The oscillator representation and the stability of three-body Coulomb systems

Within nonrelativistic quantum mechanics the Wick-ordering method, called the oscillator representation, is suggested for calculating the energy spectrum for a wide class of potentials allowing the existence of a bound state. As test cases, anharmonic (V(r) = r2σ) and screened Coulomb potentials are considered. In particular, the method is applied to three-body Coulomb systems to obtain the dependence of the bound-state energy on the masses and charges of the particles. The calculations of the bound-state energies for the molecules H- = (pee), H+2 = (ppe), (e-e-e+) and (ppμ), (ddμ), (dtμ) prove the accuracy of the zeroth approximation to be better than one per cent. For the three-body Coulomb system with charges +, -, - and arbitrary masses the region of stability is determined. For the systems (pe-C+), (A+e-e+), and (pB-e- ) the critical masses are calculated to be MC = 1.945me, MA = 4.350me and MB=1.575me. It turns out that the system (pe-e+) is unstable. (authors)