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World Journal of Nuclear Science and Technology, 2016, 6, 199205
http://www.scirp.org/journal/wjnst
ISSN Online: 21616809
ISSN Print: 21616795
DOI: 10.4236/wjnst.2016.64021 September 21, 2016
Electromagnetic Theory of the Nuclear Interaction
Bernard Schaeffer
7 Rue de l’Ambroisie, Paris, France
Abstract
After one century of nuclear physics, its underlying fundamental laws remain a pu
z
zle. 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 ma
g
netic −6
exponent. A proton attracts a not so neutral neutron as amber attracts dust.
The nucleons have magnetic moments that interact as magnets, equilibrating stat
i
cally 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.
Keywords
Electromagnetic Interaction, Coulomb, Poisson, Potential, Potential Energy,
Neutron, Proton, Deuteron, Helium, Alpha Particle, Nuclear Energy, Nuclear
Interaction, Quarks, Strong Nuclear Force, Rutherford Scattering, Anomalous
Scattering, Magnetic Moments
1. Introduction
Two millenaries ago, Thales discovered the electrical properties of amber (
ø
λ κτρ ν
,
elektron) and the magnetic properties of magnetite (from mount Magnetos) quantified
by Coulomb [1] and Poisson [2]. In 1924, Bieler [3] made an unsuccessful attempt to
explain with an attractive magnetic inverse fourthpower term in the law of force, un
fortunately with the wrong sign. Indeed, it needs only to reuse the Rutherford formula
where −2 electric is replaced by −6 magnetic [4].
The neutron, discovered in 1931 by Chadwick, seeming to be uncharged, the elec
tromagnetic hypothesis of the nuclear interaction was abandoned. The magnetic mo
ments of the proton and of the deuteron were discovered in 1932 by Stern [5] and the
magnetic moment of the neutron in 1938 by Bloch [6]. Assuming the additivity of the
How to cite this paper:
Schaeffer, B.
(2016)
Electromagnetic Theory of the Nu
clear In

teraction
.
World Journal of Nuclear Science
and Technology
,
6
, 199205.
http://dx.doi.org/10.4236/wjnst.2016.64021
Received:
August 3, 2016
Accepted:
September 18, 2016
Published:
September 21, 2016
Copyright © 201
6 by author and
Scientific
Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
4.0).
http://creativecommons.org/licenses/by/4.0/
Open Access
B. Schaeffer
200
magnetic moments, he found that, in the deuteron, the magnetic moment of the neu
tron was opposite to that of the proton. The existence of a magnetic moment in the
neutron proved the existence of electric charges and currents in the neutron, indicating
that it is not an elementary particle, as it carries no net charge but still interacts with a
magnetic field [6].
In nuclear physics, electric (except socalled Coulomb force) and magnetic interac
tions 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” [7]. Indeed, a proton attracts a neu
tron as a rubbed plastic pen attracts small pieces of paper.
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 nucle
ons is attractive or repulsive depending on the position and orientation of their mag
netic moments. First theoretical results have been obtained for hydrogen and helium
isotopes [8] [9]. The results shown in this paper are for the deuteron and the
α
par
ticle.
2. Electromagnetic Potential Energy
The sum of the electric and magnetic potential energies between electromagnetic par
ticles is the fundamental combination of Coulomb electric and Poisson magnetic po
tentials [10][12]:
( )( )
032
0
3
4π4π
i ij j ij
ij
em i j
iij ii j
ij ij ij
qq
Urrr
µ
≠≠
⋅⋅
= + ⋅−
∑∑ ∑∑ rr
µµ
µµ
(1)
The first term is the sum of the electrostatic interaction potential energy between
electric charges
i
e
and
j
e
separated by
ij
r
. The second term is the magnetic inte
raction potential energy between magnetic moments
i
µ
and
j
µ
, separated by
ij
r
.
3. Deuteron Electromagnetic Potential Energy
3.1. Deuteron Electrostatic Potential Energy per Nucleon (Coulomb)
The
electrostatic
potential energy per nucleon
e
U
of this system of the three point
charges of the deuteron is, from formula (1), where A is the atomic number:
2
H23 31
12
0 12 23 31
11
4π
e
U qq qq
qq
AA r r r
=× ++
(2)
1
q
,
2
q
and
3
q
are the three electrostatic charges.
