Relativistic Effects and Gauge Invariance in Photon Absorption and Scattering
The interaction of light with matter is often described within the semiclassical framework where light is represented by an external time-dependent vector potential. We show that the transition probabilities so obtained suffer from two drawbacks: their semi-relativistic limit is delicate and they are not gauge invariant. We describe how a gauge-invariant transition probability can be obtained, for which the semi-relativistic limit is well defined. In this way, we obtain a new spin-position term which is not negligible in x-ray magnetic circular dichroism at the K-edge of transition metals.
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