Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Static electric multipole susceptibilities of the relativistic
  hydrogen-like atom in the ground state: Application of the Sturmian expansion
  of the generalized Dirac-Coulomb Green function   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 30 (1997) 825,
erratum: 30 (1997) 2747] 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 $\alpha_{L}$, electric-to-magnetic cross-susceptibilities
$\alpha_{\mathrm{E}L\to\mathrm{M}(L\mp1)}$ and 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 non-terminating generalized hypergeometric
functions ${}_{3}F_{2}$ with the unit argument. Counterpart formulas for the
near-nucleus multipole susceptibilities --- the electric nuclear shielding
constants $\sigma_{\mathrm{E}L\to\mathrm{E}L}$, near-nucleus
electric-to-magnetic cross-susceptibilities
$\sigma_{\mathrm{E}L\to\mathrm{M}(L\mp1)}$ and near-nucleus
electric-to-toroidal-magnetic cross-susceptibilities
$\sigma_{\mathrm{E}L\to\mathrm{T}L}$ --- involve terminating ${}_{3}F_{2}(1)$
series and for each $L$ may be rewritten in terms of elementary functions.
Exact numerical values of the far-field dipole, quadrupole, octupole and
hexadecapole susceptibilities are provided for selected hydrogenic ions.
Analytical quasi-relativistic approximations, valid to the second order in
$\alpha Z$, where $\alpha$ is the fine-structure constant and $Z$ is the
nuclear charge number, are derived for all types of the far-field and
near-nucleus susceptibilities considered in the paper.

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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th