  We present an approach to extend plasma transport theory into the Warm Dense
Matter (WDM) regime characterized by moderate Coulomb coupling and electron
degeneracy. It is based on a recently proposed closure of the BBGKY hierarchy
that expands in terms of the departure of correlations from their equilibrium
value, rather than in terms of the strength of correlations. This kinetic
equation contains modifications to the collision term in addition to a second
term that models the non-ideal contributions to the equation of state. An
explicit collision operator is derived in the semiclassical limit that is
similar to that of the Uehling-Uhlenbeck equation, but where scattering is
mediated by the potential of mean force (PMF). As a demonstration, we use this
collision integral to evaluate temperature and momentum relaxation rates in
dense plasmas. We obtain degeneracy- and coupling-dependent 'Coulomb integrals'
that take the place of $\ln\Lambda$ in the scattering rates. We additionally
find a novel difference in the way in which degeneracy influences momentum
relaxation in comparison to temperature relaxation. Finally, we evaluate
electron-ion relaxation rates for the case of warm dense deuterium over a range
of density and temperature spanning the classical to quantum and weak to strong
coupling transitions. Results are compared with the Landau-Spitzer rate and
rates obtained from the quantum Landau-Fokker-Planck equation and Lee-More
model. We find that the models diverge significantly in the degenerate and
moderately coupled regime and attribute this difference to how the various
models treat the physics of Pauli blocking, correlations, large-angle
scattering, and diffraction.
