Second-order Stark effect and polarizability of a relativistic two-dimensional hydrogen-like atom in the ground state

Abstract

The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves a generalized hypergeometric function ${}_3{F}_2$ with the unit argument. Numerical values of the polarizabilities for relativistic planar hydrogenic atoms with atomic numbers $1⩽Z⩽68$ are provided in a tabular form. A simple formula for the polarizability of a nonrelativistic two-dimensional hydrogenic atom, reported previously by several other authors, is recovered from our result in the nonrelativistic limit.

12 pages, 1 table

References in corpus (3)

• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• Stark effect in low-dimension hydrogen
• Static electric multipole susceptibilities of the relativistic hydrogen-like atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function