(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 T̂² 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, T̂²)-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).