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Enhancement of Alpha Decay due to Medium Effects

Pankaj Jain, Harishyam Kumar

TL;DR

The paper investigates how a surrounding medium or external repulsive potential can modify alpha-decay rates for quasi-bound states with energy $E>0$, focusing on cases with very small final-state $Q$-values. It develops a time-dependent, spherically symmetric potential model and analyzes the decay dynamics by expanding the wavefunction in instantaneous resonant states, solving an integro-differential evolution for the amplitudes $a_k(t)$. The key finding is that as the $Q$-value becomes very small, medium effects can substantially enhance the decay rate, whereas for large $Q$ the effect is negligible. These results suggest practical avenues to control decay rates via external fields or media and may shed light on lattice-related observations of alpha-decay and related processes, with potential extensions to heavier emitted particles.

Abstract

We study the effect of medium on radioactive alpha decay and other similar decays. The initial state in these type of decays is a quasi-bound state with energy greater than zero. Such a state has very large amplitude in the nuclear region and is exponentially suppressed at larger distances. The decay rate of such states is known to decrease rapidly with decrease in the Q-value. Here we study such a decay within a medium. We assume a simple spherically symmetric repulsive potential model for the medium. This models the cumulative effect of all nuclei in the medium which at short distances present repulsive Coulomb interaction. We find that as the Q-value becomes very small, the medium effects lead to a substantial enhancement in rate. In contrast, for large Q-values, the medium effects are negligible. We briefly comment on application to real systems and the experimental implications of this result.

Enhancement of Alpha Decay due to Medium Effects

TL;DR

The paper investigates how a surrounding medium or external repulsive potential can modify alpha-decay rates for quasi-bound states with energy , focusing on cases with very small final-state -values. It develops a time-dependent, spherically symmetric potential model and analyzes the decay dynamics by expanding the wavefunction in instantaneous resonant states, solving an integro-differential evolution for the amplitudes . The key finding is that as the -value becomes very small, medium effects can substantially enhance the decay rate, whereas for large the effect is negligible. These results suggest practical avenues to control decay rates via external fields or media and may shed light on lattice-related observations of alpha-decay and related processes, with potential extensions to heavier emitted particles.

Abstract

We study the effect of medium on radioactive alpha decay and other similar decays. The initial state in these type of decays is a quasi-bound state with energy greater than zero. Such a state has very large amplitude in the nuclear region and is exponentially suppressed at larger distances. The decay rate of such states is known to decrease rapidly with decrease in the Q-value. Here we study such a decay within a medium. We assume a simple spherically symmetric repulsive potential model for the medium. This models the cumulative effect of all nuclei in the medium which at short distances present repulsive Coulomb interaction. We find that as the Q-value becomes very small, the medium effects lead to a substantial enhancement in rate. In contrast, for large Q-values, the medium effects are negligible. We briefly comment on application to real systems and the experimental implications of this result.
Paper Structure (8 sections, 52 equations, 3 figures)

This paper contains 8 sections, 52 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Basic Mechanism
  3. Evolution of the wave function
  4. Solution to the evolution equation
  5. Results
  6. Applications
  7. Conclusions
  8. Appendix A

Figures (3)

  • Figure 1: Schematic illustration of model potential
  • Figure 2: The real part of the wave function $U(r,t)$ at $t=0$ for the chosen parameters. The imaginary part is zero at this time.
  • Figure 3: The real part of the wave function $U(r,t)$ at $t=T$ for the chosen parameters. Here the time $T$ has been chosen to be unity. The imaginary part displays a similar behaviour.