A natural time-dependent generalization is given for the well-known pair distribution function g(r) of systems of interacting particles. The pair distribution in space and time thus defined, denoted by G(r, t), gives rise to a very simple and entirely general expression for the angular and energy distribution of Born approximation scattering by the system. This expression is the natural extension of the familiar Zernike-Prins formula to scattering in which the energy transfers are not negligible compared to the energy of the scattered particle. It is therefore of particular interest for scattering of slow neutrons by general systems of interacting particles: G is then the proper function in terms of which to analyze the scattering data.After defining the G function and expressing the Born approximation scattering formula in terms of it, the paper studies its general properties and indicates its role for neutron scattering. The qualitative behavior of G for liquids and dense gases is then described and the long-range part exhibited by the function near the critical point is calculated. The explicit expression of G for crystals and for ideal quantum gases is brieRy derived and discussed.

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SynopsisThis paper investigates single particle properties in a Fermi gas with interaction at the absolute zero of temperature. In such a system a single particle energy has ordy a meaning for particles of momentum [k I close to the Fermi momentum kF. These single particle states are metastable with a life-time approaching infinity in the limit Jk I --~ kF. The limiting value of the energy is called the Fermi energy EF. As a special ease of a more general theorem, it is shown that for a system with zero pressure (i.e. a Fermi liquid at absolute zero) the Fermi energy Ey is equal to the average energyper particle Eo/N of the system. This result should apply both to liquid Hes and to nuclear matter.The theorem is used as a test on the internal consistency of the theory of Brueckner 1) for the structure of nuclear matter. It is seen that the large discrepancy between the values of EF and Eo/N, as calculated by Brueckner and Gammel 2), arises from the fact that Brueckner neglects important cluster terms contributing to the single particle energy. This neglection strongly affects the calculation of the optical potential.

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