The electric dipole approximation and the calculation of free - free transition matrix elements in multiphoton processes

Abstract

In view of the arguments put forward by van Enk et al, we discuss aspects of the theory of atom-laser field interactions as they relate to the calculation of properties for which free-free transitions play a significant role. Our conclusion is that: (i) according to the standard definition of the electric dipole approximation, which is what has been employed until now in all non-perturbative calculations of multiphoton processes, the on-energy shell singularity for the length and velocity gauges is real when the one-electron continuum is represented rigorously by energy-normalized scattering functions. On the other hand, the acceleration gauge does not give rise to this singularity. (ii) When the full coupling operator A(r) · p + 1/2 A2(r) rather than A(r) · p is used, the singularity persists for the electric dipole as well as for the higher multipoles. (iii) The use of box-normalized basis sets only leads to a model space whereby even repeated (and computationally expensive) calculations with increasing box size lack intrinsic rigour and the certainty that convergence implies accuracy.