Quantum calculation of the muon depolarization function: effect of spin dynamics in nuclear dipole systems

The authors have derived formal expressions for the positive muon depolarization functions using an iterative procedure both for the longitudinal and transverse experimental geometries. They are valid at least in the motional narrowing limit and at small time. They have used formal expressions to study the depolarization functions for a muon diffusing in a lattice of nuclear dipoles neglecting the possibility of the muon returning to its original localization site. This work indicates that the effect of the spin dynamics on the depolarization functions is important at low fields for both geometries. In the case of the longitudinal geometry it is shown that a second-order iteration formula and the strong collision model with the numerically exact static function give the same result when the muon jumping rate is large enough. This has two important consequences: (i) when the muon jumping rate is sufficiently large it is possible to calculate the whole depolarization function with a modest numerical effort using the iterative formula; and (ii) the fact that the two methods give the same result in the fast diffusing limit shows that the strong collision model with the exact static function contains all the dynamics; the spin-lattice relaxation (T₁ process) is included.