Determination of Asymptotic Normalization Coefficients for the $${}^{16}$$O Nucleus in the $${}^{{12}}{\text{C}}{+\alpha}$$ Channel

A new method was used to determine the asymptotic normalization coefficient $$C_{01}$$ for the $${}^{16}\textrm{O}(0^{+};0\text{ MeV})\to{}^{12}\textrm{C}+\alpha$$ channel, which plays an important role in nuclear astrophysics. $$C_{01}$$ was found from the solution of the Schrödinger equation for a system of two clusters $${}^{12}$$ C and $$\alpha$$ , interacting with each other via the Woods–Saxon potential plus the potential of a uniformly charged sphere. The parameters of the Woods–Saxon potential were chosen from the requirement that it leads to the experimental values of the binding energies of the ground $$0_{1}^{+}$$ and the first excited $$0_{2}^{+}$$ states of $${}^{16}$$ O. The value $$C_{01}=837{-}841$$ fm $${}^{{-}1/2}$$ was obtained, which lies within a wide range of known values: $$13.9\leq C_{01}\leq 3390$$ fm $${}^{{-}1/2}$$ . The asymptotic normalization coefficient $$C_{02}$$ for the $$0_{2}^{+}$$ state was also determined: $$C_{02}=1502{-}1532$$ fm $${}^{{-}1/2}$$ .