The creation of an electron-positron pail by a photon and the bremsstrahlun
g of an electron in a medium are considered in the high-energy region, wher
e the influence of multiple scattering on the processes [the Landau-Pomeran
chuk-Migdal (LPM) effect] becomes essential. The pair photoproduction proba
bility is calculated with an accuracy up to the "next to leading logarithm.
" The integral characteristics, the radiation length and the total probabil
ity of pair photoproduction are analyzed under the influence of the LPM eff
ect, and the asymptotic expansions of these characteristics are derived.