Threshold Singularities in Appearance-Potential Spectroscopy

The model Hamiltonian used by Nozieres and De Dominicis in calculating the threshold behavior of x-ray emission and absorption in metals is applied to the situation where a core excitation is created by a fast electron. Explicit expressions are given for the exponent governing the threshold behavior. For transitions involving $s$-state core levels it is possible for stronger threshold divergences to occur than for the x-ray problem.