Analysis Of The Breakdown Of Exponential Decays Of Resonances

A simple model of alpha decay with the Dirac delta potential is studied. The model leads to breakdown of the exponential decay and to the power law behavior at asymptotic times. Time dependence of the survival probability of the particle in the potential well is analyzed numerically with two methods: integration of the Green's function representation and numerical solution of the time-dependent Schrodinger equation. The numerical results confirm power law with exponent n = 3 after the turnover into the non-exponential decay regime. Moreover, oscillations of non-escape probability are observed in the intermediate stage of the process. The simple alpha-decay model is compared to the results of the Rothe-Hintschich-Monkman experiment which was the first experimental proof of violation of the exponential law.