Functional Form of the Imaginary Part of the Atomic Polarizability
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 ω 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 ω 3 form is obtained in both gauges. The seagull term in the velocity gauge is found to be crucial in establishing gauge invariance.
U. D. Jentschura and K. Pachucki, "Functional Form of the Imaginary Part of the Atomic Polarizability," European Physical Journal D, vol. 69, no. 4, Springer New York LLC, May 2015.
The definitive version is available at https://doi.org/10.1140/epjd/e2015-50810-8
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01 May 2015