• Novel formula for decay half-life of charged particle from the resonance of δ-well decorated Coulomb barrier

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/095/0150

• # Keywords

Resonance scattering; phase-shift time; alpha decay; cluster emission; decay half-life.

• # Abstract

A nucleus, initially in a bound state akin to a Dirac δ well potential, under severe action of reflection from a repulsive electrostatic interaction at very small separation between the newly born α cluster and the daughter nucleus goes to the quasistationary state from which the decay of α sets in. The energy derivative of the phase-shift of the $S$-matrix of transition scattering from an isolated quasibound state to a scattering state is related to the width (${\Gamma}$)of the resonance and hence the half-life T$_{1/2}$= ln 2$\bar{h}$/${\Gamma}$of α-decay. Using exact solutions of the delta well driven Coulomb potential, we derive a compact expression for log10 T$_{1/2}$ in terms of Q-value and the mass and charge numbers of the α emitter with a radius parameter specifying the sum of the charge radii of α and daughter nuclei or the radius of the parent emitter. The computed results of half-lives successfully explain the experimental values of α-decay half-lives ranging from 10$^{−7}$s to 10$^{25}$s in many light, heavy and super heavy radioactive nuclei with charge number Z = 52–120 and mass number A = 106–299. Showing uniformity in the applications of formulation to the decay of positive ions, namely α and cluster ions, the universal nature of the decay rule is established.

• # Author Affiliations

1. Department of Physics, North Orissa University, Takatpur, Baripda 757 003, India

• # Pramana – Journal of Physics

Volume 95, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019