Green's Function Approach to Inclusive Electron Scattering

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A Green's function approach to the inclusive quasielastic (e,e') scattering is presented. The components of the nuclear response are written in terms of the single-particle optical model Green's function. The explicit calculation of the Green's function can be avoided by its spectral representation, which is based on a biorthogonal expansion in terms of the eigenfunctions of the non-Hermitian optical potential and of its Hermitian conjugate. This allows one to treat final state interactions consistently in the inclusive (e,e') and in the exclusive (e,e'N) reactions. Numerical results for the longitudinal and transverse response functions obtained in a nonrelativistic and in a relativistic framework are presented and discussed also in comparison with data.