Magnetic field-induced electric quadrupole moment in the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

摘要

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 theperturbing field, the only electric multipole moment induced by the field inthe ground state of the atom is the quadrupole one. Using the Sturmianexpansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J.Phys. B 30 (1997) 825; erratum 30 (1997) 2747], we derive a closed-formexpression for the induced electric quadrupole moment. The result contains thegeneralized hypergeometric function $_{3}F_{2}$ of the unit argument. Earliercalculations by other authors, based on the non-relativistic model of the atom,predicted in the low-field region the quadratic dependence of the inducedelectric quadrupole moment on $B$.