Analytic exchange integral for coupled cluster theory in the homogeneous electron gas Original Research Article

A six-dimensional integral occurring in the description of the ground state of the homogeneous electron gas was calculated analytically. This formula, together with the one of a previous work [G.G. Hoffman, Phys. Rev. B 45 (1992) 8730], reduces from seven to one the dimension of the numerical integrations to be performed in the image approximation for the correlation energy [R.F. Bishop, K.H. Lührmann, Phys. Rev. B 26 (1982) 5523].