The strong magnetic fields (B similar to 10(12)-10(13) G) characterist
ic of neutron stars make all the properties of an atom strongly depend
ent on the transverse component K-perpendicular to of its generalized
momentum. In particular, the photoionization process is modified subst
antially: (1) threshold energies are decreased as compared with those
for an atom at rest, (2) cross section values are changed significantl
y, and (3) selection rules valid for atoms at rest are violated by the
motion so that new photoionization channels become allowed. To calcul
ate the photoionization cross sections, we employ, for the first time,
exact numerical treatment of both initial and final atomic states. Th
is enables us to take into account the quasi-bound (autoionizing) atom
ic states as well as coupling of different ionization channels. We ext
end the previous consideration, restricted to the so-called centered s
tates corresponding to relatively small values of K-perpendicular to,
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 substanti
ally from those of atoms at rest. In particular, the photoionization e
dges are strongly broadened by the thermal motion of atoms; this ''mag
netic broadening'' exceeds the usual Doppler broadening by orders of m
agnitude. The decentered states of the atoms give rise to the low-ener
gy component of the photoionization cross section. This new component
grows significantly with increasing temperature above 10(5.5) K and de
creasing density below 1 g cm(-3), i.e., for the conditions expected i
n atmospheres of middle-aged neutron stars.