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arXiv · 1610.05263

Improvement of the Basis for the Solution of the Dirac Equation in Cassini Coordinates

Walter Hahn·Anton N. Artemyev·Andrey Surzhykov
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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 Ref. [1]. For the calculations in Ref. [1], 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 behaviour instead of B-splines. Thereby, we achieve a significant increase of accuracy of results as compared to Ref. [1].

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Walter Hahn, Anton N. Artemyev, Andrey Surzhykov. 2016-10-17. Improvement of the Basis for the Solution of the Dirac Equation in Cassini Coordinates. https://doi.org/10.1134/s0030400x17080094

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