Analysis of the Breakdown of Exponential Decays of Resonances

TL;DR

This paper investigates the breakdown of exponential decay in a simple alpha decay model, revealing power law behavior at long times and confirming experimental violations of exponential decay through numerical analysis.

Contribution

It introduces a simple Dirac delta potential model to study decay breakdown and provides numerical evidence of power law decay, bridging theory and experimental observations.

Findings

Power law decay with exponent n=3 after exponential regime

Interference effects observed during intermediate decay stages

Numerical results align with experimental violation of exponential decay

Abstract

In the paper, a simple model of alpha decay with Dirac delta potential is studied. The model leads to breakdown of the exponential decay and to 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 Green's function representation and numerical solution of the time-dependent Schr\"odinger equation. In particular, finite depth potential wells and behavior between the exponential and power law regimes, which are situations that could not be described in detail analytically, are studied. The numerical results confirm power law with exponent n = 3 after the turnover into the non-exponential decay regime. Moreover, the constructive and destructive interference is observed in the intermediate stage of the process. The simple alpha decay model is compared to the results of Rothe- Hintschich-Monkman experiment which was the first experimental proof of violation of the exponential law.