  We study in this work an integral formulation for the radiative transfer
equation (RTE) in anisotropic media with truncated approximation to the
scattering phase function. The integral formulation consists of a coupled
system of integral equations for the angular moments of the transport solution.
We analyze the approximate separability of the kernel functions in these
integral formulations, deriving asymptotic lower and upper bounds on the number
of terms needed in a separable approximation of the kernel functions as the
moment grows. Our analysis provides the mathematical understanding on when
low-rank approximations to the discretized integral kernels can be used to
develop fast numerical algorithms for the corresponding system of integral
equations.
