Solving the three-body Coulomb breakup problem using exterior complex scaling

摘要: Electron-impact ionization of the hydrogen atom is prototypical three-body Coulomb breakup problem in quantum mechanics. The combination subtle correlation effects and difficult boundary conditions required to describe two electrons continuum have made this one outstanding challenges atomic physics. A complete solution form a 'reduction computation' all aspects physics given by application exterior complex scaling, modern variant mathematical tool analytic continuation electronic coordinates into plane that was used historically establish formal properties scattering matrix. This review first discusses essential difficulties It then describes basis scaling as well details its numerical implementation using variety methods including finite difference, elements, discrete variable representations B-splines. Given these implementations wavefunction can be generated with arbitrary accuracy on any volume space coordinates, but there remains fundamental extracting amplitudes from it. Methods are described for evaluating amplitudes. question volume-dependent overall phase appears theory resolved. summary presented accurate results been obtained case electron-impact discussion applications double photoionization helium.