Note: Angle averaged mean-field potential (Angle averaged), mean-field potential along the symmetry axis \(z~(\theta=0^{\circ})\), and that perpendicular to the symmetry axis with \(r_{\perp}=\sqrt{x^{2}+y^{2}}~(\theta=90^{\circ})\) are presented. Here the angle averaged potential is equivalent to the spherical component of the Legendre expansion, i.e., \([V(r)+S(r)]_{\lambda=0}=\frac{1}{4\pi}\int[V(\boldsymbol{r})+S(\boldsymbol{r})]\mathrm{d}\Omega\).

Note: Angle averaged density distribution (Angle averaged), density distribution along the symmetry axis \(z~(\theta=0^{\circ})\), and that perpendicular to the symmetry axis with \(r_{\perp}=\sqrt{x^{2}+y^{2}}~(\theta=90^{\circ})\) are presented. Here the angle averaged density is equivalent to the spherical component of the Legendre expansion, i.e., \(\rho_{0}(r)=\frac{1}{4\pi}\int\rho(\boldsymbol{r})\mathrm{d}\Omega\).