The X-rays detecting system of the FAMU experiment for the measurement of the muon transfer rate to carbon

The FAMU experiment is based on spectroscopy experiment. It uses exotic atoms to measure the proton Zemach radius, a convolution of the electronic and magnetic charge distribution. Specifically, there exists a direct correlation between the Zemach radius of the proton and the hyperfine splitting (HFS) in the muonic hydrogen energy ground level (µp). It is therefore a complementary way to study the proton compared to electron scattering experiments. The FAMU experimental technique takes advantage of the fact that, for given hydrogen gas mixtures, muons pass from the µp to the heavier gas atoms at a rate that is dependent on the µp energy. This results in X-rays counting rate from the heavier muonic atoms deexcitation cascade that depends on the energy of the µp. A fast detection system and excellent energy resolution in the 20-400 keV range are needed for this high precision experiment. The LaBr3(Ce) detectors are read by PMTs in this phase of the experiment. The behavior of the muon transfer rate from hydrogen to carbon has been evaluated using a detailed analysis of the performances of the detectors, which are presented below.