Статья «Improvement of the Basis for the Solution of the Dirac Equation in Cassini Coordinates, "Оптика и спектроскопия"»

We propose an improvement of the basis for the solution of the stationary two-centre Dirac equation in Cas-sini 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 ei-genfunctions 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.