Above threshold accumulated phase in molecular potentials

Abstract

A complex accumulated phase above the threshold is defined in the quantum defect theory framework. It is the analytic continuation of the familiar accumulated phase defined below the threshold. Our phase is related to the usual parameters of the quantum defect theory (QDT). Moreover it is shown that the main part of this phase is deduced from the reflection coefficient of a wave function propagating along the external part of the potential, from the inner part to the asymptotic part, even in absence of a centrifugal barrier. Examples concern essentially the potential scattering in s partial wave and the ultracold collisions of alkali-metal atoms. It is shown how resonances or virtual states can be calculated like the bound states as poles of the cotangent of this phase. A physical interpretation of this quantity is given in a simple multichannel case.

Keywords:

• Quantum defect
• Feshbach resonance
• Van der Waals potential
• Siegart state