The Auger Transition Rate in Mixed-Coupling Scheme

An expression is derived for the Auger transition rate for elements whose initial configuration is described by $j-j$ coupling and whose final configuration is described by Russell-Saunders coupling. We use Asaad's expression for the matrix element when both configurations are described by $j-j$ coupling, and use a transformation from $j-j$ to Russell-Saunders coupling for the two-electron final-state wave function. In addition we obtain expressions for the $M_4\mathrm{NN}$ and $M_5\mathrm{NN}$ transitions which are evaluated in the following paper.