Reorientation-effect measurement of the first 2+ state in 12C: Confirmation of oblate deformation

Abstract

A Coulomb-excitation reorientation-effect measurement using the TIGRESS γ−ray spectrometer at the TRI-UMF/ISAC II facility has permitted the determination of the 2 + 1 ||Ê2 || 2 + 1 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 Coulombexcitation 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) 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.

Symmetries and order in cluster nuclei

“…i.e. a positive value, as is to be expected for a oblate deformation, and is found to be in good agreement with a recent measurement [42].…”

“…B(EL) values and charge radii for 12 C (top) and16 O (bottom). Experimental data are taken from[39,40,41,42] and[43], respectively.…”

Cluster structures in C12 from global energy density functionals

“…Furthermore, the calculated E2 transition strength from the 2 + 1 state to the ground state, B(E2; 2 + 1 → 0 + 1 ) = 8.0 e 2 fm 4 , reproduces the experimental value. We also note that the theoretical spectroscopic quadrupole moment of the 2 + 1 state, Q spec (2 + 1 ) = 5.0 efm 2 , is predicted within the error bar of the very recent experiment: Q exp spec (2 + 1 ) = (7.1 ± 2.5) efm 2 [14]. It is therefore interesting to point out that, in this specific instance, our global EDF-based approach provides a level of agreement with data that is comparable to state-of-the-art ab initio models [14].…”

“…Probably one of the most prominent examples is the self-conjugate nucleus 12 C, in which axial oblate, triangular, linear 3α, and bent arm configurations are all predicted to coexist at low excitation energies [6][7][8][9][10][11][12][13]. New reorientation-effect measurements have very recently confirmed the pronounced oblate deformation in the ground-band 2 + 1 state of 12 C [14]. First experimental evidence of triangular D 3h symmetry in 12 C was reported by Marín-Lambárri et al, with K = 0 and K = 3 bands reportedly merging to form a single rotational band built on triaxial ground state [15].…”

Odd-mass nuclei in the cluster shell model

“…B(EL) values, quadrupole moment and charge radius for 12 C. Experimental data are taken from[26,27,28], and the ACM values from[21].…”