Hyperspherical close-coupling study of hyperfine transitions in low-energy p+pμ and e^±+Ps scattering

We apply the hyperspherical close-coupling method to the elastic and spin-flip processes in p+pμ and e^-+Ps (or equivalently, e⁺+Ps) scattering at low collision energies. The spin-spin interactions V_S are included explicitly in the Hamiltonian, producing the correct hyperfine-splitting energy Δε in the separated-atom limit. A comparison is made with a simpler method in which the effect of V_S is represented only by the symmetry of the wave functions with respect to the interchange of the two identical particles. Explicit inclusion of V_S is found to be of vital importance for the calculation of the spin-flip cross sections for collision energies lower than Δε for both p+pμ and e^-(e⁺)+Ps collisions. The elastic cross sections are less sensitive to V_S, but those for p+pμ are still affected by V_S for collision energies lower than Δε.