².** According to Bohr, the chemical energy is **α²m**_{e}**c²** . According to Schaeffer, the nuclear energy is **αmc²**, intermediate. **m** is the considered mass, **m**** _{e}** the mass of the electron,

**α**= 1/137 the fine structure constant and

**c**the velocity of light. The so-called "strong force" (also referred to as the strong nuclear interaction or force) is the hypothetical force binding together the protons and the neutrons in an atomic nucleus. The word strong comes from the fact that the nuclear energy is around one million times greater than the chemical energy, for the same volume, dramatically demonstrated at Hiroshima. It is also known that the binding energy is around 1% of the mass energy mc². There are two well known fundamental forces in nature, the universal gravitation (formulated by Newton) and the electromagnetic force (formulated by Maxwell). It is fashionable to add two more hypothetical forces : the strong and weak nuclear forces. Very little is known about these forces.

According to the Bohr scheme, the electrons gravitate around the nucleus. The shell model assumes that the nucleons also gravitate (they don't on the graph) around a hypothetical force center. Indeed the nucleus has no nucleus around which the nucleons may orbite.

**The origin of the strong force**

The Rutherford scattering experiment, one century old now, consisted to collide alpha particles from a radioactive element on an atomic nucleus. The alpha particles from the radioactive element striking gold foils are scattered in different orientations. In a constant orientation, the number of particles per solid angle, called cross-section dσ/dΩ, are mesured as a function of the kinetic energy obtained by varying the number of gold foils:

In the classical theory of 'anomalous' scattering the potential energy, where r is the separation distance from the nucleus, is represented usually in the form, where B seems to be positive:

The problem was to find n. Bieler, a Rutherford student, imagined in 1924 a magnetic attraction equilibrating an electrostatic repulsion between the protons (this is valid for the nuclear energy as I have shown elsewhere). Here the minus sign is wrong. Indeed, the electric interaction discovered by Rutherford explains the diffusion of the α particle by an atomic nucleus. For high energies, it doesn't work, thus "explained by a mysterious "strong force". In fact, the magnetic force replaces the electric force, thus the electric 1/r Coulomb's law is replaced by the magnetic 1/r³ Poisson's law. The sign should be the same, thus positive instead of negative as hypothesized. The graph shows the electric part (1/r law) discovered one century ago by Rutherford and the not so anomalous magnetic part (1/r³ law), discovered by me:

The coordinates of this graph are both logarithmic, giving straight lines with -2 and -6 slopes due to the Rutherford formula where the potential exponents are multiplied by 2:

**Binding energy**

The binding energy per nucleon is given by the formula

BE/A = (Z m** _{p}** + N m

**- M)/A**

_{n}where Z is the atomic number, N the neutron number and A = Z + N is the atomic mass number. M, m** _{p}**, and m

**are the masses of one nucleus (approximately of an atom), one proton and one neutron.**

_{n}At a time when the neutron was not discovered, Aston used the packing fraction given by the formula:

f = (M - A)/A

where M is the mass of the atom measured experimentally and A the atomic number.

**The Shell Model or Independent-particle Model or Hartree Model**

The official mainstream physics model of the atomic nucleus is the shell model which the atomic model of Bohr and continuators adapted to the atomic nucleus.

The electrons are replaced by the nucleons. There are two kinds of nucleons, protons, electrically charged, and neutrons, uncharged. Contrarily to the atom, the nucleus has no nucleus. This deficiency is circumvented by the bold assumption that each nucleon experiences a central attractive force which can be ascribed to the average effect of all the other nucleons in the nucleus. On this assumption, each nucleon behaves as though it were movins independently in a central field, which is described as short-range potential well. Secondly, this potential is assumed to be the same for all values of *l,* the angular momentum quantum number of the nucleons. In the assumed central potential, each nucleon is imagined to be capable of describing an orbit of well-defined energy and angular momentum, in a manner analogous to the behavior of atomic electrons.

This assumption seems to be in conflict with the strong interaction between nucleons, as seen experimentally, and in nuclear reactions generally. This weak interaction paradox was solved by using the Pauli exclusion principle. The expected strong interaction may be present but unable to manifest itself because all the quantum states into which the nucleon might be scattered are already occupied…

The main characteristic of the shell model is the so-called "magic numbers" (Z and/or N = 2, 8, 20, 28, 50, 82, 126) corresponding to the atomic levels.

**The Liquid drop Model or Semi-empirical Mass Formula**

The liquid drop model is the antithesis of the independent-particle model. The interactions are assumed to be strong instead of weak. The initial assumptions are (Evans p. 365) :

1. The nucleus is like a droplet of incompressible matter, and all nuclei have the same density.

2. Forces between nucleons are considered to be spin-independent as well as charge-independent if the coulomb force is turned off.

3. These nuclear forces have a short-range character and are effective only between nearest neighbors. Each nucleon interacts with all its nearest neighbors.

4. The volume or exchange energy is proportional to to the number of nucleons A for A ≥ 16, giving a radius R_{0 }**A ^{1/3}**, where R

**is a constant.**

_{0 }5. The surface energy is like the surface tension of a liquid due to the fact that nucleons at the surface have fewer near neighbors than nucleons that are deep within the nuclear volume. We can expect a deficit of binding energy for these surface nucleons. A simple calculation shows that the surface energy is proportional to **A ^{2/3}**.

