A twodimensional pseudospectral HartreeFock method for lowZ atoms in intense magnetic fields
Abstract
The energy levels of the first few lowlying states of helium and lithium atoms in intense magnetic fields up to $\approx 10^810^9$~T are calculated in this study. A pseudospectral method is employed for the computational procedure. The methodology involves computing the eigenvalues and eigenvectors of the generalized twodimensional HartreeFock partial differential equations for these two and threeelectron systems in a selfconsistent manner. The method exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. It is seen that the results obtained here for a few of the most tightly bound states of each of the atoms, helium and lithium, are in good agreement with findings elsewhere. In this regard, we report new data for two new states of lithium that have not been studied thus far in the literature. It is also seen that the pseudospectral method employed here is considerably more economical, from a computational point of view, than previously employed methods such as a finiteelement based approach. The key enabling advantage of the method described here is the short computational times which are on the order of seconds for obtaining accurate results for heliumlike systems.
 Publication:

arXiv eprints
 Pub Date:
 March 2012
 DOI:
 10.48550/arXiv.1203.3437
 arXiv:
 arXiv:1203.3437
 Bibcode:
 2012arXiv1203.3437T
 Keywords:

 Quantum Physics;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 24 pages, 8 figures, 7 tables