Two approaches for self consistency in the calculation of screening electron densities

We have calculated the electronic density around an ion in metallic hydrogen using the density functional formalism of Hohenberg, Kohn and Sham. We have a set of self-consistent equations to be solved within this formalism. We have numerically solved these equations using two different approaches. In the first one we have approximate self consistency. This approach had been used previously to calculate the interionic potential and superconducting properties of metallic hydrogen. In the second approach we have full self-consistency by following the method of Manninen et al. The results for the density show small differences from one approach to the other and for the effective potentials the differences are even smaller. From the densities we have recalculated the interionic potential for both approaches. The resulting interionic potentials are practically identical. (author)