The alpha capture reaction 12C(α,γ)16O plays an important role in helium burning in massive stars and their evolution. The reaction rate at Gamow energy (E ~ 300 keV) corresponding to helium burning temperature T~ 0.2 GK determines - together with the triple alpha reaction - the relative amounts of carbon and oxygen at the end of helium burning. Subsequent advanced burning stages in stars rely on the carbon and oxygen fuel. Consequently, the 12C(α,γ)16O reaction rate further influences the nucleosynthesis of heavy elements and even the evolution of massive stars that explode as supernovae. Therefore, a more precise rate for this reaction is highly desirable. Although there have been numerous experimental efforts to measure the radiative capture cross section at low energies (~ 300 keV) in the last 50 years, the desired accuracy of better than 10% has not been obtained. This is because the cross section is very small and it is impossible to measure it directly. The only way to measure this reaction cross section is to first measure it at the lowest energy possible and then extrapolate it down to the low energy. Even the extrapolations are complicated due to the contribution from ground state as well as cascade transitions.
To address this problem, we have studied the 12C(α,γ)16O reaction indirectly through the α-transfer reactions 12C(6Li,d)16O and 12C(7Li,t)16O at the Edwards Accelerator Laboratory facility at the Ohio University, Athens, Ohio by using the 4.5-MV tandem accelerator. Two independent measurements have been performed to check the consistency of the results. The 12C(6Li,d)16O measurements have been performed by using a 6Li beam of various beam energies (5, 4, 3.5, 3.25, 3, and 2.5 MeV) to bombard 12C targets of different thicknesses (15.0, 15.3, and 20 µg/cm2). The 12C(7Li,t)16O measurements have been performed by using 7Li beam at different beam energies (6, 5, 4.5, 4, and 3.5 MeV) and 12C targets of two different thicknesses (21 and 30 µg/cm2). Both the measurements have been performed at eight different laboratory angles i.e. 37.5, 52.5, 67.5, 82.5, 112.5, 127.5, 142.5, and 157.5.
The data was analyzed to determine the asymptotic normalization coefficients for the excited sub-threshold states: 0+ (6.05 MeV), 3- (6.13 MeV), 2+ (6.92 MeV), and 1- (7.12 MeV) in 16O. The asymptotic normalization coefficients for the 2+ (6.92 MeV), and 1- (7.12 MeV) states have been previously measured and well confirmed. However, the asymptotic normalization coefficients for the 0+ (6.05 MeV) and 3- (6.13 MeV) have not been measured in the past except for a very recent measurement by another group. My measurement provides a crosscheck to that measurement, which is important since the measurements are being made for the first time. The asymptotic normalization coefficients determined from the 12C(6Li,d)16O measurements are: C20+ (6.05 MeV) = (3.39 ± 0.33) x 106, C23- (6.13 MeV) = (2.26 ± 0.23) x 104, C22+ (6.92 MeV) = (1.71 ± 0.16) x 1010, and C21- (7.12 MeV) = (5.32 ± 0.59) x 1028, respectively in the units of fm-1. The asymptotic normalization coefficients determined from the 12C(7Li,t)16O measurements are:C20+ (6.05 MeV) = (3.69 ± 0.56) x 106, C23- (6.13 MeV) = (1.80 ± 0.29) x 104, C22+ (6.92 MeV) = (1.40±0.67) x 1010, and C21- (7.12MeV) = (2.57±1.23) x 1028, respectively in the units of fm-1