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Low lying particle-hole states in $$^\mathbf{206 }$$ 206 Pb and $$^\mathbf{208 }$$ 208 Pb and the shell model
The European Physical Journal A ( IF 2.6 ) Pub Date : 2021-06-30 , DOI: 10.1140/epja/s10050-021-00500-0
A. Heusler

The nucleus \(^{206}\mathrm{Pb}\) differs from the doubly magic nucleus \(^{208}\mathrm{Pb}\) by two missing neutrons. In \(^{208}\mathrm{Pb}\) most states at \(E_x< 7.4\) MeV are described by one-particle one-hole configurations. The lowest configurations with a g \(_{{ 9}/{2}}\) particle and dominant p \(_{{ 1}/{2}}\), f \(_{{ 5}/{2}}\), p \(_{{ 3}/{2}}\) holes and admixtures from f \(_{{ 7}/{2}}\) and a few more configurations build an ensemble of two dozen states at 3.2\(<E_x< 4.9\) MeV. They are described by rather complete orthonormal transformation matrices of two dozen states with spins from 2\(^-\) to 8\(^-\) to configurations. In \(^{206}\mathrm{Pb}\) a similar ensemble of states is deduced from the analysis of angular distributions measured in 1969 for the \(^{206}\mathrm{Pb}\) \(({{{\textit{p}}}, {{\textit{p}}}' })\) reaction via the g \(_{{ 9}/{2}}\) IAR in \(^{207}\mathrm{Bi}\). An equivalent \(^{208}\mathrm{Pb}\) \(({{{\textit{p}}}, {{\textit{p}}}' })\) experiment was performed in 1968 at the Max–Planck–Institut für Kernphysik at Heidelberg (Germany). New spins are determined for 32 states and 22 levels in \(^{206}\mathrm{Pb}\). The comparison to corresponding states in \(^{208}\mathrm{Pb}\) studied especially in 1982 yields both remarkable similarities and clear differences. Sizeable g \(_{{ 9}/{2}}\) p \(_{{ 1}/{2}}\) strength found in 4\(^-\) and 5\(^-\) states is interpreted as admixtures of \({{\textit{p}}}{_{{ 3}/{2}}}^{-2}\) and \({{\textit{f}}}{_{{ 5}/{2}}}^{-2}\) components to the ground state of \(^{206}\mathrm{Pb}\) with dominant \({{\textit{p}}}{_{{ 1}/{2}}}^{-2}\) character. The description of nuclear states by shell model particle-hole configurations in the lead region needs the inclusion of collective excitations at already very low excitation energies. For the two isotopes \(^{206}\mathrm{Pb}\) and \(^{208}\mathrm{Pb}\) a rather good agreement of excitation energies and configuration mixing is observed for states at 3.7\(<E_x< 4.7\) MeV.



中文翻译:

$$^\mathbf{206 }$$ 206 Pb 和 $$^\mathbf{208 }$$ 208 Pb 中的低位粒子空穴状态和壳模型

原子核\(^{206}\mathrm{Pb}\)与双幻核\(^{208}\mathrm{Pb}\)的区别在于缺少两个中子。在\(^{208}\mathrm{Pb}\) 中\(E_x< 7.4\)  MeV 的大多数状态由单粒子一孔配置描述。具有g \(_{{ 9}/{2}}\)粒子和主导p \(_{{ 1}/{2}}\)的最低配置,f \(_{{ 5}/{2 }}\)p \(_{{ 3}/{2}}\)孔和来自f \(_{{ 7}/{2}}\) 的混合物以及其他一些配置构建了一个两打的集合状态为 3.2 \(<E_x< 4.9\)兆伏。它们由具有从 2 \(^-\)到 8 \(^-\)到配置的自旋的二打状态的相当完整的正交变换矩阵来描述。在\(^{206}\mathrm{Pb}\) 中,从 1969 年对\(^{206}\mathrm{Pb}\) \(({{ {\textit{p}}}, {{\textit{p}}}' })\)反应通过g \(_{{ 9}/{2}}\) IAR in \(^{207}\ mathrm{Bi}\)。等效的\(^{208}\mathrm{Pb}\) \(({{{\textit{p}}}, {{\textit{p}}}' })\)1968 年在德国海德堡的 Max-Planck-Institut für Kernphysik 进行了实验。为\(^{206}\mathrm{Pb}\) 中的32 个状态和 22 个级别确定新的自旋。与1982 年特别研究的\(^{208}\mathrm{Pb}\) 中的相应状态的比较产生了显着的相似性和明显的差异。在 4 个\(^-\)和 5 个\(^-\)状态中发现相当大的g \(_{{ 9}/{2}}\) p \(_{{ 1}/{2}}\)强度被解释为\({{\textit{p}}}{_{{ 3}/{2}}}^{-2}\)\({{\textit{f}}}{_{ { 5}/{2}}}^{-2}\)分量到\(^{206}\mathrm{Pb}\)的基态,具有显性\({{\textit{p}}}{_{{ 1}/{2}}}^{-2}\)字符。通过壳模型粒子-孔结构在铅区描述核状态需要在已经非常低的激发能量下包含集体激发。对于两个同位素\(^{206}\mathrm{Pb}\)\(^{208}\mathrm{Pb}\)观察到激发能和构型混合的相当好的一致性,对于 3.7 \(< E_x< 4.7\) MeV。

更新日期:2021-07-01
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