High precision proton angular distribution measurements of $^{12}$C(p,p') for determination of the $E0$ decay branching ratio of the Hoyle state

Abstract

Background In stellar environments, carbon is produced exclusively via the 3α process, where three α particles fuse to form 12 C 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 12 C(p, p ) reaction and measuring the pair decay of both the Hoyle state and the first 2 + state of 12 C.Purpose 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 (0 + 2 ) and 2 + 1 state in 12 C in 12 C(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 12 C were measured in 12 C(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 (60 µg/cm 2 ) nat C target.Results Total cross-sections for each state were extracted and the population ratio between the 2 + 1 and Hoyle state determined at each energy step. By appropriately averaging these cross-sections and taking their ratio, the equivalent population ratio can be extracted applicable for any thick 12 C 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 12 C(p, p ) cross-sections that make uncertainties resulting from the population of the 2 + 1 and 0 + 2 states by proton inelastic scattering negligible for any future measurements of the E0 branching ratio in 12 C. Implications for future measurements are discussed, as well as possible applications of this data set for investigating cluster structures in 13 N.