Determination of the Astrophysical S-factor Near Zero Energy

The astrophysical S-factor for radiative-capture reactions is reviewed at zero energy in the simplified potential models since the determination of reaction rates in astrophysics requires accurate values of radiative-capture cross sections at very low energy values. The Taylor expansion of the astrophvsical S-factor is calculated. The radial Schrodinger equation and its derivatives are solved at zero energy by taking corresponding exact asymptotic forms of wave functions into account. Explicit expressions for the S-factor and for its derivatives at zero energy are obtained. The procedure is applied to 3He(,)7Be reaction as an example.