Exact analytic relation between quantum defects and scattering phases with applications to Green's functions in quantum defect theory
Department of Physics, Voronezh State University, 394693 Voronezh, Russia
2 Department of Physics and Astronomy, The University of Nebraska, Lincoln, Nebraska 68588-0111, USA
Published online: 15 March 2000
The relation between the quantum defects, , and scattering phases, , 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 and 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 is a complex function for above-threshold energies, which is analogous to the fact that is complex for below-threshold energies. The QDT Green's function, , of the "perturbed"Whittaker equation is parameterized by the functions and for the continuous and discrete spectrum domains respectively, and a number of representations for are presented for the general case of noninteger λ. Our derivations and analyses provide a more general justification of known results for nonrelativistic and relativistic cases involving Coulomb potentials and for a Coulomb plus point dipole potential.
PACS: 31.15.-p – Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations) / 33.80.Rv – Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000