Theory of Atomic Collisions

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This research will probe strongly interacting atomic systems to develop practical computational schemes for treating them. There are five projects to be undertaken: (1.) Perturbation Series of Strongly Interacting Atoms and Ions. The new perturbation series developed for strongly interacting systems will be formally extended to treat ionization and applied to compute cross sections for the interaction of highly ionized atoms with low Z targets. Some connections of this work and QED have recently been discovered and it is expected they will be explored further. 2. New Time Dependent Variational Principle. A new time dependent variational principle akin to the Schwinger principle for time independent problems will be applied to some of the problems of part 1. The advantage of the variational formulation is to be able to derive higher order approxi- mations to the distorting potential used in the strong potential Born calculations for highly ionized systems. 3. Hyperspherical Expansions. The hyperspherical expansion developed earlier will be applied to the scattering of H+ on deuterium as a test of the "translation factor free" theory. Particular attention will be paid to electron transfer reactions. All that remains is the actual coupled channel calculation using the computed wave functions and potential curves. 4. Saddle Point Effects In Secondary Electron Spectra. Work on saddle point effects in secondary electron spectra will be continued. New approximations to the electron propagator will be developed which contain rotational effects and the new propagator will be used to compute an approximate wave function for the final state. The primary difficulty is the numerical evaluation of the multiple integrals but this seems quite tractable. There are close connections with experimental work at Nebraska and Tennessee. 5. Alignment and Orientation in the Abramov Model. Alignment and orientation parameters are a very sensitive test of collisional approximations. The Abromov model has been developed to compute these parameters for states formed by electron capture at low velocities. The model will be applied and tested against existing experiment. The hope is to stimulate further measurements. There is close co-operation with the experimental groups at Oak Ridge, Kansas State, and other highly charged ion sources such as that at Cornell.