Excited states ofHe4

The energies of highly deformed ‘‘four-particle–four-hole’’ states of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are calculated using Skyrme-like interactions. The J=0, 2, and 4 projected states are then considered. Deformed harmonic oscillator wave functions are used in which two oscillator lengths, $b_x$ and $b_0$, are allowed to vary. Both the energies and the stability of the states are studied as a function of the amount of fi- nite range energy in the interaction. Then a less restricted Hartree-Fock calculation is performed for the intrinsic state energies of both ‘‘four-particle–four-hole’’ states and ‘‘two-particle–two-hole’’ states. All the states considered come low enough in energy so as to be associated with the excited states of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in the 20 to 35 MeV range.