The delta excitation on the shell-model effective nucleon-nucleon interactions

We have calculated the Delta particle-nucleon hole core polarization diagram G(pp Delta h) to investigate the effect of the Delta three-nucleon force on the shell-model effective interactions. A realistic NN <-> N Delta transition G-matrix G(N Delta) is derived using a Delta-subtracted Paris potential and the coupled-channel approach of Lee and Matsuyama. The core-polarization diagrams G(pp Delta h), second order in G(N Delta), are found to be very small for the sd-shell valence nucleons. Satisfactory convergence is reached by including Delta excitations up to 20 oscillator shells for the summation of the Delta intermediate states in G(pp Delta h).