Electron Energy Bands in Sodium

The potential energy of a valence electron in sodium is represented by the function $V\left(r\right)=-\frac{2}{r}+\frac{A{e}^{-\beta r}}{r}$. The second term, which is repulsive in character, represents the effect of the core electrons. Values for $A$ and $\beta$ are determined from spectroscopic data. Energy levels of predominantly $s$ and $p$ symmetry are determined at four points of the Brillouin zone.