Electronic wave functions - The evaluation of the general vector-coupling coefficients by automatic computation

Abstract

A considerable number of different types of investigations on atomic and nuclear wave functions involve the use of vector-coupled functions and would be facilitated by an easy method of evaluation of the basic fundamental coefficients. This is particularly so for the present series of investigations, in which very complicated vector-coupled functions are used in convergent methods of atomic wave-function calculation. Hitherto the evaluation of these coefficients, which are independent of all aspects of a problem other than the irreducible representations of the rotational group concerned, has been extremely tedious while still requiring considerable mathematical understanding. It has now been found possible to develop a method of calculation which can be performed purely automatically by the EDSAC, proceeding from the lowest argument values indefinitely through all higher values. A substantial table, which would otherwise require over a year of computation by a mathematician, has been obtained. This investigation constitutes a significant contribution to problems of wave-function calculation and also involves some minor innovations in the vector-coupling theory.