Electric-field-induced magnetic quadrupole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

Abstract

We consider a Dirac one-electron atom placed in a weak, static, uniform electric field. We show that, to the first order in the strength of the perturbing field, the only magnetic multipole moment induced in the ground state of the atom is the quadrupole one. The tensorial structure of that moment is resolved. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997); Szmytkowski, J. Phys. B 30, 2747(E) (1997)], we derive a closed-form expression for an $E1\ensuremath{\rightarrow}M2$ cross-susceptibility of the atom in the ground state.