  The behavior of spins undergoing Lamor precession in the presence of time
varying fields is of interest to many research fields. The frequency shifts and
relaxation resulting from these fields are related to their power spectrum and
can be determined from the Fourier Transform of the auto-correlation functions
of the time varying field. Using the method of images [C. M. Swank, A. K.
Petukhov, and R. Golub, Phys. Lett. A 376, 2319 (2012)] calculated the
position-position auto-correlation function for particles moving in a
rectangular cell with specular scattering walls. In this work we present a
heuristic model that extends this work to the case of Lambert scattering walls.
The results of this model are compared to simulation and show good agreement
from the ballistic to diffusive regime of gas collisions, for both square and
general rectangular cells. This model requires three parameters, two of which
describe the distribution of images in the case of a square cell, and one of
which describes the asymmetry in the mixing of the x and y components of the
velocity in the case of non-square rectangular cells.
