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. 
C.Barbieri (TRIUMF, Vancouver), W.H.Dickhoff (Wash. Univ., St.Louis)