Static electric multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized DiracCoulomb Green function
Abstract
The ground state of the Dirac oneelectron atom, placed in a weak, static electric field of definite 2^{L} polarity, is studied within the framework of the firstorder perturbation theory. The Sturmian expansion of the generalized DiracCoulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997), 10.1088/09534075/30/4/007; erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997), 10.1088/09534075/30/11/023] is used to derive closedform analytical expressions for various farfield and nearnucleus static electric multipole susceptibilities of the atom. The farfield multipole susceptibilities—the polarizabilities α_{L}, the electrictomagnetic cross susceptibilities α_{E L} →M (L ∓1 ), and the electrictotoroidalmagnetic cross susceptibilities α_{E L} →T L —are found to be expressible in terms of one or two nonterminating generalized hypergeometric functions F_{2} with the unit argument. Counterpart formulas for the nearnucleus multipole susceptibilities—the electric nuclear shielding constants σ_{EL}→E L, the nearnucleus electrictomagnetic cross susceptibilities σ_{E L} →M (L ∓1 ), and the nearnucleus electrictotoroidalmagnetic cross susceptibilities σ_{E L} →T L —involve one or two terminating F_{2}(1 ) series and for each L may be rewritten in terms of elementary functions. Numerical values of the farfield dipole, quadrupole, octupole, and hexadecapole susceptibilities are provided for selected hydrogenic ions. The effect of a declared uncertainty in the CODATA 2014 recommended value of the finestructure constant α on the accuracy of numerical results is investigated. Analytical quasirelativistic approximations, valid to the second order in α Z , where Z is the nuclear charge number, are also derived for all types of the farfield and nearnucleus susceptibilities considered in the paper.
 Publication:

Physical Review A
 Pub Date:
 June 2016
 DOI:
 10.1103/PhysRevA.93.062502
 arXiv:
 arXiv:1602.00613
 Bibcode:
 2016PhRvA..93f2502S
 Keywords:

 Physics  Atomic Physics
 EPrint:
 66 pages, 19 tables