Precise analysis of resonance decay law in atomic physics

Straightforward high-precision results for the problem of resonance state decay within the well known Laplace method are obtained. Deviation of the resonance decay law from the conventional exponential time dependence, determined by the pole contributions, is accurately studied for a model system. The asymptote of the background contribution which dominates the decay pattern for large t is shown to be directly related to the threshold behaviour of the discrete state-continuum matrix element. A new scheme for continuum discretization with different sets of the resonance pseudostates is applied and its high accuracy in describing the system evolution over very large time intervals is demonstrated. It is shown that both pf the approaches considered do not imply any analytical form for the discrete state-continuum matrix element V(mu). A scheme is developed which allows the application of these approaches for arbitrary V(mu) including the cases when this quantity is obtained within ab initio calculations.