The scattering matrix and its meromorphic continuation in the Stark effect case

Quantum scattering in the presence of a constant electric field ('Stark effect') is considered. It is shown that the scattering matrix has a meromorphic continuation in the energy variable to the entire complex plane as an operator on L²(R^n-1). The allowed potentials V form a general subclass of potentials that are short-range relative to the free Stark Hamiltonian: Roughly, the potential vanishes at infinity, and admits a decomposition V = V_{script A sign} + V_e, where V_{script A sign} is analytic in a sector with V_{script A sign}(x) = O(〈x¹〉^-1/2-ε), and V_e(x) = O(e^μx1), for x₁ < 0 and some μ, ε > 0. These potentials include the Coulomb potential. The wave operators used to define the scattering matrix are the two Hilbert space wave operators.