6. The Coulomb repulsion energy between protons is the only known long-range force in nuclei. The total nuclear charge Ze is assumed to be spread approximately uniformly throughout the nuclear volume. Again assuming a constant-density nuclear radius R** _{0 }**A

^{1/3}and applying the Coulomb law for the potential, the Coulomb energy is proportional to

**Z**.

^{2}/A^{1/3}7. The asymmetry energy, the deficit in energy dependent on the neutron excess or deficit, is **(N - Z) ^{2}/A = **

**(A - 2Z)**.

^{2}/A8. The pairing energy δ is a correction to take into account the pairing of N and Z.

The complete Bethe-Weizsäcker formula is

The following graph shows the Bethe-Weizsäcker curve (in blue), compared with the experimental data (in red) for the N = Z nuclei. The BW formula is unable to represent the binding energies of even Z and even N. There is also no distinction for same A nuclei with even N - odd Z and even Z - odd N (mirror nuclei).

Atomic number in abscissas and binding energy per nucleon in ordinates

**Four-shell structure or α particle model**

This type of models have been initiated by Gamow who observed that the nuclei with atomic masses multiple of 4 have larger binding energies. Indeed, it can be observed peaks of the binding energies for even A, Z and N. It is maximum for both N and Z even. The addition of an α-particle adds a tetrahedron to the structure already existing and so three bonds are alloted per addition.

For example, the maximum of ³Li is smaller than for both ²He and ⁴Be. **For given Z, peaks appear for even N. They are greater if Z is also even. The amplitude diminishes when Z increases**. The peaks are small but detectable even for the heavy nuclides:

**Binding energies of 2,000 nuclides (Excel, to be downloaded)**

**Supercomputer calculations**

The following curve shows the helium isotopes total binding energies, experimental and "ab initio", calculated by a supercomputer . It shows that the total binding energy is practically constant, except for the pairing effect, for the N>2 isotopes of helium. The discrepancy with the experimental values is attributed to the "3 body force". In fact, a better approximation is obtained by assuming that the excess neutrons are unbounded (halo nuclei). The red horizontal line is nearer to the experimental values (in red) than the super computer calculated orange line. Moreover, it seems that 4H (alpha particle) has not been calculated at all : the -28 MeV is the experimental value of its total binding energy. Even the simplest bounded nucleus (2H, the deuteron or heavy hydrogen) has never been calculated "ab initio". The fundamental laws and constants of the so-called "strong force" are still inexisting after one century of nuclear physics.

Figure 5. ORNL's Jaguar, the world's second fastest computer, enables certain nuclear calculations only dreamt of a few years ago. As an example, Jaguar was used for the first ever ab initio computation of neutron-rich helium nuclei using coupled cluster theory (shown in the figure on the side of the computer). The figure shows the binding energy of these nuclei, while the inset indicates the width, related to lifetime. Experimental data are marked in red. The calculated masses show a systematic deviation from experiment; this can be attributed to a three-body force, missing in the calculation. (original legend)

**Energy per proton**

Dividing the total binding energy by the the proton number, one obtains the following curves. From selected elements of the atomic mass table, one sees that the binding energy **per proton** tends towards a limit for each chemical element :

This limit is maximum for Fe and neighbors. For heavier nuclides, the binding energy decreases, due to the Coulomb repulsion between the protons.

**Electromagnetic theory of the nuclear force**

It is believed since almost a century that the strong force cannot be electromagnetic. This is incorrect because the nucleus has no nucleus or, in other words, the angular momentum has no fixed point like the atom. Therfore such a nucleus cannot be stable. The proof is given by my calculations ("Electromagnetic Theory of the Binding Energy of the Hydrogen Isotopes", J Fusion Energy (2011) 30 :377-381 here).

**Deuteron binding energy**

For the simple case of the deuteron, I have obtained the following formula:

If you have studied electromagnetism you will recognize the Coulomb attractive force and the magnetic repulsive force. Graphically, it gives the electromagnetic nuclear potential similar to other phenomenological potentials but truly ab initio because it contains only universal constants:

The formula in the graph is the same as the previous one but with different universal constants. One may recognize the famous mc² formula for the mass energy. It is multiplied by the fine structure constant α = 1/137. R** _{P}** is the proton Compton radius. g

**and g**

_{p}**are the Landé factors of the proton and of the neutron.**

_{n}A better precision is obtained with a graphical resolution taking into account both electric charges in the neutron. Comparison is given below :

The curve at the right is the same as above. The scales are to be divided by 100. This is the first ab initio calculation of the binding energy of a nucleon (ab initio means a calculation using only fundamental constants, without adjusting parameters, and a well established theory e.g. Maxwell theory of electromagnetism).

**Binding energy of the hydrogen isotopes**

The binding energies of all the hydrogen isotopes have been calculated assuming the following structures:

**Simplified calculation for H and He nuclei with N > 2**

This method has been simplified for the hydrogen (giving the same results) and helium isotopes with N > 2. It is assumed that the total binding energy is the same when the number of nucleons is larger than 2, due to the small binding energy of the excess neutrons. These nuclei are called halo nuclei. The 4He binding energy is too low, probably due to the neglect of the positive charge of the neutron. More precise calculations are necessary for 4He. One can see that the binding energies of the N>2 isotopes are parallel to the experimental curves, justifying the approximation of almost zero binding energy of the last neutron (halo nuclei).

