https://doi.org/10.1007/s100530050044
Exact analytic relation between quantum defects and scattering phases with applications to Green's functions in quantum defect theory
1
Department of Physics, Voronezh State University, 394693 Voronezh, Russia
2
Department of Physics and Astronomy, The University of Nebraska, Lincoln, Nebraska 68588-0111, USA
Received:
25
June
1999
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
