RAPID-IONIZATION APPROACH BASED ON THE FACTORIZATION METHOD

The factorization method of Bar-Shalom, Klapisch, and Oreg [Phys. Rev. A 38, 1773 (1988)] is extended to relativistic-distorted-wave cross sections for ionization by electron impact. This leads to a very great simplification for complex ions. In particular, when mixing is confined to the states in a complex (having the same set of n values, parity, and J value), the ionization cross section takes the form of a summation over states of the product of a readily calculated quantity that depends only on target-ion properties, such as mixing coefficients and angular momenta, and a cross section having exactly the same form as a hydrogenic cross section except that the radial functions should be calculated using the appropriate potential for the ion being considered. Similar results are obtained for intermediate coupling using LS-coupling notation and for totally nonrelativistic calculations. Only slightly more complicated formulas apply when mixing is included outside a complex. It is also noted that similar expressions apply for photoionization. Sample numerical results are obtained and compared with relativistic calculations of Moores and Pindzola [Phys. Rev. A 42, 5384 (1990)]. Quite good agreement is obtained when mixing is included among the same set of states.