Analysis of realistic and empirical multipole interactions for shell-model calculations

We perform analysis of realistic nucleon-nucleon interactions, as well as of empirically-corrected interactions, fitted to reproduce in detail the spectroscopic data in p and sd shells. We focus on the multipole part of the interactions, contrary to previous studies of that type which focused on monopole parts. We analyze how the different parts of the NN force (tensor, spin-orbit and central) contribute to the leading multipoles of the interaction and how do they renormalize in medium. We show that the leading coherent terms of the realistic and effective interactions are dominated by the central component as expected from their schematic operator structure. Convergence and cutoff dependence of multipole Hamiltonians is also discussed.