# Stark-induced magnetic anapole moment in the ground state of the relativistic hydrogenlike atom: 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); R. Szmytkowski,30, 2747(E) (1997)] is used to derive an analytical formula for the static magnetic anapole (toroidal dipole) moment induced in the ground state of the relativistic hydrogenlike atom by a weak, spatially uniform, static electric field. An expression for the anapole polarizability for the system in question is found. This expression contains a single generalized hypergeometric series {sub 3}F{sub 2} with the unit argument. In the nonrelativistic limit our result agrees with that of Lewis and Blinder [Phys. Rev. A 52, 4439 (1995)].

- Authors:

- Atomic Physics Division, Department of Atomic Physics and Luminescence, Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, PL 80-952 Gdansk (Poland)

- Publication Date:

- OSTI Identifier:
- 20974572

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.73.022511; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; CORRECTIONS; DIPOLE MOMENTS; ELECTRIC FIELDS; EXPANSION; GREEN FUNCTION; GROUND STATES; MAGNETIC MOMENTS; POLARIZABILITY; RELATIVISTIC RANGE

### Citation Formats

```
Mielewczyk, Krzysztof, and Szmytkowski, Radoslaw.
```*Stark-induced magnetic anapole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.022511.

```
Mielewczyk, Krzysztof, & Szmytkowski, Radoslaw.
```*Stark-induced magnetic anapole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function*. United States. doi:10.1103/PHYSREVA.73.022511.

```
Mielewczyk, Krzysztof, and Szmytkowski, Radoslaw. Wed .
"Stark-induced magnetic anapole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function". United States.
doi:10.1103/PHYSREVA.73.022511.
```

```
@article{osti_20974572,
```

title = {Stark-induced magnetic anapole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function},

author = {Mielewczyk, Krzysztof and Szmytkowski, Radoslaw},

abstractNote = {The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997); R. Szmytkowski,30, 2747(E) (1997)] is used to derive an analytical formula for the static magnetic anapole (toroidal dipole) moment induced in the ground state of the relativistic hydrogenlike atom by a weak, spatially uniform, static electric field. An expression for the anapole polarizability for the system in question is found. This expression contains a single generalized hypergeometric series {sub 3}F{sub 2} with the unit argument. In the nonrelativistic limit our result agrees with that of Lewis and Blinder [Phys. Rev. A 52, 4439 (1995)].},

doi = {10.1103/PHYSREVA.73.022511},

journal = {Physical Review. A},

number = 2,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}

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