THE ELECTRIC-DIPOLE APPROXIMATION AND THE CALCULATION OF FREE-FREE TRANSITION MATRIX-ELEMENTS IN MULTIPHOTON PROCESSES

In view of the arguments put forward by van Enk et al, we discuss aspe cts of the theory of atom-laser field interactions as they relate to t he calculation of properties for which free-free transitions play a si gnificant role. Our conclusion is that: (i) according to the standard definition of the electric dipole approximation, which is what has bee n employed until now in all non-perturbative calculations of multiphot on processes, the on-energy shell singularity for the length and veloc ity gauges is real when the one-electron continuum is represented rigo rously by energy-normalized scattering functions. On the other hand, t he acceleration gauge does not give rise to this singularity. (ii) Whe n the full coupling operator A(r) . p + 1/2 A(2)(r) rather than A(r) . p is used, the singularity persists for the electric dipole as well a s for the higher multipoles. (iii) The use of box-normalized basis set s only leads to a model space whereby even repeated (and computational ly expensive) calculations with increasing box size lack intrinsic rig our and the certainty that convergence implies accuracy.