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In this work we define single-particle potentials for a positron and apositronium atom interacting with light atoms (H, He, Li and Be) by inverting asingle-particle Schr\"odinger equation. For this purpose, we use accurateenergies and positron densities obtained from the many-body wavefunction of thecorresponding positronic systems. The introduced potentials describe the exactcorrelations for the calculated systems including the formation of apositronium atom. We show that the scattering lengths and the low-energy s-wavephase shifts from accurate many-body calculations are well accounted for by theintroduced potential. We also calculate self-consistent two-componentdensity-functional theory positron potentials and densities for the boundpositronic systems within the local density approximation. They are in a verygood agreement with the many-body results, provided that thefinite-positron-density electron-positron correlation potential is used, andthey can also describe systems comprising a positronium atom. We argue that theintroduced single-particle positron potentials defined for single molecules aretransferable to the condensed phase when the inter-molecular interactions areweak. When this condition is fulfilled, the total positron potential can beconstructed in a good approximation as the superposition of the molecularpotentials.

Full correlation single-particle positron potentials for a positron and a positronium interacting with atoms