Comment on "Recoil saturation of the self-energy in atomic systems"

Abstract

The effective potential in low-energy two-body scattering obtained by the ``self-energy method'' is identical to the effective potential commonly defined as the Fourier transform of the scattering transition amplitude (the T matrix) with respect to the momentum transfer. Because of the convenience that may occur in the exchange of the order of integration, nonadiabatic recoil corrections may be disguised as momentum-dependent corrections. These momentum-dependent corrections are distinct from energy-dependent corrections. In certain forms, they may violate either T invariance or Hermiticity. Their origin is attributable to a mathematical artifact and there exists a systematic method of converting the momentum-dependent correction terms into truly local form. When recoil effect is important, these nonadiabatic corrections cannot be ignored even at threshold energy when all energy-dependent corrections vanish. In certain cases, such as in the extrapolation of the effective potential to short-distance behavior, each of the nonadiabatic corrections may be comparable to the leading term. On resummation, these may greatly alter the behavior of the effective potential indicated by the leading term alone. The previous analysis of J. R. Manson and R. H. Ritchie [Phys. Rev. A 35, 5249 (1987)] on the saturation effect due to recoil in the scattering of Coulombic systems is based on neglect of these nonadiabatic corrections disguised as momentum-dependent corrections while extrapolating the effective potential to short-distance behavior. The present Comment points out the flaw in such a procedure.