**Nuclear to chemical energy ratio**

The electromagnetic theory of the nuclear energy shows that it is αmc² or 1/137 of the mass energy, known to be of the order of 1%.

It is well known that the chemical energy is given by the Rydberg constant from the Bohr theory of the atom, ½α²m_{e}c² where m_{e} is the masses of the electron and α the fine structure constant.

The electromagnetic theory gives also the nuclear to chemical energy ratio, *for the same weight*, as

α^{-1}m_{p}/m_{e} = 137 x 1836 = 250,000

where m_{p} and m_{e} is the mass of the proton. This formula, a consequence of the electromagnetic theory, explains for the first time why the nuclear energy is up to one million times more concentrated than the chemical energy, f*or the same volume*.

My presentation about the Strong_Force, and the calculated binding energies of hydrogen and helium binding energies H and_He_energies, may be downloaded.

**Simple derivation of the nuclear to chemical energy ratio**

It is known since one century that radium releases a huge energy, one million times larger than any combustion energy, according to Pierre Curie and others. This is the reason why nuclear energy is expressed in MeV and chemical energy in eV. "The energy stored by the binding energy of the outer electrons to the nucleus is, inversely, very much smaller (a hundred thousand or even a million times smaller), than that stored in the binding of nucleons in the nucleus. I have often been asked why it is that the smallest particles carry the largest energy. The precise analysis of this relation would lead us too far." Using this suggestion, we shall compare theoretically the radius and energy ratios of the hydrogen atom and the deuteron nucleus. The Bohr radius of the hydrogen atom is :

where

is the fine structure constant, representing the strength of coupling between radiation and matter, appearing also in the nuclear cross section. h is Planck's constant, m_{e}, the electron mass and c, the light velocity.

H atom and ^{2}H nucleus. - Comparison between electron and neutron distances. a_{0} is the Bohr radius and R_{P} is the proton Compton radius identified with the proton radius.

There exists no formula, using fundamental constants only, for the radius of a nucleon. Therefore we shall use the proton Compton radius R_{P}, five times smaller than the experimental value of the proton radius but of the same order of magnitude, knowing that the binding energy per nucleon varies from one to ten times from deuteron to iron :

where m_{p} is the proton mass. In the deuteron, the distance between the centers of the neutron and the proton being 2R_{P} (figure), one obtains an expression of the ratio of the separation distances of the electron and of the neutron from the proton :

The separation energy of a neutron from a proton is 2.2 MeV and 13.6 eV for an electron from a proton, giving a 163,000 ratio. The Bohr formula of the binding energy of the fundamental state of the hydrogen atom is :

Multiplying by a_{0 }/ (2R_{P}) from equation above, one obtains the binding energy of the deuteron :

This value was already obtained with an electromagnetic method. It is 30 % smaller than the experimental value, 2.2 MeV. A more precise result with a three body formulation (unpublished) gives a precision of 5 %.

Dropping the 1/4 coefficient, one obtains a mean value of the order of magnitude of the nuclear binding energy per nucleon :

which is coincidentally almost that of the alpha particle, 7.02.

This calculation explains why the binding energy of the nuclei is between 0.1 % and 1 % of the mass energy, or, per nucleon, between 1 MeV for the deuteron and 10 MeV for iron.This simple calculation confirms that the order of magnitude of the binding energy of a nucleus can be found theoretically from first principles and fundamental constants without ad hoc constants.

Poster: (click to enlarge or, better, unload it)

## Groningen and Bobeszko

Presentation at Groningen:

My calculation of the deuteron 2H binding energy has been verified by A. Bobeszko:

There are some restrictions:

"The internucleon distance is much less than experimentally estimated."

The separation distances r and a are not internucleon distances, not considered here. They separate pointlike electric charges and magnetic moments.

A single horizontal inflection point is obtained by adjusting the parameter a. The corresponding potential coincides with the experimental binding energy potential not only for 2H, but also for 4He as shown on the presentation above. Physically, the inflection point may be unstable, due to the point-like approximation of the electric charges. Up to now no other theory exists to obtain the binding energy of a nucleus with fundamental laws and constants only.

"The assumption of existence of a ‘hard’ core repulsion between nucleons."

Using a ‘hard’ core destroys the fundamental nature of the above calculation. The horizontal inflection point is characteristic of a nucleus, here 2H or 4He as shown on the presentation above.

## Two or 4 Forces of Nature ?

### It is usually believed that there exists four forces like the four musketeers:

### gravitation, electromagnetic, strong, weak.

The first two forces, gravitation and electrostatic are known since two centuries. The electric force is in 1/r² and 1/r for the potential. Similarly, The magnetic force in 1/r⁴ and its potential in 1/r³.

The strong and weak forces remain hypothetical: their fundamental laws are ignored.

The strong force, varies, depending of the taste of the scientist, from 10, 137 to 1000 times stronger than the electromagnetic interaction, depending on the author. The coupling constant of the electromagnetic interaction is assumed to be 1/137, the strong force is assumed to be 1 (why? nobody knows) although it is not a constant.

