Whole fusion-fission process with Langevin approach and compared with analytical solution for barrier passage

TL;DR

This paper models the entire fusion-fission process using a Langevin approach, deriving an analytical expression for barrier crossing probability that accounts for metastable potential effects, and compares it with simulations.

Contribution

It introduces an approximate analytical expression for the modified barrier crossing probability considering reflection boundary effects, validated by Langevin simulations.

Findings

Passing probability is non-monotonous over time.

Maximum passing probability is less than stationary value.

Analytical results agree with Langevin Monte-Carlo simulations.

Abstract

We investigate time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of reflection boundary of potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of passing probability over the saddle point of inverse harmonic potential.