Relativistic finite-basis-set calculations for finite nuclear size potentials-application to hydrogenic atoms in strong magnetic fields

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 r-γ+n in the basis set is of fundamental importance, increasing the convergence in the energy eigenvalues by several orders of magnitude in the case of large nuclear charge. This conclusion applies also to one-electron potential calculations like Dirac-Hartree-Fock. The method is applied to calculations of the low-lying levels of hydrogenic atoms in strong magnetic fields. For B≤109Z2G, the finite-nuclear-size correction is of the same order as that for B=0. For B > 109Z2G, 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 the wave functions for B=0