The weak force, recently unified with electromagnetism under the name electroweak interaction, could be entirely and only electromagnetic…

The fundamental laws of the strong and weak forces remain unknown. It is not the LHC with its Higgs boson, a modern philosophical stone or Holy Graal, that will solve the problem. As it is not by swatting a fly that its internal structure may be known, the high energies are unsuitable to explore the atomic nucleus.

The fundamental constants of the strong force are still inexistent in tables like the Handbook of Chemistry and Physics. Mainstream physics still ignores the physical nature of the nuclear interaction. It is therefore unable to explain why the nuclear energy is one million larger than the chemical energy and also predict that the nuclear energy is around one percent of the Einstein mass energy **mc²**.

**The nuclear interaction is electromagnetic**

Bohr solved the problem of the atom two years only after Rutherford discovered the atomic nucleus. The nuclear shell model was imagined by analogy with the Bohr model of the hydrogen atom where the electrons orbite around the nucleus. One century later, a coherent theory of the nucleus is still inexistent : nuclear physics seems to be in a dead end.

The reason of this long unsuccessful research by thousands of distinguished scientists comes from the belief that the nucleus behaves like the atom. The nucleus contains no predominant central particle, no nucleus around which the nucleons may orbit. Therefore the angular momentum is undefined. With an orbital movement, the deuteron is comparable to binary stars whose stability is questionable.

**Structure of the simplest bound nucleus, the deuteron:**

For the sake of simplicity, let us consider the simplest compound nucleus, the deuteron, made of one proton and one neutron.

The proton contains the same electric charge as the electron, but of opposite sign. The not so neutral neutron contains electric charges with no net charge. The intrinsic spin of the nucleons generates the proton and neutron magnetic moments by the rotation of their internal electric charges. The Pauli exclusion principle does not apply because the proton and the neutron are distinguishable. The spins of the proton and the neutron are known to be parallel in the deuteron. The electric charges and the magnetic moments may be assumed to be collinear by reason of axial symmetry. Indeed, the magnetic moment of the deuteron is close to the difference between the proton and neutron magnetic moments as was shown by Rabi. The magnetic moments of the proton and the neutron in the deuteron, being collinear and opposite, the magnetic interaction between the magnetic moments of the deuteron nucleons is thus repulsive. The deuteron bindind energy can thus be calculated electromagnetically, as shown **in my paper:**

Bieler of the Rutherford laboratory imagined in 1924 a magnetic attraction equilibrating an electrostatic repulsion between the protons. Since the discovery of the neutron and the magnetic moments of the nucleons proving that the neutron contains electric charges, nobody, as far as I know, has tried to apply electromagnetism to the nuclear interaction.

## Forces between nucleons according to Evans

### Citations of R.D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1969, Chater 10 and 11, are in quotation marks. *Comments in italics.*

**Chapter 10 Forces between nucleons**

1. **General Characteristics of Specifically Nuclear Forces**

**a. Comparison of Atomic and Nuclear Forces**

"no predominant central particle" :* the nucleus has no nucleus like the atom*

The forces have a very short range of action: *the measurement of the range of action is undefined, unlike the radioactive decay period*.

"In order to confine a nucleon to a region of this size, (…) its kinetic energy must be of the order of (…) 20 MeV. * There is no experimental proof that the nucleons should have an orbital movement*.

*Is there an orbital movement of the atoms in a molecule or a crystal? No. The usual shell model is an adaptation of the atomic model of Bohr and followers not necessarily applicable to the atomic nucleus.*

**b. Inadequacy of Classical Forces**

"the total binding energy of nuclei is proportional to the number of nucleons A and not to A²". *This is well known in chemistry and crystallography*.

"The electrostatic potential energy between the same two nucleons is identically zero because the neutron is uncharged". *The neutron is not uncharged, it contains electric charges with no net charge*.

**c. The Singlet and Triplet Forces between Nucleons**

"Because the nucleons are fermions and obey the Pauli exclusion principle, there can be involved at most two neutrons (spin "up" and spin "down") and two protons in such a group". *Nothing to say about it, except that there exists no physical explanation of the exclusion principle and its applicability to the nucleons*.

"The possible forces therefore include three types of singlet forces (antiparallel spins) (…) The triplet forces (parallel spins) are restricted to one type for S states" *Not very clear*.

"The (pp) force represents the specifically nuclear attractive force between two protons and do not include their purely classical coulomb interaction". *What is the experimental basis?*

"That there exists also a strong attractive force (nn) between neutrons is shown by the fact that the neutron excess (N - Z) in nuclei varies approximately as A^{5/3 }and appears to counterbalance the disruptive coulomb forces in heavy nuclei". *Although this law (Evans p. 272) is somewhat better than the linear correlation, it is not a proof of the existence of the strong force*.

**d. Exchange Forces**

"The clear experimental evidence that nuclear forces show saturation directs our attention toward the purely quantum-mechanical concept of exchange forces". *This is a strange idea. Saturation is not specific to the nucleus: it exists also in crystals like NaCl. In fact saturation is common in all materials where the chemical binding energy is proportional to the mass*.

1. "Heisenberg forces in which there is an exchange of both the position and spin coordinates of the two interacting nucleons" *Strange hypothesis*.

