Fano effect studied with use of the recursion method

We treat the classical problem of a number of discrete states interacting with continua (Fano effect), by means of the recursion method. We first map a continuum of states on an equivalent semi-infinite linear chain; then we take advantage of the concepts and properties of the interaction and dipole carrying states to calculate the absorption spectrum. Our approach leads to a significant simplification of calculations without introducing approximations to the original problem. As an example, we consider the case of discrete states interacting with a semielliptical band: we show that resonances, antiresonances, and narrowing of levels, due to interference effects among interacting channels, can be handled in a very compact and simple way.