Anomalous Behavior of the CoulombTMatrix

Abstract

Some apparent discrepancies in the definition or calculation of the Coulomb $T$ matrix are investigated in an approach that uses shielded wave functions. It is found that the screened Coulomb $T$ matrix behaves anomalously in the neighborhood of the energy shell and is in fact discontinuous in the limit of zero screening. A closed-form expression for the $T$ matrix, which has been derived previously, is shown to be essentially correct off the energy shell.