Scattering of ultracold atoms by an absorbing nanowire

We study the scattering of ultracold atoms by a conducting cylindrical wire with total absorption near the surface of the wire. A hierarchy of approximations for the exact nonretarded atom-wire potential is explored. We show the existence of a semiclassical region near to the surface of the wire, which allows us to unambiguously define incoming boundary conditions for the description of total absorption at the wire surface. The semiclassical region is only reproduced by an accurate treatment of the potential. We calculate the complex s-wave scattering length for the effective two-dimensional atom-wire scattering problem. The scattering length tends to the wire radius R in the thick-wire limit, and it tends to 0 nearly as (ln R)^-1 in the thin-wire limit.