Calculation of density matrices in the formation of positronium

We study single collisions between spin-polarized positron beams and targets that result in the production of positronium and target ions. We consider unpolarized as well as polarized targets with 0, 1, and 2 unpaired electrons. First, we use angular momentum coupling to calculate the spin scattering matrices in all three cases. Then, for some targets, we define an angle beta between the polarization vectors of the positron beam and the target, and calculate density matrices whose elements are functions of beta. Finally, from the density matrices, we obtain the probabilities of forming para- and ortho-positronium atoms for specific spins of the target ions. We present ratios of para- to ortho-positronium yields as well as total positronium annihilation rates.