Multiple scattering of matter waves: An analytic model of the refractive index for atomic and molecular gases

We present an analytic model of the refractive index for matter waves propagating through atomic or molecular gases. The model, which combines the Wentzel-Kramers-Brillouin (WKB) treatment of the long-range attraction with the Fraunhofer model treatment of the short-range repulsion, furnishes a refractive index in compelling agreement with recent experiments of Jacquey [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.240405 98, 240405 (2007)] on Li atom matter waves passing through dilute noble gases. We show that the diffractive contribution, which arises from scattering by a two-dimensional "hard core" of the potential, is essential for obtaining a correct imaginary part of the refractive index.