标题： 变形的奇-奇核中的Gallagher-Moszkowski分裂在微观方法中 显示英文标题

标题： Gallagher-Moszkowski splitting in deformed odd-odd nuclei within a microscopic approach

摘要： 轴对称长椭球变形的奇-奇核的低能带头态长期以来基本上是在转子+两个准粒子的框架下描述的。这种方法能够解释所谓的带头态的Gallagher-Moszkowski双态，其特征是中子和质子在对称轴上的角动量投影的$K = \Omega_n \pm \Omega_p$、和与差。根据Gallagher和Moszkowski提出的经验规则，自旋对齐的构型比自旋反向对齐的构型能量更低。Robledo、Bernard和Bertsch在Phys. Rev. C 89, 021303(R) (2014)中的一项最新研究，在Gogny能量密度泛函下，对未配对核子进行自洽阻挡，表明计算在大约一半的情况下无法再现这一规则，并指出该泛函的密度依赖项是导致这一失败的原因。本文旨在进一步分析以揭示Gallagher-Moszkowski双态中能量分裂的机制。我们采用Skyrme能量密度泛函方法框架，包括BCS配对相关性以及自洽阻挡。我们使用带有时间奇数项和seniority配对矩阵元的SIII参数化，扩展了对偶偶核K同质异能态的先前研究[Phys. Rev. C 105, 044329 (2022)]。我们发现，能量分裂来源于Skyrme能量密度泛函的自旋-自旋、密度依赖和电流-电流项之间的竞争。在较大K值能量较低的双态中，SIII Skyrme能量密度泛函始终满足Gallagher-Moszkowski规则。相反，在较小K值能量较低的双态中，计算得到的能量分裂通常较小，且经常出现与Gallagher-Moszkowski规则不符的情况。 显示英文摘要

摘要： Low-lying bandhead states in axially prolate deformed odd-odd nuclei have long been described essentially within the rotor+two-quasiparticle picture. This approach allows one to explain the appearance of so-called Gallagher-Moszkowski doublets of bandheads with $K = \Omega_n \pm \Omega_p$, sum and difference of neutron and proton angular momentum projections on the symmetry axis. According to an empirical rule stated by Gallagher and Moszkowski the spin-aligned configuration lies lower in energy than the spin-anti-aligned configuration. A recent study by Robledo, Bernard and Bertsch in Phys. Rev. C 89, 021303(R) (2014) within the Gogny energy-density functional with selfconsistent blocking of the unpaired nucleons showed that calculations fail to reproduce this rule in about half of the cases and points to the density-dependent term of the functional as responsible of this failure. In this paper we aim at pushing further this analysis to exhibit the mechanism underlying the energy splitting in a Gallagher-Moszkowski doublet. We work in the framework of the Skyrme energy-density functional approach, including BCS pairing correlations with selfconsistent blocking. We use the SIII parametrization with time-odd terms and seniority pairing matrix elements extending a previous study of K-isomeric states in even-even nuclei [Phys. Rev. C 105, 044329 (2022)]. We find that the energy splitting results from a competition between the spin-spin, density-dependent and current-current terms of the Skyrme energy-density functional. In doublets where the larger K value is lower in energy the Gallagher-Moszkowski rule is always satisfied by the SIII Skyrme energy-density functional. In doublets, on the contrary, where the smaller K value lies lower, the energy splittings are calculated to be rather small and often a disagreement with the Gallagher-Moszkowski rule occurs.