An analytic and parameter-free wavefunction for studying the stability of three-body systems

An analytic wavefunction is proposed 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 the 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(-). Simple polynomial fits are provided for certain important subcases, allowing for a rapid estimate of the ground state energy and of the stability of three-body systems.