In this work, we define single-particle potentials for a positron and a positronium atom interacting with light atoms (H, He, Li, and Be) by inverting a single-particle Schrödinger equation. For this purpose, we use accurate energies and positron densities obtained from the many-body wave function of the corresponding positronic systems. The introduced potentials describe the exact correlations for the calculated systems including the formation of a positronium atom. We show that the scattering lengths and the low-energy s-wave phase shifts from accurate many-body calculations are well accounted for by the introduced potential. We also calculate self-consistent two-component density-functional-theory positron potentials and densities for the bound positronic systems within the local-density approximation. They are in a very good agreement with the many-body results, provided that the finite-positron-density electron-positron correlation potential is used, and they can also describe systems comprising a positronium atom. We argue that the introduced single-particle positron potentials defined for single molecules are transferable to the condensed phase when the intermolecular interactions are weak. When this condition is fulfilled, the total positron potential can be constructed in a good approximation as the superposition of the molecular potentials.
- effective potential
- stochastic variational method