Parametric potential determination by the canonical function method

Abstract

The canonical function method (CFM) is a powerful means for solving the Radial Schrdinger Equation. The mathematical difficulty of the RSE lies in the fact it is a singular boundary value problem. The CFM turns it into a regular initial value problem and allows the full determination of the spectrum of the Schrdinger operator without calculating the eigenfunctions.Following the parametrisation suggested by Klapisch and Green, Sellin and Zachor we develop a CFM to optimise the potential parameters in order to reproduce the experimental Quantum Defect results for various Rydberg series of He, Ne and Ar as evaluated from Moore's data.

The Canonical Function Method and its applications in quantum physics

“…Several parametric potentials are discussed extensively in the literature and we already used several functional forms (1) adapted to different atomic systems. We have studied (59) the QD of some rare gases with the Klapisch parametric potential (28) and found that in some cases it was very difficult to optimize parameters that provide an accurate representation of the experimental QD. We believe, the Green-Sellin-Zachor ( 21) is better suited to our present study as the parameter space is small (two-dimensional) which allows for an efficient search of the optimized parameters.…”

Recursive determination of phase shifts for screened Coulomb potentials

“…Due to configuration mixing, the number of involved radial integrals can be very large, and analytical potentials can be an alternative to self-consistent field methods. Tannous et al [10] tried to determine potentials which incorporate the effect of exchange while keeping a local character. Parametric potentials are often used [11], and are the key ingredient of a number of atomic-structure codes, such as Hebrew University Lawrence Livermore Atomic Code [12][13][14][15], OPAL [16], super transition arrays [17][18][19] or flexible atomic code [20].…”

Low Energy (E, 2E) Ionization of Argon in the Equal Energy Sharing Geometry

“…Several parametric potentials are discussed extensively in the literature and we already used several functional forms [2] adapted to different atomic systems. We studied recently [8] the QD of some rare gases with the Klapisch parametric potential [13] and found that in some cases it was very difficult to optimize parameters that provide an accurate representation of the experimental QD. We believe, the Green-Sellin-Zachor [6] is better suited to our present study as the parameter space is small (two-dimensional) which allows for an efficient search of the optimized parameters.…”