Skyrme, Peierls-Yoccoz, and statistical approximations for the inertia parameter

Abstract

Angular momentum operator identities are used to show that Skyrme's expression can be written using the $y$ component of angular momentum only. It is shown that the Gaussian approximation for the matrix element of ${{J}_{y}}^{4}$ leads to the Peierls-Yoccoz expression. A new approximation based on the theory of probability is introduced. The numerical calculations for the $2s\ensuremath{-}1d$ shell nuclei show that the inverse of the inertia parameter using the statistical approximation is much closer to Skyrme's value than the one given by the Peierls-Yoccoz approximation.[NUCLEAR STRUCTURE Approximations for nuclear inertia parameter.]