R-MATRIX FLOQUET THEORY OF MULTIPHOTON PROCESSES .2. SOLUTION OF THE ASYMPTOTIC EQUATIONS IN THE VELOCITY GAUGE

A unified R-matrix-Floquet theory of multiphoton ionization and laser-assisted electron-atom collisions for a general atom has been proposed recently by Burke, Francken and Joachain. The present paper describes two new computational methods for solving the asymptotic equations which occur in the external R-matrix region in the velocity gauge. The first method extends the Light and Walker propagator approach to include the first derivative coupling terms which arises in the velocity gauge. The second method extends the Burke and Schey asymptotic expansion to include the first derivative coupling terms and the long-range multipole potential terms. These new methods, combined with the solution in the internal R-matrix region, enable the complete solution of the R-matrix-Floquet equations to be obtained. By introducing a small r expansion of the one-electron system in the velocity gauge, numerical results are presented for multiphoton ionization of atomic hydrogen and compared with results obtained using other approaches.