Resonances and exterior complex scaling

Abstract We have implemented the technique of exterior complex scaling via inward numerical integration of the complex-eigenvalue Schrodinger equation for resonances. The method has been tested successfully on three physically meaningful model potentials, the (12, 6) Lennard-Jones, the cubic anharmonic oscillator and the exponential, and on the vibrational resonances of He 2 2+ , 1 Σ g + , whose potential goes asymptotically as 1/ R . Widths as small as 10 −15 au have been computed.