12
r
,
23
r
and
31
r
are their separa
tion distances along their common axis. The total electrostatic potential energy between
the 3 electric charges of the deuteron (Equation (2)) becomes fundamental, except for
a
,
adjusted to obtain a horizontal inflection point, replacing a real minimum (
np
r
and
a
are defined on Figure 1). The electric potential, being negative, is attractive:
B. Schaeffer
201
Figure 1. Schematic deuteron structure. The punctual proton contains an
electrostatic
elementa
ry charge
e+
. The neutron contains
electrostatic
charges with no net charge, assumed to be
e+
and
e−
, the elementary electric charges (no proof of the quarks existence found). The
electros
tatic
field of the proton produces the 2
a
dipole separation distance between the two opposite
electrostatic
charges of the not so neutral neutron, distant by
np
ra+
and by
np
ra−
from the
proton center. The proton attracts
electrically
the neutron as amber (elektron) attracts dust. The
magnetic
moments of the proton and of the neutron are known to be collinear and opposite,
North against North (or South against South). The
magnetic
repulsion equilibrates statically the
electrostatic
attraction. The nuclear binding energies of simple nuclei such as 2H and 4He have been
calculated for the first time by applying electromagnetic Coulomb and Poisson fundamental laws.
2
H2
0
1 1 11
0
4π2
e
np np
Ue
A A r ar a a
=× − −<
+−
(3)
3.2. Deuteron Magnetic Potential Energy per Nucleon (Poisson)
According to the general formula (1) the total
magnetic
potential energy of the deute
ron is:
( )( )
2
H0
32
3
4π
n np p np
mnp
np np
UArA r
µ
⋅⋅
= ⋅−
rr
µµ
µµ
(4)
The
magnetic
moments of the proton and of the neutron in the deuteron are known
to be collinear and opposite, (
0
n
µ
<
and
0
p
µ
>
), as shown on Figure 1. The coeffi
cient in the brackets above being equal to
( )
13 2−−− =+
, the
magnetic
potential is
positive, repulsive:
2H
3
20
4π
np
m
np
UAA r
⋅
−
=×>
µµ
(5)
3.3. Deuteron Electromagnetic Potential Energy per Nucleon
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 2H:
2
H20
3
0
1 1 11
24π24π
np
em
np np np
Ue
A r ar a a r
µµµ
=× − −+
+−
(6)
or,
numerically
(see Appendix):
2
H
3
1 1 1 0.085
0.72 MeV
2
em
np np np
UA r ar a a r
= − −+
+−
(7)
B. Schaeffer
202
There is one variable
np
r
and one parameter
a
in formula (7). In order to find the
binding energy it is necessary to adjust the parameter
a
of the curve to obtain a poten
tial minimum (in fact, a local minimum, a horizontal inflection point) for both
np
r
and
a
. This is not to be confused with fitting to adjust the binding energy. A real mini
mum [13] would be better, of course, but, needing an empirical parameter, would break
the fundamental nature of the theory. The horizontal inflection part of the curve cor
responds to the deuteron binding energy. The result, obtained by applying
electrostatic
Coulomb’s law and
magnetic
Poisson’s law with the corresponding fundamental con
stants, is in compliance with the experimental value of the deuteron binding energy per
nucleon −1.11 MeV (Figure 1). There is only one horizontal inflection point per nuc
leus, adjusted manually by trial and error (Figure 2). It coincides, as by chance, with
the binding energy of the nucleus.
4. Alpha Particle Electromagnetic Energy per Nucleon
4.1. Interactions between Neutrons and between Protons
The single neutronneutron and protonproton bonds, being small in comparison with
the 4 neutronproton bonds, have been neglected provisionally. The electric interac
tions 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 4He is shown on Figure 3. The graphical so
lution (Figure 2) gives, for the
α
particle, a binding energy per nucleon of −7.6 MeV,
stronger than the experimental value, −7.07 MeV, by 10 per cent, due probably to the
neglect, in a first approximation of the magnetic repulsion between neutrons and be
tween protons. More precise results should be obtained by taking into account these
interactions.
