Calculation and Application of the Density Propagator for a Self-Bound Fermion System. I. Theory

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Abstract
The Martin-Schwinger-Puff theory for a many-fermion system is applied to a calculation of the appropriate density propagator. The real part of this function, the system's polarizability, is a measure for the lowest order change in energy due to a harmonic density ripple enforced on the infinite system. The imaginary part, the linear response function, yields the inelastic cross section for the scattering of a weak external agent. The linear response contains additional information on excited states and, in particular, on collective states, excited by an external field. The formalism necessitates the calculation of the self-energy of a particle and from it the optical model for nucleon scattering can be derived. The relation of the theory to perturbative and other nonperturbative approaches is discussed and a comparison is made with a calculation of the polarization energy of nuclear matter by Koltun and Wilets.