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Static magnetic multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

Abstract

We study far- and near-field magnetic and electric multipole moments induced in the ground state of the Dirac one-electron atom placed in a weak 2L-pole magnetostatic field. The analysis is carried out within the framework of the first-order Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997);J. Phys. B 30, 2747(E) (1997)]. Closed-form analytical expressions for multipole magnetizabilities χL, magnetic nuclear shielding constants σML→ML, the far-field magnetic-to-electric cross-susceptibilities χML→E(L∓1), and the near-field counterparts σML→E(L∓1) of the latter are derived. The formulas obtained for χL and σML→ML are much simpler than those available in the literature. We establish the relationship χML→E(L∓1)=αE(L∓1)→ML, where αE(L∓1)→ML are the multipole far-field electric-to-magnetic susceptibilities discussed in our previous paper [Szmytkowski and Łukasik, Phys. Rev. A 93, 062502 (2016)]. It is also found that when the atom is placed in superimposed weak and static electric and magnetic fields of respective multipolarities 2L1 and 2L2, such that L1=L2∓1, then the second-order correction to the ground-state energy contains an additional term entangling both fields and involving the cross-susceptibility αEL1→ML2=χML2→EL1.

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Details

Category:
Magazine publication
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
PHYSICAL REVIEW A no. 98, edition 2, pages 1 - 22,
ISSN: 2469-9926
Language:
English
Publication year:
2018
Bibliographic description:
Szmytkowski R., Łukasik G.: Static magnetic multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function// PHYSICAL REVIEW A. -Vol. 98, iss. 2 (2018), s.1-22
DOI:
Digital Object Identifier (open in new tab) 10.1103/physreva.98.022502
Sources of funding:
  • Działalność statusowa
Verification:
Gdańsk University of Technology

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