在广义液滴模型中系统研究PDMATHAAB、$\boldsymbol{N=126}$壳层封闭体周围核的$α$衰变预形成因子
Systematic study of the $α$ decay preformation factor of nuclei around the $\boldsymbol{Z=82}$, $\boldsymbol{N=126}$ shell closures within a generalized liquid drop model
摘要：
本文基于广义液滴模型，系统地研究了152个核在$Z$ = 82，$N$ = 126封闭壳层附近的$α$衰变预形成因子$P_α$和$α$衰变半衰期，其中$P_α$是从计算的$α$衰变半衰期与实验值的比值中提取的。结果表明，$P_α$与价质子（空穴）$N_p$和价中子（空穴）$N_n$的乘积有明显的线性关系。同时，我们从Sun \textit{et al.} [\href {https：//doi.org/10.1088/1361-6471/aac981}}{J. Phys. G：Nucl.Part. Phys. $\bm{45}$，075106（2018）}]，其中$P_α$可以通过两个不同的显微公式计算。我们发现$P_α$也与$N_pN_n$有关。结合我们以前的工作[Sun \textit{et al.}，\href {https：//www.example.com PhysRevC.94.024338}{Phys. Rev. C $\bm{94}$，024338（2016）}; Deng \textit{et al.}，\href {https：//doi.org/10.1103/PhysRevC 96.024318}{ibid. $\bm{96}$，024318（2017）}; Deng \textit{et al.}，\href {https：//doi.org/10.1103/PhysRevC.97.044322}{ibid. $\bm{97}$，044322（2018）}]和Seif \textit{et al.}的工作[\href {http：{Phys. Rev. C $\bm{84}$，064608（2011）}]，我们怀疑这些封闭壳层周围的核的线性关系的这种现象是模型无关的。这可能是由于壳层封闭物周围的价质子（空穴）和价中子（空穴）的作用引起的。最后，利用由广义液滴模型（GLDM）计算的$P_α$拟合得到的公式，计算了这些核的$α$衰变半衰期。计算结果与实验数据吻合较好。
英文摘要：
In this work, we systematically study the $α$ decay preformation factors $P_α$ and $α$ decay half-lives of 152 nuclei around $Z$ = 82, $N$ = 126 closed shells based on a generalized liquid drop model while $P_α$ is extracted from the ratio of the calculated $α$ decay half-life to the experimental one. The results show that there is an obvious linear relationship between $P_α$ and the product of valance protons (holes) $N_p$ and valance neutrons (holes) $N_n$. At the same time, we extract the $$P_α$ values of even-even nuclei around $\emph{Z}$ = 82, $\emph{N}$ = 126 closed shells from the work of Sun \textit{et al.} [\href {https://doi.org/10.1088/1361-6471/aac981} {J. Phys. G: Nucl. Part. Phys. $\bm{45}$, 075106 (2018)}], in which the $P_α$ can be calculated by two different microscopic formulas. We find that the $P_α$ are also related to $N_pN_n$. Combining with our previous works [Sun \textit{et al.}, \href {https://doi.org/10.1103/PhysRevC.94.024338} {Phys. Rev. C $\bm{94}$, 024338 (2016)}; Deng \textit{et al.}, \href {https://doi.org/10.1103/ PhysRevC 96.024318} {ibid. $\bm{96}$, 024318 (2017)}; Deng \textit{et al.}, \href {https://doi.org/10.1103/PhysRevC.97.044322} {ibid. $\bm{97}$, 044322 (2018)}] and the work of Seif \textit{et al.} [\href {http://dx.doi.org/10.1103/PhysRevC.84.064608}{Phys. Rev. C $\bm{84}$, 064608 (2011)}], we suspect that this phenomenon of linear relationship for the nuclei around those closed shells is model independent. It may be caused by the effect of the valence protons (holes) and valence neutrons (holes) around the shell closures. Finally, using the formula obtained by fitting the $P_α$ calculated by the generalized liquid drop model (GLDM), we calculate the $α$ decay half-lives of these nuclei. The calculated results are agree with the experimental data well.
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