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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

✍ Scribed by Patrycja Stefańska; Radosław Szmytkowski


Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
143 KB
Volume
112
Category
Article
ISSN
0020-7608

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✦ Synopsis


Abstract

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
$(\sigma_{E})$
and magnetic $(\sigma_{M})$
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 $\sigma_{E}=Z^{-1}$
(as it should be) and

where
$\gamma_{1}=\sqrt{1-(Z\alpha)^{2}}$
(α is the fine‐structure constant). This expression for $\sigma_{M}$
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. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012