Single and double ionization of helium: the axial symmetry

Transition amplitudes and probabilities are the basic quantities of numerous theoretical approaches for the interpretation of collisional processes. These quantities are often evaluated from the transition matrix via Fourier transformation. However, a modification of the axial symmetry of the collision has sometimes been introduced to simplify the calculation. The present study shows that such a simplification is in general not justified and a source of highly unrealistic results. This is demonstrated in studies of single and double ionization of helium by ion impact.