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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