Analytical Properties and Nonperturbative Calculation of the Optical Potential for Nuclear Matter

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Abstract
Within the framework of Green's functions techniques, a definition is discussed of the optical potential in terms of the self-energy of a particle. A theoretical expression for this potential is given based on a version of the independent pair approximation for nuclear matter. Identical dispersion relations are shown to be valid for both the exact and the approximated self-energy. A discussion is presented regarding the relation between the independent pair approximation and the impulse approximation. The region of validity for the latter has been estimated. Quantities related to the self-energy, spectral function, and optical potential for a particle above the Fermi sea have been calculated for a given nuclear force. Tolerable agreement with experiment is obtained for the real part of the optical potential. Reasons why only the trend of the imaginary part is reproduced can be partly understood. An effective mass approximation is shown to be valid for a wide range of particle and hole energies. In conclusion, a discussion of related approaches is presented.