forces2.htm 3-3-99

**NUCLEAR FORCES**

The discovery of the neutron in 1932 launched the modern era of nuclear physics.

In 1977, at the University of Minnesota, there was a Symposium
"Nuclear Physics in Retrospect", which dealt with the beginning of modern
nuclear physics in the 1930's. Many of the nuclear physicists from that
era were at the symposium. The proceedings were edited by Roger H. Stuewer
and published by the University of Minnesota in 1977. Unfortunately, this
book has been out of print, but it still is in several libraries.

Two of the talks given at the symposium, by Bethe "The Happy Thirties" by
Hans Bethe and "The Developments of Our Ideas of the Nuclear Forces" by
Rudolf Peierls, are particularly noteworthy for the insight into the early
days. I have taken
the liberty of integrating some of what was said by Bethe and Peierls into
the material below. However, I have also added some other remarks on how
new developments after the 30's changed our thinking.

Nuclear stability and saturation

Wigner gave reasons for considering also an interaction which depends only on interparticle distance without any exchange,i.e. V(r).

At the time, only very low energy phenomena (up to a few MeV) could be investigated. It was already known that the deuteron, which later was found to have spin 1, is slightly bound, by 2.23 MeV, while a neutron-proton system with spin 0 was slightly unbound. This difference also shows up in low energy scattering of protons by neutrons. There is a story that Bethe and Peierls (on Wigner's suggestion) came up with the currently accepted explanation, namely spin-dependence of the nuclear forces, while riding in the New York subway!

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. Two-Body only,b. Central,

c. Static, depending only on interparticle distances, not on momenta

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 and Majorana, since such interactions, if purely attractive, would lead to nuclear collapse.

f. Spin-independent.

g. One sign only , viz. purely attractive. This assumption was made mainly for aesthetic reasons, i.e. desire for mathematical simplicity.

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.

The role of the tensor force in nuclei is still a somewhat open problem.
It certainly plays an important role at large interparticle distances.
However, there are good reasons to believe that quark degrees of freedom
reduce the effect of the tensor force at short distances and also its role
in nuclear stability.

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 at the time. 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.
Such many body forces, which arise from more basic degrees of freedom
(quarks in the case of nuclei, and nuclei & electrons in the case of atoms),
made the physics of the
system easier to understand, not harder!

Still, it is useful to keep in mind an admonition given in the talk by
Peierls:" We may hope that, for the sake of the sanity of nuclear physicists,
we can confine ourselves to forces that are predominantly a sum of two-body
terms, though it is likely that there exist some corrections involving several nucleons at a
time."