Numerical study of the “two components” model and background effects in muonic hydrogen experiments

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Abstract In this study, we explore the X-ray time spectra of muonic oxygen in various H 2 + O 2 gaseous mixtures by means of numerical simulations based on a sophisticated kineticrate equations model. Our primary focus is on the “two components” hypothesis, which was put forward to account for the experimentally observed two successive exponential behaviors in the radiation time-distribution. To ensure an accurate representation of the physical processes in the experiments, we incorporate precise transition rate coefficients for the elastic and inelastic scattering between the muonic hydrogen atoms and other gas constituents, in our simulation code. Specifically, a crucial aspect in our approach is the utilization of the energy dependence of the muon transfer rate to oxygen, recently extracted from experimental data by the FAMU collaboration. The accurate knowledge of such muonic oxygen X-ray time spectra is vital for cutting-edge experiments like FAMU, where the hyperfine splitting in muonic hydrogen atoms is to be determined with high accuracy, as this time spectra serves as a significant part of the background for the desired signal.

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