Numerical approach to energy-dependent complex-potential surfaces of metastable negative molecular ions

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Abstract
An ab initio method for the treatment of metastable negative ions is presented, which is applicable to larger and especially polyatomic molecules. This method is based on Feshbach’s projection-operator formalism. The ‘‘discrete component’’ Φ of the resonance is thereby represented by a large-scale configuration-interaction expansion, calculated as the ground-state eigenfunction of a perturbed Hamiltonian related to the negative system. The real part of the complex potential is given by the energy expectation value of Φ and the level shift Δ, and the imaginary part is the negative half width Γ/2 of the resonance. Level shift and resonance width are calculated energy-dependently by using a Green’s-operator approach. The Lippmann-Schwinger equation for this Green’s operator is defined by the free Green’s operator and the background potential. The latter includes correlation effects of the target system as well as the polarization of energetic lower orbitals according to the additional captured electron. The complex potential contains all information for calculation of vibrational excitation in resonant electron-molecule scattering processes.

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