Generalized quantum defects: Their variations with energy and radius

Abstract

A unified interpretation of single-channel quantum-defect behavior is presented, and illustrated with the example of a square well. As an application the quantum defects for the lowest three partial waves of potassium are calculated and discussed as continuous functions of the energy above, near, and far below the ionization threshold, with emphasis on their non-Rydberg spectral properties; results for other atoms are discussed. The quantum defect for the radial motion of a ${}_{}{}^1{}_{}{}^{}P_{}^{\circ }{}_{}{}^{}$ electron pair of ${\mathrm{H}}^{-}$ is also calculated, thereby combining Macek's hyperspherical-coordinate approach with quantum-defect theory.