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 |
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Authors: | Patrycja Stefańska Radosław Szmytkowski |
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Institution: | Atomic Physics Division, Department of Atomic Physics and Luminescence,Faculty of Applied Physics and Mathematics, Gdańsk University of Technology,Narutowicza 11/12, 80‐233 Gdańsk, Poland |
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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 |
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Keywords: | electric nuclear shielding magnetic nuclear shielding Dirac one‐electron atom Dirac‐Coulomb Green function Sturmian functions |
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