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Electromagnetic Theory of the Nuclear

Interaction.Application to the Hydrogen and

Helium Isotopes

Bernard Schaeffer, Paris, France

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The neutron is not so neutral

The strong force is not so strong

The electromagnetic interaction is not so feeble

The nuclear interaction may be electromagnetic

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Estimate of2H binding energy

At an internucleon distance of R = 0.65 fmthe electrostatic potential energy is equal to thebinding energy of the deuteron :

Unp

em = e2

4

!"0R

= 2.2 MeVThis calculation proves that the

electromagnetic interaction

is not so feeble as it is incorrectly assumed.

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Deuteron nuclear potential

electrostatic attractionbetween a neutron and a nearby proton is

due to the well known electrostatic induction

+magnetic repulsion

between nucleons is due to opposite and

collinear magnetic moments

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Shell model useless

No orbital movement of the nucleons existsin the deuteron and in the ! particle

ground states

where l = 0

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Dipole and polarizability formulas

The dipole and polarizability formulas arevalid only in a uniform electric field

It is better to use the originalCoulomb law

for point charges

The electric fieldis not uniform within a

neutronnear to a proton

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Deuteron electromagnetic structure

Electrostatic

induction means

neutron-proton

attractive force

Opposite magneticmoments means

repulsive force

+e

"e+e

+e neglected

Spin

+e

Deuteron

non-zero

quadrupole

Neutron

dipole

induced bythe proton

"e+e

Deuteronmagnetic

momentD = p" |n| > 0

Neutronn < 0

Protonp > 0

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Deuteron binding energyfrom laws of electrostatics and

magnetostatics

The experimental binding energy is intermediate between the two

graphically obtained binding energies.

This justifies the 2 point charge approximation

3 electric charges + " + 2 electric charges " +

(approximation)

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Electromagnetic interaction

between the proton and the

neutron in the deuteron

The neutron has a locally effective negative charge "e due to theneglect of its positive charge, farther away from the proton.

U em = U e + U m = !e2

4"#0rnp

+

0

n

p

2"r3np

Summing the Coulomb attractive charge-charge potential and the

magnetic repulsive dipole-dipole potential gives the deuteron potential :

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Calculated equilibrium distance

F = !dU em rnp

drnp= !

e2

4"#0rnp

1 !6

n

p

e2c2r2np= 0

This gives the neutron-proton equilibrium distance :

rnp =6

n

pec

= 0.60 fm

The minimum potential (without orbital kinetic energy: l = 0)gives the binding energy at equilibrium (force = 0) :

Phenomenological potentials give also values around 0.6 fm

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Deuteron binding energy

Replacing rnp

at equilibrium in the potential

gives the binding energy of the deuteron :

B = ! e

3

c6"#

06

n

p

J = ! 1.6 MeV

Experimental value : 2.2 MeV

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! : fine structure constant

mp : proton mass

c : light speed

Published online 29 January 2011, J. Fusion Energy

Deuteron electromagnetic potential

RP : proton Compton radius

gn, gp : Land factors

Uem = !"mpc2 RPr ! gngp8 RPr3

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3H and 3He

Experiment : 8.5 MeV 7.7 MeV

TritonHelion

3H has a higher binding energy than 3He due to the lower magnetic

repulsion between neutrons than between protons

Calculated triton

binding energy:

Replacing gn by gp gives

the helion binding energy :

B3Hem = !4 2

gn

" mpc2 = !10 MeV

B3Heem = !

4 2

gp" mpc

2 = !6.9 MeV

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4He potentialThe electromagnetic potential for an almost regular tetrahedron is :

The structure of4He being

unknown the magnetic

moments are assumed to be

opposite but inward-outward

and the 4He tetrahedron 20 %

flattened:

rnn = rpp = 1.20 rnp.

This gives the binding energyof4He : " 28 MeV.

rnp

rpp = 1.20 rnp

rnn = 1.20 rnp

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Calculated and experimental binding energies B/A of the

H and He isotopes

Total binding energy of the N > 2 isotopes assumed to be constant

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Nuclear and chemical energiesChemical energy is the electron-proton separation energy:

Nuclear energy is the neutron-proton separation energy

Calculated Experimental

2.2 MeV

13.6 eV= 160,000

! Ry = ! 12"2mec

2 = ! 13.6 eV

! 14 "mpc2 ~!1.6 MeV

Ratio nuclear / chemical energy :

1

2

mp!me

=1.6 MeV

13.6 eV= 120,000

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Electromagnetism clarifies:

Strong force : electrostatic attraction

Hard core : magnetic repulsion

Ratio nuclear / chemical energy :

Thank you for your attention

1

2

mp

!me= 120,000