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

Abstract

The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$ polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997); erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997)] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities - the polarizabilities $\alpha_{L}$, the electric-to-magnetic cross susceptibilities $\alpha_{\mathrm{E}L\to\mathrm{M}(L∓1)}$, and the electric-to-toroidal-magnetic cross susceptibilities $\alpha_{\mathrm{E}L\to\mathrm{T}L}$ - are found to be expressible in terms of one or two nonterminating generalized hypergeometric functions ${}_{3}F_{2}$ with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities - the electric nuclear shielding constants $\sigma_{\mathrm{E}L\to\mathrm{E}L}$, the near-nucleus electric-to-magnetic cross susceptibilities $\sigma_{\mathrm{E}L\to\mathrm{M}(L∓1)}$, and the near-nucleus electric-to-toroidal-magnetic cross susceptibilities $\sigma_{\mathrm{E}L\to\mathrm{T}L}$ - involve one or two terminating ${}_{3}F_{2}(1)$ series and for each $L$ may be rewritten in terms of elementary functions. Numerical values of the far-field dipole, quadrupole, octupole, and hexadecapole susceptibilities are provided for selected hydrogenic ions. The effect of a declared uncertainty in the CODATA 2014 recommended value of the fine-structure constant $\alpha$ on the accuracy of numerical results is investigated. Analytical quasirelativistic approximations, valid to the second order in $\alpha Z$, where $Z$ is the nuclear charge number, are also derived for all types of the far-field and near-nucleus susceptibilities considered in the paper.

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DOI:
Digital Object Identifier (open in new tab) 10.1103/PhysRevA.93.062502
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Copyright (2016 American Physical Society)

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Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
PHYSICAL REVIEW A no. 93, edition 6, pages 1 - 40,
ISSN: 2469-9926
Language:
English
Publication year:
2016
Bibliographic description:
Szmytkowski R., Łukasik G.: Static electric 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. 93, iss. 6 (2016), s.1-40
DOI:
Digital Object Identifier (open in new tab) 10.1103/physreva.93.062502
Verified by:
Gdańsk University of Technology

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