An Analytical Model for the Time Distribution of Muonic Oxygen X-Rays in Muonic Experiments

We propose an analytical model and perform numerical simulations to study the time distribution of the characteristic muonic oxygen X-ray emission following muon transfer from muonic hydrogen to oxygen in a H2 + O2 gas mixture. The model accounts for all fundamental processes that alter the kinetic energy and spin distribution of muonic hydrogen atoms. The impact of the uncertainties in various experimental parameters on the precision of the computed results is studied in detail by means of the Monte Carlo method. Specifically, we observe the presence of a minimum in the time dependence of the relative standard deviation of X-ray emission for realistic parameter combinations, which can serve as a benchmark for comparing experiments and numerical simulations. Verification against available experimental data reveals the potential of this approach for both description and parameter optimization in the planning and analysis of muonic experiments