  The process of pair creation by a photon in a strong magnetic field is
investigated basing on the polarization operator in the field. The total
probability of the process is found in a relatively simple form. The
probability exhibits a "saw-tooth" pattern because of divergences arising when
the electron and positron are created at threshold of the Landau energy levels.
The pattern will be washed out at averaging over any smooth photon energy
distribution. The new results are obtained in the scope of the quasiclassical
approach: 1) in the case when the magnetic field $B \ll B_0, (B_0$ is the
critical field) the new formulation extends the photon energy interval to the
case when the created particles are not ultrarelativistic; 2) the correction to
the standard quasiclassical approximation is found showing the range of
applicability of the approach at high photon energy as well. The very important
conclusion is that for both cases $B \ll B_0$ and $B \geq B_0$ the results of
the quasiclassical calculation are very close to averaged probabilities of
exact theory in a very wide range of photon energies. The quasiclassical
approximation is valid also for the energy distribution if the electron and
positron are created on enough high levels.
