Self-consistent field theory of collisions I. Scattering channels |
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Authors: | E Zerrad Y Hahn |
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Institution: | (1) Department of Physics, Delaware State University, Dover, DL 19901, USA, US;(2) Physics Department, University of Connecticut, Storrs, CT 06269, USA, US |
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Abstract: | The conventional Hartree and Hartree-Fock approaches for treating many-electron bound systems have been extended recently
to positive energy scattering problems, in which both the bound and continuum orbitals are determined by the requirement of
full self-consistency. Serious consequences of such a theory are that the target orbitals become energy dependent and the
asymptotic boundary conditions are satisfied only approximately, in lowest order. It is important therefore to test the theory
for its convergence under configuration mixing. This self-consistent field (SCF) theory for scattering has been tested here
for scattering from hydrogenic target as a model where the target function is determined dynamically. Penetration of the projectile
inside the bound target orbital is manifest through the SCF for the bound state. Our results show that the theory converges
to the correct amplitudes and to the exact boundary conditions as more configurations are added. The use of the amputated
functions and the weak asymptotic condition (WAC) upon which the SCF theory is based, is justified as the WAC converges to
the correct limit. It is then applied to the positron-helium and electron-helium scattering systems where the helium function
is calculated simultaneously together with the scattering function. The resulting phase shifts and the SCF target functions
are compared with those obtained with the pre-determined target functions in the conventional approaches.
Received 22 September 1999 |
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Keywords: | PACS 34 10 +x General theories and models of atomic and molecular collisions and interactions (including statistical theories transition state stochastic and trajectory models etc ) - 31 10 +z Theory of electronic structure electronic transitions and chemical binding - 24 10 -i Nuclear-reaction models and methods |
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