Four-particle—four-hole states inHe4

Deformed states in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, in which four nucleons are placed in the $1p$ shell, are considered. An interaction consisting of a Gaussian attraction and zero range density dependent repulsion is employed. The parameters are chosen so that the ground state energy of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is -28 MeV, and the oscillator length parameter $b$ is 1.4 fm. The method of variation after projection is employed, using the techniques of Evans and Elliot, to obtain the energies of $J=0^{+},2^{+},\mathrm{and} 4^{+}$ states. The results are studied as a function of the range of the Gaussian interaction. Connection is made with the more extensively studied problem of four-particle—four-hole states in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$.