Electron impact excitation cross sections

McDowell, M R C; Morgan, L A; Myerscough, V P

doi:10.1016/0010-4655(74)90055-1

Cited by 25 publications

(16 citation statements)

References 3 publications

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“…corrections. Practically identical results were obtained using the Aymar-Crance parametric potentials to generate the distorted wavefunctions for ejected electron b, and using wavefunctions obtained from the distorted wave polarised orbital code of McDowell et al [21]. The correlated wavefunction of Tweed and Langlois [22] was used to describe the target.…”

Section: Resultsmentioning

confidence: 99%

Quantum-mechanical analogies for classical post-collision interaction effects in (e, 2e) collisions

Robaux

Tweed

Langlois

1992

Z Phys D - Atoms, Molecules and Clusters

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Abstract.A method is proposed for approximately computing the post collisional interaction of the two escaping electrons in otherwise standard first order ionisation calculations. At intermediate energies and in asymmetric kinematics the effects are found to be very small. The interactions of these electrons with the residual ion are considered through the use of distorted waves. For the slow one the latter are used in the calculations but for the fast one their effect is investigated using Fourier transforms. These interactions play a significant role.

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Section: Resultsmentioning

confidence: 99%

Quantum-mechanical analogies for classical post-collision interaction effects in (e, 2e) collisions

Robaux

Tweed

Langlois

1992

Z Phys D - Atoms, Molecules and Clusters

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“…This integro-differential equation can be transformed to the following system of coupled differential equations, which is the starting point for McDowell et al [15,16]:…”

Section: The Integro-differential Equationmentioning

confidence: 99%

“…Almost all previous methods require a starting solution in the region near to the origin, where numerical integration of the coupled equations cannot be directly initiated because of the singular behaviour of the potentials which contain terms proportional to r −1 and r −4 and the angular momentum terms which are proportional to r −2 . It is possible to follow McDowell et al [15,16] in obtaining a series expansion of the regular solution at the origin, which requires the potentials to be expressable in an analytical form and their series expansions about the origin to be known. The solutions are continued by numerical integration of the coupled equations using one or another of the well-known integrators, such as the method of Numerov (1933).…”

Section: The Canonical Function Technique For Solving the Dwpo Ementioning

confidence: 99%

“…This is the Distorted Wave Polarised Orbital (DWPO) method of McDowell et al [15] which was developed for Distorted Wave Born calculations of excitation of Hydrogen (McDowell et al [16]) and of Helium [18] and replaces the integro-differential equation by coupled differential equations. In both cases, only an s-state of the atom is considered and the central potentials are expressed in analytical form.…”

Section: Introductionmentioning

confidence: 99%

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Distorted waves with exact nonlocal exchange: A canonical function approach

Fakhreddine¹,

Tweed²,

Vien³

et al. 2006

Can. J. Phys.

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It is shown how the Canonical Function approach can be used to obtain accurate solutions for the distorted wave problem taking account of direct static and polarisation potentials and exact non-local exchange. Calculations are made for electrons in the field of atomic hydrogen and the phaseshifts are compared with those obtained using a modified form of the DWPO code of McDowell and collaborators: for small wavenumbers our approach avoids numerical instabilities otherwise present. Comparison is also made with phaseshifts calculated using local equivalentexchange potentials and it is found that these are inaccurate at small wavenumbers. Extension of our method to the case of atoms having other than s-type outer shells is dicussed.

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“…In the present "modified" VCCPB prior form model calculations one has to solve three coupled differential equations for the radial distorted wave. The method described earlier by McDowell et al [11,12] was utilized with suitable modifications to achieve the solutions. The wavefunctions that we have used for the ground state of He has been taken from Byron and Joachain [13] while for the 23S state the target wavefunction is taken from Van den Bos [14].…”

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confidence: 99%

On the variable-charge Coulomb-projected Born approximation

et al. 1984

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Total cross-sections for electron impact excitation of 11S-23S transition in helium have been calculated using variable-charge Coulomb-projected Born approximation and also using a distorted wave model in which the prior form of the T-matrix is used. The comparison of the two sets of results enables us to make certain observations about the suitability of the variable-charge Coulomb-projected Born approximation.The variable-charge Coulomb-projected Born (VCCPB) approximation proposed by Schaub-Shaver and Stauffer [-1] is the most generalized form of Coulomb-project Born (CPB) approximation initially suggested by Geltman [23. It is easy to show that the VCCPB model, in which the effective nuclear charge as seen by the incident particle depends on its position with respect to the target nucleus, is essentially a form of the distorted wave Born (DWB) approximation with distortion included in the final channel only. The screening parameter determines the static potential of the target in its initial state and the distortion of the scattered particle-wavefunction by this potential is considered. The results obtained in the VCCPB model for the 11S-23S electron impact excitation cross section of helium (since we are neglecting relativistic effects, this transition occurs only through exchange) are however, in very poor agreement with the results of other distorted wave (DW) models [3-53. Further the VCCPB method when applied to electron impact excitation of the 11S-21S transition in helium like ions [-6], yields cross section results, at low incident energies (where again exchange contributions are significant), which are in very poor agreement with the results obtained by Bhatia and Temkin [73 (herein after referred as BT model). This particular form (BT model) of the DW model is very similar to the VCCPB model differing only in the choice of channel in which distortion is included -BT model includes distortion in the initial channel while the VCCPB model includes it in the final channel. Both models do not take any account of polarisation. So the large discrepancy between the VCCPB results and the other DW results in the case of electron impact IIS-21S excitation in helium [-8] (at least for low incident energies) and for the 11S-23S transition does not seem likely to be caused only by the neglect of distortion in one channel and/or the neglect of polarisation, in the former. We use a VCCPB type DW model utilizing the prior form of the T-matrix in order to remove this discrepancy and show why this choice leads to a better representation of the collision process. If we examine the DW methods used so far for the calculation of electron-beam (ion) collisions (either already referred to above or cited in these references) and the VCCPB method we readily make the following observations: (ii) The wavefunction ~/+ is properly antisymmetrized.(iii) In the various DW models it is the function ~/+ in which the distortion is included. Some more accurate studies [5] include distortion in both channels.(iv) The VCCPB method includ...

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Electron impact excitation cross sections

Cited by 25 publications

References 3 publications

Quantum-mechanical analogies for classical post-collision interaction effects in (e, 2e) collisions

Quantum-mechanical analogies for classical post-collision interaction effects in (e, 2e) collisions

Distorted waves with exact nonlocal exchange: A canonical function approach

On the variable-charge Coulomb-projected Born approximation

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