Perpendicular Plane Geometry Research Articles

Analysis of electron induced single ionisation differential cross-section of CO2 molecules in different kinematics

Theoretical investigations of electron-impact ionisation for carbon dioxide (CO2) in low to intermediate energy ranges are presented. In addition to the energy range, we have estimated triple differential cross-section (TDCS) in coplanar and perpendicular plane geometry. We have calculated the TDCS for electron impact using the modified distorted wave formalism up to the second order. Post-collision interaction effects have also been introduced to describe the collision dynamics accurately. There is a good correlation between the distorted-wave Born approximation results and the experimental results in terms of forward and backward scattering regions.

Triply differential cross sections for electron and positron impact on methane.

We here report theoretical triply differential cross sections (TDCS) for 250eV electron and positron impact ionization of the methane molecule calculated within the second-order distorted-wave Born approximation (DWBA2) for various momentum transfer conditions. The experimental data taken from Işık et al. [J. Phys. B: At., Mol. Opt. Phys. 49, 065203 (2016)] will be compared with the current theoretical predictions as well as molecular three body distorted wave (M3DW) approximation and generalized Sturmian function (GSF) theoretical models in a non-coplanar geometry. In the low analyzer scattering plane, the results obtained within the DWBA2 theory show better agreement with the experimental results compared to the GSF results. The M3DW results also exhibit agreement with the experimental results, in particular in the perpendicular plane geometry. Furthermore, significant differences between electron and positron TDCS were observed.

Energy-sharing(e,2e)collisions: Ionization of the inert gases in the perpendicular plane

The triple differential cross section for ionization of the inert gases He, Ne, Ar, Kr, and Xe in energy-sharing perpendicular plane geometry is investigated. Encouraging agreement with recent experiments is found using the distorted-wave Born approximation (DWBA). Mechanisms are discussed which explain the He and Ne data but which seem to be masked by the greater distortion effects in the heavier targets. The inclusion of postcollisional interaction is explored using Gamow, ${N}_{ee}$, and Ward-Macek, ${M}_{ee}$, factors. While both help to improve the shape of the cross section for He and Ne at the lower energies, they are not successful for the other targets, and both factors prove to be too strong for all the inert gases with increasing impact energy. It is well known that ${N}_{ee}$ destroys normalization. Comparing DWBA $+\phantom{\rule{0.16em}{0ex}}{M}_{ee}$ results with some absolute experimental points at 1 and 2 eV indicates that it is also not to be trusted on normalization. An interesting situation with Ar is highlighted near 25 eV, where the cross section may be tending towards a strong interference minimum or zero.

Low energy (e,2e) coincidence studies of NH3: Results from experiment and theory

Experimental and theoretical triple differential cross sections (TDCS) from ammonia are presented in the low energy regime with outgoing electron energies from 20 eV down to 1.5 eV. Ionization measurements from the 3a1, 1e1, and 2a1 molecular orbitals were taken in a coplanar geometry. Data from the 3a1 and 1e1 orbitals were also obtained in a perpendicular plane geometry. The data are compared to predictions from the distorted wave Born approximation and molecular-three-body distorted wave models. The cross sections for the 3a1 and 1e1 orbitals that have p-like character were found to be similar, and were different to that of the 2a1 orbital which has s-like character. These observations are not reproduced by theory, which predicts the structure of the TDCS for all orbitals should be similar. Comparisons are also made to results from experiment and theory for the iso-electronic targets neon and methane.

Strong Dynamical Screening of the ( e, 2e) Processes for Electron Impact Ionization of Helium in the Perpendicular Plane Symmetric Geometry

We apply BBK, DS3C model and the new modified Sommerfeld parameters of the present DS3C model to calculation of the triple differential cross sections (TDCS) for electron impact ionization of helium in the perpendicular plane symmetric geometry. The results of the present are compared with the measurements and those of other theoretical models. It was found that the present results give a better description for the experimental data and the dynamical screening effects are strong in this geometry. The influence of the Sommerfeld parameters on the triple differential cross sections is also analyzed and discussed in the perpendicular plane geometry.

C6+-impact ionization of helium in the perpendicular plane: Ionization to the ground state, excitation-ionization, and relativistic effects

In search of the discrepancy between theory and experiment in perpendicular plane geometry for C{sup 6+} ionization of He at 100 MeV/amu, we have used the first and second Born approximations to examine whether ionization to an excited He{sup +} state could be significant, whether relativistic effects could be important, and whether there is substantive sensitivity to the He wave functions used in the calculations. We fail to find any explanation of the discrepancy. Of the three possibilities, only relativistic effects turn out to be significant but then only in changing the overall normalization of the cross section, not in changing its shape, which is a prerequisite to getting agreement with experiment. The second Born calculations are in excellent accord with previous impact parameter coupled pseudostate results [Phys. Rev. A 81, 042704 (2010)] and confirm, yet again, that elastic scattering of the projectile by the target nucleus cannot explain the discrepancy. The calculations are extended to the lower impact energy of 2 MeV/amu. Here, in perpendicular plane geometry, ionization to excited He{sup +} states becomes significant and we find an interesting ''oscillatory'' structure in both the ground- and excited-state cross sections. Comparison is made with some relative experimental data and,more » although the agreement is poor, possibly because of the need to include experimental resolutions, there are nuances in the data that mirror the structures in the calculations.« less

