Anisotropic muonium atoms: Energy levels and electron spin exchange - art.no. 042505

The time evolution of the muon spin in fully anisotropic muonium (Mu=mu(+)e(-)) in the presence of Heisenberg spin exchange has been investigated the oretically. First, the energy levels of anisotropic Mu as a function of fie ld are investigated analytically with a particular emphasis on the crossing and avoidance of energy levels at certain magnetic fields, which have impo rtant consequences in muon spin dynamics. Second, the knowledge of the ener gy levels is applied to investigate the muon spin depolarization due to ele ctron spin exchange with spin-1/2 paramagnetic species, where the muon spin depolarization rate and the precession amplitude observed by the muon-spin -rotation (mu SR) technique are explicitly expressed solely in terms of the matrix that diagonalizes the anisotropic Mu hyperfine Hamiltonian. The tre atment presented here represents a special systematic and practical method that allows one to investigate the time evolution of the muon spin in aniso tropic Mu in the presence of electron spin exchange. Several concrete examp les are discussed in detail, including those in which all the mu SR observa bles can be obtained analytically. The method developed in this work is use d to explain the relaxation rate maximum in anisotropic Mu in semiconductor s observed at the longitudinal fields at which two of the Mu energy levels avoid each other due to a strong level mixing or avoidance, where the prese nt formalism takes the tensor nature of the anisotropic hyperfine interacti on fully into account without invoking the convenient but not necessarily c orrect notion of an effective magnetic field in an anisotropic Mu. Also dis cussed is the possibility of observing additional relaxation maximum at a l ow-avoidance field, where the effective magnetic-field approximation comple tely breaks down. Observation of such a maximum will provide valuable infor mation on the parameters characterizing the anisotropic Mu in question. The formalism presented here can also be applied to anisotropic positronium on surfaces, anisotropic Mu undergoing both charge exchange and spin exchange , and fast spin exchange.