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2024年10月30日
Chinese Physics C> 2009, Vol. 33> Issue(9) : 737-742 DOI: 10.1088/1674-1137/33/9/005

Microscopic calculation of the magnetic field of neutron stars

  • Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pz=0, n=0, and m≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.

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    [1] . Shapiro S L, Teukolsky S A. The Physics of Compact Ob-jects. Wiley, New York, 19832. Backer D C. Ap J., 1976, 209: 8953. CHEN Wei, LIU Liang-Gang. HEP NP, 2005, 29: 119-123. (in Chinese)4. Kouveliotou C et al. Nature, 1994, 368: 1255. Chakrabarty S, Bandyopadhyay D, Pal S. Phys. Rev. Lett.,1997, 78: 28986. Dipankar B. J Astrophy Astro., 2002, 23: 672727. Ito H, Yamada S, Sumiyoshi K et al. Theor. Phys., 2006,114: 995-10208. DUAN Huai-Yu, QIAN Yong-Zhong. Astro-ph., 2005, 29:72-939. MAO Guang-Jun, Iwamoto A, LI Zhu-Xia. Astro-ph/010922110. Kutschera M, Wojcik W. Phys. Lett. B, 1983, 223: 1111. Kutschera M, Wojcik W. Acta Magnetica. 1997, 8: 212. JIA Wen-Zhi, WANG Shun-Jin. HEP NP, 2006, 30(6):530-536 (in Chinese)13. JIA Wen-Zhi, WANG Shun-Jin. Commun. Theor., 2008,50: 335-340

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LIU Jun, JIA Wen-Zhi and WANG Shun-Jin. Microscopic calculation of the magnetic field of neutron stars[J]. Chinese Physics C, 2009, 33(9): 737-742. doi: 10.1088/1674-1137/33/9/005
LIU Jun, JIA Wen-Zhi and WANG Shun-Jin. Microscopic calculation of the magnetic field of neutron stars[J]. Chinese Physics C, 2009, 33(9): 737-742.  doi: 10.1088/1674-1137/33/9/005 shu
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Received: 2008-12-30
Revised: 2009-03-21
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Microscopic calculation of the magnetic field of neutron stars

    Corresponding author: WANG Shun-Jin,
  • Received Date: 2008-12-30
  • Accepted Date: 2009-03-21
  • Available Online: 2009-09-05

Abstract: 

Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pz=0, n=0, and m≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.

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