arXiv subjects

K. Fakhreddine

Publications and source records attributed to K. Fakhreddine.

4 recordsLinked to original sources

arXiv2007

The Canonical Function Method and its applications in Quantum Physics

The Canonical Function Method (CFM) is a powerful method that solves the radial Schrödinger equation for the eigenvalues directly without having to evaluate the eigenfunctions. It is applied to various quantum mechanical problems in Atomic and Molecular physics with presence of regular or singular potentials. It has also been developed to handle single and multiple channel scattering problems where the phaseshift is required for the evaluation of the scattering cross-section. Its controllable accuracy makes it a valuable tool for the evaluation of vibrational levels of cold molecules, a sensitive test of Bohr correspondance principle and a powerful method to tackle local and non-local spin dependent problems.

quant-ph↗

arXiv2002

Low energy (e,2e) ionization of Argon in the equal energy sharing geometry

Quantum Defect theory is a well established theoretical concept in modern spectroscopy. We show that this approach is useful in electron impact ionization problems where state of the art theoretical methods are presently restricted mostly to simple atomic targets. For the well documented Argon ionization case in equal energy sharing geometry the approach suggested leads to significant improvements compared to previous calculations.

quant-ph↗

arXiv2002

Distorted Waves with Exact Non-Local Exchange: a Canonical Function Approach

It is shown how the Canonical Function approach can be used to obtain accurate solutions for the distorted wave problem taking account of direct static and polarisation potentials and exact non-local exchange. Calculations are made for electrons in the field of atomic hydrogen and the phaseshifts are compared with those obtained using a modified form of the DWPO code of McDowell and collaborators: for small wavenumbers our approach avoids numerical instabilities otherwise present. Comparison is also made with phaseshifts calculated using local equivalent-exchange potentials and it is found that these are inaccurate at small wavenumbers. Extension of our method to the case of atoms having other than s-type outer shells is dicussed.

quant-ph↗

arXiv2001

Parametric Potential Determination by the Canonical Function Method

The canonical function method (CFM) is a powerful means for solving the Radial Schrodinger 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 Schrodinger 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.

quant-ph↗