Scattering Amplitudes

Abstract

Electrons are constantly colliding with atoms and molecules: in chemical reactions, in our atmosphere, in stars, plasmas, in a molecular wire carrying a current, or when the tip of a scanning tunneling microscope injects electrons to probe a surface. When the collision occurs at low energies, the calculations become especially difficult due to correlation effects between the projectile electron and those of the target. These bound-free correlations are very important. For example, it is due to bound-free correlations that ultra-slow electrons can break up RNA molecules [Hanel 2003] causing serious genotoxic damage. The accurate description of correlation effects when the targets are so complex is a major challenge. Existing approaches based on wavefunction methods, developed from the birth of quantum mechanics and perfected since then to reach great sophistication [Morrison 1983, Burke 1994, Winstead 1996], cannot overcome the exponential barrier resulting from the many-body Schrödinger equation when the number of electrons in the target is large. Wavefunction-based methods can still provide invaluable insights in such complex cases, provided powerful computers and smart tricks are employed (see, e.g., [Grandi 2004] for low-energy electron scattering from uracil), but a truly ab-initio approach circumventing the exponential barrier would be most welcome. The purpose of this chapter is to describe several results relevant to this goal.