Comments on the triple differential ionisation cross sections in the second Born approximation

Pathak, A; Srivastava, M. K.

doi:10.1088/0022-3700/14/23/004

Cited by 7 publications

(11 citation statements)

References 7 publications

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“…Recently, Dal Cappello et al [7] have shown that the second Born approximation works very well for the ionization of atomic hydrogen for an incident energy of 250 eV and an energy of 5 eV for the ejected electron but completely fails for higher values of the energy of the ejected electrons (50 eV). This result was also found by Pathak and Srivastava [8] who only used the closure approximation. In our studies, the incident electron is described by a plane wave.…”

Section: Introductionsupporting

confidence: 84%

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Ionization of atomic hydrogen by electrons: the role of the contributions of the pseudo-states in the second Born approximation

Cappello

Hmouda

Naja

et al. 2013

J. Phys. B: At. Mol. Opt. Phys.

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The second Born approximation is often used, particularly when we study double processes such as the ionization-excitation and the double ionization of atoms and molecules by charged particles. But when we apply this approximation, it needs the knowledge of all excited states of the target. In this study, we apply the second Born approximation by using 294 excited and pseudo-states for the ionization of atomic hydrogen by electrons. We compare the results of our model with those given by other models and to all experiments performed with an incident energy of 250 eV. We show that our new version of the second Born approximation gives better agreement than previous versions even for high values of the energy of the ejected electrons (50 eV).

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Section: Introductionsupporting

confidence: 84%

“…We also study in greater detail the closure approximation. We have known for a long time that the closure approximation works very well for low energy for the ejected electrons [7,9,21,22], but fails for higher energies [7,8]. We decide to investigate this issue mostly in the highest possible energy regime 50 eV of the ejected electron.…”

Section: Introductionmentioning

confidence: 99%

Ionization of atomic hydrogen by electrons: the role of the contributions of the pseudo-states in the second Born approximation

Cappello

Hmouda

Naja

et al. 2013

J. Phys. B: At. Mol. Opt. Phys.

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“…From this good agreement between the two theories (CDW-EIS and CCC) they conclude that the experimental data of Ehrhardt et al (1985Ehrhardt et al ( , 1986 . These experiments are interesting because Pathak and Srivastava (1981) conclude that the second Born approximation is not able to bring about a general improvement in the values of the TDCS over the first Born results. These authors use the closure approximation with a high average excitation energy w =1 au.…”

Section: Results and Discussion A) Ionization Of Atomic Hydrogen By Ementioning

confidence: 93%

“…We only notice small differences between the two calculations and find results close to those of Byron et al (1982): the first and second Born triple differential cross sections differ by only 17% at the binary peak, with the second Born result being smaller than the first Born result (as in the case of atomic hydrogen).We also find that the ratio of the binary peak to the recoil peak is reduced from the first Born value of 8.43 to the second Born value of 5.63 in better agreement with experiment. Thus, as written by Byron et al (1982), the results of Pathak and Srivastava (1981) in this case are incorrect.…”

Section: C) Single Ionization Of Helium By Electronsmentioning

confidence: 97%

The second Born approximation for the single and double ionization of atoms by electrons and positrons

Cappello

Haddadou

Menas

et al. 2010

J. Phys. B: At. Mol. Opt. Phys.

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have shown that the second Born approximation is necessary to describe the experimental results of the double ionization of atoms and molecules. The second Born approximation needs a difficult triple numerical integration and often many authors find some controversial results. We now investigate, in greater detail, the application of the second Born approximation for the easier case: the ionization of atomic hydrogen by electrons. The ionization of atomic hydrogen allows us to check accurately this approximation because the wavefunctions describing the target are known exactly. Moreover, sophisticated models such as convergent close coupling (CCC) and the continuum distorted wave eikonal initial state (CDW-EIS) exist and give closer results leading to easier comparisons. We report accurate second Born results for differential cross sections for the ionization of atomic hydrogen using a basis including 100 discrete states, and another basis including 32 discrete states and pseudo-states. The results of the present method are compared with other calculations and experiment. The single ionization of helium is also investigated in order to answer an old controversy between two different theoretical results. Finally, an application of the second Born approximation to the double ionization of helium has been performed.

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“…Pathak and Srivastava [32] used the second Born approximation for the ionization of atomic hydrogen and compared their results to the first (e, 2e) experiments of Weigold et al [33], Then they also made calculations for the ionization of helium by using the closure approximation and compared their results to those of Ehrhardt et al [34], Byron et al [35] also calculated TDCSs for the ionization of helium by using the closure approximation and found results which disagreed with those of Pathak and Srivastava [32], Later on, Byron et al [36] applied the second Born approximation by using very few discrete states as intermediate states and by taking into account the closure approximation and adding the contribution of the third Born approximation calculated with the Glauber approximation. It was found that the second Born PACS number(s): 34.50.Rk, 34.80.Dp, 34.50.Fa calculation plays a crucial role in understanding the (e, 2e) process.…”

Section: Introductionmentioning

confidence: 99%

Exchange effects and second-order Born corrections in laser-assisted(e,2e)collisions with helium atoms

et al. 2015

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The triple differential cross section for laser-assisted ionization of a helium target by slow electrons is analyzed within the framework of the second Born approximation. We evaluate the S-matrix elements using Volkov and Coulomb-Volkov wave functions for describing the continuum states of the scattered and the ejected electrons, respectively. The required scattering amplitudes are performed by expanding the atomic wave functions onto a complex-scaled Sturmian basis, which allows us to exactly take into account the contribution of the continuous spectrum to the dressing of the atomic states. Our results have been improved by taking into account exchange effects. Furthermore, the second-order Born correction is seen to be important and significantly affects the magnitudes of the binary and recoil peaks.

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Comments on the triple differential ionisation cross sections in the second Born approximation

Cited by 7 publications

References 7 publications

Ionization of atomic hydrogen by electrons: the role of the contributions of the pseudo-states in the second Born approximation

Ionization of atomic hydrogen by electrons: the role of the contributions of the pseudo-states in the second Born approximation

The second Born approximation for the single and double ionization of atoms by electrons and positrons

Exchange effects and second-order Born corrections in laser-assisted(e,2e)collisions with helium atoms

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