Description and performances of a transition radiation detector for a Gran Sasso underground experiment

A transition radiation detector module, 6 x 2 x 2 m(3) in size, has been developed, tested and then installed on the MACRO detector at the Gran Sasso National Laboratory. The modular structure consisting of proportional tubes interleaved with polyethylene foam radiators allows to cover a large area. This detector measures the residual energies, up to 1 TeV, of penetrating muons. We discuss the possibility to obtain more physical information from these muons by measuring their residual energy and the performances of the first module. Calibration results of prototypes operated in a test beam at the CERN P.S. are also given