Deep minima in the Coulomb-Born triply differential cross sections for ionization of helium by electron and positron impact

Previously, a deep minimum in the measurements of the triply differential cross section (TDCS) for electron-helium ionization at an incident energy of 64.6 eV was interpreted in terms of a vortex. We apply the Coulomb-Born (CB1) and modified CB1 approximations to this process at the same incident energy and obtain a deep minimum whose position is in reasonable accord with time-dependent close-coupling results and experimental data. We also obtain the deep minimum in the TDCS that was measured for an energy of 74.6 eV. For both incident energies, but at slightly different gun angles to those used experimentally, we obtain a very deep minimum in the TDCS that is related to a vortex in the velocity field associated with the CB1 transition matrix element. We determine for energies of 44.6 eV-79.6 eV the gun and polar angles for a deep minimum in the CB1 TDCS. We apply both approximations to positron-helium ionization. For an incident energy of 205.25 eV we find a deep minimum in the TDCS that is related to a vortex in the velocity field associated with the CB1 transition matrix element.