4.2. ProtonNeutron Interactions Only, Provisionally
We shall calculate the 4He binding energy per nucleon from the deuteron 2H potential
energy, which is, as seen before (Equation (6)):
2
H20
3
0
1 1 11
24π24π
np
em
np np np
Ue
A r ar a a r
µµµ
=× − −+
+−
(8)
A neutronproton 4He bond is one total attractive 2H 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 (Figure 3), according to
formula (1), the Poisson formula has a coefficient of 3 instead of 2 for the deuteron.
The potential energy per nucleon is thus:
4He 20
3
0
1 1 13
24π22
4π
np
em
np np np
Ue
A r ar a a r
µ µµ
=× − − +×
+−
(9)
or, numerically (see Appendix):
B. Schaeffer
203
Figure 2. The binding energies per nucleon of 2H and 4He are calculated with Coulomb, electric,
and Poisson, magnetic, fundamental laws, without phenomenological parameters. It can be seen
that the socalled Coulomb singularity is not a real problem: it just need to replace the minimum
by a horizontal inflection point, the radius of the elementary electric charges being unknown, as
sumed to be pointlike. The binding energy is calculated graphically as −1.2 for an experimental
value of −1.1 for 2H and −7.6 MeV for an experimental value of −7.1 MeV for 4He.
Figure 3. The deuteron 2H has one neutronproton bond, as shown on Figure 1, thus a total bind
ing energy of −2.2 MeV. 4He has 4 deuteron bonds, inclined at 60˚, thus multiplying twice by 4 the
total 2H binding energy, giving an approximate total binding energy of
2.2 4 4 35 MeV− ××=−
somewhat larger than the experimental value, −28 MeV. The difference is probably due to the
repulsive neutronneutron and protonproton potentials, not taken into account.
B. Schaeffer
204
4
He
3
1 1 1 0.128
2.88 MeV
2
em
np np np
U
A r ar a a r
= − −+
+−
(10)
The graphical solution (Figure 2) gives, for the
α
particle, a binding energy of −7.6
MeV, stronger than the experimental value, −7.07 MeV, too large by 10 per cent, due
probably to the magnetic repulsion between neutrons and between protons, neglected
in a first approximation. More precise results should be obtained by taking into account
these interactions.
5. Conclusions
The binding energies of the deuteron and of the
α
particle have been calculated by ap
plying 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 neutronneutron and protonproton 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 hypo
thetical strong force and quarks.
Acknowledgements
Thanks to persons at Dubna for their interest to my electromagnetic theory of the nuc
lear 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 [14].
References
[1] Coulomb, C.A. (1785) Mémoire sur l’électricité et le magnétisme. 2nd Edition, Mémoires
de l’Académie Royale des Sciences, Paris.
[2] Poisson (1824) Théorie du magnétisme, Mémoires de l’Académie Royale des Sciences. Par
is.
[3] Bieler, E.S. (1924) LargeAngle Scattering of AlphaParticles by Light Nuclei.
Proceedings
of the Royal Society of London
,
Series A
, 105, 434450.
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[4] Schaeffer, B. (2016) Anomalous Rutherford Scattering Solved Magnetically.
World Journal
of Nuclear Science and Technology
, 6, 96102. http://dx.doi.org/10.4236/wjnst.2016.62010
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Zeitschrift für Physik
, 85, 416.
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., 8, 6378.
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Appendix: Fundamental Constants Used (CODATA)
• Light velocity:
6
299 10 m sc= ×
• Fundamental Electric charge
19
1.60 10 Ce
−
= ×
(11)
• Electric constant
2
0
1.44 MeV fm
4π
e= ⋅
(12)
• Magnetic constant
272
00
4π10 N A
c
µ
−−
==×⋅
(13)
• Proton mass:
27
1.67 10 kg
p
m
−
= ×
(14)
• Proton magnetic moment
26 1
1.41 10 J T
p
µ
−−
=×⋅
(15)
• Neutron magnetic moment
26 1
0.97 10 J T
n
µ
−−
=−× ⋅
(16)
• Protonneutron magnetic moments combined
03
0.085 MeV fm
4π
np
µµµ
= ⋅
(17)
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