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arXiv 2005.03134nucl-th
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狄拉克振子：原子核结构计算的另一种基础

The Dirac oscillator: an alternative basis for nuclear structure calculations

Junjie Yang, J. Piekarewicz

备注：
10 pages, 2 figures
发表信息：
Phys. Rev. C 102, 054308 (2020)
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摘要：

背景资料：由强自旋轨道相互作用补充的各向同性谐振子自七十多年前成立以来一直是原子核结构的基石。在本文中，我们介绍-或更确切地说重新介绍-“狄拉克振荡器”，一个完全相对论的基础上，具有所有所需的属性的普通谐振子，同时自然纳入一个强大的自旋轨道耦合。目的：第一次评估--据我们所知--狄拉克振子基在协变密度泛函理论框架内解决原子核结构问题的能力和灵活性。研究方法：自洽计算的结合能和基态密度为选定的一组双魔术魔术进行使用的狄拉克振荡器的基础上，然后与经常使用的龙格-库塔方法得到的结果进行比较。结果如下：使用狄拉克振荡器的基础上得到的结果与高精度的再现那些来自使用龙格-库塔方法，并提出了一个明确的路径概括为系统的轴对称。结论：虽然具有自旋轨道修正的三维谐振子从一开始就一直是核壳模型的主要组成部分，但狄拉克振子在核物理界实际上是未知的。在本文中，我们说明的权力和灵活性的狄拉克振荡器，并建议扩展到系统的研究，没有球对称的核激发的约束计算所需的。

英文摘要：

Background: The isotropic harmonic oscillator supplemented by a strong spin-orbit interaction has been the cornerstone of nuclear structure since its inception more than seven decades ago. In this paper we introduce---or rather re-introduced---the "Dirac Oscillator", a fully relativistic basis that has all the desired attributes of the ordinary harmonic oscillator while naturally incorporating a strong spin-orbit coupling. Purpose: To assess---to our knowledge for the first time---the power and flexibility of the Dirac Oscillator basis in the solution of nuclear structure problems within the framework of covariant density functional theory. Methods: Self-consistent calculations of binding energies and ground-state densities for a selected set of doubly-magic magic are performed using the Dirac-oscillator basis and are then compared against results obtained with the often-used Runge-Kutta method. Results: Results obtained using the Dirac oscillator basis reproduced with high accuracy those derived using the Runge-Kutta method and suggest a clear path for a generalization to systems with axial symmetry. Conclusions: Although the three-dimensional harmonic oscillator with spin-orbit corrections has been the staple of the nuclear shell model since the beginning, the Dirac oscillator is practically unknown among the nuclear physics community. In this paper we illustrate the power and flexibility of the Dirac oscillator and suggest extensions to the study of systems without spherical symmetry as required in constrained calculations of nuclear excitations.

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