Deep minima in the Coulomb-Born triply differential cross section for electron and positron ionization of hydrogen and helium

Using the Coulomb-Born (CB1) and modified CB1 approximation we have obtained a deep minimum or minima in the triply differential cross section (TDCS) for e$^{\mathrm{-}}$-H, e$^{\mathrm{+}}$-H, e$^{\mathrm{-}}$-He and e$^{\mathrm{+}}$-He ionization [1,2]. At the position of a deep minimum, the CB1 transition matrix element~is zero. Corresponding to a zero in~the CB1 transition matrix element, there is a vortex in the velocity field associated with this element.~Interestingly, we found, for the geometries and the kinematics that we considered, the velocity field rotates in the same direction for e$^{\mathrm{-}}$-H, e$^{\mathrm{+}}$-H and e$^{\mathrm{-}}$-He ionization, but in an opposite direction for e$^{\mathrm{+}}$-He ionization. For e$^{\mathrm{-}}$-He ionization, we varied the incident energy from 44.6 eV to 79.6 eV (in steps of 5 eV) and determined the polar and gun angles [3] for a deep minimum in the TDCS at each incident energy [1].