Theory of the density expansion of the dynamic structure factor: The pair contribution

We have derived, from a general quantum-mechanical statistical approach, the density expansion of the neutron-scattering dynamic structure factor both for coherent and incoherent scattering. The theory is based on the differentiation of appropriate functionals and leads to a series in which the first term is the perfect-gas contribution, the second the contribution of pairs, the third the contribution of triplets. The term due to pairs has been analyzed in detail, and quantum-mechanical rigorous expressions have been given that can be calculated once the pair-interaction potential is known and wave functions of the pairs are derived. Also the exact expressions of the first four moments of the pair contribution are given.