Positronium scattering from hydrogen and helium atoms at low energies

We investigate the elastic scattering of Ps-H and Ps-He below the Ps($n=2$) excitation threshold using the confined variational method with explicitly correlated Gaussians as basis functions. As an extension of the previous work (EPL, $\textbf{99}$ 43001 (2012)), we calculate phase shifts for the elastic Ps-H scattering for partial waves $1 \leq \ell \leq 3$. We expect that the Ps-H calculation is to determine the contribution of the mixed symmetry terms to phase shifts for partial waves $\ell > 2$ and to resolve the convergence problems that occur in the calculations of Woods et al. for $^{1,3}\!D$ with the S-matrix complex Kohn variational method (PRA $\textbf{92}$ 022713 (2015)). For the Ps-He scattering below the excitation threshold of Ps($n = 2$), we compute phase shifts, pick-off annihilation rates, and momentum-transfer cross sections for partial waves $\ell \leq 3$ to resolve the huge discrepancies between theory and experiment.