The Approximate Model Independence of the Asymptotic Normalization Coefficient

Radiative capture reactions play an important role in nuclear astrophysics, but their cross sections are difficult to measure directly or obtain through theoretical calculations. The asymptotic normalization coefficient (ANC) provides an indirect approach to determining radiative capture cross sections from measured transfer reaction cross sections. Extracting the ANC requires solving the Schrödinger equation to obtain the bound-state wave function of the residual nucleus in the transfer reaction. This paper investigates the approximate model independence of the ANC and the parameters of the Woods–Saxon potential used in solving the Schrödinger equation. Firstly, we provided a mathematical analysis of the approximate model independence of the ANC. Subsequently, based on [Formula: see text] transfer reaction experimental data, we calculated ANCs for the ground state, first excited state, second excited state and third excited state of 13 C, and presented their variations with model parameters. The results further confirm the approximate model independence of the ANC.