  The strong magnetic fields (B ~ 10^{12} - 10^{13} G) characteristic of
neutron stars make all the properties of an atom strongly dependent on the
transverse component K_\perp of its generalized momentum. In particular, the
photoionization process is modified substantially: (i) threshold energies are
decreased as compared with those for an atom at rest, (ii) cross section values
are changed significantly, and (iii) selection rules valid for atoms at rest
are violated by the motion so that new photoionization channels become allowed.
To calculate the photoionization cross sections, we, for the first time, employ
exact numerical treatment of both initial and final atomic states. This enables
us to take into account the quasi-bound (autoionizing) atomic states as well as
coupling of different ionization channels. We extend the previous
consideration, restricted to the so-called centered states corresponding to
relatively small values of K_\perp, to arbitrary states of atomic motion. We
fold the cross sections with the thermal distribution of atoms over K. For
typical temperatures of neutron star atmospheres, the averaged cross sections
differ substantially from those of atoms at rest. In particular, the
photoionization edges are strongly broadened by the thermal motion of atoms;
this "magnetic broadening" exceeds the usual Doppler broadening by orders of
magnitude. The decentered states of the atoms give rise to the low-energy
component of the photoionization cross section. This new component grows
significantly with increasing temperature above 10^{5.5} K and decreasing
density below 1 g/cm^3, i.e., for the conditions expected in atmospheres of
middle-aged neutron stars.
