Nucleon-pair truncation of the shell model for medium-heavy nuclei
Nucleon-pair truncation of the shell model for medium-heavy nuclei
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DOI：
10.1103/physrevc.106.044309
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发表时间：
2022-08
影响因子：
3.1
通讯作者：
Y. Yu;Y. Lu;G. Fu;C. Johnson;Z. Ren
中科院分区：
文献类型：
--
作者：
Y. Yu;Y. Lu;G. Fu;C. Johnson;Z. Ren
背景：可计算的原子核模型是核结构物理学长期追求的目标。一个容易包含激发态和多体关联的灵活框架是构型-相互作用壳模型（SM），但基的指数增长意味着需要一个有效的截断方案，理想的截断方案是同时包含变形和配对关联。目的：提出一种有效的SM截断方案：从Hartree-Fock单粒子态的对凝聚变分定义和粒子数守恒的Bardeen-Cooper-Schrieffer （NBCS）近似出发，对具有良好角动量的态进行投影。方法：在SM空间中生成具有Kramers简并的Hartree-Fock单粒子态后，通过最小化能量来优化NBCS中的对幅值，然后对具有良好角动量的态进行线性代数投影（LAP）。NBCS和LAP的计算速度都很快。结果：在$^{44,46,48}$Ti、$^{48,50}$Cr、$^{52}$Fe、$^{60,62,64}$Zn、$^{66,68}$Ge、$^{68}$Se和$^{108,110}$Xe等中、重质量区域，我们的计算结果与具有轴对称和三轴变形的过渡核和旋转核低空态的全构型相互作用SM计算结果吻合得很好。我们预测了$^{112-114}\textrm{Ba}$和$^{116-120}\textrm{Ce}$的低洼态，这些原子核很难通过大规模SM计算得到。结论：对相关和不同本征态之间的组态混合在再现集体和形状共存中发挥了关键作用，证明了SM截断方案在研究过渡核和变形核方面的实用性。
Background: Computationally tractable models of atomic nuclei is a long-time goal of nuclear structure physics. A flexible framework which easily includes excited states and many-body correlations is the configuration-interaction shell model (SM), but the exponential growth of the basis means one needs an efficient truncation scheme, ideally one that includes both deformation and pairing correlations. Purpose: We propose an efficient truncation scheme of the SM: starting from a pair condensate variationally defined by Hartree-Fock single-particle states and the particle-number conserved Bardeen-Cooper-Schrieffer (NBCS) approximation, we carry out projection of states with good angular momentum. Methods: After generating Hartree-Fock single-particle states with Kramers degeneracy in a SM space, we optimize the pair amplitudes in the NBCS by minimizing the energy, and then use linear algebra projection (LAP) of states with good angular momentum. Both NBCS and LAP are computationally fast. Results: Our calculations yield good agreement with full configuration-interaction SM calculations for low-lying states of transitional and rotational nuclei with axially symmetric and triaxial deformation in medium- and heavy-mass regions: $^{44,46,48}$Ti, $^{48,50}$Cr, $^{52}$Fe, $^{60,62,64}$Zn, $^{66,68}$Ge, $^{68}$Se, and $^{108,110}$Xe. We predict low-lying states of $^{112-114}\textrm{Ba}$ and $^{116-120}\textrm{Ce}$, nuclei difficult to reach by large-scale SM calculations. Conclusions: Both pair correlation and the configuration mixing between different intrinsic states play a key role in reproducing collectivity and shape coexistence, demonstrating the utility of this truncation scheme of the SM to study transitional and deformed nuclei.