Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

Abstract

The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997] is exploited to derive a closed-form expression for the magnetizability of the relativistic one-electron atom in an arbitrary discrete state, with a pointlike, spinless and motionless nucleus of charge Ze. The result has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument. Our general expression agrees with formulas obtained analytically earlier by other authors for some particular states of the atom. We present also numerical values of the magnetizability for some excited states of selected hydrogenlike ions with 1 Z 137 and compare them with data available in the literature.

Magnetizabilities of relativistic hydrogenlike atoms in some arbitrary discrete energy eigenstates

“…In Ref. [10] we have shown that it remains valid for an arbitrary discrete energy eigenstate. However, the aforementioned article contains only two representational tables with values of the relativistic magnetizabilities for some excited states of selected hydrogenlike ions.…”

“…Present calculations have been performed with the current value 137.035 999 139 of the inverse of the fine-structure constant recommended by the Committee on Data for Science and Technology (CODATA) [11], in contrast to those described in Ref. [10], in which we have used α −1 = 137.035 98 95 (CODATA 1986), to be able to compare our results with the previous results of other authors [12]. To show how the change in the value of the fine structure constant affects the value of the magnetizability, additionally, we performed calculations for χ with α −1 = 137.035 999 074, recommended by CODATA 2010 (i.e.…”

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We present the results of numerical calculations of magnetizability (χ) of the relativistic one-electron atoms with a pointlike, spinless and motionless nuclei of charge Ze. Exploiting the analytical formula for χ recently derived by us [P. Stefańska, 2015], valid for an arbitrary discrete energy eigenstate, we have found the values of the magnetizability for the ground state and for the first and the second set of excited states (i.e. : 2s 1/2 , 2p 1/2 , 2p 3/2 , 3s 1/2 , 3p 1/2 , 3p 3/2 , 3d 3/2 , and 3d 5/2 ) of the Dirac one-electron atom.

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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

“…Basing on the analysis of such kind of expressions as the one in the last equation, carried out by us in the appendix to Ref. [12], particularly, using Eq. (A.11) from that article, one may easily prove that F n κ (1) = −1.…”

Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

“…In Ref. [13], we have analyzed the magnetic dipole moment induced in the relativistic hydrogenlike atom by a weak, static, uniform magnetic field. Actually, we derived analytically an expression for the magnetizability of the atom in an arbitrary excited state, which allowed us then to find numerical values of this quantity for a few low-lying discrete energy eigenstates [14].…”