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We have measured the 12C(?, 3?) 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 HI?S 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 2+2 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. The predicted rotation-vibration spectrum of a triangular shape oblate spinning top (with a D3h 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 model radius parameter of the Hoyle state of 3.22(8) fm ( time the r.m.s. radius of the ground state) which is close to the radius extracted from 12C(x,x') data.

The structure of the Hoyle state via a measurement of the 'Hoyle Rotational Band' in12C

The structure of the Hoyle state via a measurement of the 'Hoyle Rotational Band' in¹²C