To make Eq. 37 highly accurate for the UEG, we begin with the σx term of Eq. 37 whose role is to reduce w MRF λ=1 (r) to w λ=0 (r) when the correlation terms are omitted. We computed this object for the UEG in Section 4, and its value is given in Eq. 35 and it does not depend on r s . The N L term is given by Eq. 38, and the L term remains the only one to be built for