Theory of muon spin relaxation of Mu+CO

In previous papers [Phys. Rev. A 50, 4743 (1994); 54, 4815 (1996)] a theoretical description of the signals associated with the muon spin relaxation of simple muonated gaseous radicals has been presented. These gaseous radicals were assumed to have been formed during the slowing down process of the muons in the gaseous target and assumed to be stable chemical species at the initial observation time. The observed signals were attributed to these stable radicals. In this paper the theoretical description is extended to include situations where the radicals are formed in slow processes as opposed to fast processes with the assumption that the muon exists as muonium at the initial observation time. This muonium then reacts for the time duration of the experiment, which is limited by the muon’s lifetime. The theoretical treatment is based on an operator expansion of the spin density operators for muonium and for the molecular radicals whose time dependences are described by a set of coupled linearized quantum kinetic equations. Relaxation of the signals is due to two effects, namely, the chemical reactions themselves and the collisions that reorient the molecular radical’s rotational angular momentum. This affects the muon’s spin via intramolecular couplings between the muon’s spin, the radical’s free-electron spin, and the radical’s rotational angular momentum. The coefficients of the radical’s spin Hamiltonian, the collisional reorientation lifetimes (cross sections), and the chemical reaction rates may be used as fitting parameters to describe the experimental signals. These could also be calculated from first principles. [S1050-2947(98)00212-1].