Microscopic Calculation of the Optical Model Potential from One Boson Exchange Poten­tials

A new method for calculating the optical model potential from One Boson Exchange Potentials (OBEPs) is developed. The G-matrix is calculated by solving the Bethe-Goldstone equation in momentum space. Using vector brackets these G-matrix elements can be transformed from the center of mass representation into the laboratory system. This allows the evaluation of the (r-matrix interaction between nucleons in bound states and those in a plane-wave state. The lowest order contribution to the real part of the potential comes from the Hartree-Fock term, while the lowest order contribution to the imaginary part comes from the two-particle-one-hole (2p1h) diagram. Calculations for 16O and 40Ca have been carried out. Local approximations are obtained by describing the results for the central part in terms of a Woods-Saxon potential and those for the spin-orbit part in terms of the corresponding derivatives. The dependence of these potentials on energy and angular momentum is discussed. The parameters for these local approximations are in good agreement with empirical fits.