Explicit expressions for the semiclassical transition probabilities of atomic $K$- and $L$-shell electrons into the continuum as a result of proton collisions are obtained as functions of proton-impact parameter and energy transfer, using first-order time-dependent perturbation theory with undeflected proton trajectories. Calculated energy distributions for the ejected electrons are compared with the plane-wave Born-approximation cross sections. The contributions from various partial waves are shown in illustrations. The validity of the calculation is limited by the neglect of the Coulomb deflection of the protons.

• Received 22 August 1968

DOI:https://doi.org/10.1103/PhysRev.177.233