A simple parameter-free wavefunction for the ground state of three-body systems

Abstract

We propose a simple wavefunction for the ground state of general atomic three-body systems in which two light particles are negatively charged and the third (heavy) is positively charged. By construction this wavefunction (i) has the same analytical form for all systems; (ii) is parameter-free; (iii) is nodeless; (iv) satisfies all two-particle cusp conditions; and (v) yields reasonable ground-state energies for several three-body systems, including the prediction of a bound state for H−, D−, T− and Mu−. For illustration, results are given for several three-body systems, and in particular for variants of helium-like ions. We provide analytical formulae, as well as simple polynomial fits for certain subcases, which allow one to have a rapid estimate of the ground-state energy and to study the stability for quite general cases.