  Theoretical spectra of X-ray bursting neutron star (NS) model atmospheres are
widely used to determine the basic NS parameters such as their masses and
radii. We construct accurate NS atmosphere models using for the first time an
exact treatment of Compton scattering via the integral relativistic kinetic
equation. We also compare the results with the previous calculations based on
the Kompaneets operator. We solve the radiation transfer equation together with
the hydrostatic equilibrium equation accounting exactly for the radiation
pressure by electron scattering. We thus construct a new set of plane-parallel
atmosphere models in LTE for hot NSs. The models were computed for six chemical
compositions (pure H, pure He, solar H/He mix with various heavy elements
abundances Z = 1, 0.3, 0.1, and 0.01 Z_sun, and three log g = 14.0, 14.3, and
14.6. For each chemical composition and log g, we compute more than 26 model
atmospheres with various luminosities relative to the Eddington luminosity
L_Edd computed for the Thomson cross-section. The maximum relative luminosities
L/L_Edd reach values of up to 1.1 for high gravity models. The emergent spectra
of all models are redshifted and fitted by diluted blackbody spectra in the
3--20 keV energy range appropriate for the RXTE/PCA. We also compute the color
correction factors f_c. The radiative acceleration g_rad in our luminous,
hot-atmosphere models is significantly smaller than in corresponding models
based on the Kompaneets operator, because of the Klein-Nishina reduction of the
electron scattering cross-section, and therefore formally "super-Eddington"
model atmospheres do exist. The differences between the new and old model
atmospheres are small for L / L_Edd < 0.8. For the same g_rad / g, the new f_c
are slightly larger (by approximately 1%) than the old values.
