Quasi-spin method for jj coupling in the theory of many-electron atoms

Abstract

A new modification of the theory of many-electron atoms is described in which tensorial properties of the quasi-spin operator are taken into account. The properties of tensorial operators, including the second quantisation operators, and their reduced matrix elements are studied with respect to quasi-spin space in the case of jj coupling in a shell of equivalent atomic electrons. The methods of angular momentum theory are generalised for the quasi-spin space. The properties of the wavefunctions and the coefficients of fractional parentage are studied with respect to quasi-spin space. Redmond's formula is generalised. Algebraic expressions for the wavefunctions and coefficients of fractional parentage are found for the shell jN(j<or=7/2). Some useful algebraic formulae are obtained for the scalar products of irreducible tensors as well as the matrix elements of the operators corresponding to certain physical quantities. The method described can easily be generalised to cover the case of complex electronic configurations.