We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the perturbing field, the only electric multipole moment induced by the field in the ground state of the atom is the quadrupole one. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997)], we derive a closed-form expression for an induced electric quadrupole moment. The result contains the generalized hypergeometric function 3 F 2 of the unit argument. Earlier calculations by other authors, based on a nonrelativistic model of the atom, predicted in the low-field region the quadratic dependence of the induced electric quadrupole moment on B.

The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997] is exploited to derive a closed-form expression for the magnetizability of the relativistic one-electron atom in an arbitrary discrete state, with a pointlike, spinless and motionless nucleus of charge Ze. The result has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument. Our general expression agrees with formulas obtained analytically earlier by other authors for some particular states of the atom. We present also numerical values of the magnetizability for some excited states of selected hydrogenlike ions with 1 Z 137 and compare them with data available in the literature.

ABSTRACT:The Sturmian expansion of the generalized Dirac-Coulomb Green function (Szmytkowski, J Phys B, 1997, 30, 825; erratum 1997, 30, 2747) is exploited to derive closed-form expressions for electric (σ E ) and magnetic (σ M ) dipole shielding constants for the ground state of the relativistic hydrogen-like atom with a point-like and spinless nucleus of charge Ze. It is found that σ E = Z −1 (as it should be) andwhere γ 1 = 1 − (Zα) 2 (α is the fine-structure constant). This expression for σ M agrees with earlier findings of several other authors, obtained with the use of other analytical techniques, and is elementary compared to an alternative one presented recently by Cheng et al. (J Chem Phys 2009, 130, 144102), which involves an infinite series of ratios of the Euler's gamma functions.

We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997)], we derive a closed-form expression for the electric quadrupole moment induced in the atom in an arbitrary discrete energy eigenstate. The result, which has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument, agrees with the earlier relativistic formula for that quantity, obtained by us for the ground state of the atom.

We present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless and of charge Ze. Calculations are based on the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); erratum 30, 2747(1997], combined with the theory of hypergeometric functions. The final result is of an elementary form and agrees with corresponding formulas obtained earlier by other authors for some particular states of the atom.