Nuclear moments of inertia and effective nucleon mass

Abstract

The nuclear moment of inertia may be calculated as the sum of individual contributions by treating the dynamics of one sample nucleon in the ellipsoidal harmony oscillator potential representing its interaction with the others, on the plauside assumption that the moment of inertia due to all the other nucleons is simply associated with the orientation of the axes of the distortion ellipsoid. The ellipsoid is allowed to move freely (in two dimensions) with conservation of angular momentum, but the is rather similar to that given earlier on the basis of a constant angular velocity of the ellipsoid (“cranked model”), and the result is the same. The moment of rigid value when the magnitude of the distortion of an open-shell nucleus is obtained in the most simple manner, by minimizing the sum of the oscillator energies with constant nuclear volume. The analogous problem of linear translation may be similarlyThe moments of inertia of highly distorted nuclei are observed to be about half of the rigid value. One might hope to understand this discrepancy in terms of the “effective mass” Me … 12M which appears in some problems involving through nuclear matter, and is required in the shell model to binding energies. The shell-model-type assumption considered most the effective mass arises from simple dependence of the potential not on the momentum but on the nucleon velocity relative to the axes of the and this is the assumption whose analogue gives a sensible result in the linear The velocity dependence is taken to be a quadratic cue, giving a simple Me. It is shown that, with these assumptions, Me is not effective for the moment of inertia problem and one still obtains the rigid value.