A procedure is presented which leads to a well-defined, convergent method for extending ordinary distorted-wave Born-approximation (DWBA) analysis to the calculation of scattering to long-lived resonant states. This method is based upon the use of a normalized wave function for the resonant state. The cross section calculated with this wave function is correct to terms of the order of $\frac{\Gamma }{E_0}$, the ratio of the resonance width to its energy. To illustrate this technique the cross section for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(d,p)\mathrm{}{}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ transfer reaction to the resonant 5.08-MeV state of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ is calculated. The results are compared to those obtained by other methods and are found to agree to order $\frac{\Gamma }{E_0}$.

• Received 14 June 1972

DOI:https://doi.org/10.1103/PhysRevC.6.2047