New Measurement of ^{12}C+^{12}C Fusion Reaction at Astrophysical Energies

Extending the Hoyle-State Paradigm to ^{12}C+^{12}C Fusion

Carbon burning is a key step in the evolution of massive stars, Type 1a supernovae and superbursts in x-ray binary systems. Determining the ^{12}C+^{12}C fusion cross section at relevant energies by extrapolation of direct measurements is challenging due to resonances at and below the Coulomb barrier. A study of the ^{24}Mg(α,α^{'})^{24}Mg reaction has identified several 0^{+} states in ^{24}Mg, close to the ^{12}C+^{12}C threshold, which predominantly decay to ^{20}Ne(ground state)+α. These states were not observed in ^{20}Ne(α,α_{0})^{20}Ne resonance scattering suggesting that they may have a dominant ^{12}C+^{12}C cluster structure. Given the very low angular momentum associated with sub-barrier fusion, these states may play a decisive role in ^{12}C+^{12}C fusion in analogy to the Hoyle state in helium burning. We present estimates of updated ^{12}C+^{12}C fusion reaction rates.

The 12C+12C fusion reaction at stellar energies

The carbon fusion reaction is crucial in stellar evolution. Despite six decades of studies, there is still a large uncertainty in the reaction rate which limits our understanding of various stellar objects, such as massive stars, type Ia supernovae, and superbursts. In this paper, we review the experimental and theoretical studies of the carbon fusion reaction at sub-barrier energies. An outlook for future studies is also presented.

Carbon burning rates on the compound nucleus formation

The 12C+12C reaction rates based on the compound nucleus formation seem to be concordant with the standard rates. The resonant contribution in 12C+12C is also discussed. To put the rates on firm ground, the resonances below Ec.m. = 3 MeV will have to be studied further.

Direct measurements of the 12C(12C,p)23Na and 12C(12C,α)20Ne reactions at low energies for Nuclear Astrophysics

12C+12C reactions are crucial in the evolution of massive stars and explosive scenarios. The measurement of these reactions at astrophysical energies is very challenging due to their extremely small cross sections, and the presence of beam induced background originated by the natural 1,2H contaminants in the C targets. In addition, the many discrepancies between different data sets and the complicated resonant structure of the cross sections make the extrapolation to low energies very uncertain. Recently, we performed a direct measurement of the 12C+12C reactions at the CIRCE Laboratory in Italy. Results from a study on target contamination were used, allowing us to measure cross sections at Ec.m. =2.51 − 4.36 MeV with 10-25 keV energy steps. Two stage ΔE-Erest detectors were used for unambiguous particle identification. Branching ratios of individual particle groups were found to vary significantly with energy and angular distributions were also found to be anisotropic, which could be a potential explanation for the discrepancies observed among different data sets.

Direct Measurement of Carbon Fusion at Astrophysical Energies with Gamma-Particle Coincidences

We present 12C+12C direct fusion measurements with STELLA UKFATIMA, that reach into the region of astrophysics interest relevant to massive stars (M⊙ ≈ 25) using self-supporting thin rotating carbon foils [1]. We demonstrate that detecting gammas and light charged particles in coincidence with nanosecond timing is key for effective background reduction achieving reliable measurements in the sub-nanobarn range. We give details about core developments of the detection apparatus as well as the coincidence-analysis procedure of low count statistics. The present data largely follows the phenomenological hindrance interpolation and shows indication for resonant behaviour at the lowest energy explored.

Recent Achievements of the ERNA Collaboration

For more than two decades, the ERNA collaboration has investigated nuclear processes of astrophysical interest through the direct measurement of cross sections or the identification of the nucleosynthesis effects. Measurements of cross-section, reported in this publication, of radiative capture reactions have been mainly conducted using the ERNA Recoil Mass Separator, and more recently with an array of charged particle detector telescopes designed for nuclear astrophysics measurements. Some results achieved with ERNA will be reviewed, with a focus on the results most relevant for nucleosynthesis in AGB and advanced burning phases.

Newtonian dynamics of imaginary time-dependent mean field theory

A Time Dependent Hartree-Fock (TDHF) based classical model is applied to sub-barrier fusion reactions using the Feynman Path Integral Method (FPIM). The fusion cross-sections and modified astrophysical S*-factors are calculated for the 12C+12C reactions and compared to direct and indirect experimental results. Different channels cross-sections are estimated from the statistical decay of the compound nucleus. A good agreement with the direct data is found. We suggest a complementary observable given by the (imaginary) action A easily derived from theory and experiments. When properly normalized by the action in the Gamow limit it has an upper value of 1 at zero beam energies. It becomes negative at the Coulomb barrier which is Vcb=5.05±0.05MeV from direct data and Vcb=5.5MeV from model calculations.