Orthopositronium scattering off H and He

Exploiting an approach similar to the R-matrix theory, the diffusion Monte Carlo method is employed to compute phase shifts and threshold cross sections for the elastic scattering of positronium off light atoms. We briefly review the main ideas behind the use of quantum Monte Carlo techniques in scattering problems and, as applications, we present results for Ps-H and Ps-He. We find scattering lengths of 4.375(34) and 2.228(50) a.u. for the singlet and the triplet states of Ps-H, and of 1.4046(6) a.u. for Ps-He. A discussion of the agreement with other recent estimates for the same quantities is included. In particular, the scattering length for the Ps-H singlet agrees within 1% with the stochastic variational minimization (SVM) estimate by Ivanov, Varga, and Mitroy [Phys. Rev. A 65, 32703 (2002)] and the R-matrix one by Blackwood, McAlinden, and Walter [Phys. Rev. A 65, 32517 (2002)]. The Ps-H triplet scattering length, which still shows good agreement (1%) with the SVM one, appears to be 10% larger than the R-matrix value. As far as Ps-He is concerned, the calculation has been performed in a fully many-body framework. Comparison of the diffusion Monte Carlo scattering length with other estimates allows us to qualitatively and quantitatively assess the degree of approximation involved in other approaches.