  Octupole vibrations are studied in some doubly magic nuclei using the
time-dependent Hartree-Fock (TDHF) theory with a Skyrme energy density
functional. Through the use of the linear response theory, the energies and
transition amplitudes of the low-lying vibrational modes for each of the nuclei
were determined. Energies were found to be close to experimental results.
However, transition amplitudes, quantified by the deformation parameter
$\beta_3$, are underestimated by TDHF. A comparison with single-particle
excitations on the Hartree-Fock ground-state shows that the collective octupole
vibrations have their energy lowered due to attractive RPA residual
interaction.
