Classical model of atomic polarisability in the presence of radiation damping

What is it about?

A simple classical-oscillator model of atomic polarisability is derived to account for radiation damping. The model is corroborated by quantum-mechanical perturbation theory. A wide-spread analytically incorrect expression for the polarisability is pointed out and improved. The resulting polarisability is in agreement with conclusions from the most general treatment of radiation damping by Spohn (2004) who uses the mathematically sophisticated method of singular perturbation theory applied to the equations of motion of a charged particle. The present investigation presents a pedestrian's view on the problem by starting from the unique solution of the classical Abraham-Lorentz equation.

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Why is it important?

The erroneous expression for the atomic polarisability has spread widely in quantum optics literature during the last decades. In view of increasing experimental achievements with ultra-cold gases, a correct analytical form for the polarisabilty seems more necessary than ever.