Techniques for the calculation of atomic structures and radiative data including relativistic corrections

Abstract

The theory incorparated in a general-purpose automatic atomic-structure program is formulated in detail. The computer program, which is called SUPERSTRUCTURE, will be published soon. SUPERSTRUCTURE can calculate term energies, intermediate-coupling energy levels, term-coupling coefficients, radiative data which includes permitted and forbidden transition probabilities, and cascade coefficients. The program uses multi-configuration type expansions. Relativistic corrections are made by means of the Breit-Pauli approximation. Special attention is paid to those features of the formulation which make it particularly suited to the computer. Such principal features are: 1. (i) Wave functions are effectively expanded in Slater determinants. 2. (ii) Expressions for the matrix elements of the relativistic operators are given in a concise form. These matrix elements are expressed in terms of coefficients c λ lm, l′m′, related to the corresponding coefficients of Condon and Shortley, and coefficients d λ( lm, l′m′), which we introduce. Relativistic operators whose matrix elements have similar angular parts are grouped together to avoid superfluous calculation of angular coefficients. 3. (iii) Radial functions can be either statistical-model functions of user-supplied functions. SUPERSTRUCTURE will calculate the statistical-model radial functions if they are required, and user-supplied functions will be processed to suite the internal requirements of the program. Checking procedures used for testing the various parts of SUPERSTRUCTURE are discussed. We also give a critique of the techniques described, and, where appropriate, discuss them in relation to techniques used by other workers. The wide range of atomic structure data which the program can calculate makes it highly suitable for astrophysical applications. The formulation developed here should be of wide application in various problems relating to atomic structure.