Direct variational methods resonance calculations

Recent years have seen the development of a number of methods for direct calculation of complex resonance energies, both In the context of electron scattering from atoms and molecules and In the context of heavy-particle scattering. This article Is not Intended as a review of that literature. Rather, I present here a brief summary of some of our own work together with a description of a few other approaches with the intention of exhibiting the common theme they employ. That theme is a generalized complex variational... 

Kohn-variational (12), Schwinger-variational, (13) R-Matrix (14), and linear algebraic techniques (15,16) have been quite successful in calculating collisional and phH oTo nization cross sections in both resonant and nonresonant processes. These approaches have the advantage of generality at the cost of an explicit treatment of the continuous spectrum of the Hamiltonian and the requisite boundary conditions. In the early molecular applications of these scattering methods, a rather direct approach based on the atomic collision problem was utilized which lacked in efficiency. However in recent years important conceptual and numerical advances in the solution of the molecular continuum equations have been discovered which have made these approaches far more powerful than those of a decade ago... 

---