Triple Differential Cross Sections For Ionization Research Articles

Triple Differential Cross-Sections for Ionization of H(3d) by Incident Electron

Triple differential cross sections (TDCS) are estimated for the ionization of metastable 3d-state hydrogen atoms by electron at 250 eV for various kinematic conditions pursuing a multiple scattering theory. The present new results are compared with the theoretical results of hydrogenic different metastable states as well as the hydrogenic ground state experimental data. Obtained new finding results are in good qualitative agreement with those of compared theories. The present results give an immense opportunity for experimental trial in the field of ionization problems.

Theoretical study of (e, 2e) process of atomic and molecular targets*

Triple differential ionization cross sections (TDCSs) by electron impact are calculated for some atomic and molecular targets by using several models where Post Collisional Interaction (PCI) is taken in account. We also investigate the effect of the short range potential and describe the ejected electron either by a Coulomb wave or by a distorted wave. Significant differences are observed between these models. A better agreement with experimental data is achieved when the short range potential and distortion effects are included.

The First Born Triple Differential Cross-Section for Ionization of H(3P) by Electron Impact in the Asymmetric Coplanar Geometry

First Born triple differential cross sections (TDCS) for ionization of metastable 3P-state hydrogen atoms by electrons are calculated for various kinematic conditions in the asymmetric coplanar geometry. A multiple scattering theory is used in this study. The present results are compared with other existing related theoretical results for ionizations of hydrogen atoms from metastable 2S-state and 2P-state, showing a good qualitative agreement. There is no available theoretical study for ionization of metastable 3P-state hydrogen atoms by electrons. We are expecting that the present results provide a wide scope for further study of such ionization problems.

Ionization of diatomic molecules by electron impact

An analytical expression for the amplitude of ionization of the hydrogen molecule by electron impact in the first Born approximation with a one-center Coulomb continuum wave function is derived. The case where the incident electron energy is much greater than the ejected electron energy is considered. The molecular wave functions were constructed in the approximation of linear combination of atomic orbitals with overlapping configurations. The role of the orthogonalization of the initial and final wave functions of the active electron of the target is elucidated. The triple differential ionization cross sections for the different orientations of the molecular axis and that averaged over all orientations are calculated. The secondary electron angular distribution is represented in the form of three-dimensional images. A comparison with the results of other theoretical calculations and experimental data is performed.

Absolute cross sections for the ionization-excitation of helium by electron impact

In a recent publication we presented detailed experimental and theoretical results for the electron-impact-induced ionization of ground-state helium atoms. The purpose of that work was to refine theoretical approaches and provide further insight into the Coulomb four-body problem. Cross section ratios were presented for transitions leading to excited states, relative to those leading to the ground state, of the helium ion. We now build on that study by presenting individual relative triple-differential ionization cross sections (TDCSs) for an additional body of experimental data measured at lower values of scattered-electron energies. This has been facilitated through the development of new electron-gun optics which enables us to accurately characterize the spectrometer transmission at low energies. The experimental results are compared to calculations resulting from a number of different approaches. For ionization leading to ${\mathrm{He}}^{+}{(1{s}^{2})}^{1}S$, cross sections are calculated by the highly accurate convergent close-coupling (CCC) method. The CCC data are used to place the relative experimental data on to an absolute scale. TDCSs describing transitions to the excited states are calculated through three different approaches, namely, through a hybrid distorted-$\text{wave}+R$-matrix (close-coupling) model, through the recently developed four-body distorted-wave model, and by a first Born approximation calculation. Comparison of the first- and second-order theories with experiment allows for the accuracy of the different theoretical approaches to be assessed and gives insight into which physical aspects of the problem are most important to accurately model.

(e, 2e) triple differential cross-sections for ionization beyond helium: the neon case at large energy transfer

We report new coplanar (e, 2e) results for ionization of the He 1s and Ne 2p and 2s subshells under kinematics which have remained rather unexplored to date and characterized by large energy transfer and close to minimum momentum transfer from the projectile to the target. The experimental results obtained in two laboratories are used as a sensitive test of a number of state-of-the-art available theoretical models for multi-electron atoms. The He results are in excellent agreement with convergent close-coupling predictions as well as with distorted-wave + Gamow and hybrid distorted-wave + R-matrix models. In the Ne case, an overall satisfactory agreement with experiments is obtained for all considered models. The importance of post-collisional interaction effects is demonstrated whereas second-order effects in the projectile-target interaction at small distances are shown to be negligibly small. Remaining discrepancies between theories and experiments are discussed.

Low-energy electron-impact single ionization of helium

A study is made of low-energy electron-impact single ionization of ground-state helium. The time-dependent close-coupling method is used to calculate total integral, single differential, double differential, and triple differential ionization cross sections for impact electron energies ranging from 32 to $45\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. For all quantities, the calculated cross sections are found to be in very good agreement with experiment, and for the triple differential cross sections, good agreement is also found with calculations made using the convergent close-coupling technique.

