Calculation of the 1s-2s Electron Excitation Cross Section of Hydrogen

Marriott, R. A.

doi:10.1088/0370-1328/72/1/317

Cited by 141 publications

(20 citation statements)

References 3 publications

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“…It is easy to understand the difference from Eqs. (19) above, since in the exchange case the second channel contains no energy, and a inhomogeneous term is present, while both features are absent in the inelastic coupled channel case.…”

Section: Equations and Notationsmentioning

confidence: 94%

“…The reason that it is possible here to replace a nonlocality by an equivalent added channel is that the Green's function which corresponds to the operator d 2 /dx 2 is given by the product The above equations (19) are a set of inhomogeneous coupled equations which can be solved by conventional numerical means. However for more general semi-separable nonlocalities, which cannot be reduced to a set of equivalent coupled equations, the methods of solving Eq.…”

Section: Equations and Notationsmentioning

confidence: 99%

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A novel method for the solution of the Schrödinger equation in the presence of exchange terms

Rawitscher¹,

Kang²,

Koltracht³

et al. 2003

The Journal of Chemical Physics

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In the Hartree-Fock approximation the Pauli exclusion principle leads to a Schrödinger Eq. of an integro-differential form. We describe a new spectral noniterative method (S-IEM), previously developed for solving the Lippman-Schwinger integral equation with local potentials, which has now been extended so as to include the exchange nonlocality. We apply it to the restricted case of electron-Hydrogen scattering in which the bound electron remains in the ground state and the incident electron has zero angular momentum, and we compare the acuracy and economy of the new method to three other methods. One is a non-iterative solution (NIEM) of the integral equation as described by Sams and Kouri in 1969. Another is an iterative method introduced by Kim and Udagawa in 1990 for nuclear physics applications, which makes an expansion of the solution into an especially favorable basis obtained by a method of moments. The third one is based on the Singular Value Decomposition of the exchange term followed by iterations over the remainder. The S-IEM method turns out to be more accurate by many orders of magnitude than any of the other three methods described above for the same number of mesh points.2

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Section: Equations and Notationsmentioning

confidence: 94%

Section: Equations and Notationsmentioning

confidence: 99%

A novel method for the solution of the Schrödinger equation in the presence of exchange terms

Rawitscher¹,

Kang²,

Koltracht³

et al. 2003

The Journal of Chemical Physics

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“…(2.9) and (2.10). This type of equation is quite common in nuclear and atomic collision theory: see Bransdenj Smith and Tate (1958) for the scattering of nucleons on deuterons, and Marriott (1958) for the scattering of electrons by hydrogen atoms. In general, we shall write the N coupled equations as where k(x is the wave number of the emerging projectile, which can be calculated directly from the energy of the incident projectile using energy conservation [see, for example, Eq.…”

Section: Numerical Details An Iterative Methods For Calculating Cromentioning

confidence: 99%

“…-32 kgj (xx') + 64 (2x'2 + x2) kSj (xx')j For a pair of coupled equations, i, e., a single terna taken in the eigenfunction expansions, the explicit expression for inelastic cross section is given in Marriott (1958). For three, or more, coupled equations the relevant matrix expressions for the cross sections have been derived by Smith (I960).…”

Section: }*^*'-Tl^-^•i]mentioning

confidence: 99%

The Scattering of Positrons by Atomic Hydrogen: Formulation

Cody¹,

Smith²

1960

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“…(13) can be reduced to a single integro-differential equation [25,26], the solution of which has been discussed several times before [27]. Such solutions would correspond to the exact static-exchange (ESE) continuum solutions of the scattering problem at the collision energy E if one also assumes that the target atomic wave function is an exact solution of the SchrSdinger equation and not just its Hartree-Fock solution.…”

Section: N+i N~almentioning

confidence: 99%

Elastic electron scattering from rare gases with exact exchange: a new correlation-polarisation potential

Gianturco

Rodriguez-Ruiz

1994

Nuov Cim D

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(ricevuto il 17 Marzo 1994; approvato il 21 Aprile 1994)Summary. --The many-body correlation forces which act between the impinging electron and the bound electrons of the target atoms are treated here using a newly developed correlation-polarisation potential that originates from the calculation of correlation energies in electronic bound states of atoms and molecules. The new formulation of such forces is shown to be particularly effective for the present systems once all the other forces at play are treated exactly within the Hartree-Fock scheme. The calculations of this paper compare our new density functional theory (DFT) approach (Gianturco and Rodriguez-Ruiz, 1993) with an earlier homogeneous electron gas (FEG) model for correlation forces (O'Connell and Lane, 1983) and clearly indicate the superior quality of a more realistic Hartree-Fock description of the density functional for the bound electrons. Excellent accord is obtained between experimental cross-sections and theoretical results, both for differential and integral elastic electron scattering cross-sections, over a very broad range of collision energies. PACS 34.80.Bm -Elastic scattering of electrons by atoms and molecules.

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Calculation of the 1s-2s Electron Excitation Cross Section of Hydrogen

Cited by 141 publications

References 3 publications

A novel method for the solution of the Schrödinger equation in the presence of exchange terms

A novel method for the solution of the Schrödinger equation in the presence of exchange terms

The Scattering of Positrons by Atomic Hydrogen: Formulation

Elastic electron scattering from rare gases with exact exchange: a new correlation-polarisation potential

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