Variation-Iteration Method for Many-Particle Bound States

A method is presented to remedy the defects of the projection-operator technique for calculating electron resonances in scattering from many-electron targets. Specifically it is shown that if the projection operator (i. e. , idempotent) Q is replaced by a quasi-projection operator Q such that limQ+ =0 as any r~-~, then the spectrum of QHQ is discrete, and can be made to be in essentially a unique correspondence with resonance energies. Belaxation of the idempotency requirement allows us to define two forms of Q operator. The simpler of the two forms is tested on e-H and e-He' systems; the two lowest resonant energies differ by

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Effects of Approximate Cluster Functions on Scattering Parameters and an Improved Pseudostate Expansion for Many-Particle Scattering

Hahn

1972

Phys. Rev. A

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The effects on scattering parameters of approximate cluster functions which appear in the asymptotic boundary conditions are examined by a model calculation of the elastic electronhydrogen scattering. It is shown that (i) the resonance energies calculated with functions which are orthogonal to the approximate open-channel functions could be spurious, (ii) the phase shifts could deviate from the correct values as much as the relative error in the cluster functions, and (iii) the threshold mismatch may cause an enhancement of phase shifts. An improved pseudostate expansion is studied in which the prediagonalization of the cluster energy matrix is emphasized. This is seen not only to improve the threshold energies and incorporate the effect of the continuum states, but also to optimize the input functions in a given calculation. An additional diagonalization of the closed-channel energy matrix provides a set of quasistates far the resonance and distortion potentials.

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Variation-Iteration Method for Many-Particle Bound States

Cited by 3 publications

References 21 publications

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

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

Resonance Quasi-Projection Operators: Calculation of theS2Autoionization State ofHe
Temkin
¹
,
Bhatia
²
,
Bardsley
³

1972
Phys. Rev. A
74
0
5
0
View full text Add to dashboard Cite

Effects of Approximate Cluster Functions on Scattering Parameters and an Improved Pseudostate Expansion for Many-Particle Scattering

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Variation-Iteration Method for Many-Particle Bound States

Cited by 3 publications

References 21 publications

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

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

Resonance Quasi-Projection Operators: Calculation of theS2Autoionization State ofHeTemkin1, Bhatia2, Bardsley3 1972Phys. Rev. A74050View full textAdd to dashboardCite

Effects of Approximate Cluster Functions on Scattering Parameters and an Improved Pseudostate Expansion for Many-Particle Scattering

Contact Info

Product

Resources

About

Resonance Quasi-Projection Operators: Calculation of theS2Autoionization State ofHe
Temkin
¹
,
Bhatia
²
,
Bardsley
³

1972
Phys. Rev. A
74
0
5
0
View full text Add to dashboard Cite