R-MATRIX-FLOQUET THEORY OF MULTIPHOTON PROCESSES .8. A LINEAR-EQUATIONS METHOD

A new linear equations method for calculating the R-matrix, which aris es in the R-matrix-Floquet theory of multiphoton processes, is introdu ced. This method replaces the diagonalization of the Floquet Hamiltoni an matrix by the solution of a set of linear simultaneous equations wh ich are solved, in the present work, by the conjugate gradient method. This approach uses considerably less computer memory and can be readi ly ported onto parallel computers. It will thus enable much larger pro blems of current interest to be treated. This new method is tested by applying it to three-photon ionization of helium at frequencies where double resonances with a bound state and autoionizing states are impor tant. Finally, an alternative linear equations method, which avoids th e explicit calculation of the R-matrix by incorporating the boundary c onditions directly, is described in an appendix.