Studies of electron-molecule collisions using the Schwinger variational principle with plane waves as a trial basis set

Lino, J.L.S.; Lima, Margareth Guimarães

doi:10.1590/s0103-97332000000200028

Cited by 7 publications

(24 citation statements)

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“…In this manner, substituting Eqs. (23), (26) and (29) in Eq. (21) the K-matrix is provided for a given ℓm pair of quantum numbers, where the type of confining geometry is not specified.…”

Section: Scattering Observables In Terms Of the Schwinger Variatiomentioning

confidence: 99%

“…The evaluation of the term in the denominator of Eq. ( 21) is complicated by the fact that the Ĝc is simple in a different coordinate system from that of |ψ s and Vs [24,26,[28][29][30]. However, these complications can be avoided by adding and subtracting the Green's function for a free particle, Ĝf ,…”

Section: K-matrix For Two Potentials: Application Of the Schwinger Va...mentioning

confidence: 99%

“…We restrict our treatment in this paper to the situation of symmetric confining potentials in x, y and no force in z; the more general case of asymmetric potentials and/or forces in z will be treated else-where. Note that the Schwinger variational principle has been successfully used for the quantitative study of Rydberg molecules [24], Rydberg atoms [25], electron scattering [26,27] and electron-molecule collisions [28][29][30]. However, in most of these studies, the trial function is composed from a superposition of basis functions (often Gaussian orbitals), which requires numerical evaluation of complicated volume integrals.…”

Section: Introductionmentioning

confidence: 99%

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Schwinger-variational-principle theory of collisions in the presence of multiple potentials

2015

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A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and extends its capabilities. Specifically, the Schwinger variational approach gives results without the divergences that need to be regularized in other methods. Furthermore, it provides a framework to identify the origin of these singularities and possibly improve the local frame transformation. We have used the method to obtain the scattering parameters for different confining potentials symmetric in x, y. The method is also used to treat photodetachment processes in the presence of various confining potentials, thereby highlighting effects of the infinitely many closed channels. Two general features predicted are the vanishing of the total photoabsorption probability at every channel threshold and the occurrence of resonances below the channel thresholds for negative scattering lengths. In addition, the case of negative ion photodetachment in the presence of uniform magnetic fields is also considered where unique features emerge at large scattering lengths.

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“…In this manner, substituting Eqs. (23), (26) and (29) in Eq. (21) the K-matrix is provided for a given ℓm pair of quantum numbers, where the type of confining geometry is not specified.…”

Section: Scattering Observables In Terms Of the Schwinger Variatiomentioning

confidence: 99%

Section: K-matrix For Two Potentials: Application Of the Schwinger Va...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Schwinger-variational-principle theory of collisions in the presence of multiple potentials

2015

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“…A first study using this idea was to implement the so-called C-functional originally proposed by Kolsrud [17] and subsequently discussed more fully by Takatsuka and McKoy [18] and Tao et al [19] for electron scattering and by Lino for positron scattering [20] (the C-functional consists in writing the wave function as a sum of a plane wave plus a combination of L 2 trial functions). In the present work we expand the scattering wave function as a combination of plane waves [21] (We will refer it to SMC-PW). In order to do this, we have develop computer codes involving matrix elements of the type second Born terms with no restrictions on molecular geometries.…”

Section: Introductionmentioning

confidence: 99%

“…In order to do this, we have develop computer codes involving matrix elements of the type second Born terms with no restrictions on molecular geometries. [20,21] Our study has several goals. First, as is known, the effect of electron exchange [22] is usually included in a quantum dynamical calculation through the antisymetrization of the wave function, which introduces nonorthogonal functions to these calculational schemes including the usual staticexchange model.…”

Section: Introductionmentioning

confidence: 99%

Elastic Scattering of CH ₄ by Electron Impact

Lino

2008

Commun. Theor. Phys.

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In this work we present a theoretical study on electrons scattering by CH 4 in the intermediate energy range.More specifically, we report integral and differential cross sections for electron scattering by CH 4 in the (10 ∼ 300) eV range by the Schwinger multichannel method using plane waves as a trial basis set (SMC-PW). To include exchange effects we have used the Born-Ochkur model. Our aim is to study the numerical stability of the cross sections and our calculated results compared with experimental data and theoretical studies are encouraging.

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Improving the wavefunction of the Schwinger multichannel method: application for positron elastic scattering by He atom

Lino¹

2007

Phys. Scr.

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In the present paper, we propose a development to the Schwinger multichannel (SMC) method (Germano and Lima 1993 Phys. Rev. 47 3976) for the elastic scattering of positrons by targets of arbitrary geometry. The essence of this work is based on the fact that the main limitation of the SMC method resides on what makes it a general method, i.e. the expansion of the scattering function is done in a L2 basis (Cartesian Gaussian functions) and this is very effective only for short range potentials. Our effort now is to improve the SMC through the use of plane waves as trial functions (SMC-PW). In order to do this, we have to evaluate reliable codes involving matrix elements which are a straightforward modification of the SMC method. We also discuss a mechanism for the Buckingham potential (polarization effects) where the cutoff parameter is adjustable to the positronium formation threshold. Our results to positron-He illustrate convergence characteristics for several incident positron energies.

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Studies of electron-molecule collisions using the Schwinger variational principle with plane waves as a trial basis set

Cited by 7 publications

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Schwinger-variational-principle theory of collisions in the presence of multiple potentials

Schwinger-variational-principle theory of collisions in the presence of multiple potentials

Elastic Scattering of CH ₄ by Electron Impact

Improving the wavefunction of the Schwinger multichannel method: application for positron elastic scattering by He atom

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Studies of electron-molecule collisions using the Schwinger variational principle with plane waves as a trial basis set

Cited by 7 publications

References 0 publications

Schwinger-variational-principle theory of collisions in the presence of multiple potentials

Schwinger-variational-principle theory of collisions in the presence of multiple potentials

Elastic Scattering of CH 4 by Electron Impact

Improving the wavefunction of the Schwinger multichannel method: application for positron elastic scattering by He atom

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Product

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Elastic Scattering of CH ₄ by Electron Impact