A new calculation technique of muonium formation rate Original Research Article

In condensed matter the formation of a muonium atom from a positive muon and an election is described usually with a first order kinetic equation which assumes that the process is random and that the charge distribution is uniform. According to this model the muon polarization function as a function of time should reduce to an exponential law. Experiments in superfluid helium demonstrates that this is incorrect.Our proposed technique allows to reconstruct the muonium formation rate function from the μSR histogram in low transverse magnetic field without presupposing a particular theoretical form, i.e. with no parametrization. The technique is based on solving the integral equation of the first kind for the muon polarization function using the maximum likelihood method. The obtained results are of fundamental importance for the analysis of the charge kinetics in superfluid helium.