The Two-Body Interaction in Nuclear Shell Model Calculations

Abstract

I would like to start by emphasizing that the work I will discuss here is the result of a lengthy and close collaboration between Edith Halbert at Oak Ridge, Hobson Wildenthal at Michigan State, and myself. In recent years, we have been making an intensive study of the properties of low-lying bound states of light mass nuclei in terms of the conventional nuclear shell model. In particular, we have studied the structure of nuclei in the Op-shelly the Od-ls shelly and the Of-lp shell. The discussion here can be broken down into five sections. I will first describe what I mean by a conventional shell-model calculation, and indicate how the effective two-body interaction is introduced in the calculation. I will also discuss here the types of two-body interactions we have used in these calculations, which are typical of interactions used in most shell-model calculations. Second, I will illustrate the type of agreement with experimental data we have obtained for nuclei in the s-d shell for energy levels, strengths in single- nucleon-transfer reactions, and for electric-quadrupole and magnetic-dipole moments and transition rates. Third, I will discuss the sensitivity of these calculated results to the differences between the various interactions we have used. The material in these two sections represent a quick review of a recently published, detailed discussion of shell-model calculations of nuclei with A = l8–22. Unless otherwise noted, all references to experimental data will be found in that article. Fourth, I will discuss the renormalization of the effective two-body interaction which occurs when the model space is truncated to include only part of a complete oscillator shell.

Research sponsored by the U. S. Atomic Energy Commission under contract with The Union Carbide Corporation.