Eur. Phys. J. D (2015) 69: 118
https://doi.org/10.1140/epjd/e2015-50810-8

Regular Article

Functional form of the imaginary part of the atomic polarizability

¹ Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
² Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland

^a e-mail: ulj@mst.edu

Received: 11 November 2014
Received in final form: 25 January 2015
Published online: 28 April 2015

Abstract

The dynamic atomic polarizability describes the response of the atom to incoming electromagnetic radiation. The functional form of the imaginary part of the polarizability for small driving frequencies ω has been a matter of long-standing discussion, with both a linear dependence and an ω³ dependence being presented as candidate formulas. The imaginary part of the polarizability enters the expressions of a number of fundamental physical processes which involve the thermal dissipation of energy, such as blackbody friction, and non-contact friction. Here, we solve the long-standing problem by calculating the imaginary part of the polarizability in both the length (“d·E”) as well as the velocity-gauge (“p·A”) form of the dipole interaction, verify the gauge invariance, and find general expressions applicable to atomic theory; the ω³ form is obtained in both gauges. The seagull term in the velocity gauge is found to be crucial in establishing gauge invariance.