We calculate the S-3(e) and S-1(e) scattering lengths in low-energy e(-) Rb(Ss), Cs(Gs), and Fr(7s) collisions. Our approach is based on the relativ
istic version of the modified effective range theory (MERT) and extrapolate
s eigenphases provided by Dirac R-matrix calculations to zero energy. To te
st the accuracy of our MERT extrapolation method, we compare the fine-struc
ture components for the lowest P-3(o) resonance of Fr- ion with full Dirac
R-matrix calculations.