An explicit method for calculating the scattering matrix from a given structure-model Hamiltonian is presented. The special technique adopted uses nonorthogonal eigenfunctions of the basic model Hamiltonian to represent the scattering wave functions in the interaction region. Application of this approach is mode to neutron scattering by ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. The weak-coupling particle-rotator model has been used for the positive-parity states of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$. The results obtained agree closely with the experimental total neutron cross section, both the background and resonant behavior being well reproduced by the theory.

• Received 4 April 1969

DOI:https://doi.org/10.1103/PhysRev.185.1279