  In this paper we investigate the effects of the band shifts induced by the
interband spin-fluctuation coupling on the optical sum rule in pnictides. We
show that, despite the shrinking of the Fermi surfaces with respect to
first-principle calculations, the charge-carrier concentration in each band is
almost unchanged, with a substantial conservation of the total optical sum
rule. However, a significant transfer of spectral weight occurs from low-energy
coherent processes to incoherent ones, with practical consequences on the
experimental estimate of the sum rule, that is carried out integrating the data
up to a finite cut-off. This has profound consequences both on the absolute
value of the sum rule and on its temperature dependence, that must be taken
into account while discussing optical experiments in these systems.
