Randomphase approximation to onebody transition matrix elements for openshell atoms
Abstract
A graphical procedure is presented for evaluating each term in the equation satisfied by the firstorder transition matrix for an arbitrary (openshell) atom. For those terms involving the interaction of excited virtual pairs of electrons with the ionic core, we introduce the approximation that there is no exchange of orbital or spin angular momentum with the ionic core. This approximation is shown to lead to the randomphase approximation (RPA) equations in the closedshellatom case; we use it to define the RPA for openshell atoms. The single equation satisfied by the firstorder transition matrix is used to obtain a set of N+N' coupled differential equations for N finalstate radial functions and N' initialstate radial functions, which together, completely determine the firstorder transition matrix for an atomic system having N finalstate channels. (The relation of N' to N depends on the particular atom studied). The N+N' differential equations are shown to reduce to familiar forms in the following cases: (1) When initialstate correlations are ignored, one obtains the closecoupling equations and (2) when closedshell atoms are considered, N=N' and one obtains the 2N coupled differential equations of the ChangFano version of the RPA. Finally, our RPA firstorder transition matrix is used to evaluate the matrix element of the electricdipole operator for an arbitrary (openshell) atom. These RPA electricdipole transition matrix elements may be used to calculate nonrelativistically all experimentally observable quantities resulting from a singleelectron atomic photoabsorption process.
 Publication:

Physical Review A
 Pub Date:
 April 1982
 DOI:
 10.1103/PhysRevA.25.2135
 Bibcode:
 1982PhRvA..25.2135S