Multiple scattering formalism for the effective interaction

A general formalism is proposed for evaluating the effective interaction between valence nucleons, taking into consideration the low-lying contributions of two-particle two-hole (2p2h), two-particle one-hole (2p1h), three-particle one-hole (3p1h), three-particle two-hole (3p2h), and four-particle two-hole (4p2h) correlations. The formalism consists of solving a hierarchy of multiple scattering type equations with coupling between various correlations and is naturally combined with the Q-box approach for folded diagram theory. The energy dependence of the reaction matrix is included in the formalism. The effect of 4p2h correlations is studied for a simple two-level model for mass 42 by solving the hierarchy of coupled equations numerically by neglecting the coupling to 2p1h and 3p1h configurations. The 4p2h correlation with 4p coupled to isospin 0 has dominant contributions as expected. For a reasonable choice of the energy denominator, the 4p2h contribution to the two-body effective interaction is sizably attractive