Zeros in (inverse) bremsstrahlung matrix elements

Abstract

We discuss the possibility of zeros in the nonrelativistic radiative continuum-continuum matrix element for electron-atom (inverse) bremsstrahlung. As demonstrated earlier for upward transitions from bound states, the occurrence of different signs for the free-free matrix element in limiting cases, plus the requirement of continuity, implies the existence of zeros. Using knowledge of the sign of the dipole matrix element in the soft- and hard-photon limits with one continuum electron energy held fixed, we show that zeros can occur in the $s$-$p$ matrix element. We discuss the connection of our results to elastic scattering and to Ramsauer-Townsend minima. We consider the observability of zeros in this $(s$-$p)$ matrix element manifested as minima in the cross sections.