"Heisenberg forces are ruled out by the clear experimental fact that the α particle is the saturation subunit". *I would better say that the nucleons with Z and N larger than 2 contain α particles*.

2."Majorana forces,in which there is exchange of the position coordinates but not of spin. *Variant of Heisenberg forces.*

3. "Bartlett forces, in which there is exchange of the spin coordinates but not of the position coordinates". *Variant of Heisenberg forces*.

**e. Tensor Forces**

"With central forces, the probability density of nucleons S states must be spherically symmetric". *Of course*.

"the strength of this noncentral force, or tensor force, depends not only on the separation between the interacting pair of particles but also on the angle between the spins of the particles and the line joining the particles, like the force between two magnets". *This force may be actually magnetic, not only a imitation*.

"some other small effects are explicable if there is admixed with the dominant central force a small amount of a noncentral force." *This is a second order effect, the first order effect needs the knowledge of the universal constants characterizing the nuclear forces, still unknown*.

**f. Charge Independence of Singlet Forces between Nucleons**

"It is found that the singlet forces between all pairs of nucleons are substantially equal, i.e. ¹(np) = ¹(nn) = ¹(pp)".

*No information given about the experimental method used to obtain this result*.

**2. Ground Level of the Deuteron**

**a. Wave Function for the Rectangular-well Approximation**

"For simplicity, we may choose at first the rectangular potential well, of depth D and radius b (…) where r is the distance between the proton and neutron. (…) The radial wave equation for the relative motion becomes

where M is the reduced mass of the proton and neutron (…). and W is their total energy (…). For the ground level of the deuteron, the total energy W is restricted to the single constant value W = - B where B =2.225 MeV is the observed binding energy of the deuteron". *The calculation continues to obtain* "the rationalized de Broglie wavelength λ of the relative motion of two particles having reduced mass M and sharing kinetic energy equal to the binding energy B of the deuteron".

*This binding energy has never been calculated. C**alculations i*** mproperly called ab initio never use universal constants because the universal constants of the nuclear forces are unknown**.

**Chapter 11 Models of Nuclei**

**1****. Summary of Experimental Evidence Which Should Be Represented by the Model**

**1. Nuclear angular momenta I of ground levels**

For even-Z even-N nuclides, *I=0*.

For odd-Z odd-N nuclides, *I *= 1, 2, 3,…

For odd-A nuclides, *I* = ½, 3/2…

Mirror nuclei have equal *I*.

Extremes of triads have equal *I*.

*No justification is given. Odd-A nuclides are of two different kinds : odd-Z even-N and even-Z odd-N. The independent parameters of a nucleus are N and Z, not A which is composite.*

**2. Magnetic dipole moments μ**

They are summarized in Schmidt diagrams. *Very low precision, due to theory or to measure?*

**3. Electric quadrupole moments Q**

Systematic empirical variation with Z or N.

**4. Existence of isomers**

Statistical concentration in "islands of isomerism".

**5. Relative parity of nuclear levels**

As seen in β and γ decay.

**6. Discontinuities of nuclear binding energy **

and of neutron or proton separation energy, as seen for particular values of N and Z, especially 50, 82 and 126. *These discontinuities at the so-called "magic numbers" are relatively small and diffuse. *

**7. Frequency of stable isotones and isotopes**

Statistical concentration for particular values of N and Z (Chap. 8, Fig. 3.1?).

**8. Pairing energy for identical nucleons**

as seen in the occurrence of stable, nonadjacent, isobars (Chap. 8, Fig. 3.3). They correspond to a sequence of completed "four-shells" and suggest an α model for light nuclei (p. 298, Chap. 9, Fig. 3.1).* They are very large for the light nuclei, particularly around ⁴He. They are very small but still detectable for the heaviest nuclides. There are peaks for even N independently of Z parity and also foreven Z independently of N parity.*

9. Constant density of nuclei

10. Neutron excess N-Z dependent on A^{5/3}

**2. The Nuclear Shell Model**

**a Assumptions in the Independent-particle Model**

In contrast with the situation with atoms, the nucleus contains no central bodywhic can act a force center. This deficiency is circumvented by the bold assumption that each nucleon experiences a central attractive force which can be ascribed to the average effect of all the other (A - 1) nucleons in the nucleus. On this assumption, each nucleon behaves as thought it were moving independently in a central field which is described as a short range potential well.

*The Weak-interaction Paradox for Low-lying States*.

"In the assumed central potential, each nucleon is imagined to be capable of describing an orbit of well-defined energy and angular momentum, in a manner analogous to the behavior of atomic electrons. (…) Thus it is possible to accept the model of weak interaction between the constituent nucleons within a nucleus at low excitation energies, without denying the inherently strong character of the interaction between free nucleons."

**b. The Sequence of Nucleon States for the Ground Levels of Successive Isotopes and Isotones**.

"The value of the independent-particle model lies mainly in its ability to give a nearly correct energy sequence for nucleon states having different values of the orbital angular momentum l. A simple rectangular well having a great depth and a radius about equal to the nuclear radius R is a sufficiently good representation of such a short-range force."

