Theoretical investigations of the ¹²C(α,γ)¹⁶OE2 cross section

The E2 component of the ¹²C(α,γ)¹⁶O cross section is investigated in three ways: by a microscopic cluster model, by R-matrix fits and by a combination of both. The microscopic calculation leads to an estimate of the S-factor at a typical energy of 300 keV of S_E2(300 keV)≈ 50 keV-b for ground-state transitions. Cascade transitions to the 0₂⁺ and 2₁⁺ excited states of ¹⁶O are also studied. Then the S-factor is analyzed in the phenomenological R-matrix theory. We show that the background term plays a crucial role, and cannot be determined without ambiguity. Consequently only an upper limit on the extrapolated S-factor can be obtained [S_E2(300 keV)< 190 keV-b]. Finally, we use the microscopic Asymptotic Normalization Constant (ANC) of the 2₁⁺ level, well known to be a cluster state to constrain the R-matrix analysis. This procedure strongly reduces the uncertainties on the R-matrix fits, and we end up with a recommended value of S_E2(300 keV) = 42 ± 2 keV-b. (author)