  We consider a quasi one-dimensional quantum dot composed of two Coulombically
interacting electrons confined in a Gaussian trap. Apart from bound states, the
system exhibits resonances that are related to the autoionization process.
Employing the complex-coordinate rotation method, we determine the resonance
widths and energies and discuss their dependence on the longitudinal
confinement potential and the lateral radius of the quantum dot. The stability
properties of the system are discussed.