Coincidence studies of He ionized byC6+,Au24+, andAu53+

A recently developed [Phys. Rev. A 79, 042707 (2009)] impact parameter coupled pseudostate approximation (CP) is applied to calculate triple differential cross sections for single ionization of He by ${\mathrm{C}}^{6+}$, ${\mathrm{Au}}^{24+}$, and ${\mathrm{Au}}^{53+}$ projectiles at impact energies of $100$ and 2 MeV/amu for ${\mathrm{C}}^{6+}$ and $3.6$ MeV/amu for ${\mathrm{Au}}^{24+}$ and ${\mathrm{Au}}^{53+}$. For ${\mathrm{C}}^{6+}$, satisfactory, but not perfect, agreement is found with experimental measurements in coplanar geometry, but there is substantial disagreement with data taken in a perpendicular plane geometry. The CP calculations firmly contradict a projectile-nucleus interaction model which has been used to support the perpendicular plane measurements. For ${\mathrm{Au}}^{24+}$ and ${\mathrm{Au}}^{53+}$, there is a complete lack of accord with the available experiments. However, for ${\mathrm{Au}}^{24+}$ the theoretical position appears to be quite firm with clear indications of convergence in the CP approximation and very good agreement between CP and the completely different three-distorted-waves eikonal-initial-state (3DW-EIS) approximation. The situation for ${\mathrm{Au}}^{53+}$ is different. At the momentum transfers at which the measurements were made, there are doubts about the convergence of the CP approximation and a factor of 2 difference between the CP and 3DW-EIS predictions. The discord between theory and experiment is even greater with the experiment giving cross sections a factor of 10 larger than the theory. A study of the convergence of the CP approximation shows that it improves rapidly with reducing momentum transfer. As a consequence, lower-order cross sections than the triple are quite well converged and present an opportunity for a more reliable test of the experiment.

Three-body coupling for electron impact ionization of helium in the perpendicular plane geometry

Dynamically screened three-Coulomb-wave (DS3C) model is applied to study single ionization of helium by 102 eV electron impact. Fully differential cross sections (FDCS) are calculated at different scattering angle of (8°, 10°, 15°, 20°) in the perpendicular plane asymmetric geometry. The results are compared with experimental data and theoretical predictions from a three-Coulomb wave function (3C) approach, convergent close-coupling calculation (CCC), as well as second-order distorted-wave Born method (DWB2). It is shown that three-body coupling effects are important for the perpendicular plane geometry.

The effect of dynamical screening on helium (e, 2e) fully differential cross-sections

This paper presents the fully differential cross sections (FDCS) for 102eV electron impact single ionization of helium for both the coplanar and perpendicular plane asymmetric geometries within the framework of dynamically screened three-Coulomb-wave theory. Comparisons are made with the experimental data and those of the three-Coulomb wave function model and second-order distorted-wave Born method. The angular distribution and relative heights of the present FDCS is found to be in very good agreement with the experimental data in the perpendicular plane geometry. It is shown that dynamical screening effects are significant in this geometry. Three-body coupling is expected to be weak in the coplanar geometry, although the precise absolute value of the cross section is still sensitive to the interaction details.

Fully differential cross sections for 102eV electron-impact ionization of helium in non-coplanar geometry

DS3C model is applied to study single ionization of helium by 102eV electron impact. Fully differential cross sections are calculated at different scattering angles of θ1 (8°，10°，15°，20°) for the perpendicular plane geometry. The results of 3C and CCC model were compared with experimental data, which sho ws that DS3C model can give a successful description of the (e，2e) process for noncoplanar geometry qualitatively，indicating the existence of strong dynamic correlations effect between the three particles in the final channel for noncoplanar geometry.

Triple differential cross-sections of Ne (2s 2 ) in coplanar to perpendicular plane geometry

The distorted wave Born approximation (DWBA) with the spin averaged static exchange potential has been used to calculate the triple differential cross-sections (TDCSs) for Ne (2s 2) ionization by electron impact in coplanar to perpendicular plane symmetric geometry at 110.5 eV incident electron energy. The present theoretical results at gun angles \(\Psi = 0^\circ\) (coplanar symmetric geometry) and \(\Psi = 90^\circ\) (perpendicular plane geometry) are in satisfactory agreement with the available experimental data. A deep interference minimum appears in the TDCS in the coplanar symmetric geometry and a strong peak at scattering angle \(\xi = 90^\circ\) caused by the single collision mechanism has been observed in the perpendicular plane geometry. The TDCSs at the gun angles \(\Psi = 30^\circ\), and \(\Psi = 60^\circ\) are predicted.

