(Ĵ2,T̂2)—adapted graphs

Abstract

The eigenspace of the total angular and spin momentum operator Ĵ2 in the j — j coupling and of the isospin operator T2 is the most appropriate for calculation of the nuclear properties. Due to the nature of nuclear forces solutions of nuclear equations are sought in full many-particle spaces built from primitive functions, called in context of nuclear shell-model calulations’orbits’, that are almost always taken as harmonic oscillator functions (cf Wong 1981; Brussaard and Glaudemans 1977). The full spaces have very high dimensions and therefore shell-model calculations in nuclear physics are concentrated mainly in the sd shell, with only a modest studies of other shells (McGrory and Wildenthal 1980). A program determining the dimensionalities of such model spaces has recently been published (Draayer and Valdes 1985). Calculation of matrix elements in (Ĵ2, T2)-adapted space is not simple, therefore computer programs performing calculations of nuclear structure work frequently in the ‘M-scheme’ or determinantal spaces where calculation of matrix elements is simpler but the dimension of the space is much bigger (Duch 1986b).