Centrifugal-corrected harmonic oscillator model for spherical proton emitters

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 $\log_{10}{γ^2}$ 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.

Figures (5)

• Figure 1: (color online) The schematic diagram of the total interaction potential $V(r)$ and the modified harmonic oscillator potential $V_N(r)$ versus $r$.
• Figure 2: (color online) The linear relationship between the logarithm of spectroscopic factors $S_{p}^{\rm{{cal}}}$ calculated by Eq. (\ref{['Spcal']}) and the fragmentation potential $V_{frag}$.
• Figure 3: (color online) The logarithmic differences between experimental half-lives and calculate ones for unfavored proton radioactivity. The different colors represent the different angular momentum taken away by the proton emitters. For each angular momentum cases, the squares and circles are represented by Eq. (\ref{['logT']}), while the pentagrams and triangles are denoted by Eq. (\ref{['logTT']}), respectively.
• Figure 4: (color online) Deviations between the theoretical proton radioactivity half-lives and the experimental ones.
• Figure 5: (color online) Relationship between the predictions of these models and/or formulas given in Table \ref{['table3']} and $(Z_d^{0.8}+l)+Q_p^{-1/2}$.