Asymptotic behavior of photoionization cross section in a central field
  We demonstrate that the high energy nonrelativistic asymptotic for the photoionization cross section in a central field $V(r)$ can be expressed in terms of the asymptotic of the Fourier transform $V(p)$ of the field. We show that the cross sections drop in the same way for the fields with the Coulomb short distance behavior. The character of the cross sections energy behavior is related to the analytical properties of the function $V(r)$. The cross sections exhibit power drop for the potentials which have singularities an the real axis. They suffer the exponential drop if $V(r)$ has singularities in the complex plane. 
E. G. Drukarev, A. I. Mikhailov
quant-ph