Electric and magnetic dipole shielding constants for the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

摘要

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 (σE) and magnetic (σM) 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 σE = Z?1 (as it should be) and σM = ?(2Zα~2/27)-4γ ~31 + 6γ ~21 ? 7γ1 ? 12-/[γ1(γ1 + 1)(2γ1 ? 1)], where γ1 = 1 ? (Zα)~2 (α is the fine-structure constant). This expression for σM 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.