The dissociation of an orbiting resonance : calculation of eigen-energies and widths of the quasi-bound states of ⁴HeH⁺

Abstract

Born-Oppenheimer eigenergies (E_nJ ) of the ro-vibrational (n, J) quasibound levels of ⁴HeH⁺ in the X¹Σ⁺ electronic state are calculated using an improved outer boundary condition and their values are compared with those of three other methods, namely, the uniform JWKB quadratic approximation, the application of an outer boundary condition pertaining to the irregular Bessel function and the maximization of the time-delay function. The widths (Γ _nJ ) of these states obtained by semiclassical and quantum techniques are also compared. The boundary condition may be applied to other diatomic ionic orbiting complexes (i.e. H₂ ⁺) which dissociate via the decay of quasibound states to an ion and a neutral atom. For the broader resonances, the differences between various estimates of a particular E_nJ can exceed the diagonal nuclear-motion correction.