Low-Energy Scattering Properties of Ground-State and Excited-State Positronium Collisions

Low-energy elastic and inelastic scattering in the Ps(1s)-Ps(2s) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet (TT), singlet-singlet (SS), and singlet-triplet (ST) spin symmetries in the spin representation of coupled electrons ($S_-$) and coupled positrons ($S_+$), with total angular momentum $L=0$ and charge conjugation and parity both equal to $+1$. Multichannel scattering calculations were performed to obtain preliminary estimates of the $s$-wave scattering length in the asymptotic Ps(1$s$)-Ps(2$s$) channel for each spin configuration. Spin re-coupling is implemented to obtain scattering lengths and cross-sections for collisions of Ps atoms in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross-sections are carried-out for collisions with total spin, $S_{\mathrm{tot}}=0$, $1$, and $2$.