A convergent analysis of radiative matrix elements in atomic lineshape theory

For dipole-allowed atomic transitions the radiative matrix element which defines the pressure-broadened atomic lineshape is only conditionally convergent. Using a commutator technique to redefine the integral, the authors isolate, and ultimately reject, the contribution of an indeterminate asymptotic surface integral that is associated with the energy normalisation of the continuum wavefunctions which describe the binary collision of the atom and its perturber. The remaining contributions, which are absolutely convergent, give the multichannel atomic lineshape which includes effects of non-adiabatic and inelastic scattering. Further, the authors show the relationship of the commutator integral to the exact requirements of close-coupled scattering theory for radiatively induced collisions. This scattering analysis suggests the interpretation of the convergent lineshape as an expression of multichannel inelastic collisions between field-dressed atomic states. This same interpretation applies both in the impact and the static limit. The authors make explicit comparisons which demonstrate the equivalence between the commutator integral and the numerical close-coupled results in the weak-field limit. They emphasize the static limit, well in the wings of the atomic line, where the Jablonski stationary-phase JWKB analysis is often applied to good effect.