The Dirac oscillator: an alternative basis for nuclear structure calculations

Abstract

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.

10 pages, 2 figures

References in corpus (5)

• Neutron-Rich Nuclei in Heaven and Earth
• Building relativistic mean field models for finite nuclei and neutron stars
• Nuclear Structure in the Framework of the Unitary Correlation Operator Method
• Optimizing the relativistic energy density functional with nuclear ground state and collective excitation properties
• Covariant Density Functional Theory in Nuclear Physics and Astrophysics

Cited by in corpus (4)

• Towards accurate nuclear mass tables in covariant density functional theory
• Effect of Quantum Gravity on Specific Heat of Solid
• The Dirac oscillator in the curved spacetime of a cloud of strings
• Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime