Electrical conductivity of metallic hydrogen in the nearly-free-electron model

Abstract

The electrical resistivity of metallic hydrogen has been calculated. To do this, the perturbation theory in terms of electron-proton interaction for the reciprocal relaxation time characterizing the electrical conductivity has been employed. The second-and third-order terms as well as an approximate expression for the series sum have been calculated in detail. In doing so, the random-phase approximation with allowance for exchange interaction and correlations in the local-field approximation has been used for an electron subsystem and the exact solution of the Percus-Yevick equation for the hard-sphere model has been employed for the proton subsystem. In this case, at given density and temperature, the only parameter of the theory is the hard-sphere diameter. To determine this parameter, the effective pairwise interproton interaction has been calculated. The hard-sphere diameter has been determined from the dependence of the interproton interaction on the distance and the known temperature of the system. The dependence of the resistivity of metallic hydrogen on the density and temperature has been examined in a wide range of the latter quantities. In the entire range of densities and temperatures considered, the resistivity proves to be close to its limiting value for which the nearly-free-electron model is applicable.