*Article* **Calculation of Low-Energy Positron-Atom Scattering with Square-Integrable Wavefunctions**

**Sarah Gregg \* and Gleb Gribakin**

> School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, UK; g.gribakin@qub.ac.uk **\*** Correspondence: sgregg07@qub.ac.uk

**Abstract:** The variational method is applied to the low-energy positron scattering and annihilation problem. The ultimate aim of the investigation is to find a computationally economical way of accounting for strong electron–positron correlations, including the effect of virtual positronium formation. The method is applied to the study of elastic *s*-wave positron scattering from a hydrogen atom. A generalized eigenvalue problem is set up and solved to obtain *s*-wave positron–hydrogen scattering phase shifts within 8 × 10−<sup>3</sup> rad of accepted values. This is achieved using a small number of terms in the variational wavefunction; in particular, only nine terms that depend on the electron– positron distance are included. The annihilation parameter *Z*eff is also calculated and is found to be in good agreemen<sup>t</sup> with benchmark calculations.

**Keywords:** theoretical atomic and molecular physics; positron; hydrogen; annihilation; phase shift; scattering
