Muon capture rates from precision measurements of the muon disappearance

In a typical experiment the nuclear \mu-capture rate is determined from measurements of the time constant of the muon decay exponential in a target. We propose a new approach for the evaluation of the \mu-capture rate, which is based on direct measurements of the \mu^- disappearance rate in the target. Considering, as an example, the reaction of \mu-capture on proton, we demonstrate that measurements of the \mu^- disappearance at different values of the hydrogen gas pressure in the target could be used to avoid a pressure-dependent correction and determine the "vacuum" \mu p -> \nu n reaction rate with accuracy better than 10^{-2} after extrapolation to zero gas density. The proposed method could be used to perform precision measurements of the \mu^- capture rate on different types of nuclei in one experiment.