"Therefore, in each state of a given I, there can be (21 + 1) identical nucleons when spin is neglected or 2(21 + 1) identical nucleons if the energy is independent of spin orientation. The order of energy states for the deep rectangular well turns out to be 1s, 1p, 1d, 2s, 1f, 2p, 1g with 2, 8, 18, 20, 34, 40, 58 nucleons. This sequence fails to give any indication of a closed shell at 50 nucleons and fails even more clearly for still larger nucleon numbers. With more assumptions it is possible to match the higher magic numbers 50, 82, and 126, called major closed shells. The shell model, "periodic system for nuclei", with strong spin-orbit coupling, gives the first satisfactory representation of the angular momentum, parity, and magnetic dipole moment of the ground levels and the lowlying excited levels of nuclei. "

## I didn't know it was impossible

My theory of the electromagnetic origin of the nuclear interaction has been published in an american journal under the title "Electromagnetic Theory of the Binding Energy of the Hydrogen Isotopes", Journal of Fusion Energy (2011) 30 :377-381. Ma presentation in Glasgow is easier.

**Official objections of the french Académie des Sciences (December 5, 2008):**

"*1) Pourquoi les spins ne s'orienteraient-ils pas de façon à ce que l'énergie **soit négative, dont attractive?*"

It is the Bieler hypothesis in 1924, abandonned since because the neutron was not yet discovered. In the deuteron, the magnetic moments of the proton and the neutron repulse themselves like aligned and opposite magnets. They are aligned by reason of symmetry along their common rotation axis. I assume that there is no orbital movement as in the Bohr atom. Indeed the nucleus has no nucleus.

"*2) Quid du mouvement quantique de point zéro, dont l'amplitude est sûrement **très supérieure à la valeur dE calculée au paragraphe 2 (avant-dernière **formule)?*"

There is no experimental proof of a zero point quantum movement in a nucleus. It is only a theoretical assumption.

"*3) L'auteur pense expliquer l'attraction entre le neutron et le proton en **supposant que le neutron est fait de 2 particules. Mais comment **explique-t-il l'attraction qui tient ces 2 particules ensemble?*"

The neutron contains electric charges equal and opposite. They are separated under the electrostatic induction of the nearby proton. Everybody can observe that a pen rubbed on a cloth attracts small neutral pieces of paper.

*4) Si le neutron est fait de 2 particules A et B, dont l'une, soit A, est **très proche du proton alors que B est éloignée, comment ne par considérer **que c'est A et le proton qui constituent une particule?*"

There are three electric charges in the deuteron giving a quadrupole by fusion of the proton and the neutron.

*5) L'auteur évoque brièvement les quarks... mais des quarks, il y en 3 dans **le neutron, et pas 2, et puis il y en a aussi 3 dans le proton!*

The magnetic moments of the quarks have not yet been measured as far as I know, therefore cannot be used.

**Objections by an academician**

"*L'énergie d'origine électromagnétique de la paire proton-neutron est très* *petite par rapport à l'énergie de liaison, déjà assez faible, du deutéron.*"

The electromagnetic energy of the proton-neutron pair is of the order of magnitude of the binding energy of the deuteron as shows the Coulomb force between the protons (inexistent in the deuteron). It is taken into account in the Bethe-Weizsäcker model.

"*Ceci n'a rien à voir avec l'approximation du dipôle, qui est, d'ailleurs, **assez bonne pour la distance moyenne de deux nucléons dans le deutéron.*"

Surely not : the distance between the electric charges in the deuteron is given by the deuteron quadrupole moment which separation distance is 2.738 x 10^{-27} cm^{2 }. Its quadrupole moment is 0.5 fm, of the same order of magnitude as that of a nucleon. The proton is not far enough from the neutron to allow the use only of the dipole approximation.

*"Vous pouvez faire le même calcul en prenant les vraies distributions des **charges à l'intérieur du proton et du neutron. Ces distributions sont **mesurées aux expériences de diffusion profondément inélastiques, (c'est à **dire à haute énergie et à grand moment de transfert), d'électrons sur du **deutérium. Vous pouvez calculer l'énergie électrostatique, avec le dégré **de précision que vous le souhaitez, à l'aide des formules classiques que **vous trouvez dans les manuels de physique niveau lycée.*"

The precision of diffusion is much less than mass measures of the nuclides. High energy bombardment is like swatting a fly to know its anatomy.

"*Je dois avouer que votre calcul me paraît totalement incompréhensible*."

In the past, the editor Gallimard refused to publish Proust, supposed *incompréhensible*. This academician seems to ignore electromagnetism, preferring the charm of the quarks and variable constants.

Another academician accepted to discuss but withdrawed, saying that I should call a nuclear specialist. In fact, a specialist is limited in his specialty and has no hindsight on it.

**Objections of Nuclear Physics A:**

"*it is incorrect to calculate the np electromagnetic interaction by disregarding the `positive' fraction of charge in the neutron and using only the `negative' fraction*"

Although it is an approximation giving an error of 30%, it gives an analytical formula.

"*It is incorrect to use np mean distances as small as 0.6 fm in deuterium and 0.14 fm in tritium*"

The distance of 0.6 fm corresponds to that predicted by the nuclear potentials. The low value calculated for tritium is compatible with its low quadrupole moment. It experimental value seems to be unknown.

