Numerical determination of scattering and bound states via self-consistent field theory
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Abstract
Interpretation of atomic spectra and the applications of atomic spectroscopy to current problems in astrophysics, laser physics, and thermonuclear plasma require a precise knowledge of atomic structure and dynamics. The collisional excitation and ionization of atomic targets by electron impact is distinct in that one or more electrons are in the continua, which makes the theory complicated and also drastically disturbs the system for probing and detection.
Analysis of interacting atomic systems is complex and many approximate methods have been developed in the past. The most prominent of these methods is the Hartree-Fock procedure and its relativistic and multiconfiguration extensions. This self-consistent-field (SCF) approach has been limited to treating only fully bound, negative energy states whose corresponding wave functions are square-integrable. Recently, the SCF extension to scattering in which continuum (positive-energy) states are involved, has been formulated. The non-integrability of the continuum functions can be overcome by an amputation procedure that retains all of the physical essentials of the scattering system. It is extended here to the electron-hydrogenic scattering system in the zero angular momentum coupling models. In this project, the focus is on devising a numerical algorithm for solving such systems of integro-differential equations stemming from the SCF theory. The method is compared with results obtained by several other approaches. It is shown that the newly devised numerical approach converges as the amputated continuum functions provide an effective projection of the scattering function.