AI 中文总结
研究手征三核子力张量秩分量对钙同位素单粒子结构的影响，通过导出有效壳模型哈密顿量，发现3NF增强SO分裂主要由秩 - 1分量导致，其不同张量秩分量对结构性质有不同影响，明确了相关机制在0f1p壳中的延续。
AI 中文摘要
背景：手征三核子力（3NFs）在核壳演化的微观描述中起关键作用。最近的一项工作引入了手征3NF在下一个次领先阶的不可约张量分解，并表明在p壳核中，0p3/2 - 0p1/2自旋 - 轨道（SO）分裂的增强主要由其秩 - 1分量驱动。目的：我们将上述分析扩展到0f1p壳，以研究相同机制在更重的价空间中是否持续，以及3NF的不同张量秩分量如何影响钙同位素的结构性质。方法：从手征双核子力加3NF导出双幻核40Ca核心外中子的有效壳模型哈密顿量。后者通过其秩 - λ分量（λ = 0,1,2,3）逐步包含，使我们能够分离它们对中子单粒子结构演化的影响。结果：手征3NF产生的1p和0f轨道的SO分裂的显著增强主要由其秩 - 1分量引起。秩 - 2项贡献较小，而秩 - 3项可忽略不计。发现秩 - 0分量以及在较小程度上的秩 - 1分量在确定具有不同轨道角动量的轨道之间的间距方面起重要作用。3NF在单粒子结构中引起的所有修改对48Ca的壳闭性质有相关影响。结论：3NF的秩 - 1双π交换分量在解释SO分裂增强方面的主导地位 - 先前在p壳中确定 - 在0f1p壳中持续。观察到的与轨道不同角动量依赖性相关的3NF效应基本上源于其秩 - 0和秩 - 1分量。
英文摘要
Background: Chiral three-nucleon forces (3NFs) play a key role in the microscopic description of nuclear shell evolution. A recent work introduced an irreducible tensor decomposition of the chiral 3NF at next-to-next-to-leading order and showed that, in $p$-shell nuclei, the enhancement of the $0p_{3/2}$--$0p_{1/2}$ spin--orbit (SO) splitting is mainly driven by its rank-1 component. Purpose: We extend the aforementioned analysis to the $0f1p$ shell to investigate whether the same mechanism persists in a heavier valence space, and how the different tensor-rank components of the 3NF affect structure properties of calcium isotopes. Methods: Effective shell-model Hamiltonians for neutrons outside the doubly magic $^{40}$Ca core are derived from chiral two-nucleon force plus 3NF. The latter is progressively included through its rank-$λ$ components ($λ=0,1,2,3$), allowing us to isolate their impact on the evolution of the neutron single-particle structure. Results: The significant enhancement of the SO splittings for both $1p$ and $0f$ orbitals produced by the chiral 3NF is mainly induced by its rank-1 component. The rank-2 term gives a smaller contribution, while the rank-3 term is negligible. The rank-0 component, and to a lesser extent the rank-1 component, are found to play an important role in determining the spacings between orbitals with different orbital angular momenta. All modifications induced by the 3NF in the single-particle structure have a relevant impact on the shell-closure properties of $^{48}$Ca. Conclusions: The dominance of the rank-1 two-pion-exchange component of the 3NF in explaining the enhancement of SO splitting -- previously identified in the $p$ shell -- persists in the $0f1p$ shell. Observed effects of the 3NF related to the different angular-momentum dependence of the orbitals are shown to arise essentially from their rank-0 and rank-1 components.
Comments9 pages, 5 figures, 2 tables
