球形质子发射体的离心修正谐振子模型
Centrifugal-corrected harmonic oscillator model for spherical proton emitters
AI总结：
提出一种改进的谐振子模型，通过引入离心势修正项，系统评估球形原子核的质子放射性半衰期，并利用实验数据拟合得到离心参数和核势深度，验证了归一化宽度对数与碎裂势的线性关系，推导出离心势可调参数的解析表达式，提高了质子放射性研究的精度。
摘要：
在本工作中，我们提出了一种改进的谐振子模型，通过引入离心势效应，系统评估球形原子核的质子放射性半衰期。通过拟合实验数据，得到修正项 $dl(l+1)$ 的离心参数 $d = 0.143$ 和核势深度 $V_0 = 62.4$ MeV。该模型结合了基于 DD-ME2 力的相对论平均场（RMF）理论和 BCS 方法，以确定谱因子 $S_p$。此外，通过验证归一化宽度对数 $\log_{10}{γ^2}$ 与碎裂势 $V_{frag}$ 之间的线性关系，确认了核结构与隧穿动力学之间的联系，并推导出离心势对应的可调参数 $d$ 的解析表达式为 $d^{ m{Ae}}$ $\approx$ 0.167。与 $d^{ m{Ae}}$ 相比，基于 $d$ 的修正模型得到的结果与实验半衰期更吻合，并能将实验数据的误差控制在 2.4 倍以内。此外，扩展后的改进模型被用于预测 NUBASE2020 中一些能量允许或已观测到但尚未量化的可能质子放射性候选核的半衰期。本工作提高了质子放射性研究的精度，并为未来的核结构研究提供了稳健的理论框架。
英文摘要：
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 $S_p$. 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 radioactivity candidates in NUBASE2020 that are energetically allowed or have been observed but not yet quantified. This work improves the accuracy of proton radioactivity studies and provides a robust theoretical framework for future nuclear structure research.
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