  The aim of the FAMU experiment is to realize the first measurement of the
hyperfine splitting (hfs) in the 1S state of muonic hydrogen $\Delta
E^{hfs}_{1S}$, by using the RIKEN-RAL intense pulsed muon beam and a
high-energy mid-infrared tunable laser. This requires a detailed study of the
muon transfer mechanism at different temperatures and hence at different
epithermal states of the muonic system. The experimental setup involves a
cryogenic pressurized gas target and a detection system based on silicon
photomultipliers-fiber beam hodoscopes and high purity Germanium detectors and
Cerium doped Lanthanium Bromide crystals, for X-rays detection at energies
around 100 keV. Simulation, construction and detector performances of the FAMU
apparatus at RAL are reported in this paper.
