Reorientation-effect measurement of the first 2+ state in 12C: 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 $〈2_1^{+}\Vert \widehat{E2}\Vert 2_1^{+}〉$ diagonal matrix element in ¹²C 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 ¹²C have been calculated using chiral NN N⁴LO500 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 ¹²C. Spectroscopic quadrupole moments of $Q_S\left(2_1^{+}\right)=+0.053\left(44\right)$ eb and $Q_S\left(2_1^{+}\right)=+0.08\left(3\right)$ eb are determined, respectively, yielding a weighted average of $Q_S\left(2_1^{+}\right)=+0.071\left(25\right)$ eb, in agreement with recent ab initio calculations. The present measurement confirms that the 2${}_1^{+}$ state of ¹²C is oblate and emphasizes the important role played by the nuclear polarizability in Coulomb-excitation studies of light nuclei.