arXiv subjects

H. Ouerdane

Publications and source records attributed to H. Ouerdane.

40 records · Page 3Linked to original sources

arXiv2006

Scattering states of coupled valence-band holes in point defect potential derived from variable phase theory

In this article we present a method to compute the scattering states of holes in spherical bands in the strong spin-orbit coupling regime. More precisely, we calculate scattering phase shifts and amplitudes of holes induced by defects in a semiconductor crystal. We follow a previous work done on this topic by Ralph [H. I. Ralph, Philips Res. Rept. 32 160 (1977)] to account for the p-wave nature and the coupling of valence band states. We extend Ralph's analysis to incorporate finite-range potentials in the scattering problem. We find that the variable phase method provides a very convenient framework for our purposes and show in detail how scattering amplitudes and phase shifts are obtained. The Green's matrix of the Schroedinger equation, the Lippmann-Schwinger equation and the Born approximation are also discussed. Examples are provided to illustrate our calculations with Yukawa type potentials.

cond-mat.mtrl-sci↗

arXiv2005

The variable phase method used to calculate and correct scattering lengths

It is shown that the scattering length can be obtained by solving a Riccati equation derived from variable phase theory. Two methods of solving it are presented. The equation is used to predict how long-range interactions influence the scattering length, and upper and lower bounds on the scattering length are determined. The predictions are compared with others and it is shown how they may be obtained from secular perturbation theory.

physics.atom-ph↗

arXiv2005

A note on the calculation of the effective range

The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining the effective range, by fitting a numerical solution of the Schrödinger equation to known asymptotic boundary conditions, can be modified to include the first order contribution of a long range interaction.

physics.atom-ph↗

arXiv2005

Scattering parameters for cold-Li-Rb and Na-Rb collisions derived from variable phase theory

We show how the scattering phase shift, the s-wave scattering length and the p-wave scattering volume can be obtained from Riccati equations derived in variable phase theory. We find general expressions that provide upper and lower bounds for the scattering length and the scattering volume. We show how, in the framework of the variable phase method, Levinson's theorem yields the number of bound states supported by a potential. We report new results from a study of the heteronuclear alkali dimers NaRb and LiRb. We consider $ab$ $initio$ molecular potentials for the X${}^1Σ^+$ and $a{}^3Σ^+$ states of both dimers and compare and discuss results obtained from experimentally based X${}^1Σ^+$ and $a{}^3Σ^+$ potentials of NaRb. We explore the mass dependence of the scattering data by considering all isotopomers and we calculate the numbers of bound states supported by the molecular potentials for each isotopomer.

physics.atom-ph↗