On a relation between the scattering cross-section in dense media and the energy of a dilute electron gas

In some scattering problems a certain role is played by an integral over the pair distribution function of the scattering system. On the other hand, the energy of a dilute electron gas may be expressed in terms of a slightly different integral over the pair distribution function. The close relation between these two integrals is pointed out and the question of the system configurations for which these integrals would attain their maximum value is discussed