We present a scattering kernel to describe the interactions of low-energy neutrons in superfluid 4He at temperatures below ∼1.3K. The kernel was developed on the basis of the separation of the single-phonon and multi-phonon excitations. The single-phonon excitations are described exactly by the dispersion relation and the multi-phonon excitations are included using the phonon expansion approach in the Gaussian approximation. For this purpose, a weighted frequency distribution, derived from the experimentally observed phonon-roton excitations, is used as input. We demonstrate that this approach reproduces very well the measured total cross-sections, scattering functions, and ultra-cold neutron production spectrum, including both the single-phonon and multi-phonon components.