Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

Z. X. Ren (任政学), S. Q. Zhang (张双全), and J. Meng (孟杰)
Phys. Rev. C 95, 024313 – Published 10 February 2017

Abstract

A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in a 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single-particle energy are smaller than 104 MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial-deformed, nonaxial-deformed, and octupole-deformed potential are provided and discussed.

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  • Received 30 October 2016
  • Revised 6 January 2017

DOI:https://doi.org/10.1103/PhysRevC.95.024313

©2017 American Physical Society

Physics Subject Headings (PhySH)

Nuclear Physics

Authors & Affiliations

Z. X. Ren (任政学)1, S. Q. Zhang (张双全)1, and J. Meng (孟杰)1,2,3,4,*

  • 1State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
  • 2School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
  • 3Department of Physics, University of Stellenbosch, Stellenbosch, South Africa
  • 4Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

  • *mengj@pku.edu.cn

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Issue

Vol. 95, Iss. 2 — February 2017

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