Extension of the random phase approximation including the self-consistent coupling to two-phonon contributions

A microscopic formalism is developed that includes the coupling to two particle-hole phonons in the particle-hole propagator by extending the dressed random phase approximation (DRPA) equation for a finite system. The resulting formalism is applied to study the low-lying excitation spectrum of ¹⁶O. It is observed that the coupling to two-phonon states at low energy generates excited states with quantum numbers that cannot be obtained in the DRPA approach. Nevertheless, the two-phonon states mix weakly with particle-hole configurations and participate only partially in the formation of the lowest-lying positive-parity excited states. The stability of the present calculation is tested vs the truncation of model space. It is demonstrated that when single-particle strength fragmentation is properly considered, the present formalism exhibits convergence with respect to the chosen model space within the confines of the chosen approximation scheme.