Nonadiabatically Coupled Hyperspherical Equations Applied to the Collisional Spin Flip of Muonic Hydrogen

Abstract

Nonadiabatically coupled equations in terms of hyperspherical coordinates are solved for the elastic and hyperfine transitions F→F′ of muonic hydrogen isotopes pμ, dμ, and tμ in collisions pμ(F)+p→p+μp(F′), dμ(F)+d→d+μd(F′), and tμ(F)+t→t+μt(F′), as an extension of our previous work on pμ [Igarashi et al., Phys. Rev. A 58 (1998), 1166]. Converged cross sections are obtained for collision energies 10⁻³ to 10² eV and for the total orbital angular momentum L=0 and 1 including the spin–spin interactions V _S explicitly in the Hamiltonian, and for L≥2 neglecting V _S because of the large interparticle separations. The inclusion of V _S for L=0 and 1 reproduces the correct hyperfine-splitting energy Δ∈ in the separated-atom limit, and is found to be of vital importance for the calculation of the spin-flip cross sections for collision energies lower than Δ∈.