A Computational Perspective on Multichannel Scattering Theory with Applications to Physical and Nuclear Chemistry

In this chapter we discuss a general theoretical framework, based on the generalization of Fano's approach to discrete–continuum interaction, able to describe a variety of resonant phenomena and decay events, ranging from core-electron spectroscopies to the description of universal properties in ultracold Fermi gases, and from the investigation of β-decay in heavy nuclei to the nucleosynthesis of the elements in stars. This method is capable of analyzing the dynamics of atoms, molecules, and solids under the influence of incident radiation or electronic beams and, simultaneously, to predict quantitatively the spectral line shapes correlating their features with the internal dynamic of the perturbed system. On the computational side, we demonstrate by using the concept of the multichannel scattering T-matrix that our approach is amenable to efficient program implementations for determining numerically continuum wave functions including the main correlation effects. For each application we present a detailed description of the main algorithms and computational procedures used to implement our scattering approach and to limit the computational cost of the calculations.