Time-Dependent Hartree-Fock Theory Applied toNe20andMg24

The time-dependent Hartree-Fock method is applied to the even-even nuclei ${\mathrm{Ne}}^{20}$ and ${\mathrm{Mg}}^{24}$. The starting point of the calculation is a static Hartree-Fock solution, with the assumptions that in both the ground and the excited state, the deformed nuclei are axially symmetric, that the self-consistent wave functions have the usual shell-model radial dependence, and that the two-body interaction is the Rosenfeld mixture proposed by Elliott and Flowers. Application of the method yields intrinsic excited states corresponding to the rotational bands of the nuclei being considered. The calculated differences in energy between the lowest lying members of these bands agree quite well with experiment. The spurious solutions or states, corresponding to the invariance of the system under rotation about the axis of symmetry, occur with zero excitation energy, as predicted, when correlation effects in the ground state are included. The effect of these correlations on the energy spectra for the nonspurious solutions is shown to be negligible.