Abstract.The results of a previous Breit-Pauli R-matrix calculation are further analyzed by investigating the effects of various approximations to account for relativistic effects and by studying the convergence of the close-coupling expansion. At very low collision energies (below 2 eV), the complicated resonance structure causes significant differences between the results obtained from one-state, three-state and seven-state expansions. In addition, the competition between Mott scattering and the "fine-structure effect" in the elastic channel makes the results for the spin asymmetry function SA extremely sensitive to the details of the theoretical approximation.PACS: 34.80.Dp between the projectile and the target electrons) and to the convergence of the close-coupling expansion. Since the effects are most pronounced for the case of elastic scattering, we will restrict the present discussion to this channel.In Sect. 2, we will briefly summarize the main differences between the present Breit-Pauli R-matrix calculation and our earlier work (Bartschat and Scott [2]) on electron scattering from thallium atoms. This is followed by numerical results for elastic scattering at a few selected energies. These results are compared with recent experimental data of the Mfinster group [5,6] as well as those from a fullrelativistic calculation based on the "generalized density Ihnctional" (GDF) theory [7,8]. Finally, some conclusions are drawn in Sect. 4.