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arXiv 2406.03378nucl-thnucl-ex
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量子性在原子核及多体系统中的应用

Use of quantality in nuclei and many-body systems

J. -P. Ebran, L. Heitz, E. Khan

AI总结:

本文探讨了量子性在原子核及多体系统中的应用,揭示了其与散射长度、极限半径及自旋-轨道效应的关系,发现原子核因所有无量纲量接近1而成为特殊系统。

摘要:

本文讨论了量子性在原子核及其他多体系统(如原子电子)中的应用。这一无量纲量已知可用于指示多体系统何时表现得像晶体或量子液体。通过展示其与散射长度的关系,进一步分析了它的作用。此外,还展示了一个基本长度尺度——极限半径的出现。在核子的情况下,它对应于核子-核子相互作用的硬核;在原子电子的情况下,它对应于接近玻尔半径的值。通过量子性与局域化参数的关系,分析了原子核中团簇相的出现,从而确定核子数和密度均为该相出现的控制参数。量子性与相互作用大小的关系还揭示了第三个无量纲参数,通过实现赝自旋对称性来监测有限系统中自旋-轨道效应的大小。比较了量子性对自旋-轨道效应在不同多体系统中的影响。在原子核中,还分析了量子性在结合能与壳层能相对效应中的作用。最后,通过量子性的推广提出了额外的无量纲量。研究发现,原子核是特殊的系统,因为其所有无量纲量均接近1的量级,与其他多体系统不同。

英文摘要:

The use of quantality is discussed in the case of nuclei and other many-body systems such as atomic electrons. This dimensionless quantity is known to indicate when a many-body system behaves like a crystal or a quantum liquid. Its role is further analyzed by showing its relation to the scattering length. The emergence of a fundamental lengthscale, the limit radius, is also shown. It corresponds to the hard-core of the nucleon-nucleon interaction in the case of nucleons, and to a value close to the Bohr radius in the case of atomic electrons. The occurrence of a cluster phase in nuclei is analyzed using the quantality through its relation to the localization parameter, allowing for the identification of both the number of nucleons and the density as control parameters for the occurrence of this phase. The relation of the quantality to the magnitude of the interaction also exhibits a third dimensionless parameter, monitoring the magnitude of the spin-orbit effect in finite systems, through the realization of the pseudo-spin symmetry. The impact of quantality on the spin-orbit effect is compared in various many-body systems. The role of quantality in the relative effect of the binding energy and the shell one is also analyzed in nuclei. Finally, additional dimensionless quantities are proposed from the generalization of the quantality. Nuclei are found to be exceptional systems because all their dimensionless quantities are close to the order of unity, at variance with other many-body systems.

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