Closed-form expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

摘要

We present analytical derivation of the closed-form expression for the dipolemagnetic shielding constant of a Dirac one-electron atom being in an arbitrarydiscrete energy eigenstate. The external magnetic field, by which the atomicstate is perturbed, is assumed to be weak, uniform and time independent. Withrespect to the atomic nucleus we assume that it is pointlike, spinless,motionless and of charge Ze. Calculations are based on the Sturmian expansionof the generalized Dirac- Coulomb Green function [R. Szmytkowski, J. Phys. B30, 825 (1997); erratum 30, 2747 (1997)], combined with the theory ofhypergeometric functions. The final result is of an elementary form and agreeswith corresponding formulas obtained earlier by other authors for someparticular states of the atom.