Reorientation-effect measurement of the first 2 + state in 12 C: Confirmation of oblate deformation
A Coulomb-excitation reorientation-effect measurement using the TIGRESS γ-ray spectrometer at the TRIUMF/ISAC II facility has permitted the determination of the $\langle$2$^+_1$ || $\hat{E2}$ || $2^+_1$$\rangle$ diagonal matrix element in 12 C from particle-γ coincidence data and state-of-the-art no-core shell model calculations of the nuclear polarizability. The nuclear polarizability for the ground and first-excited (2$^+_1$) states in 12 C have been calculated using chiral NN N 4 LO500 and NN+3NF350 interactions, which show convergence and agreement with photo-absorption cross-section data. Predictions show a change in the nuclear polarizability with a substantial increase between the ground state and first excited 2$^+_1$ state at 4.439 MeV. The polarizability of the 2$^+_1$ state is introduced into the current and previous Coulomb-excitation reorientation-effect analyses of 12 C. Spectroscopic quadrupole moments of $Q_S$(2$^+_1$) =+0.053(44) eb and $Q_S$(2$^+_1$) =+0.08(3) are determined, respectively, yielding a weighted average of $Q_S$(2$^+_1$)=+0.071(25) eb, in agreement with recent ab initio calculations. The present measurement confirms that the 2$^+_1$ state of 12 C is oblate and emphasizes the important role played by the nuclear polarizability in Coulomb-excitation studies of light nuclei.