Analytic solution of Lipmann-Schwinger equation for gas-solid quantum scattering via harmonic confinement

Confined fluids in nano-sized geometry can be found everywhere, in natural media such asbiological systems and rocks, and in man-made systems such as NEMS and purificationsystems. For describing behavior of them, the continuum model may not be applied becauseof being very small geometry and very much diluted fluid [1]. Because of the importance ofnano-confined fluid, we were motivated to consider it. The goal of our work is to investigatethe next behavior of an atom of fluid after incidence to the wall of nanochannel. Thereforewith considering an atomic fluid flowing in a nanochannel and introducing a Hamiltonianequation for short range movement of it, near the surface, we obtained its exact wavefunction. We considered the nonlocal separable potential with rank 1. It can reduce threebodyinteractions to two-body interactions. In our theoretical investigations, the scatteringapproach was used because it is the most useful method for studying the structure of matter insmall geometry.