The U(7) structure of [sup 12]C and the Hoyle 2+ state

Abstract

We measured the 12C(γ,3α) reaction with an Optical Time Projection Chamber (O-TPC) detector operating at 100 torr with the CO2(80%)+N2(20%) gas mixture and gamma-ray beams from the HIγS facility of the TUNL at Duke. The measured complete angular distributions (between 9.1 - 10.7 MeV) determine the cross section yield curve and phase shifts leading to an unambiguous identification of the second 2+ state in 12C at 9.94 MeV. Hence the long sought for "Hoyle 2+ state" is unambiguously established. The observed spectrum of 12C below 12 MeV including the 2+2 (and a hint of a third 2+) observed in this work is analyzed in the theoretical framework of the rotationvibration spectrum predicted for a triangular shape oblate spinning top with a D3h symmetry, in which the Hoyle state is the first vibrational breathing mode of the triangular three alpha particle system. We also observed a hint of the 2+3 state which is predicted by this U(7) model as a member of the 1− bending mode band, but the existence of this 2+3 is yet to be confirmed.