forces2.htm 3-3-99


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.

Before the discovery of the neutron, it was believed that nuclei are made up of protons and electrons. Heisenberg considered the possibility that the nuclear forces involve electron exchange, analogous to the interactions which bind H2+ ions or H2 molecules. Once the neutron was discovered, it quickly became accepted that nuclei were made up of protons and neutrons. Until the discovery of quarks in the 1960's, these nucleons were considered as elementary particles. But the idea of the nuclear forces being some kind of exchange force, where nucleons are exchanged, remained a subject of active investigation. The question of nuclear stability For more details on nuclear saturation, quickly came to the fore. For more details on nuclear stability, see:
  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!


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."

  Nuclear Fission