  The setting of Moessbauer nuclei embedded in thin-film cavities has
facilitated an aspiring platform for x-ray quantum optics as shown in several
recent experiments. Here, we generalize the theoretical model of this platform
that we developed earlier [Phys. Rev. A 88, 043828 (2013)]. The theory
description is extended to cover multiple nuclear ensembles and multiple modes
in the cavity. While the extensions separately do not lead to qualitatively new
features, their combination gives rise to cooperative effects between the
different nuclear ensembles and distinct spectral signatures in the
observables. A related experiment by Roehlsberger et al. [Nature 482, 199
(2012)] is successfully modeled, the scalings derived with semiclassical
methods are reproduced, and a microscopic understanding of the setting is
obtained with our quantum mechanical description.
