We demonstrate for the first time that the phase shift in elastic positronium-atom scattering can be precisely determined by the confined variational method, in spite of the fact that the Hamiltonian includes an unphysical confining potential acting on the center of mass of the positron and one of the atomic electrons. As an example, we study the S-wave elastic scattering for the positronium-hydrogen scattering system, where the existing ∼ 4% discrepancy between the Kohn variational calculation and the R-matrix calculation is resolved.
The parameters for S-wave elastic scattering of near-zero-energy electrons and positrons by H 2 molecules are calculated using the stabilization method with explicitly correlated Gaussians. The confined variational method is applied to optimize the Gaussians to describe the short-range interaction of incident e ± with H 2 in the fixed-nuclei approximation. For e +-H 2 scattering the scattering length of previous work [Phys. Rev. Lett. 103, 223202 (2009)] is substantially improved. More importantly, for e −-H 2 scattering, from first principles, the scattering length is computed as a function of the internuclear distance. In the case that the two nuclei are at the equilibrium distance the results are in a good agreement with values derived from fitting experimental total and diffusion cross sections to the modified effective range theory.
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