Centrifugal-corrected harmonic oscillator model for spherical proton emitters

TL;DR

This paper introduces an enhanced harmonic oscillator model incorporating centrifugal effects to accurately predict proton radioactivity half-lives in spherical nuclei, integrating relativistic mean field theory and spectroscopic factors.

Contribution

The work develops a modified model with a centrifugal correction parameter, improving agreement with experimental data and enabling predictions for unmeasured proton emitters.

Findings

Model achieves better half-life predictions within a factor of 2.4.

Linear relationship between $ ext{log}_{10}{ ext{width}}$ and $V_{frag}$ is verified.

Predicts half-lives for potential proton emitters in NUBASE2020.

Abstract

In the present work, we propose an improved harmonic oscillator model to systematically evaluate the proton radioactivity half-lives in spherical nuclei, incorporating centrifugal potential effects. By fitting the experimental data, the centrifugal parameter $d = 0.143$ for the correction term $dl(l+1)$ and nuclear potential depth $V_0 = 62.4$ MeV are obtained. The model integrates the relativistic mean field (RMF) theory with the BCS method based on the DD-ME2 force to determine spectroscopic factors $S_p$, which represent the probability of proton emission. Moreover, by verifying the linear relationship between the logarithm of the normalized width $\log_{10}{\gamma^2}$ and fragmentation potential $V_{frag}$, the connection between nuclear structure and tunneling dynamics is confirmed, and an analytical expression for the adjustable parameter $d$ corresponding to the centrifugal potential is derived as $d^{\rm{Ae}}$ $\approx$ 0.167. Compared with $d^{\rm{Ae}}$, the modified model based on $d$ yields results in better agreement with experimental half-lives, and is able to control the error of the experimental data within a factor of 2.4. Furthermore, the extended improved model is used to predict the half-lives of some possible proton emission candidates in NUBASE2020 that are energetically allowed or have been observed but not yet quantified. This work improves the accuracy of proton emission studies and provides a robust theoretical framework for future nuclear structure research.