  We have constructed an approximate microscopic model for the neutron dynamic
structure factor of solid methane in phase II. We expect our model to apply for
neutron energies below 1\textit{eV} at pressures near 1 bar and temperatures
below 20K, where solid methane exists in a phase, called phase II, in which the
tetrahedral hydrogens exist in a mixed phase of free rotors and hindered
rotors. Certain matrix elements needed for the dynamic structure factor $S(Q,
\omega)$ are adapted from a calculation by Ozaki \textit{et
al.}\cite{ozaki:3442}\cite{ozaki2}. The model treats the effects of molecular
translations, intramolecular vibrations and the free and hindered rotational
degrees of freedom as uncoupled ones. Total scattering cross sections
calculated from the model agree with the cross section measurements of
Grieger\cite{grieger:3161} and Whittemore\cite{Wittemore} for the incident
neutron energies of 0.5 \textit{meV} $\sim$ 1\textit{eV}. The effective density
of states extracted from the model was compared with the Harker $&$ Brugger
frequency spectrum extracted from neutron scattering measurements conducted at
22K\cite{HARKER1967}.
