Procedures for the evaluation of atomic transition matrix elements in the interaction with laser light Original Research Article

Analytical and numerical procedures for the calculation of atomic transition matrix elements in the interaction with linearly and circularly polarized laser light are presented. The laser—atom interaction is treated beyond the dipole approximation. The procedures are derived explicitly for hydrogen but may be readily generalized to other one-electron systems with, e.g., quantum defect type radial wavefunctions. The numerical procedure is programmed in Matlab and tested for main quantum numbers up to n = 30. The results clearly indicate when the dipole approximation breaks down in connection with laser excitation of angular Rydberg wavepackets.