Faddeev treatment of long-range correlations and the one-hole spectral function of ${}^{16}\mathrm{O}$

The Faddeev technique is employed to study the influence of both particle-particle and particle-hole phonons on the one-hole spectral function of ${}^{16}\mathrm{O}.$ Collective excitations are accounted for at a random phase approximation level and subsequently summed to all orders by the Faddeev equations to obtain the nucleon self-energy. An iterative procedure is applied to investigate the effects of the self-consistent inclusion of the fragmentation in the determination of the phonons and the corresponding self-energy. The present results indicate that the characteristics of hole fragmentation are related to the low-lying states of ${}^{16}\mathrm{O}.$