  In the theory of resonant scattering, the double differential cross section
involves the computation of a multifold integral of a 4-point correlation
function, which generalizes the traditional 2-point correlation function of
Van-Hove for potential scattering. In the case of a neutron-crystal
interaction, the numerical computation of these multifold integrals is
cumbersome. In this paper, a new approximation is suggested. It is based on a
factorization of the differential cross section into one function describing
the exchange of kinetic energy between the neutron and the bound nucleus
(phonons dynamic) and a function related to the nuclear scattering amplitude.
This formalism is then applied to the modeling of resonant scattering of a
neutron by $^{238}U$ in a $UO_2$ crystal lattice.
