Asymptotic normalization coefficients for α+C12 synthesis and the S factor for C12(α,γ)O16 radiative capture

Abstract

: The C12(α,γ)O16 reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. A specific feature of the O16 nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, 2+) and (7.12 MeV, 1−), that dominate the behavior of the low-energy S factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs), which need to be known with high accuracy. : The objective of this research is to examine how the subthreshold and ground-state ANCs impact the low-energy S factor, especially at the key astrophysical energy of 300keV. The S factors are calculated within the framework of the R-matrix method using the code. Our total S factor takes into account the E1 and E2 transitions to the ground state of O16 including the interference of the subthreshold and higher resonances, which also interfere with the corresponding direct captures, and cascade radiative captures to the ground state of O16 through four subthreshold states: 02+,3−,2+, and 1−. To evaluate the impact of subthreshold ANCs on the low-energy S factor, we employ two sets of the ANCs. The first selection, which offers higher ANC values, is attained through the extrapolation process [Blokhintsev , ]. The set with low ANC values was employed by deBoer []. A detailed comparison of the S factors at the most effective astrophysical energy of 300 keV is provided, along with an investigation into how the ground-state ANC affects this S factor. : The contribution to the total E1 and E2S factors from the corresponding subthreshold resonances at 300keV are (71–74)% and (102–103)%, respectively. The correlation of the uncertainties of the subthreshold ANCs with the E1 and E2S(300keV) factors is found. The E1 transition of the subthreshold resonance 1− does not depend on the ground-state ANC but interferes constructively with a broad (9.585MeV;1−) resonance giving (for the present subthreshold ANC) an additional 26% contribution to the total E1S(300keV) factor. Interference of the E2 transition through the subthreshold resonance 2+ with direct capture is almost negligible for small ground-state ANC of 58fm−1/2. However, its interference with direct capture for higher ground-state ANC of 337fm−1/2 is significant and destructive, contributing −27%. The low-energy SE2(300keV) factor experiences a smaller increase when both subthfreshold and the ground-state ANCs rise together due to their anticorrelation, compared to when only the subthreshold ANCs increase.Published by the American Physical Society2024