Multidetection (e,2e) electron spectrometer

An electron-pair coincidence spectrometer, using only a single electrostatic toroidal analyzer, has been developed for the study of final-state electron pairs following ionization by electron impact. The system allows the angular and energy distribution of electron pairs emitted in a selected plane to be detected by a single planar microchannel plate stack followed by two position-sensitive semicircular wedge-and-strip anodes. The output signals are decoded into energy, angle and nanosecond coincidence timing information from which relative energy and angular triple differential ionization cross sections are determined. The performance of the instrument is indicated by He I photoionization of krypton and the first measurements of differential cross sections for electron-impact ionization of the P3∕22 and P1∕22 states of krypton. For perpendicular-plane scattering and an excess energy of 10 eV for the P3∕22 state and 0.67 eV less for the P1∕22 state, these cross sections are significantly different for the two states and indicate the importance of the final state of the ion in the scattering process.

Electron Correlation in the Final Continuum of IonizationHydrogen by 150-eV Electron Impact

Electron correlation in triple differential cross sections forionization of atomic hydrogen by electron impact is analysed forthe case of coplanar asymmetric geometry within the framework of thetwo-potential formulae. Based on the approximations of projectile andfaster-electron plane wave, the transition matrix element isanalytically expressed to be a product of two factors: the correlationfactor of two electrons in the final channel and thestructure-scattering factor. The contribution of both the factors tothe angular distribution of the triple differential cross section iscalculated. The present results are compared with the experimental dataand the other theoretical calculations for the incident energy of 150 eV.

Triple differential cross-sections for near threshold (e, 2e) process for hydrogen

The triple differential cross-sections for ionization of hydrogen at incident energies in the range 17.6 eV to 13.7 eV are calculated in the distorted-wave Born approximation in the equal energy sharing andϑab = 180° kinematics. It is found that a maximum in the cross-section, as was observed in the case of helium under similar conditions is also found here at excess energyEex ≤ 1.0 eV. This ‘maximum’ becomes more pronounced asEex decreases indicating dominance of short rangee-e correlations at these low energies. The angular distribution of the singlet and triplet partial waves and the asymmetry parameter have been analysed.

Spin asymmetries in spatially resolved processes of ionization of heavy atoms by relativistic electrons

The triple-differential cross section for ionization of a heavy atom is shown to depend on the spin of the incident electron even if this is polarized entirely parallel or antiparallel to its direction of propagation, the atom is unpolarized, and the spins of the ejected electrons are not resolved. Quantitative predictions for the spin asymmetry are presented in a relativistic distorted-wave Born approximation. Simple physical models are introduced to understand both these results and further symmetry properties involving the reversal of a spatial momentum component also.

Theoretical and experimental investigation of the triple-differential cross sections for electron-impact ionization of Kr(4p) and Xe(5p) at 1-keV impact energy

The triple-differential cross sections for the ionization of $\mathrm{Kr}(4p)$ and $\mathrm{Xe}(5p)$ by a fast electron where the exiting electrons have energies of 20 eV and 1 keV have been measured and compared with distorted-wave Born calculations. Difficulties were encountered when trying to place the relative data on an absolute scale by extrapolation to the optical limit: an extensive study of this normalization process is presented and it is argued that it is not applicable to the heavier atoms considered here, but can be used effectively for helium targets.

Triple differential cross sections for ionization of hydrogen atoms by positrons in a Schwinger variational calculation

Schwinger variational principle has been used to calculate triple differential cross-sections for ionization of hydrogen atoms by positrons at intermediate and high energies for Ehrhardt type asymmetric geometry. The results agree in general with the calculations of Brauneret al [8] and with the second Born calculation.

Triple differential ionisation cross-section of hydrogen atom bye �-impact including exchange

The Triple Differential Cross-Sections for ionisation of hydrogen atom bye± impact are calculated including exchange effect. A correlated three-body continuum wave function is used here for the final state. Attention is paid to equal energy sharing at the final channel where scattered and ejected energies are each 200 ev., and it is found that the exchange effect is remarkably high in this case. Present electron impact results are compared with the recent work of McCarthy et al. [1].

Coplanar asymmetric (e,2e) experiments on xenon 4d and 5p orbitals.

Relative triple-differential cross sections for ionization of Xe 4[ital d] and 5[ital p] orbitals have been measured in coplanar asymmetric kinematics. The scattered-electron energy is held at 1000 eV while the ejected-electron energy is changed so as to select energy-loss values [Delta][ital E] in or out of the region characterized by the giant resonance in the 4[ital d][r arrow][var epsilon][ital f] channel. The ionization mechanism as well as the interference between the direct and resonant processes have been investigated by varying the momentum transfer in a collision at each ejected-electron energy. Strong interchannel coupling between the 5[ital p] and 4[ital d] shells in the region of the giant resonance has been observed in ([ital e],2[ital e]) experiments. Distorted-wave-Born-approximation calculations have been compared with the experimental triple-differential cross section and used to guide the discussion.

