The electron cloud (of the outermost electrons) of an ensemble of atoms of atomic number Z is described by a continuous charge density ρ(r) that adjusts itself so that the electrons at the Fermi level have zero energy. If V(r) is the local electrostatic potential, then ρ(r) is
1
\(\frac{e}{3 \pi^2 \hbar^3}\left[2 m_e e V(\mathbf{r})\right]^{3 / 2}\)
2
\(\frac{Z e}{3 \pi^2 \hbar^3}\left[2 m_e e V(\mathbf{r})\right]^{3 / 2}\)
3
\(\frac{e}{3 \pi^2 \hbar^3}\left[Z m_e e V(\mathbf{r})\right]^{3 / 2}\)
4
\(\frac{e}{3 \pi^2 \hbar^3}\left[m_e e V(\mathbf{r})\right]^{3 / 2}\)