(e,2e)triple-differential cross sections of helium and argon at 64.6 eV

The distorted-wave Born approximation with spin averaged static exchange potential and modified semiclassical exchange potential has been used to calculate the triple-differential cross section of He (1s 2 ) and Ar (3p 6 ) in the coplanar to perpendicular plane geometry. Similar to helium a strong interference minima in the cross section has been observed for the argon atom for all the incident electron angles. The triple-differential cross section in the case of argon at low- and high-scattering angles is in very good agreement with the present experiment. Inclusion of postcollision interaction gives a dip at 45° (characteristic feature of p-orbital targets), which has not been observed exactly at 45° by the experiment and calculations without postcollision interaction. The agreement with experiment in case of helium is quite good, but in the case of argon, some discrepancies are still there.

The triple differentialcross sections of ionic targets in the coplanar to perpendicularplane geometry

The distorted wave Born approximation with spin averaged staticexchange potential has been used to calculate the tripledifferential cross sections of Li+(1s2),Rb+(4p6), Cs+(5p6), Cu+(3d10)and Ag+(4d10) ions in the coplanar to perpendicularplane geometry. The incident electron energy has been chosen at40 eV above the ionization potential. The calculations have beencarried out with three sets of detection energies for theoutgoing electrons, namely (20, 20 eV) symmetric, (15, 25 eV)asymmetric and (5, 35 eV) highly asymmetric. The incidentelectron angle has been varied from 0° (coplanarsymmetric geometry) to 90° (perpendicular plane geometry)with angular increments of 22.5°. The effect of post-collision interaction has also been studied. An interferencedip in the cross section has been noticed for each target. Inthe perpendicular plane geometry it has been seen that Zhanget al's model is applicable only to the targets with s- andp-orbital electrons.

Geometry effects on the(e,2e)triple differential cross sections ofLi+,Na+,andK+

The three-body distorted-wave Born and impulse approximations with spin-averaged static exchange potential have been used to calculate the electron-impact triple-differential ionization cross sections (TDCS's) of ${\mathrm{Li}}^{+},$ ${\mathrm{Na}}^{+},$ and ${\mathrm{K}}^{+}$ ions in different geometries and kinematics. In coplanar geometry at high incident energy (>500 eV) and scattering angle $\ensuremath{\sim}10\ifmmode^\circ\else\textdegree\fi{},$ both recoil and binary peaks split into two in case of p-electron targets $({\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ ions). In noncoplanar geometry a strong interference resulting in a dip in TDCS's has been noticed. In the perpendicular plane geometry, single- and double-scattering mechanisms together produce an oscillatory structure in the TDCS's of a ${\mathrm{K}}^{+}$ ion. The values of the binary-to-recoil peak ratio for specific values of the momentum transfer have been determined to understand collision dynamics.

PCI, polarisation and exchange effects in (e,2e) collisions

The role of post-collisional, polarisation and exchange effects in energy sharing (e,2e) collisions is considered. Methods of including such effects are assessed. Results are presented for the ionisation of hydrogen and helium gases in coplanar geometry. Results are also presented for the ionisation of helium, argon and xenon in perpendicular plane geometry

Evolution from the coplanar to the perpendicular plane geometry of helium (e,2e) differential cross sections symmetric in scattering angle and energy.

Experimentally determined differential cross sections are presented for the (e,2e) process in helium, in which the two outgoing electrons have the same energy and the same scattering angle with respect to the incident beam. At four incident energies from 20 to 50 eV above the ionization threshold the detection plane defined by the outgoing electrons was varied from being coplanar with the incident beam to being perpendicular to the beam. The differential cross section evolves from a two-peak structure in coplanar geometry to a three-peak structure in the perpendicular plane. At the lowest energy the forward-scattering coplanar peak is smaller than the backscatter peak, in contrast to the results at higher energies. A deep minimum is seen at an intermediate plane angle of 67.5\ifmmode^\circ\else\textdegree\fi{}, this minimum being deepest at 40 eV above the ionization threshold. The results are normalized to an absolute scale using previous coplanar measurements as discussed in the text. The spectrometer used to collect these results is fully computer controlled and real-time computer optimized.

Distorted-wave Born approximation calculations of (e, 2e) reactions

The distorted-wave Born approximation (DW-BA) is discussed and samples of calculations are presented for ionization of the 2p inner shell of Ar, the 5p, 5s and 4d shells of Xe, and for ionization of He in asymmetric perpendicular plane geometry. Agreement with measurements of inner shell ionization of Ar is excellent. It is pointed out that triple differential cross sections for ionization of heavy atoms can exhibit much structure, which presents a challenge to both theory and experiment. Particular cases of 5s and 4d ionization of Xe are given as examples of situations worthy of experimental investigation. Comparison is made with very recent measurements of ionization of He in asymmetric perpendicular plane geometry. In agreement with experiment, DWBA shows at all incident energies a single main peak at φ=180°, where φ is the angle between the outgoing electrons. It is demonstrated that at high energies this peak arises from a double collison mechanism. This contrasts with energy-sharing ionization into the perpendicular plane where the double collision mechanism, dominant at high energies, gives a peak at φ=90°, and where with reducing energy this peak is replaced by one at φ=180° coming from the single collision mechanism. Suggestions are made for further experiments.