A new calculation technique of muonium formation rate

E.L.Kosarev, and E.P.Krasnoperov

P.L.Kapitza Institute for Physical Problems, Moscow 117334, Russia
and
RRC Kurchatov Institute, Moscow 123182, Russia

Report to the International Conference "Modern Trends in Computational Physics", Dubna, Russia, June 1998

Abstract:

Usually the formation of a muonium from a positive muon and an election is described 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 muonium formation rate $d(\log n(t))/dt=-k$ is constant and 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 the function n(t) to be reconstructed from the $\mu SR$ 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.