Microscopic Theory of the Optical-Model Potential and the Hole-Particle Model in Nuclear Spectroscopy
Approximate expressions for the optical-model potential Uopt in terms of the nucleon-nucleon interaction are discussed. The identity of all the A+1 nucleons of the scattering problem is approximately taken into account in our final formulas. The imaginary part of Uopt is calculated for the case of 12C and the incident-nucleon energy of 20 MeV. The spherical-model random-phase-approximation (RPA) eigenvalues and eigenvectors are assumed for the complete set of intermediate nuclear states involved. The results are rather insensitive to the exchange-force mixture assumed for our zero-range nucleon-nucleon potential. The anti-symmetrization of our V-matrix elements is extremely important as it reduces our ImUopt by a factor of 2-3. For a reasonable set of our RPA intermediate eigenvalues and eigenvectors we obtain a semiquantitative agreement with the best phenomenological ImUopt available for our case. The most important contribution to ImUopt corresponds to the first excited T=0, 2+ state in 12C.