Extremely large oblate deformation of the first excited state in ${}^{12}$C: a new challenge to modern nuclear theory

Abstract

A Coulomb-excitation study of the high-lying first excited state at 4.439 MeV in the nucleus ${}^{12}$C has been carried out using the ${}^{208}$Pb(${}^{12}$C,${}^{12}$C${}^{\ast }$)${}^{208}$Pb${}^{\ast }$ reaction at 56 MeV and the {\sc Q3D} magnetic spectrograph at the Maier-Leibnitz Laboratorium in Munich. High-statistics achieved with an average beam intensity of approximately 10${}^{11}$ ions/s together with state-of-the-art {\it ab initio} calculations of the nuclear dipole polarizability permitted the accurate determination of the spectroscopic quadrupole moment, $Q_{{}_S}(2_{{}_1}^{+})=+0.076(30)$~eb, in agreement with previous measurements. Combined with previous work, a weighted average of $Q_{{}_S}(2_{{}_1}^{+})=+0.090(14)$ eb is determined, which includes the re-analysis of a similar experiment by Vermeer and collaborators, $Q_{{}_S}(2_{{}_1}^{+})=+0.103(20)$~eb. Such a large oblate deformation challenges modern nuclear theory and emphasizes the need of $\hat{I}\pm$ clustering and associated triaxiality effects for full convergence of $E2$ collective properties.

(11 pages, 6 figures)