The energy distribution of neutrons thermalized in an infinite homogeneous medium containing a crystalline moderator and absorbing material is investigated with the aid of a simplified model of the crystal. A Debye phonon spectrum is assumed, and a formal expansion in powers of the ratio of neutron mass to moderator atom mass is used. The inelastic scattering is approximated by the term of first order in the mass ratio, and interference effects are neglected. The resulting energy-change kernel is not correct in detail at high energies, but it correctly gives the average logarithmic energy loss, and therefore can be used in the age theory approximation at energies well above thermal. Solutions of the integral equation for the energy spectrum have been obtained on the IBM-650 for (1/υ) absorption. These are compared to solutions of the differential equation for a heavy gaseous moderator. It is found that the thermal spectra are very insensitive to the choice of scattering model, even when large departures from thermal equilibrium occur.