Pair-hypernetted-chain closure for three-body potentials: Results for argon with the Axilrod-Teller triple-dipole potential

The hypernetted-chain closure is modified to include three-body potentials. The latter is reduced to a state-dependent effective pair potential. Explicit expressions for the Helmholtz free energy and for the chemical potential are derived for the modified closure. The approximation is shown to be relatively self-consistent and in qualitative agreement with perturbation results. An argonlike fluid is discussed using the Lennard-Jones pair potential and the Axilrod-Teller triple-dipole potential. In agreement with earlier work, it is found that the effective three-body contribution is positive, increasing the pressure and the internal energy by about 10% in the liquid state.