The structure of the Hoyle state and its 2⁺partner state in¹²C

Abstract

Abstract. We have measured the 12 C(γ, 3α) reaction with an Optical Time Projection Chamber (O-TPC) detector operating with the CO 2 (80%) + N 2 (20%) gas mixture and gamma-ray beams from the HIγS facility of the TUNL at Duke. We measured complete angular distributions (between 9.1 -10.7 MeV) from which we determine the cross section yield curve and E1 − E2 relative phases leading to an unambiguous identification of the second 2 + state in 12 C at 10.03(11) MeV. The observed spectrum of 12 C below 12 MeV including the 2 + 2 state observed in this work resembles the rotation-vibration spectrum predicted for a triangular shape oblate spinning top 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 the U(7) model as a member of the 1 − bending mode band, but the existence of this 2 + 3 is yet to be confirmed. The predicted rotation-vibration spectrum of a triangular shape oblate spinning top (with a D 3h symmetry) allows us to compare the moment of inertia of the predicted Hoyle rotational band to the ground state rotational band and in this way extract the (large) rms radius of the Hoyle state of 3.22(8) fm. We compare the deduced rms radius with recent ab-initio theories and cluster models as well as the radius extracted from 12 C(p, p ) data.