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

Experimental measurements of a deep minimum in the triply differential cross section (TDCS) for electron-impact ionization of helium [1,2] for an energy of 64.6 eV have previously been interpreted in terms of a vortex in the velocity field [3]. The measurements are for out-of-plane symmetric geometry and for a specific gun angle of 67.5°. We have applied the Coulomb-Born (CB1) approximation for the gun angle of 67.5° and for the energies of 64.6eV and 74.6 eV and obtained a minimum in the TDCS for each energy [4]. However, to obtain deep minima in the CB1 TDCSs that corresponds to zeros in the CB1 transition matrix element we varied the gun angle. Corresponding to each zero there is a vortex in the velocity field that is associated with the transition matrix element. Using the CB1 approximation and considering symmetric geometries we also obtained a deep minimum in the TDCS for electron-hydrogen ionization of hydrogen [5], positron-hydrogen ionization [5] and positron-helium ionization [4]. For electron-impact ionization of both helium and hydrogen the CB1 TDCS results have been compared with both the TDCC and 3DW results [4-6]. [1] A. J. Murray and F. H. Read, J. Phys. B 26, L359 (1993). [2] A. J. Murray and F. H. Read, Phys. Rev. A 47, 3724 (1993). [3] J. H. Macek, J. B. Sternberg and S. Yu. Ovchinnikov, Phys. Rev. Lett. 104, 033201 (2010). [4] C. M. DeMars and S. J. Ward, Eur. Phys. J. D. 74, 48 (2020). [5] C. M. DeMars, S. J. Ward, J. Colgan, S. Amami and D. H. Madison, Atoms 8, 26 (2020). [6] J. Colgan, O. Al-Hagan, D.H. Madison, A.J. Murray and M.S. Pindzola, J. Phys. B 42, 171001 (2009).