  We have investigated the influence of X-ray irradiation on the vertical
structure of the outer accretion disk in low-mass X-ray binaries by performing
a self-consistent calculation of the vertical structure and X-ray radiation
transfer in the disk. Penetrating deep into the disk, the field of scattered
X-ray photons with energy $E\gtrsim10$\,keV exerts a significant influence on
the vertical structure of the accretion disk at a distance
$R\gtrsim10^{10}$\,cm from the neutron star. At a distance $R\sim10^{11}$\,cm,
where the total surface density in the disk reaches
$\Sigma_0\sim20$\,g\,cm$^{-2}$, X-ray heating affects all layers of an
optically thick disk. The X-ray heating effect is enhanced significantly in the
presence of an extended atmospheric layer with a temperature
$T_{atm}\sim(2\div3)\times10^6$\,K above the accretion disk. We have derived
simple analytic formulas for the disk heating by scattered X-ray photons using
an approximate solution of the transfer equation by the Sobolev method. This
approximation has a $\gtrsim10$\,% accuracy in the range of X-ray photon
energies $E<20$\,keV.
