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

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