The action of product tensor operators within and between pure and mixed configurations

Abstract

Atomic and nuclear shell Hamiltonians can be represented in terms of one- and two-body product tensor operators which act both in spin and orbital spaces. In this paper, equivalence conditions for the matrix elements of these operators are used to find their normalization constant. The results obtained for one-body operators are tabulated for all pure and mixed shells with l≤3. The normalization constants for two-body operators are proved to be products of two one-body normalization constants with the corresponding ranks. Subsequently, expressions for the matrix elements of one- and two-body double tensor operators within all pure configurations are found for arbitrary ranks. Since these generalized product tensor operators may include polar components, they are allowed to participate in configuration mixing. Therefore, reduced matrix elements for these operators have also been calculated both within mixed configurations and between all possible combinations of mixed and pure configurations. These formulas have been used in a computer program and selected numerical results have been provided in this paper.