An analytic model for description of muonic oxygen X-ray time distribution 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 $H_2+O_2$ 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 Monte Carlo method. Verification against available experimental data reveals the potential of this approach for both description and parameter optimization in planning and analysis of muonic experiments.