Single-particle formulation of electron-atom scatterings with strong correlation effects

Hahn, Yukap

doi:10.1016/0003-4916(70)90241-1

Cited by 27 publications

(3 citation statements)

References 26 publications

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“…V S and V B are the self-consistent field potentials for u and ψ, respectively. Evidently, V B has never been derived before, because of the difficulty (9).…”

Section: Generalization Of the Hartree And Hartree-fock Methods To Scmentioning

confidence: 97%

“…One is then forced to pre-determine the ψ since the ψ equation contains the difficulty (9). Furthermore, the strong asymptotic condition (Eq.…”

Section: Generalization Of the Hartree And Hartree-fock Methods To Scmentioning

confidence: 99%

“…In the past, numerous attempts to extend the approach to scattering problems involving continuum (positiveenergy) orbitals have been made [7][8][9][10], but, no correspondingly satisfactory methods have been found until very recently [11,12]. The principal difficulties in extending the theory are well-known: (i) the non-normalizability of the continuum scattering function makes the SCF determination of the potentials inoperative, and (ii) the strong asymptotic boundary condition which requires exact target internal wave functions for all the open (allowed) channels.…”

Section: Introductionmentioning

confidence: 99%

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Self-consistent field theory of collisions I. Scattering channels

Zerrad

Hahn

2000

The European Physical Journal D

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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.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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“…V S and V B are the self-consistent field potentials for u and ψ, respectively. Evidently, V B has never been derived before, because of the difficulty (9).…”

Section: Generalization Of the Hartree And Hartree-fock Methods To Scmentioning

confidence: 97%

“…One is then forced to pre-determine the ψ since the ψ equation contains the difficulty (9). Furthermore, the strong asymptotic condition (Eq.…”

Section: Generalization Of the Hartree And Hartree-fock Methods To Scmentioning

confidence: 99%