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 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 (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.
Highlights
The second 0+ state at 7.654 MeV in 12C that was first predicted by Hoyle [1] plays a central role in nuclear physics
The predicted as a member of the 1− bending rotation-vibration spectrum of a triangular shape oblate spinning top 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 rms radius of the Hoyle state of 3.22(8) fm
In this paper we deduce the rms radius of the Hoyle state from the moment of inertia of the rotational band built on top of the Hoyle state and we conclude that the rms radius of the Hoyle state is considerably (35%) larger than the ground state
Summary
The second 0+ state at 7.654 MeV in 12C that was first predicted (in 1953) by Hoyle [1] plays a central role in nuclear physics. The predicted as a member of the 1− bending 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 (large) rms radius of the Hoyle state of 3.22(8) fm. In the U(7) model and the FMD model the Hoyle state is predicted to be an oblate triangular three alpha-particle configuration.
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