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

Abstract

We consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength B of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); 30, 2747(E) (1997)], we derive a closed-form expression for the electric quadrupole moment induced in the atom in an arbitrary discrete energy eigenstate. The result, which has the form of a double finite sum involving the generalized hypergeometric functions 3F2 of the unit argument, agrees with the earlier relativistic formula for that quantity, obtained by us for the ground state of the atom.

Nuclear magnetic shielding constants of Dirac one-electron atoms in some low-lying discrete energy eigenstates

“…In Refs. [16][17][18][19][20] we have considered an arbitrary discrete energy eigenstate of relativistic hydrogenlike atom, in order to obtain analytical expressions (and further -the numerical values) for some properties illustrating the influence of the external electromagnetic perturbations on the atom. In particular, in Ref.…”

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

“…[1][2][3][4][5][6][7][8][9]. Utilizing the Sturmian series representation of the first-order GDCGF [1], we derived analytically the closed-form expressions for the magnetizability [12,13] and the electric quadrupole moment induced by the dipole magnetic field [14] in an arbitrary discrete energy eigenstate of the atom. The final results from Refs.…”

“…The final results from Refs. [12,14] have the form of the double finite sum of hypergeometric functions 3 F 2 with the unit arguments. However, the comparison of their counterparts for the atomic ground state [5,8] (which contain only one 3 F 2 function) with the elementary formula describing the dipole magnetic shielding constant provided e.g.…”

“…[6], suggests that such general expression for the later atomic parameter should have a bit simpler form than the corresponding results presented in Refs. [12,14].…”

Probing the resonance of Dirac particle by the application of complex momentum representation

“…However, probing the resonance of Dirac particle by the application of complex momentum representation is still missing. As the resonance of Dirac particle is widely concerned in many fields [47][48][49][50] and almost all the methods have been developed for description of the relativistic resonance [19,25,27,35,[51][52][53], in this paper we will establish a new scheme for the resonance of Dirac particle using the complex momentum representation, which can be implemented straightforwardly to the relevant studies in other fields. In the following, we first introduce the theoretical formalism.…”