Calculations of many-particle–many-hole deformed state energies: Near degeneracies, deformation condensates

In deformed Hartree-Fock calculations with Skyrme interactions we observe a near degeneracy of the mean energies of many-particle–many-hole deformed intrinsic states. For example, in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ the np-nh states with n=2, 3, 4, 5, 6, 7, and 8 are nearly degenerate. The deformation parameter β increases steadily from n=2 to 8. The intrinsic state energy of the 8p-8h state is lower than that of the 4p-4h state for the interactions used here—SK III, SK IV, and SK VI. The calculations are also performed with the Skyrme III interaction for the even-even calcium and titanium isotopes. For ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ there is a near degeneracy of 6p-2h and 8p-4h. For the N>Z isotopes above, the two protons excitation lies lowest. Whereas the intrinsic state energies are much higher than the observed energies of the lowest-lying deformed states, the results when projection of J${=0\mathrm{}}^{+}$ states is carried out and pairing effects are taken into account, are encouraging.