Theoretical description of the muon spin depolarization in the crystalline phase of 3He

We present a theoretical description of the behavior of a positive muon stopped in a solid helium target that allows the results of experiments for the crystalline phase of 3He to be explained. The forming linear (He2μ)+ molecular ion is shown to have time to be thermalized in the muon lifetime and to be in a state with the rotational quantum numbers K = 1 and K = 0 for ions with the total nuclear spins I = 1 and I = 0, respectively. The thermalization mechanism is attributable to the interaction between the electric quadrupole moment of the ion and the helium lattice. This interaction removes the three-fold angular momentum component degeneracy and there is no spin-rotation interaction. We derive the Hamiltonian of the spin-phonon interaction between the helium ion nuclei and the lattice. Depolarization is observed only for the ion with I = 1 and is attributable to the spin-exchange interaction between the lattice nuclei and the 3He nuclei bound with the muon with the emission of phonons in the lattice deformed by the strong Coulomb field of the positively charged ion