We extend a modified Newton-Sabatier method for the solution of the fixed energy, coupled channels, inverse scattering problem to deal with a set of cluster transfer reactions. The method is tested by using analytic model potentials for the transfer reaction ${}^{16}\mathrm{O}(\alpha {,}^8\mathrm{Be}{)}^{12}\mathrm{C}.$ For low energy scattering we show that inclusion of S matrices for nonphysical, noninteger angular momenta are required to find stable solutions. The possibility of application to actual experimental data is discussed.

• Received 16 August 2000

DOI:https://doi.org/10.1103/PhysRevC.62.064610