For excitation to very high levels or ionization of a complex ion there are sometimes several possible final states for the remaining core (next higher stage of ionization in the case of ionization). Then formulas, such as the widely used ionization formula of Lotz or other ionization and excitation formulas in which the cross section is expressed essentially as a product of the number of electrons in the initial subshell times a cross section having the form of a hydrogenic ion cross section, must be multiplied by an additional factor giving the relative probability or branching ratio for the particular final state of the core. This problem was considered previously by Bely and Schwartz [Astron. Astrophys. 1, 281 (1969)] for the case of ionization. They used LS coupling, exchange was neglected and the remaining core was assumed to contain one or two partially filled subshells. Here we have included exchange and we have obtained the branching ratios for jj coupling as well as LS coupling for the general situation that any number of filled and partially filled subshells are present. The results apply for both collisional and radiative transitions.

• Received 14 April 1986

DOI:https://doi.org/10.1103/PhysRevA.34.986