Theory of muon spin relaxation of gaseous C(2)H(4)Mu

A theoretical study of the muon spin relaxation of the gaseous muonated ethyl radical C(2)H(4)Mu is expanded in this paper to include both longitudinal and transverse signals. This study is based upon an operator expansion of the spin-density operator for the radical with its time dependence described by the linearized quantum Boltzmann equation. Relaxation is due to collisions which reorient the radical’s rotational angular momentum while effects on the muon’s spin are due to 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 and the collisional lifetimes (cross sections) are used as fitting parameters to describe the transverse signals. A fit to the transverse data by itself and a global fit to both the transverse and longitudinal data are obtained with good accuracy.