We present the results of a microscopic theory of the scattering, transmission, and sticking of 4He atoms impinging on a zero temperature 4He slab at near normal incidence. The theory includes coupling between different modes and allows for inelastic processes. The present work focuses on the elastic reflection and transmission of a 4He atom in the sense that we examine these intensities for atoms which have the same energy as the incident atoms. We find a considerable loss of total intensity due to scattering into multiple excitations. The reflected signal is in qualitative and semi-quantitative agreement with experimental results for 4He atoms scattered from the surface of bulk helium. The transmission intensity — which has not been measured — shows a very strong energy dependence. Moreover, we show that this dependence is substantially different from the Feynman level theory, which doesn't permit the decay of the single excitation into multiple excitations, and thus cannot describe a reduction in total intensity. In our theory, the major source of decay of elastic transmission and reflection (i.e., sticking) is from the production of ripplons at the liquid-vacuum interfaces.