Rotation and Vibrations of Nuclei

Abstract

Surface deformations of nuclei. We shall examine the states associated with the excitation of collective degrees of freedom of nuclei. The shell model of the nucleus is based on the simplifying assumption that the individual nucleons move independently, the interaction between them being described by a self-consistent field. The liquid-drop model of the nucleus is based on the assumption of the existence of strong coupling between the nucleons, as a result of which the mean free path of a nucleon in nuclear matter is small compared with the dimensions of the nucleus. Whereas in the shell model of the nucleus one considers one-particle excitations associated with changes of the states of individual nucleons, in the liquid-drop model of the nucleus collective excitations associated with a simultaneous change of the states of many nucleus are taken into account. Lying at the basis of the so-called generalized model of the nucleus, which is a synthesis of the shell and liquid-drop models, is the assumption that the individual nucleons move independently in a slowly varying self-consistent field. In this model, as in the shell model, degrees of freedom associated with the motion of one nucleon or several weakly coupled nucleons in the self-consistent field are taken into account. In the generalized model, as in the liquid-drop model, collective degrees of freedom associated with change of the shape of the nucleus and of its orientation in space are taken into account.