Comment on the photon number bound and Rayleigh scattering

We discuss photon number bounds for a system of non-relativistic particles coupled to the quantized electromagnetic field (non-relativistic QED), below the ionization threshold. Such a bound was assumed in the proof of asymptotic completeness for Rayleigh scattering in our paper [3] (Condition (1.20) of Theorem 1.3 in [3]). We show how this assumption can be weakened and verified for a class of hamiltonians.