Unearthing radial independence for prediction of alpha-decay half-lives

TL;DR

This paper derives an analytical formula for alpha-decay half-lives based on an effective potential model, identifying a radial independence region to improve decay predictions for various nuclei.

Contribution

It introduces a novel analytical approach linking radial independence to decay half-life calculations using the Frahn potential form.

Findings

Identified a radial region where decay time remains nearly constant.

Derived a closed-form expression for half-life in terms of potential parameters.

Predicted half-lives for multiple nuclei using the analytical formula.

Abstract

Nuclear radial distance is a prerequisite for generating any alpha-decay half-life formula by taking a suitable effective potential. We study the emission process of alpha particles from an isolated quasi-bound state generated by an effective potential to a scattering state. The effective potential is expressed in terms of Frahn form of potential which is exactly solvable and an analytical expression for half-life is obtained in terms of Coulomb function, wave function and the potential. We then derive a closed form expression for the decay half-life in terms of the parameters of the potential, Q-value of the system, mass and proton numbers of the nuclei valid for alpha-decay as well as proton-decay. From the nature of variations of half-life as a function of radial distance, we trace the radial independence region where decay time is almost constant. Finally by overviewing our results and picking that particular radial distance we predict the half-lives of a series of nuclei by using the closed form expression.