New Investigation of the 1<i>Se</i>Autoionizing States of He and H−

Holøien, E.; Midtdal, John

doi:10.1063/1.1727912

Cited by 101 publications

(27 citation statements)

References 14 publications

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“…(A6). Equation (14) predicts that, for the one-term cases, the DA products are expected to have an angular distribution relative to£ e «, which is the same as the partial wave absorbed from the continuum by the target in forming the resonance.…”

Section: Dissociative Attachmentmentioning

confidence: 99%

See 1 more Smart Citation

Angular Dependence of Scattering Products in Electron-Molecule Resonant Excitation and in Dissociative Attachment

O'Malley¹,

Taylor

1968

Phys. Rev.

210

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For the processes mentioned in the title, the general rearrangement formalism of a previous paper is applied with specific consideration to the effect of molecule orientation on the electronic matrix elements and on the total and differential cross sections. Formulas are given for two cases: when one can and when one cannot treat the effect of rotation as a semiclassical orientation average. A short discussion is given of selection rules and of the use of these formulas in (a) ab initio calculation of the cross section, (b) approximate prediction of angular dependence, and (c) parametrization of experimental data.

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Section: Dissociative Attachmentmentioning

confidence: 99%

“…Therefore, while the present paper supplements I by giving the correct angular distribution for o r DA (^) through Eqs. (13) and (14), it makes no change in the formulas (1-5.19 and 5. 24) for the total cross section.…”

Section: Dissociative Attachmentmentioning

confidence: 99%

Angular Dependence of Scattering Products in Electron-Molecule Resonant Excitation and in Dissociative Attachment

O'Malley¹,

Taylor

1968

Phys. Rev.

210

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“…Instead of testing various methods proposed to determine the discrete state (such as a stabilization method [8,9], applied to electron collisions with H 2 [18] and N 2 [20] molecules, or a recently proposed Feshbach-Fano R-matrix method [10,11]) we will choose several welldefined states and show what problems we can encounter if the nonlocal approximation is used to study the dynamics of electron-molecule collisions.…”

Section: Sensitivity Of the Nonlocal Approximation To Choice Of Tmentioning

confidence: 99%

“…The same numerical techniques that we used for solving the two-dimensional problem can be efficiently applied to solve the nonlocal approximation equations (see Section IV for details) and thus we are able to obtain reliable results for any given discrete state. Several alternative definitions of the discrete state can be found in the literature (see for example [7][8][9][10][11]) including the unique definition of Lippmann and O'Malley [12] based on the physical significance of this state. But implementation of these definitions is elaborate and it is not the purpose of this paper to decide which of these definitions gives the best nonlocal approximation.…”

Section: Introductionmentioning

confidence: 99%

Probing the nonlocal approximation to resonant collisions of electrons with diatomic molecules

2008

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A numerically solvable two-dimensional model introduced by the authors [Phys. Rev. A 73, 032721 (2006)] is used to investigate the validity of the nonlocal approximation to the dynamics of resonant collisions of electrons with diatomic molecules. The nonlocal approximation to this model is derived in detail, all underlying assumptions are specified and explicit expressions for the resonant and non-resonant (background) T matrix for the studied processes are given. Different choices of the so-called discrete state, which fully determines the nonlocal approximation, are discussed and it is shown that a physical choice of this state can in general give poorer results than other choices that minimize the non-adiabatic effects and/or the background terms of the T matrix. The background contributions to the cross sections, which are usually not considered in the resonant theory of electron-molecule collisions, can be significant not only for elastic scattering but also for the inelastic process of vibrational excitation.

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“…Along theu axis this procedure is equivalent to that of the Holaien and Midtdal [9]. The real eigenvalues W of the unrotated Hamiltonian A are computed as a function of the scale factor 77 = 1771.…”

Section: Stability Of the Resonance Solutionmentioning

confidence: 99%

Study of predissociation resonances by the complex coordinate method

Moiseyev

1981

Int J of Quantum Chemistry

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The complex coordinate method is applied to the predissociation resonances of two-state model system. The stability of the resonance positions and their widths, as well as the affect of using real and complex basis sets are studied. A. Autoionization and Predissociation ResonancesAutoionization and predissociation resonances are quasibound states that are associated with non-normalizable solution of the time-independent Schrodinger equation. Therefore, the description of resonance states within the framework of Hilbert space is not straightforward. The complex coordinate (or scaling) method [l] has the advantage that it enables us to obtain the resonance positions and lifetimes by using techniques of bound state approximation theory. Up to the present, attention has primarily been drawn to the application of the complex coordinate method to electron scattering processes, i.e., to atomic [2] and molecular [3] autoionization resonances. In this work we investigate the application of the complex coordinate method to predissociation processes.In the framework of the Born-Oppenheimer approximation, the only type of predissociation resonances that can be observed are the shape-type resonances [4]. These resonances result from the existence of a centrifugal barrier, or from the interaction between two potential curves, in which it is assumed that the electronic eigenfunctions of the Born-Oppenheimer Hamiltonian are independent of nuclear position R: N q = C Ci(R)qi(r). i = lAs presented in Figure 1 for a two-state model ( N = 2 ) , the crossing of the two potentials El and Ez is avoided. The new potential (the dashed lines in Fig. 1) has only shape-type resonance states. In order to obtain the Feshbach resonances that lie above the crossing point of the two curves in Figure 1, one has to go beyond the Born-Oppenheimer approximation. The

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New Investigation of the 1SeAutoionizing States of He and H−

Cited by 101 publications

References 14 publications

Angular Dependence of Scattering Products in Electron-Molecule Resonant Excitation and in Dissociative Attachment

Angular Dependence of Scattering Products in Electron-Molecule Resonant Excitation and in Dissociative Attachment

Probing the nonlocal approximation to resonant collisions of electrons with diatomic molecules

Study of predissociation resonances by the complex coordinate method

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