SPIN DYNAMICS OF THE POSITIVE MUON RADICALS IN THE PRESENCE OF RAPID ELECTRON-SPIN EXCHANGE - FREQUENCY-SHIFT AND RELAXATION

The spin dynamics of the positive muon in a muonium-like radical has been investigated in the case where the unpaired electron of the radical undergoes rapid spin flip collisions. If the spin flip rate lambda-SF is much faster than the hyperfine frequency of the radical, the behaviour of the muon spin is very similar to that of a positive muon in diamagnetic environments. It has been shown that in a transverse field, the relaxation rate and precession frequency of the apparent diamagnetic muon are related to the time evolution function of the muon spin in muonium G(T)(t) by R(D) = -lambda-SF<Re ln G(T)(t)>SF and omega-D = -lambda-SF<Im ln G(T)(t)>SF, respectively, where <...>SF means the average over the statistical time distribution of spin flip events, and Re and Im represent the real and imaginary parts, respectively. The relaxation rate of such an apparent diamagnetic signal has a characteristic field dependence which is very sensitive to the hyperfine frequency of the radical. The fractional frequency shift with respect to the positive muon precession frequency (omega-D - omega-mu)/omega-mu is shown to be field-dependent, in contrast to the case of Knight shifts in metals. The field dependence of the relaxation and frequency shift will provide a tool to distinguish experimentally the muon in a radical which behaves like a free positive muon from a genuine diamagnetic muon. This work can be applied to a variety of fields involving muonium and hydrogen, such as spin dynamic in the gas phase and the muonium-like (hydrogen-like) states in semiconductors. The case where the muon undergoes both spin flip and charge transfer collisions is also discussed.