K-matrix analysis of theC12(α,γ) reaction at low energy

The most recent data for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(α,γ${)}^{16}$O reaction are parametrized in terms of a K matrix in order to derive the astrophysical S(E) factor at stellar energies. This straightforward parametrization introduces neither boundary condition constants nor channel radii. To constrain the free parameters, all the available data for the phase shifts ${\delta }_l$(l=1,2) of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(α,α${)}^{12}$C were simultaneously fitted with those for the E1 and E2 radiative captures. For each of the three sets of capture data we have analyzed, ${\chi }^2$ tests have been performed with different types of energy-dependent background terms, namely, polynomials and nonresonant echo poles (in the sense of McVoy). The introduction of such poles is motivated by the falling of the ${\delta }_l$ phase shift at higher energies. On the basis of the present analysis, it is concluded that, from the data available, one can derive an allowed range for S(0.3), from 0.00 to 0.17 MeV b. No confidence can be given to a so-called best value of S(0.3) within this range because such a value is dependent on both the data set analyzed and the type of background terms introduced into the parametrized K matrix.