The scattering matrix and its meromorphic continuation in the stark effectcase

Quantum scattering in the presence of a constant electric field ('Stark eff ect') is considered. It is shown that the scattering matrix has a meromorph ic continuation in the energy variable to the entire complex plane as an op erator on L-2(Rn-1). The allowed potentials V form a general subclass of po tentials that are short-range relative to the free Stark Hamiltonian: Rough ly, the potential vanishes at infinity, and admits a decomposition V = V-A + V-e,where V-A is analytic in a sector with V-A(x) = O([x(1)](-1/2-epsilon )), and V-e(x) = O(e(mu x1)), for x(1) < 0 and some mu, epsilon > 0. These potentials include the Coulomb potential. The wave operators used to define the scattering matrix are the two Hilbert space wave operators.