12C(α, γ)16O E2 cross section:: R-matrix fits combined with a microscopic cluster model

The E2 component of the C-12(alpha,gamma)O-16 cross section is investigated in two ways: by a microscopic cluster model, and by R-matrix fits. The alpha+C-12 microscopic calculation is performed in the framework of the generator coordinate method (GCM) by including all C-12 states (T = 0) within the p shell. Using different nucleon-nucleon interactions we find S-E2(300 keV) approximate to 50 keV . b for ground-state transitions. We also study cascade transitions to the 0(2)(+) and 2(1)(+) excited states of O-16. 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. Using the experimental phase shifts and capture cross sections, only an upper limit on the extrapolated S factor can be obtained [S-E2(300 keV)< 190 keV center dot b]. To constrain the R-matrix analysis, we use the GCM asymptotic normalization constant (ANC) of the 2(1)(+) level, well known to be a cluster state. This procedure strongly reduces the uncertainties on the R-matrix fit, and we end up with a recommended value of S-E2(300 keV) = 42 +/- 2 keV center dot b. We show that ANC values derived from indirect methods are not consistent with the C-12(alpha, gamma)O-16 cascade transitions to the 2(1)(+) state, and suggest that a remeasurement of this cross section is desirable.