Nonrelativistic variationally optimized exchange potentials for Ne-like atomic ions having large atomic number

In an earlier study, the exchange energy density ${\epsilon }_x\mathrm{}\left(r\right)\mathrm{}$ has been calculated analytically for Ne-like atomic ions in the nonrelativistic limit of large atomic number Z. Here, though now by numerical methods based on the optimized exchange potential approximation, corresponding results are obtained for $V_x\mathrm{}\left(r\right)\mathrm{}$ for such ten-electron ions at large Z. The approach to the bare Coulomb limiting form of the $1/Z$ expansion is considered in some detail, as are corrections to the Slater potential $V_x^{\mathrm{Sl}}\mathrm{}\left(r\right),$ given in terms of the exchange energy density and ground-state density $\rho \mathrm{}\left(r\right)\mathrm{}$ by $2{\epsilon }_x\mathrm{}\left(r\right)/\rho \mathrm{}\left(r\right).$