  The Mu2e calorimeter is composed by 1400 un-doped CsI crystals coupled to
large area UV extended Silicon Photomultipliers arranged in two annular disks.
This calorimeter has to provide precise information on energy, timing and
position. It should also be fast enough to handle the high rate background and
it must operate and survive in a high radiation environment. Simulation studies
estimated that, in the hottest regions, each crystal will absorb a dose of 300
Gy and will be exposed to a neutron fluency of 6 x 10^{11} n/cm^2 in 3 years of
running.
  Test of un-doped CsI crystals irradiated up to 900 Gy and to a neutron
fluency up to 9 x 10^{11} n/cm^2 have been performed at CALLIOPE and FNG ENEA
facilities in Italy. We present our study on the variation of light yield (LY)
and longitudinal response uniformity (LRU) of these crystals after irradiation.
The ionization dose does not modify LRU while a 20% reduction in LY is observed
at 900 Gy. Similarly, the neutron flux causes an acceptable LY deterioration
(<15%). A neutron irradiation test on different types of SIPMs (two different
array models from Hamamatsu and one from FBK) have also been carried out by
measuring the variation of the leakage current and the charge response to an
ultraviolet led. We concluded that, in the experiment, we will need to cool
down the SIPMs to 0 C reduce the leakage current to an acceptable level.
