Group Theory and Mixed Atomic Configurations

A group‐theoretical scheme is introduced to classify the states of an atomic system having two open shells. States labeled according to this scheme may be written $${\mathrm{|(l}}_A{\mathrm{+\; l}}_B{\mathrm{)\alpha Q}}_A{\mathrm{(S}}_A{L}_A{\mathrm{)J}}_A{\mathrm{\times \; \beta Q}}_B{\mathrm{(S}}_B{L}_B{\mathrm{)J}}_B{\mathrm{,\hspace{0.17em}QM}}_Q{\mathrm{JM}}_J〉$$ , where the quasispins Q_A and Q_B are coupled together to form a total quasispin Q. Although these states are, in general, mixtures of different configurations $l_A^k{l}_B^q$ , it is found that they serve as a convenient basis for the calculation of matrix elements in (l_A + l_B)^N. The matrix elements of operators between the states of two configurations are obtained from these matrix elements by means of a unitary transformation. As an example matrix elements of the Coulomb interaction within (f + p)^N are calculated.