  The main goal of the FAMU experiment is the measurement of the hyperfine
splitting (hfs) in the 1S state of muonic hydrogen $\Delta E_{hfs}(\mu^-p)1S$.
The physical process behind this experiment is the following: $\mu p$ are
formed in a mixture of hydrogen and a higher-Z gas. When absorbing a photon at
resonance-energy $\Delta E_{hfs}\approx0.182$~eV, in subsequent collisions with
the surrounding $H_2$ molecules, the $\mu p$ is quickly de-excited and
accelerated by $\sim2/3$ of the excitation energy. The observable is the time
distribution of the K-lines X-rays emitted from the $\mu Z$ formed by muon
transfer $(\mu p) +Z \rightarrow (\mu Z)^*+p$, a reaction whose rate depends on
the $\mu p$ kinetic energy. The maximal response, to the tuned laser
wavelength, of the time distribution of X-ray from K-lines of the $(\mu Z)^*$
cascade indicate the resonance. During the preparatory phase of the FAMU
experiment, several measurements have been performed both to validate the
methodology and to prepare the best configuration of target and detectors for
the spectroscopic measurement. We present here the crucial study of the energy
dependence of the transfer rate from muonic hydrogen to oxygen ($\Lambda_{\mu p
\rightarrow \mu O}$), precisely measured for the first time.
