Sum rule for optical scattering rates

An important quantity in electronic systems is the quasiparticle scattering rate (QPSR). A related optical scattering rate (OSR) is routinely extracted from optical data and, while it is not the same as the QPSR, it nevertheless displays many of the same features. We consider a sum rule that applies to the area under a closely related quantity, almost equal to the OSR in the low-energy region. We focus on the readjustment caused by, for example, a quasiparticle density-of-state change due to the superconducting transition. Unfortunately, no general statement about mechanism can be made solely on the energy scale in which the spectral weight readjustment in the OSR occurs.