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Exact Analytic Relation Between Quantum Defects And Scattering Phases With Applications To Green’S Functions In Quantum Defect Theory, V. E. Chernov, N. L. Manakov, Anthony F. Starace

Anthony F. Starace Publications

The relation between the quantum defects, μ_λ, and scattering phases, δ_λ, in the single-channel Quantum Defect Theory (QDT) is discussed with an emphasis on their analyticity properties for both integer and noninteger values of the orbital angular momentum parameter λ. To derive an accurate relation between μ_λ and δ_λ for asymptotically-Coulomb potentials, the QDT is formally developed for the Whittaker equation in its general form “perturbed” by an additional short-range potential. The derived relations demonstrate that μ_λ is a complex function for above-threshold energies, which is analogous to the fact that δ …