Effective three-body interactions in the f7/2 shell

The contributions of effective three-body forces to the interaction energy of three particles in the 0f72 shell are calculated using reaction matrix elements derived from the Hamada and Johnston potential. The results obtained by second-order perturbation theory are found to be much smaller than those obtained from phenomenological fits. An effective interaction is then derived for the 0f72 shell performing a shell-model calculation for three particles in the whole 0f-1p major shell and through the use of biorthogonal states; effective three-body contributions turn out to be large, as expected from the results of phenomenological fits