LetH=−Δ+V+Fx1 withV(x1,x⊥) analytic in the first variable andV(x1+ia, x⊥) bounded and decreasing to zero asx → ∞ for eacha ∈ ℝ. Let ψ be an eigenvector of −Δ+V with negative eigenvalue. Among our results we show that forF≠0, (ψ,e−Hψ) decays exponentially at a rate governed by the positions of the resonances ofH. This exponential decay is in marked contrast to “conventional” atomic resonances for which power law decay is the rule.