Nuclear Forces, S.A. Moszkowski, 2-18-99
III. NUCLEAR FORCES
BETHE 1932 Neutron
Heisenberg - Exchange forces analogous to H2+ ion and H2 molecule,
even is neutron is pure.
Majorana - Saturation from Exchange forces
Wigner favored ordinary interactions V(r),
Bethe and Peierls (on Wigner's suggestion) hit on spin-dependence
of nuclear forces (In NY subway)
Saturation with Wigner forces - need repulsive core -
not introduced till 1950's.
At the time physicists believed that the nuclear forces must be simple,
i.e. purely attractive.
NUCLEAR FORCES - FROM SIMPLICITY TO APPARENT COMPLEXITY
It is interesting to review the assumptions that were made about the nuclear forces before more became known:
a. 2 body only,
b. Central,
c. Static,
d. Short ranged. For a time, Wigner even proposed a zero range interaction.
It was quickly learned (from comparing the binding energies of the two
and three nucleon system), that this assumption was too crude.
However, some of the ideas that inspired Wigner to postulate
such a zero range interaction have returned with the quark model.
The modern Nambu-Jona-Lasinio model actually leads to an interaction
which is velocity dependent, but has some similarity to a zero range
interaction.
e. Ordinary (no exchange) This was abandoned after the work of Heisenberg
nd Majorana
f. Spin-independent.
g. One sign only , viz. purely attractive
h. n-p force only. (This was before anything was known about nn and pp
forces, other than the Coulomb force which also acts between two
protons.)
i. Charge symmetry. i.e. force between nn is the same as between pp,
excluding the Coulomb effect.
j. Charge independence.
It was quickly found, however, that most of these assumptions had to be abandoned.
Only the last two charge symmetry and independence, hold quite well.
(Except for small corrections, which appeared since the 1960's).
About 1939, it was found that the deuteron has a finite electric
quadrupole moment. This required a tensor, i.e. non-central,
component in the nuclear force.
Tensor forces even acting by themselves can also lead to nuclear saturation,
but would give non-spherical shapes.
Only after World War II did people measure nucleon-nucleon crosssections
at energies sufficiently high to test the validity of the exchange
interaction.
It was found that, in order to fit the empirical results, the interaction
had to be small in odd spatial states. This is known as a Serber force.
Such a force is roughtly a 50-50 mixture of ordinary and space exchange
forces. (For an ordinary force, it is essentially the same ,i.e.
attractive in odd as in even states, while a space exchange force has
opposite sign, i.e. repulsive, for odd states.) In addition, it was
found that a short range repulsion is needed. Also, evidence for a strong
spin-orbit interaction emerged from nucleon-nucleon scattering.
So in all respects the nuclear forces appeared to be much more complex
than had originally been thought!
Finally, many body, i.e. non-additive interactions, were not considered at
all in the 1930's. There was no need for these. Indeed, such interactions
were only established in the 1980's, and even now they are somewhat
controversial. However, in the 1930's theories of metals did have
non-additive effective interactions, due to electron screening, and in the
1950's a classical field theory of nuclei was proposed by Johnson and
Teller. Both of these involved the equivalent of many body forces in the
many body system.
However, in both cases, such many body forces made the physics of the
system easier to understand, not harder!