# Radial Hartree and exchange-correlation potentials

According to [1] the one-dimensional Kohn-Sham equation is given by $$\left( -\frac{1}{2} \frac{d^2}{dr^2} + \frac{l(l+1)}{2r^2} + V[\rho;r]\right) rR_{nl}(r) = \varepsilon_{nl} rR_{nl}(r)$$ where $$V[\rho;r] = -\frac{Z}{r} + V_\textrm{H}[\rho;r]+V^\textrm{LDA}_\textrm{xc}(\rho(r))$$ How are the radial Hartree potential $$V_\textrm{H}[\rho;r]$$ and radial exchange-correlation potential $$V^\textrm{LDA}_\textrm{xc}(\rho(r))$$ computed?

[1] Troullier and Martins. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B vol. 43, no. 3, pp. 1993-2006 (1991).