Pion exchange and the NN Potential

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Lecture 6
Pion exchange and the N-N Potential
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Neutron-proton scattering
a ?
For Ep lt few MeV ? gt nucleon size
a 5?
Thus we expect scattering cross section to get
more complex as Ep increases (? decreases), i.e.
l?1,2..
a 10?
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Expected n-p scattering cross section
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Classically why AD of high-energy n-p Scattering
is forward peaked
Classically the angle of deflection depends on
the impulse. If P is large (fast) , then ?p is
small.
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Classically why AD of high-energy n-p Scattering
is forward peaked
Classically the angle of deflection depends on
the impulse. If P is large (fast) , then ?p is
small.
?p/p F?t/p   F(r/v)/mv r width of
potential   V0/mv2 (F -dV/dr)  
V0/K  If K gt V0 angle of scattering is small
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High-energy n-p scattering
What we might expect for high-energy scattering
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Observed high-energy n-p scattering
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Observed high-energy n-p scattering
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High-energy n-p scattering
The interpretation with N-P exchange
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High-energy n-p scattering
The interpretation with N-P exchange
In about 50 of interaction the proton becomes a
neutron and the neutron becomes a proton! Why is
this and how can we explain this exchange effect?
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The exchange term in the N-N potential
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The exchange term in the N-N potential
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The exchange term in the N-N potential
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The exchange term in the N-N potential
The effect of V on the initial state can be
written as
The operation of P (interchange of p and n) is
equivalent to spatial exchange, or the parity
operation. So
Thus if l is odd V is near zero!
i.e. Nuclear potential depends strongly on l.
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Nucleon-nucleon potential
central potential derived from study of the
deuteron (l 0, S 1)
effect of spin coupling between the 2 nucleons.
e.g. from deuteron S1 stronger than S0,
tensor component. Evident from Deuteron admixed
WF
interaction of nucleon spin (s) and orbital AM l.
V deeper for l and s parallel
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Neutron-proton scattering

• N-N potential depends on
• Coupling of spins
• Coupling between l and s
• s and r (tensor component)

For Lgt0, and study of repulsive core need higher
energy scattering.
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Pion exchange as N-N field propagator
The explanation for this strange phenomenon was
given by Hideki Yukawa in 1934
nucleons are surrounded by a field of massive
(virtual) particles
Yukawa won the Nobel Prize in 1949
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Pion exchange as N-N field propagator
The ? meson was not discovered until 1947 in
cosmic-ray data by C. W. Powell of Bristol
University
Powell won the Nobel Prize in 1950
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Pion exchange as N-N field propagator
The 90 MeV n-p scattering data A.D. was
unexpectedly symmetric about 90 degrees. This was
explained in terms of a p ? n.
The possible mechanisms are   n ? p ?- and p
? n ? at the time of scattering
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Pion exchange as N-N field propagator
According to the One Pion Exchange Potential
(OPEP), each nucleon spontaneously emits pions,
which exist for a finite time and then are
re-absorbed.
The possible mechanisms are   n ? p ?- and p
? n ?
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Pion exchange as N-N field propagator
According to the One Pion Exchange Potential
(OPEP), each nucleon spontaneously emits pions,
which exist for a finite time and then are
re-absorbed.
The possible mechanisms are   n ? p ?- and p
? n ?
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Pion exchange as N-N field propagator
If within the lifetime of the virtual pion, it
encounters another nucleon, it can be absorbed,
The possible mechanisms are   n ? ? p and
p ?- ? n
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Pion exchange as N-N field propagator
So the net result is   n ? p and p ? n
.as was observed for high-energy (n,p) scattering
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Meson Exchange Theory of Nuclear Force
1. Why doesnt the existence of these virtual
particles violate energy conservation?
2. How does exchange of particles lead to an
attractive potential?
3. Does the model fit the bill?
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How can pions be created without violating
conservation of energy?
6.5 10-16 (eV-s)/140 106 (eV) 4.6 10-24 sec
Assuming that the pion has a velocity close to
that of light (an over estimate) it can travel a
distance ?t x c 4.6 10-24 x 3 108
m.
About the range of the nuclear force!!
1.4 10-15 m, 1.4 fm
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Properties of the pions
Spin of pion S 0
  There are 3 types of pion   ?, ?- and ?o.
  The masses are   ?and ?- 140 MeV/c2
?o 135 MeVc2   This small difference has
some implications that we will look at later.
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The isospin of the pion
The pion is a particle that has an isospin t 1.
(the nucleon is a particle that has an
isospin t1/2 )
It is an isospin triplet. (the nucleon is an
isospin doublet, 2 projections p and n)
It can have 3 projections
tz -1 is a ?, tz 0 is a ?o tz 1 is a ?-.
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Meson Exchange Theory of Nuclear Force
In the (p,n) scattering experiment, the p ? n and
n ? p, exchange accounted for about half of the
events those with unexpectedly large scattering.
The non-charge exchange region is accounted for
by the creation of a virtual ?0 meson.
i.e. p ? p ?o and n ? n ?o.
Half of p-n interactions involve ?o exchange. p-p
and n-n interactions can only come about by
exchange of a neutral pion.
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Meson Exchange Theory of Nuclear Force
These possibilities dictate that
A proton can have in its meson field either a ?
or a ?o, but never a ? -. 
A neutron can have in its meson field either a ?-
or a ?o, but never a ?. 
Thus the charge distributions of these two
nucleons will be markedly different.
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The distribution of charge for protons and
neutrons
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Meson Exchange Theory of Nuclear Force
In high-energy (p,n) scattering experiments, the
p ? n and n ? p due to ? and ?- exchange
accounted for the backward scattering
So if (p,p,) and (n,n) scattering only involve
exchange of ?o mesons, what would you expect the
AD for high energy scattering to look like?
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Meson Exchange Theory of Nuclear Force
The ultimate source of the exchange meson lies
within the nucleons
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How does exchange lead to an attractive force?
The H2 ion
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How does exchange lead to an attractive force?
The H2 ion
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The 2H ion Potential energy as a function of
proton separation
-54.4 eV
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Form of the OPEP (One Pion Exchange Potential)
For the meson with mass m the energy equation
becomes  E2 p2c2 mo2c4 which leads to
an equation
The electrostatic potential is obtained from the
relativistic energy of a photon
E2 p2c2 or
-p2 E2/c2 0  
replacing p and E with the appropriate operators
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