A consistent generalization of the random phase approximation (RPA) for odd nuclei is suggested. The derivation is based on the Green function method using the equation for the three-particle Green function. The model developed combines properties of both the standard RPA, and the particle-vibration coupling model. This gives a possibility to describe both the single-particle and collective parts of the excitation spectrum including giant resonances in the continuum and splitting of discrete collective states [particle (hole) $\otimes$ phonon multiplets] on a common basis. In the framework of this model, where the single-particle continuum is taken into account exactly, the $E1\mathrm{}$ photoabsorption cross section and the isoscalar $E1\mathrm{}$ resonance in ${}^{17}\mathrm{O}$ are calculated. The comparative RPA calculations of the same $E1\mathrm{}$ modes in ${}^{16}\mathrm{O}$ nucleus are presented. The results obtained are compared with experiment for the $E1\mathrm{}$ resonance in ${}^{16}\mathrm{O}$ and ${}^{17}\mathrm{O}.$ For the isoscalar $E1\mathrm{}$ strength in ${}^{17}\mathrm{O}$ we obtained an additional and noticeable low-lying contribution below 12.5 MeV caused by the odd neutron only.

• Received 22 September 2000

DOI:https://doi.org/10.1103/PhysRevC.63.034304