  In the present work, an improved numerical solution for determining the
ratio,$\mathcal{R}^{\rm Mott}$, of the unscreened Mott differential cross
section (MDCS) with respect to Rutherford's formula is proposed for the
scattering of electrons and positrons on nuclei with $1\leq Z \leq 118$. It
accounts for incoming lepton energies between 1\,keV and 900\,MeV. For both
electrons and positrons, a fitting formula and a set of fitting coefficients
for the ratio $\mathcal{R}^{\rm Mott}$ on nuclei are also presented. The found
average error of the latter practical interpolated expression is typically
lower than 1% also at low energy for electrons and lower than 0.05% for
positrons for all nuclei over the entire energy range.
