Cross section expansion for direct neutron radiative capture

Cross sections for neutron radiative capture multiplied by the relative velocity can be expressed as a Taylor expansion in powers of the relative energy. The coefficients of this expansion are expressed in the potential model as integrals involving solutions of the radial Schrodinger equation and of its inhomogeneous energy derivatives calculated at zero energy. Similarities and differences with charged-particle capture are emphasized. The C-12 (n, gamma) C-13 capture reaction is treated as an example. The coefficients of the Taylor expansion lead to simple parametrizations of the experimental partial cross sections for neutron capture to each C-13 bound state.