Background] An electron localization function was originally introduced to visualize in positional space bond structures in molecules. It became a useful tool to describe electron configurations in atoms, molecules, and solids. In nuclear physics, a nucleon localization function (NLF) has been used to characterize cluster structures in light nuclei, formation of fragments in fission, and pasta phases appearing in the inner crust of neutron stars. [Purpose] We use the NLF to study the nuclear response to fast rotation. [Methods] We generalize the NLF to the case of nuclear rotation. The extended expressions involve both time-even and time-odd local particle and spin densities and currents. Since the current density and density gradient contribute to the NLF primarily at the surface, we propose a simpler spatial measure given by the kinetic energy density. Illustrative calculations for the superdeformed yrast band of ${}^{152}$Dy were carried out using the cranked Skyrme-Hartree-Fock method. We also employed the cranked harmonic oscillator model to gain insights into spatial patterns revealed by the NLF at high angular momentum. [Results] In the case of deformed rotating nucleus, several NLFs can be introduced, depending on the definition of the spin quantization axis, direction of the total angular momentum, and self-consistent symmetries of the system. Contributions to the NLF from the current density, spin-current tensor density, and density gradient terms are negligible in the nuclear interior. The oscillating pattern of the simplified NLF can be explained in terms of a constructive interference between kinetic-energy and particle densities. The characteristic nodal pattern seen in the NLF in the direction of major axis of a rotating nucleus comes from single-particle orbits carrying large aligned angular momentum. The variation of the NLF along the minor axis of the nucleus can be traced back to deformation-aligned orbits. [Conclusions] The NLF allows a simple interpretation of the shell structure evolution in the rotating nucleus in terms of the angular momentum alignment of individual nucleons. We expect that the NLF will be very useful for the characterization and visualization of other collective modes in nuclei and time-dependent processes.

中文翻译：

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旋转核中的核子定位功能

背景技术最初引入电子定位功能是为了可视化分子中的位置空间键结构。它成为描述原子，分子和固体中电子构型的有用工具。在核物理学中，核子定位功能（NLF）已用于表征轻核中的簇结构，裂变中碎片的形成以及中子星内壳中出现的面食相。[目的]我们使用NLF研究快速旋转的核反应。[方法]我们将NLF推广到核旋转的情况。扩展的表达式同时包含了偶时和奇时局部粒子以及自旋密度和电流。由于电流密度和密度梯度主要在表面上对NLF起作用，我们提出了一种由动能密度给出的更简单的空间度量。超变形拉斯特带的说明性计算。${}^{152}$Dy使用Skyrme-Hartree-Fock曲柄法进行。我们还使用了曲柄谐波振荡器模型来洞察NLF在高角动量下揭示的空间模式。[结果]在旋转核变形的情况下，根据自旋量化轴的定义，总角动量的方向以及系统的自洽对称性，可以引入几个NLF。在核内部，电流密度，自旋电流张量密度和密度梯度项对NLF的贡献可忽略不计。简化的NLF的振动模式可以用动能和颗粒密度之间的相长干涉来解释。在NLF中沿旋转核长轴方向看到的特征性节点模式来自携带大的对准角动量的单粒子轨道。NLF沿着原子核短轴的变化可以追溯到变形对准的轨道。[结论] NLF可以根据单个核子的角动量对齐来简单解释旋转核中的壳结构演化。我们希望NLF对原子核和时间相关过程中其他集体模式的表征和可视化非常有用。[结论] NLF可以根据单个核子的角动量对齐来简单解释旋转核中的壳结构演化。我们希望NLF对原子核和时间相关过程中其他集体模式的表征和可视化非常有用。[结论] NLF可以根据单个核子的角动量对齐来简单解释旋转核中的壳结构演化。我们希望NLF对原子核和时间相关过程中其他集体模式的表征和可视化非常有用。