Functional Form of the Imaginary Part of the Atomic Polarizability

TL;DR

This paper resolves a long-standing debate by deriving the imaginary part of atomic polarizability for small frequencies, confirming the omega^3 dependence in both length and velocity gauges, and emphasizing the importance of gauge invariance.

Contribution

The authors derive the functional form of the imaginary part of atomic polarizability, demonstrating gauge invariance and confirming the omega^3 dependence using both length and velocity gauges.

Findings

The omega^3 dependence of the imaginary polarizability is confirmed in both gauges.

Gauge invariance is verified through the inclusion of the seagull term.

General expressions for atomic polarizability are provided.

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 omega has been a matter of long-standing discussion, with both a linear dependence and an omega^3 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 omega^3 form is obtained in both gauges. The seagull term in the velocity gauge is found to be crucial in establishing gauge invariance.