Theoretical investigation of scattering of an atomic projectile confined in a harmonic surface potential

In this paper, scattering of a projectile atomic gas confined in an atomic harmonic surface is studied using the Lippmann-Schwinger. The nonlocal separable potential of rank one has been assumed between the projectile gas and surface, because this potential is useful to investigate the few-body systems. The analytical solution of Lippmann-Schwinger equation has been derived, and the scattering properties including transition and scattering matrices, phase shift, scattering amplitude and time delay are calculated analytically as a function of incident atomic gas energies.