Structure of thallium and lead calculated from Shaw local pseudopotential and molecular dynamics

Recently, we (Es Sbihi Phil. Mag 2010) have successfully calculated, by molecular dynamics, the static structure factor of liquid bismuth at different temperatures. Our results were in very good agreement with the Waseda experimental data. Our assumption was to consider the true density of states which presents a gap as measured by Indlekofer (J. Non-Cryst. Solids 1989) and calculated by Hafner-Jank (Phys. Rev. B 1990) for liquid bismuth. The number of electrons at the Fermi energy has been calculated with three conduction electrons for bismuth (number of p electrons). With this assumption, the structures were determined with an effective ion-ion potential constructed from the Shaw local Optimised Model Potential (OMP) and the Ichimaru-Utsumi dielectric function. In the present paper, we generalize our assumptions to liquid thallium and lead which also present such a gap. Their calculated structures are also very close to the experimental ones. This confirms that the number of conduction electrons on the Fermi sphere is consistent with the number of p electrons as has been even shown for our electronic transport properties of liquid lead (A. Ben Abdellah, Phys. Rev. B 2003)