Hyperspherical harmonics expansion of the ground state of the Ps - ion

TLDR: In this article, the ground state of the positronium negative ion (Ps−) was treated by a hyperspherical harmonics expansion method in which the center of mass motion was properly accounted for.

Abstract: We have treated the ground state of the positronium negative ion (Ps−) by a hyperspherical harmonics expansion method in which the centre of mass motion is properly accounted for. The resulting system of coupled differential equations has been solved by the renormalized Numerov method. We find that the convergence in the Binding Energy (BE) with respect to inclusion of higher hyperspherical partial waves is quite slow for this diffuse system. Using our exact numerical results up to a maximum of 28 for the hyper angular momentum quantum number (KM) in an extrapolation formula basd on the hyperspherical convergence theorems, we get the binding energy of the ground state of Ps− as 0.261 668 9 au.