*Lastly, the scale of energy given in Eq.(20) is no more than arbitrary manipulation of the fine structure constant alpha together with the proton mass.*"

It is purely coincidental that the same letter is used for the fine structure constant and the alpha particle.The fact that αm_{p}c² is practically equal to the binding energy of the α particle is a consequence of the electromagnetic theory of the nuclear interaction.

**Objection of the European Physical Journal A**

"*the ms does not meet the scientific standards of the EPJ A*"

The scientific standards of EPJ A do not exist : I asked them but I got no answer.

**Objections of the journal Few-Body Systems**

*"The work is based on qualitative estimations of the electromagnetic interactions in the deuteron and does not fit with the minimal scientific standards of the review." *

My calculation is quantitative and in accord, at least approximate, with the measured binding energy of the deuteron never calculated by anybody even with supercomputers.

**Objections of Physics Letters B**** by a member of the "Commissariat aux Energies Alternatives (CEA)**

*"The things that you discuss are not so simple."*

If it were simple everybody would know it.

*"Your considerations, for instance, ignore completely quantum mechanics,"*

If I had ignored quantum mechanics, the fine structure constant would not appear in my formulas".

*"and just to give you one example where this is important, the binding energy is NOT the minimum of the interaction potential, kinetic energy will reduce this by a large amount (may even destroy the binding)."*

Contrarily to the atom, the nucleus has no nucleus where to apply the angular momentum. Therefore the nucleons cannot orbite like the electrons in the atom.

*"The issues that you are raising touch upon the polarizabilities of nucleons, and this has been very much studied, both theoretically and experimentally."*

The polarizabilities of the nucleons are valid only in a uniform electric field. The electric field of the proton is in 1/r², therefore not uniform in its vicinity where lies the neutron.

**Objection of the Physical Review C**

*Regrettably, your response reemphasizes the previous concerns that the manuscript is not at a level of present-day research in nuclear physics. Among other concerns, it does not consider quantum mechanics which is indispensable for objects the size of the atomic nucleus*.

With the shell model, based on quantum mechanics, it is impossible to calculate the binding energy of the simplest nucleus, the deuteron 2H.

**Objections of Europhysics Letters**

"*Your theory is on the level of knowledge* of **hundred years ago.** It is absolutely wrong and has nothing to do with the current *level of nuclear science. We would like to advise you to study one of the textbooks on nuclear physics.*"

The modern nuclear physicists ignore electromagnetics known since two * hundred years ago*.

"The head of the laboratory gave him (Schechtman, the 2011 Nobel prize winner) a textbook of crystallography and suggested he should read it."

"*This article has to be rejected with no further consideration. The author seems to be unaware that there are in nature strong nuclear forces that cannot be reduced to electromagnetic ones*

**.**"

I guess that Dr Z is unable to calculate the binding energy of the simplest nucleus beyond the proton, the deuteron. There is no experimental proof of the existence of the so-called strong force. It is usually assumed that its coupling constant αs is 1, but it varies depending on the authors. It is now a variable constant (a good joke) : "the coupling constant of the strong force becomes weaker at high energies". This proves that the laws of the nuclear interaction remain unknown after one century of nuclear physics and it is impossible to calculate ab initio from the strong force the binding energy of the nuclides.

**Rejected without justification**:

* "On behalf of the FFP12 Scientific Organizing committee, I am sorry to inform you that your abstract ID's:34 Titled:**Discovery of a formula for the nuclear to chemical energy ratio; *

*has been rejected*."

**The European Physical Journal - Plu**s

Reviewer #1: The author claims that only electromagnetic forces would be necessary to determine nuclear stability. This means the nuclear interaction can be disregarded to discuss the stability and nuclear dynamics. Even admitting this controversy hypothesis, the discussion of the deuteron bound state using the proposed electromagnetic interaction should be done in the quantum mechanics context. It is the solution of the eigenstates of the proposed quantum electromagnetic Hamiltonian, that should be compared with the experimental data. Otherwise, we would be denying also quantum mechanics treatment in nuclear scenery.

In my opinion the presented manuscript has no scientific meaning including **erroneous conceptions** in its proposal. Its publication should be refused.

We regret to inform you that we are unable to publish your paper in Nuclear Physics A as it does not match the **state of the art** in nuclear physics studies.

They take me for an illuminated guy.

The Supervisory Editors of **Nuclear Physics A** have now carefully considered your submission.

We regret to inform you that we are unable to publish your paper in Nuclear Physics A as **it does not match the state of the art in nuclear physics studies.**

**At last almost an encouragement**

"*Je ne connais rien a la physique nucleaire (car je viens de la physique atomique). **Il me semble cependant que le calcul que vous proposez est trop beau pour etre vrai.*"

## ANOMALOUS RUTHERFORD SCATTERING IS MAGNETIC

The physical nature of the nuclear interaction has been discovered to be electromagnetic.

