Resonances as viscosity limits for exponentially decaying potentials

We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to case of exponentially decaying potentials. That means eigenvalues $-\Delta + V - i\epsilon x^2$, $|V(x)|\leq C e^{-2\gamma |x|}$ converge, as $ \epsilon\to 0+ $, poles meromorphic continuation ( -\Delta -\lambda^2 )^{-1} uniformly on compact subsets $\textrm{Re}\,\lambda>0$, $\textrm{Im}\,\lambda>-\gamma$, $\arg\lambda > -\pi/8$.