Exchange and correlation effects in the strongly interacting He-Ps system

The density functional theory has been used to calculate the total energy of the system comprising a He and a positronium atom. The single particle orbitals have been used to calculate the non-interacting kinetic energy, while the electron and positron densities were used for the Hartree energy, the electron exchange-correlation energy and the external potential energies. The electron exchange-correlation energy has been calculated within the Local Density Approximation and the General Gradient Approximation (PBE). For the electron-positron correlation energy the formula by Boronski and Nieminen has been used. The results have been compared to many-body wavefunction calculations employing the exact diagonalization of an explicitly correlated gaussians basis. While the many-body value result predicts that HePs is not bound, the density functional approach predicts a bound state with mean nucleus-positron distance of ~9 a.u. To discuss the origin of this discrepancy the exchange-correlation energy has been deduced from the many-body result and it has been compared to the density functional scheme.