The structure of the Hoyle state and its 2⁺ partner state in ¹²C

Laboratory for Nuclear Science at Avery Point University of Connecticut, 1084 Shennecossett Rd, Groton, CT 06340-6097, USA

Abstract

We have measured the ¹²C(γ, 3α) reaction with an Optical Time Projection Chamber (O-TPC) detector operating with the CO₂(80%) + N₂(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 ¹²C at 10.03(11) MeV. The observed spectrum of ¹²C below 12 MeV including the 2₂⁺ 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 2₃⁺ state which is predicted by the U(7) model as a member of the 1^- bending mode band, but the existence of this 2₃⁺ 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 ¹²C(p, p′) data.