theory of the nuclear strong force (presentation)
TRANSCRIPT
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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