High-precision proton angular distribution measurements of C 12 (p,p′) for the determination of the E0 decay branching ratio of the Hoyle state

Background: In stellar environments, carbon is produced exclusively via the 3α process, where three α particles fuse to form C12 in the excited Hoyle state, which can then decay to the ground state. The rate of carbon production in stars depends on the radiative width of the Hoyle state. While not directly measurable, the radiative width can be deduced by combining three separately measured quantities, one of which is the E0 decay branching ratio. The E0 branching ratio can be measured by exciting the Hoyle state in the C12(p,p′) reaction and measuring the pair decay of both the Hoyle state and the first 2+ state of C12.Purpose: We aim to reduce the uncertainties in the carbon production rate in the universe by measuring a set of proton angular distributions for the population of the Hoyle state (02+) and 21+ state in C12 in C12(p,p′) reactions between 10.20 and 10.70 MeV, used in the determination of the E0 branching ratio of the Hoyle state. Method: Proton angular distributions populating the ground, first 2+, and the Hoyle states in C12 were measured in C12(p,p′) reactions with a silicon detector array covering 22°<θ<158° in 14 small energy steps between 10.20 and 10.70 MeV with a thin (60μg/cm2) natC target. Results: Total cross sections for each state were extracted and the population ratio between the 21+ and Hoyle state determined at each energy step. By appropriately averaging these cross sections and taking xtheir ratio, the equivalent population ratio can be extracted applicable for any thick C12 target that may be used in pair-conversion measurements. This equivalent ratio agreed with a direct measurement performed with a thick target. Conclusions: We present a general data set of high-precision C12(p,p′) cross sections that make uncertainties resulting from the population of the 21+ and 02+ states by proton inelastic scattering negligible for any future measurements of the E0 branching ratio in C12. Implications for future measurements are discussed, as well as possible applications of this data set for investigating cluster structures in N13.