General form of the quantum-defect theory for−1/rαtype of potentials withα>2

Bo Gao
2008 Physical Review A. Atomic, Molecular, and Optical Physics  
We present a general formulation of the quantum-defect theory for systems with an attractive 1 / r ␣ type of asymptotic potentials with ␣ Ͼ 2. Its structural differences from the standard theory for ␣ Յ 2, or from the semiclassical theory, is fully explained through a systematic understanding of quantum reflection above the threshold, and quantum connection formulas below the threshold.
doi:10.1103/physreva.78.012702 fatcat:6uabjog3avg77n6vqaenc6ohkm