The atomic nucleus was discovered by Rutherford, explaining electrically nuclear scattering, with a slope -2 in log-log coordinates. For high kinetic energies, the slope is -6, magnetic:

The Rutherford scattering is electromagnetic. Details here: Rutherford

**NUCLEAR BINDING ENERGY IS ELECTROMAGNETIC**

A proton attracts a not so neutral neutron as a rubbed plastic pen attracts small pieces of paper. Quantitatively, one has to use the exact dipole formula shown on the graph and not the approximate 2a/r² (cf Feynman vol. 2, § 6-2, formula 6.8). The binding energies of ²H and ⁴He nuclei have been calculated, WITHOUT FITTING, from the STATIC equilibrium between the attractive 1/r electric Coulomb potential and the repulsive short range 1/r³ magnetic Poisson potential. As shown on the graph below, the saddle points coincide with the ²H and ⁴He experimental nuclear binding energies:

The nuclear energy is electromagnetic, details here: AEM

After one century of modern phenomenological formalism, the binding energy of even the simplest bound nucleus, the deuteron, remains a puzzle: charge independence, centrifugal barrier, strong force with strength 1, magic numbers, unobservable observables, virtual particles, exchange forces, ab initio… The nucleus having no nucleus, nucleons cannot orbit as the electrons:

**The agreement between electromagnetic theory and experiment is significant for both electric and magnetic (not so anomalous) Rutherford scattering and also for the (not so strong) nuclear interaction.**

**AN EXAMPLE OF INTERESTING CRITICS** (No comment):

This paper concerns my calculation with Schrödinger equation, later published in China: WJNST_Schrodinger

Manuscript #2013-1465RR:

Editor's Comments:

Reviewer Comments:

Reviewer #1 Evaluations:

RECOMMENDATION: Reject

Original Paper required: Yes

Well Organized and Clear required : Yes

Free From Errors required : No

Conclusions Supported required : No

Satisfactory English required : Yes

Appropriate Title required : Yes

Good Abstract required : Yes

Clear Figures required : Yes

Adequate References required : Yes

Reviewer #1 (Comments to the Author required ):

I have read the rebuttal comments carefully. I am afraid that my objections were not adequately addressed and serious problems remain.

Regarding the more general and issues relevant to this work:

It is an experimental fact (explained or not) and a very basic and important one in nuclear phenomenology, that the force between two protons, two neutrons or a proton and a neutron is almost the same except for an electromagnetic part. If a theoretical model contradicts the observed fact, then the theoretical model is wrong. In this work no effort has been made to explain the almost equal force in the three cases and in fact the rebuttal document seems to dismiss the question as a detail.

It is maintained that the present theory is more fundamental (in any case, simpler indeed) than QCD and hence preferable. Now, a sphere is a more fundamental and elegant shape than the shape of a cow's body, which is largely determined by her bone structure and flesh. Should we represent our cow as a sphere and expect her to simply roll down the hill - then birch her for failing to do so?

It is also pointed out that the number of parameters in empirical nucleon-nucleon potentials is ridiculous. I definitely sympathize. Nuclear theorists would kill (so to say) for a simpler nuclear potential, but this is what nature gave us, explained or not. We can't make it go away.

To ensure that I would not judge unfairly based on epistemological arguments only, I took some time to check the calculations more closely. Unfortunately, I found genuine and fundamental errors and misconceptions.

For example:

In Eqs. (11) and (15), E is the eigenenergy of a solution to the respective Schroedinger equations. These E's should be constants, namely, all r-dependent terms should vanish. That indeed leads from (11) to (13), while for (15) it means that the last term should vanish. What went wrong? The exponential function exp^{-r/b} was wrongly assumed to be an eigenfunction for the corresponding Schroedinger equation. But it is not. The potential is different from that in the Hydrogen atom and the eigenfunction's radial dependence is different too.

The minimum of the quantity E(r,b) or E(a,b,r) is meaningless. The eigenenergy shall not be a function of r. The meaningful result in the context of quantum mechanics would be the eigenenergy and the eigenfunction (and the corresponding density).

I estimate also that, for the neutron polarization vector to have a length of the order of 0.1 fm (cf quantity a in Fig.2), and for an electric field at a distance comparable to the deuteron size, the neutron polarizability required would be at least 10 times larger than the value extracted experimentally (which is about 10^-3fm^3).

Unfortunately, I find the present work scientifically unsound and unsuitable for publication.

.

## My presentation at Groningen

"The strong nuclear force is one of the four fundamental forces in nature; the other three are gravity, electromagnetism and the weak force. As its name implies, the strong force is the *strongest *force of the four. It is responsible for binding together the fundamental particles of matter to form larger particles."

According to Wikipedia, "The nuclear force (or nucleon–nucleon interaction or residual strong force) is the force between protons and neutrons, subatomic particles that are collectively called nucleons. The nuclear force is responsible for binding protons and neutrons into atomic nuclei."

"In particle physics, the strong interaction is the mechanism responsible for the strong nuclear force (also called the strong force, nuclear strong force or colour force), one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. Effective only at a distance of a femtometer, it is approximately 100 times stronger than electromagnetism, a million times stronger than the weak force interaction and 1038 times stronger than gravitation at that range."

**Unfortunately,** t**he strong force, alias QCD, has no known fundamental laws. It is thus impossible to calculate the binding energy of even the simplest bound nucleus, the deuteron ^{2}H.**

In contrast, the electromagnetic theory is able to solve the mystery of the nuclear energy. Below is my presentation at Groningen EuNPC conference where I showed two proofs of the magnetic nature of the so-called Rutherford anomalous scattering and of the electromagnetic nature of the nuclear binding energy of the simplest bound atomic nucleus, the deuteron ²H.