  We consider photoionization of a system bound by the central potential
$V(r)$. We demonstrate that the high energy nonrelativistic asymptotics of the
photoionization cross section can be obtained without solving the wave
equation. The asymptotics can be expressed in terms of the Fourier transform of
the potential by employing the Lippmann--Schwinger equation. We find the
asymptotics for the screened Coulomb field. We demonstrate that the leading
corrections to this asymptotics are described by the universal factor. The high
energy nonrelativistic asymptotics is found to be determined by the analytic
properties of the potential $V(r)$. We show that the energy dependence of the
asymptotics of photoionization cross sections of fullerenes is to large extent
model dependent. We demonstrate that if the fullerene field $V(r)$ is
approximated by the function with singularities in the complex plane, the power
drop of the asymptotics is reached at the energies which as so high that the
cross section becomes unobservably small. The preasymptotic behavior with a
faster drop of the cross sections becomes important in these cases.
