On the Semiclassical Description of Nuclear Fermi Liquid Drops

Abstract

Recent years have seen quite some developments in the understanding and application of semiclassical methods to gross properties of nuclei1–4. Talking about gross properties we mean in fact properties of the nucleus where in a systematic and well defined way the influence of individual shells has been averaged out. One typical quantity to be considered is the single particle level density where the average part of say a fully quantal distribution (corresponding e.g. to some sort of Wood-Saxon or H.F. potential) is easily conceivable. The average part of nuclear groundstate masses is another such quantity and in fact represented by the well known Bethe Weizsacker mass formula. These are two very well known examples where the average nuclear properties have been studied since long and in very great detail. There are however many more quantities and properties whose average behavior could be investigated in the same way and what in fact is interesting to do. Among those we want to cite e.g. the moment of inertia of rotating nuclei, average nuclear pairing properties, average m-particle-n-hole level densities, average behavior of collective nuclear vibrations, average current distributions in rotating and vibrating nuclei, and many things more. In short, we would like to describe semiclassically all nuclear properties which survived could we artificially blow up nuclei to quasi macroscopic dimensions — like e.g. droplets of liquid He3 — where it is clear that the continuum limit is reached, i.e. no shell effect present any more, but still all quantities depending on the size parameters like e.g. volume, surface, curvature,and deformation of the nuclear droplets. In this region we would like to establish the laws the different quantities obey as a function of these parameters which in most cases can be resumed in a per law dependence on the cubic root of the nucleon number A. These laws should then be taken and extrapolated back to the sizes of real nuclei which at the same time then also define their behavior on the average. We know by now that the well known Strutinsky averaging procedure 5 for nuclei of realistic sizes is exactly equivalent to this point of view for the purely theoretical approaches to the nucleus; but also on the experimental side a specific quantity measured as a function of a large number of nuclei allows to extract exactly the corresponding experimentally determined average of the same quantity. Agreement of average experimental and theoretical numbers then allows us to conclude about our understanding of the nucleus. A whole realm of nuclear properties is thus open to our semiclassical investigations.