Relativistic variational calculations with finite nuclear size: Application to hydrogenic atoms in strong magnetic fields.

Abstract

A finite-basis-set method is introduced for calculations involving an electron in the presence of a finite-size nucleus. It is found that the inclusion of powers of the form ${\mathit{r}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}+\mathit{n}}$ in the basis set, where \ensuremath{\gamma} is a real number and n an integer, is of fundamental importance, increasing the convergence in the energy eigenvalues by several orders of magnitude in the case of a large nuclear charge. This conclusion applies also to one-electron potential calculations such as Dirac-Hartree-Fock. The method is applied to calculations of the low-lying levels of hydrogenic atoms in strong magnetic fields. For B\ensuremath{\lesssim}${10}^{9}$${\mathit{Z}}^{2}$ G, the finite-nuclear-size correction is of the same order as that for B=0. For B\ensuremath{\gtrsim}${10}^{9}$${\mathit{Z}}^{2}$ G, the correction increases linearly with B for the ground state, and assumes a more complicated dependence for the excited states due to the presence of more than one peak in each radial wave function for B=0.