Optimal path of diffusion over the saddle point and fusion of massive nuclei

TL;DR

This paper analyzes the diffusion process over a saddle point in a two-dimensional potential, deriving an exact passing probability formula, and applies it to optimize nuclear fusion by identifying the best initial conditions and deformations.

Contribution

It provides an exact expression for passing probability over a saddle point considering off-diagonal inertia and friction, and identifies optimal initial conditions for maximizing nuclear fusion probability.

Findings

Passing probability is strongly affected by off-diagonal inertia and friction.

Optimal initial velocity direction enhances the probability of crossing the saddle point.

Maximum fusion probability occurs at an intermediate deformation of nuclei.

Abstract

Diffusion of a particle passing over the saddle point of a two-dimensional quadratic potential is studied via a set of coupled Langevin equations and the expression for the passing probability is obtained exactly. The passing probability is found to be strongly influenced by the off-diagonal components of inertia and friction tensors. If the system undergoes the optimal path to pass over the saddle point by taking an appropriate direction of initial velocity into account, which departs from the potential valley and has minimum dissipation, the passing probability should be enhanced. Application to fusion of massive nuclei, we show that there exists the optimal injecting choice for the deformable target and projectile nuclei, namely, the intermediate deformation between spherical and extremely deformed ones which enables the fusion probability to reach its maximum.