Calculation of thermalization rate of molecular ions Heμ+ and He2μ+ ion crystalline phase of helium

A behaviour of a diamagnetic component of a muon spin polarization in solid phase of 3He could be explained theoretically if μ+ forms a molecular ion with the 3He atom. Two molecular ions containing positive muon could be formed in helium: Heμ+ and He2μ+. The binding energy of the ion He2μ+ is higher than for the ion Heμ+. The behaviour of the muon spin polarization strongly differs in thermalized and nonthermalized states of the ions. Calculations of thermalization rates of two types of the ions are carried out. It is shown that rotational and vibrational relaxation times are of the same order and sufficiently short (less than 10-9s). The ion Heμ+ turns out to be in the ground state with v=0,K=0 after the thermalization process. The He2μ+ turns out to be in the ground state with v=0 and K=0 only if the total nuclear spin I=0 (para-ion). If the total nuclear spin I=1 (ortho-ion), the ground state of the molecular ion He2μ+ is characterized by nonzero quantum number K=1 and v=0. Hyperfine interactions are not equal to zero only for the ortho-ion He2μ+. The experimental observation of the muon spin depolarization shows that the molecular ion He2μ+ is formed in crystalline phase of 3He.