A non-relativistic model of two-particle decay III. The pole approximation

Abstract

In the third part of the paper, we are concerned mostly with the problem of justifying the approximation in which the reduced resolvent is replaced by the pole term alone. Imposing additional regularity assumptions on the functionν, which specifies the interaction, we are able to estimate the difference of the corresponding reduced propagators. This result is used further to derive an estimate of the deviations from the exponential decay law which results from the pole approximation. With exception of very small and very large times, the obtained bound is proportional to fourth power of the coupling constant. We prove also Fermi golden rule for the model under consideration, and compare the present method to the one previously used by Demuth.