Abstract
The Crilin (CRystal calorImeter with Longitudinal INformation) calorimeter is a semi-homogeneous calorimeter based on Lead Fluoride (PbF$_2$) crystals readout by surface-mount UV-extended Silicon Photomultipliers (SiPMs). It is a proposed solution for the electromagnetic calorimeter of the Muon Collider. The calorimeter should operate in a very harsh radiation environment, withstanding yearly a neutron flux of 10$^{14}$n$_{1MeV}$ /cm$^2$ and a dose of 100 krad. The proposed Crilin calorimeter is characterized by a modular architecture based on stackable submodules composed of matrices of PbF$_2$ crystals, with each crystal readout by 2 series of UV-extended SiPMs. To evaluate the effect of this high radiation environment on the PbF$_2$ crystal, two crystals have been irradiated both with photons and neutrons to study the changes in their transmittance. The results of an intense R\&D study to improve the performance of the electronics will be also described
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