Three-Dimensional Approach Applied to Quasi-stationary States of Deformed $\alpha$-Emitters

TL;DR

This paper introduces a three-dimensional approach to study the quasi-stationary states of deformed alpha-emitters, revealing significant differences from traditional one-dimensional models, especially for highly deformed nuclei.

Contribution

The paper develops a 3D method for analyzing alpha decay in deformed nuclei, improving accuracy over 1D models by accounting for anisotropic potentials.

Findings

3D decay widths differ significantly from 1D results for highly deformed nuclei.

The method separates internal and external potential regions for better modeling.

Deformation effects are crucial in accurately predicting alpha decay properties.

Abstract

We apply a three-dimensional (3D) approach to investigate the quasi-stationary states of well-deformed $\alpha$-emitters. With a splitting of the anisotropic 3D potential into internal and external parts at a separation surface, the 3D $\alpha$-cluster decay width is determined by the initial wave function of a true bound state of an anisotropic harmonic oscillator potential and a non-resonance scattering wave function of Coulomb potential. Substantial difference between the 1D and 3D decay width is found for typical $\alpha$-emitters with large quadrupole and hexadecapole deformations.