Isoscalar monopole and quadrupole strength of 16O in an alpha +12C cluster and symplectic mixed basis.

Abstract

The isoscalar monopole (E0) and quadrupole (E2) transition strength of $^{16}\mathrm{O}$ is used to study how well the \ensuremath{\alpha}${+}^{12}$C cluster model works for explaining the strength distributions observed up to the isoscalar giant resonance region. The cluster model reproduces 54% of the E0 and 65% of the E2 energy weighted sum-rule strength. A symplectic basis, which naturally reproduces the sum rule, is mixed with the cluster basis to see how much of the missing strength is accounted for. A mixed basis calculation shows that the symplectic basis does not ruin the successful agreement of the cluster model with experiment obtained in the low-energy region and increases the strength by 30% for E0 and 20% for E2 below ${E}_{x}$\ensuremath{\le}40 MeV. It is predicted that both of the E0 and E2 strengths are split into two peaks in the giant resonance region with a greater spread over the excitation energy than expected.