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

Details 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 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

2011-02-18

arxiv.org/abs/1102.3853v1

Physics

Atomic Physics

LaTeX, 12 pages

Scientific paper

The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive closed-form expressions for electric ($\sigma_{\mathrm{E}}$) and magnetic ($\sigma_{\mathrm{M}}$) 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 $\sigma_{\mathrm{E}}=Z^{-1}$ (as it should be) and $$\sigma_{\mathrm{M}}=-(2Z\alpha^{2}/27)(4\gamma_{1}^{3}+6\gamma_{1}^{2}-7\gamma_{1}-12) /[\gamma_{1}(\gamma_{1}+1)(2\gamma_{1}-1)],$$ where $\gamma_{1}=\sqrt{1-(Z\alpha)^{2}}$ ($\alpha$ is the fine-structure constant). This expression for $\sigma_{\mathrm{M}}$ 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 \emph{et al.} [J. Chem. Phys. 130 (2009) 144102], which involves an infinite series of ratios of the Euler's gamma functions.

Affiliated with

Also associated with

No associations

Rating

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 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with 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, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and 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 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-212997