DILATION ANALYTICITY IN CONSTANT ELECTRIC-FIELD .1. 2 BODY PROBLEM

The resolvent of the operator H0(ε, θ)=-Δe-20+εx1eθ is not analytic in θ for θ in a neighborhood of a real point, if the electric field ε is non-zero. (One manifestation of this singular behavior is that for 0<|Im θ|<π/3, H0(ε, θ) has no spectrum in the finite plane.) Nevertheless it is shown that the techniques of dilation analyticity still can be used to discuss the long-lived states (resonances) of a system described by a Hamiltonian of the form H=-Δ+εx1+V(x). © 1979 Springer-Verlag.