Nuclear masses and deformations

Abstract

A semi-empirical theory of nuclear masses and deformations is presented. The potential energy of a nucleus, considered as a function of N, Z and the nuclear shape, is assumed to be given by the liquid-drop model, modified by a shell correction. The shell correction is a simple function of N and Z and is supposed to disappear as the nucleus is distorted away from the spherical shape. The resulting semi-empirical expression for the nuclear deformation energy has seven adjustable parameters, four in the liquid-drop part and three in the shell correction. By making the deformation energy stationary with respect to distortions, the equilibrium deformations (i.e., the quadrupole moments) and the ground-state masses of nuclei are derived as functions of N and Z. In addition, from unstable shapes of equilibrium corresponding to saddle-point configurations, barrier energies for nuclear fission are deduced. The predictions of the theory are compared with some 1200 experimental nuclear masses, 240 quadrupole moments and 40 fission barriers. The results lead, on the one hand, to a re-assessment of the accuracy of the liquid-drop model and a firmer determination of its characteristic constants and, on the other, to a semi-quantitative understanding of the effects of shell structure on nuclear masses and deformations. A number of minor anomalies are isolated, one apparently related to the so-called Wigner term in the binding energy and one relevant for the understanding of fission barriers. Applications to the analysis of the centrifugal stretching of nuclei and to the possible existence of “islands of stability” in the region of super-heavy nuclei are mentioned.