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

physical review. a/physical review, a

Magnetic-field-induced electric quadrupole moments for relativistic  hydrogenlike atoms: Application of the Sturmian expansion of the generalized  Dirac-Coulomb Green function