Nucsat1.htm, S.A.Moszkowski, 3-3-99

NUCLEAR STABILITY AND SATURATION

As is pointed out by Peierls in his talk, it became quickly evident that there must be strong and short range forces among neutrons and protons. These are quite different from the well known Coulomb interactions in atoms, but many nuclear physicists had the faith that the nuclear forces also had to be simple. Heisenberg and Majorana introduced the idea of exchange interactions as a way to insure nuclear saturation, i.e. the fact that nuclear binding energies are, except for the lightest nuclei, approximately proportional to the mass number A.
To obtain saturation with two-body forces depending only, on interparticle distances, it is necessary to have a repulsion at short distances. Such "repulsive core" potentials were not introduced till 1950's.
Part of this was due to the lack of empirical information during the 1930's, and part was due to the general belief that the nuclear forces must be simple, i.e. have only one sign, namely attraction. Although this belief turned out to mistaken, it was quite reasonable at the time. Keep in mind that until quarks were discovered in the 1960's (and only integrated into nuclear physics starting in the 1980's), it was the nucleons are the elementary particles in nuclei.

Now, in principle, nuclear saturation can be due to a number of mechanisms :
1. Exchange forces
2. Repulsive core
3. Velocity dependence
4. Many body forces.

However, in the 1930's, only exchange forces were seriously considered. There simply was not much thought about the possible role of the other three mechanisms. While we now believe that all four of these play a significant role in obtaining saturation, it is still interesting to understand the thinking of nuclear physicists in the 1930's. Some of this thinking had been shaped in the 1920's, before the discovery of the neutron, when it was believed that electrons are present in the nucleus. If this were the case, then the binding energies would be much larger than the electron rest mass, and the electrons would have to be highly relativistic. Such a model would likely be quite complicated to implement. With the development of the proton-neutron model, the theory became non-relativistic, (Nuclear binding energies are only about 1 % of the rest mass.) It was also believed that it would be simpler. Now clearly there had to be an attraction which had to be there to give binding in the first place, and this attraction had to of much shorter range and greater strength than any other force known at the time. One argument against considering the possibility of a repulsion is that this repulsion would have to be of even shorter range, say 0.3 fm, and larger strength say 100 to 1000 MeV, than the attraction. Such numbers were well outside anything that there was empirical evidence for at the time. Thus there was a general prejudice against the idea of a short range repulsion in nuclei. Now the interaction between neutral atoms does have both a fairly short range attraction (the Van der Waals interaction) and a shorter ranged attraction (due to electron kinetic energy of overlap)..

However, both of these interactions owe their existence of the composite (nucleus & electrons) nature of atoms. Nucleons were not believed to be composite anymore after the neutron came on the scene, thus it was not thought that there was any analogy that could be made between neutral atoms and nucleons, as far as interactions were concerned. However, jumping ahead to modern times, where we know that nucleons are composite particles, made of quarks, the atomic analogy again has some appeal. In fact, it provides a ready mechanism for short range repulsion, namely the extra quark kinetic energy when two nucleons overlap. Regarding the possibility of velocity dependence of the nuclear forces: If the interactions depend not only on distances, but also on momenta, in such a way as to get weaker with increasing momenta, then this will tend to avoid nuclear collapse. With increasing density, the Fermi momentum of the nucleons will increase. It turns out that relativity provides a natural basis for such velocity dependence. Basically, with increasing density, i.e. Fermi momentum, the interaction volume undergoes a Lorentz contraction. Back to Forces