A new method for constructing periodic orbits of the time-dependent Hartree-Fock equations is proposed. It is based on a perturbative expansion in the amplitude of the collective vibration. We present applications to the case of octupole vibrations in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. From calculations performed up to second order we determine the splitting of the two-phonon states. We discuss the problems which, for the quadrupole mode, arise from a resonant coupling of the vibration with states of the continuum.

• Received 6 January 1992

DOI:https://doi.org/10.1103/PhysRevC.45.2205