Theoretical and computational study of the energy dependence of the muon transfer rate from hydrogen to higher-Z gases

•Method for measuring the energy dependence of muon transfer rate to higher-Z gases.•Thermalization and depolarization of muonic hydrogen studied by Monte Carlo method.•Optimal experimental conditions determined by Monte Carlo simulations.•Mathematical model and for estimating the uncertainty of the experimental results.

The recent PSI Lamb shift experiment and the controversy about proton size revived the interest in measuring the hyperfine splitting in muonic hydrogen as an alternative possibility for comparing ordinary and muonic hydrogen spectroscopy data on proton electromagnetic structure. This measurement critically depends on the energy dependence of the muon transfer rate to heavier gases in the epithermal range. The available data provide only qualitative information, and the theoretical predictions have not been verified. We propose a new method by measurements of the transfer rate in thermalized target at different temperatures, estimate its accuracy and investigate the optimal experimental conditions.