  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.