Electron-hydrogen-atom ionization collisions at intermediate (5I0-20I0) and high ( >~ 20I0) energies.

Triple-differential cross sections for ionization of hydrogen atoms by electrons have been calculated both for small- as well as large-momentum-transfer cases at intermediate (5[ital I][sub 0]--20[ital I][sub 0]) and high ([approx gt]20[ital I][sub 0]) energies ([ital I][sub 0] being the ionization potential) following a method which uses a final-channel three-particle wave function determined by one of the authors. This wave function resulted from an analysis of the three-particle wave equation in momentum space and is correct to the first order in the interaction potentials. Incidentally, it is also the first-order Faddeev wave function. The wave function has been suitably normalized before it is used. The computed results are generally good. The small-momentum-transfer results are in nice agreement with the experimental data except for a certain angular region which includes the recoil peak. The domain over which the present results agree in trend with the experimental measurements is somewhat larger than that for the distorted-wave-Born-approximation calculation. Large-momentum-transfer results are also in qualitative agreement with experiments. There are indications that quantitatively the present results may be better there. Total-ionization cross-section results are also in excellent agreement with experiment above 200-eV energy. These facts together with the simplicity of the calculation establish thatmore » the present method has certain advantages over other existing methods. The present calculation may be the starting point for a more elaborate calculation which will take into account more accurately the correlation and higher-order effects in the final-channel three-particle wave function.« less

Symmetric scattering ine ±-H ionization collisions

Triple differential cross-sections for ionization of hydrogen atoms by electrons and positrons have been calculated for symmetric coplanar geometry following a multiple scattering method suggested and used earlier by the authors. Results show single binary peaks exactly at 45° and double binary peaks exactly at 135° for higher energies as are expected from an analysis of Briggs [3]. At lower energies there are certain deviations from these values. An analysis of scattering mechanism at peaks are also given. This supports Briggs’ explanation.

Dynamic mechanisms of He single ionization by fast proton impact.

Triple-differential ionization cross sections ${\mathit{d}}^{3}$\ensuremath{\sigma}/d${\mathrm{\ensuremath{\vartheta}}}_{\mathit{p}}$${\mathit{dcphi}}_{\mathit{p}}$${\mathit{dp}}_{\mathrm{rec}}$, the momentum distributions of singly charged recoil ions transverse to the beam direction as a function of the projectile polar (${\mathrm{\ensuremath{\vartheta}}}_{\mathit{p}}$), and azimuthal (${\mathit{cphi}}_{\mathit{p}}$) scattering angle were measured in order to elucidate the dynamics of 3-MeV ${\mathrm{H}}^{+}$ on He single ionization. For projectile polar deflections 0.2 \ensuremath{\le}${\mathrm{\ensuremath{\vartheta}}}_{\mathit{p}}$\ensuremath{\le}1 mrad and azimuthal scattering angles ${0}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$\ensuremath{\le}${\mathit{cphi}}_{\mathit{p}}$\ensuremath{\le}360\ifmmode^\circ\else\textdegree\fi{}, the kinematic regimes where two-body interactions dominate the three-body momentum exchange of the single-ionization reaction were separated experimentally.

(e,2e) ionization of helium leading to the n=2 final state under asymmetric Bethe-ridge conditions

The (e,2e) triple differential cross-sections for ionization of helium leading to the ground ( n=1) and first excited ( n=2) states of the ion are measured under high energy asymmetric Bethe-ridge kinematics, at scattered and ejected electron energies of 5500 and 75 eV respectively. With respect to older experiments, the present data are free from electron distortion effects. Hence, when compared with calculations using different correlated wavefunctions, it is found that the best agreement for the n=1 to n=2 ratio is obtained with the variationally best wavefunction in energy space. This is in contrast with the experimental findings of Cook et al. [J.P.D. Cook, I.E. McCarthy, A.T. Stelbovics and E. Weigold, J. Phys. B, 17 (1984) 2339] and supports the theoretical arguments given by Smith et al. [A.D. Smith, M.A. Coplan, D.J. Chornay, J.H. Moore, J.A. Tossell, J. Mrozek, V.H. Smith, Jr. and S. Chant, J. Phys. B, 19 (1986) 969].

Triple-differential cross sections for the ionization of helium by fast electrons.

The triple-differential cross section for the single ionization of helium in the coplanar asymmetric geometry has been calculated by using a second Born approximation which employs an improved choice of the target continuum-state wave function. The contribution of still higher-order terms of the scattering amplitude is also considered via the usual Glauber approximation. The results are compared with the recent data of Jung et al. at an incident energy of 600 eV and are found to be in very good agreement with them.