Reorientation-effect measurement of the first 2$^+$ state in $^{12}$C: confirmation of oblate deformation

TL;DR

This study measures the diagonal matrix element of the 2+ state in carbon-12 using Coulomb excitation, confirming its oblate shape and highlighting the importance of nuclear polarizability in such analyses.

Contribution

First determination of the 2+ state diagonal matrix element in carbon-12 via Coulomb excitation with advanced no-core shell model calculations of polarizability.

Findings

Confirmed oblate deformation of the 2+ state in carbon-12.

Determined spectroscopic quadrupole moments consistent with ab initio calculations.

Showed larger polarizability than previously expected, affecting Coulomb-excitation analysis.

Abstract

A Coulomb-excitation reorientation-effect measurement using the TIGRESS $\gamma-$ray spectrometer at the TRIUMF/ISAC II facility has permitted the first determination of the $\langle 2^+_1\mid\mid \hat{E2} \mid\mid 2^+_1\rangle$ diagonal matrix element in $^{12}$C from particle$-\gamma$ coincidence data. Required state-of-the-art no-core shell model calculations of the nuclear polarizability for the ground and first-excited (2$^+_1$) states in $^{12}$C using chiral NN N$^4$LO500 and NN+3NF350 interactions have been performed. Consistent predictions show a larger polarizability than previously anticipated. The polarizability of the 2$^+_1$ state is introduced into the current and previous Coulomb-excitation reorientation-effect analysis of $^{12}$C. Spectroscopic quadrupole moments of $Q_{_S}(2_1^+)= +0.053(44)$ eb and $Q_{_S}(2_1^+)= +0.08(3)$ eb 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.