Computational Methods for Shell-Model Calculations

Abstract

The nuclear shell model has a very long history, during most of which as much effort has gone into the development of the formal and technical aspects of the model as into applying it to the description of nuclear properties. This has been partly due to the formidable difficulties attendant on what would seem at the start to be an idiotic pursuit — the description of a complicated many-body system by means of a model lacking any theoretical justification and using a Hamiltonian about which nothing was known. It was also due in part to the utterly fascinating and beautiful mathematical structures that were devised in order to make the calculations possible at all. The earliest shell-model calculations, those of Feenberg and Wigner (FW 37), used methods based on group theory (supermultiplet theory). Racah (Rac 43, 49) further developed the algebra of angular momentum and the method of fractional parentage to the point where they became usable in atomic shell-model calculations. This work was taken up and extended to the case of protons and neutrons by H. A. Jahn and his collaborators (Jah 50, 51; JvW 51) and by Flowers (Flo 52). The problem tackled by them was that of ascribing sufficient approximate quantum numbers or labels to distinguish the different states arising from the filling of a shell and to produce tables of the corresponding coefficients of fractional parentage for use in calculating matrix elements.