Improvement of the basis for the solution of the Dirac equation in Cassini coordinates


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Abstract

We propose an improvement of the basis for the solution of the stationary two-centre Dirac equation in Cassini coordinates using the finite-basis-set method presented in our earlier article [J. Phys. B 43, 235207 (2010)]. For the calculations in the above article, we constructed the basis for approximating the energy eigenfunctions by using smooth piecewise defined polynomials, called B-splines. In the present article, we report that an analysis of the employed representation of the Dirac matrices shows that the above approximation is not efficient using B-splines only. Therefore, we include basis functions which are defined using functions with step-like behavior instead of B-splines. Thereby, we achieve a significant increase of accuracy of results.

About the authors

W. Hahn

Skolkovo Institute of Science and Technology; Institut für Theoretische Physik

Author for correspondence.
Email: w.hahn@skoltech.ru
Russian Federation, Moscow, 143026; Heidelberg, 69120

A. N. Artemyev

Institut für Physik

Email: w.hahn@skoltech.ru
Germany, Kassel, 34132

A. Surzhykov

Physikalisch-Technische Bundesanstalt; Technische Universität Braunschweig

Email: w.hahn@skoltech.ru
Germany, Braunschweig, D-38116; Braunschweig, D-38106

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