Projection-operator calculations for shape resonances: A new method based on the many-body optical-potential approach

The projection-operator formalism of Feshbach defines a separation of the T matrix into a smooth background term and a resonant T matrix which may vary rapidly with energy. The resonance is characterized by an unperturbed energy epsilon/sub d/, a width function GAMMA(E), and a level-shift function Δ(E). Such a separation of the fixed-nuclei electron-molecule scattering T matrix is of considerable practical relevance for the treatment of nuclear dynamics in resonant electron-molecule scattering. We present an explicit realization of the projection-operator formalism for electron-molecule scattering within the framework of the many-body optical-potential approach. In contrast to the approach of Hazi [J. Phys. B 11, L259 (1978)] which is based on the use of Stieltjes moment techniques to compute GAMMA(E), we obtain explicitly the background T matrix as well as the information on the angular distribution of the resonant scattering. The performance of the method is illustrated for the well-known 2.3-eV shape resonance in electron scattering from the nitrogen molecule. The two-particle-hole Tamm-Dancoff approximation (2ph-TDA) is adopted for the optical potential and the Schwinger variational principle is used to solve the background scattering problem. The resulting resonance parameters epsilon/sub d/, GAMMA(E), Δ(E), and the resonant eigenphase sum are in excellent agreement with results obtained previously by Hazi using different computational methods