Comparison of the symplectic shell model and Hartree-Fock results for excited 0(+) states of 4He.

Abstract

We show that with a saturating interaction V=-${\mathit{V}}_{0}$exp(-${\mathrm{r}}^{2}$/${\mathrm{a}}^{2}$)+${\mathrm{t}}_{3}$\ensuremath{\delta}(${\mathrm{r}}_{1}$-${\mathrm{r}}_{2}$)\ensuremath{\delta}(${\mathrm{r}}_{1}$-${\mathrm{r}}_{3}$), whose parameters are chosen, for any given range a, to fit the ground state binding energy and radius of $^{4}\mathrm{He}$, the excitation energy of the breathing mode state decreases as the range a increases. The same interaction is used to calculate the energy of the deformed intrinsic ``four-particle excitation.'' It is found that the energy of this state is low for the smallest value of a. As we change a, the volume is not conserved. Our results are compared with those of a Toronto group who performed a symplectic shell model calculation with a B1 interaction. Their conclusion, that the energy of the breathing mode state is low, is valid only when the range a is large. We obtain energies for the ``four-particle excitation'' which are higher than theirs when we constrain the volume to be constant, but lower than theirs when we remove that condition. Singularities and instabilities in the variational approach are discussed.