Ultracold homonuclear and heteronuclear collisions in metastable helium

Scattering and ionizing cross sections and rates are calculated for ultracold collisions between metastable helium atoms using a fully quantum-mechanical close-coupled formalism. Homonuclear collisions of the bosonic ${}^4$He$^{} +{}^{4}$He$^{}$andfermionic${}^{3}$He$^{} + {}^{3}$He$^{}$ systems, and heteronuclear collisions of the mixed ${}^3$He${}^{\ast }+{}^4$He${}^{\ast }$ system, are investigated over a temperature range 1 $\mu$K to 1 K. Carefully constructed Born-Oppenheimer molecular potentials are used to describe the electrostatic interaction between the colliding atoms, and complex optical potentials used to represent loss through ionization from the ${}^{1,3}\mathrm{\Sigma }$ states. Magnetic spin-dipole mediated transitions from the ${}^5\mathrm{\Sigma }$ state are included and results reported for spin-polarized and unpolarized systems. Comparisons are made with experimental results, previous semi-classical models, and a perturbed single channel model.