Triple Differential Cross Sections Research Articles

First-order distorted wave Born approximation for single ionization of Ar by electron impact in a coplanar doubly symmetric geometry

The first-order distorted wave Born approximation (DWBA) has been performed for single ionization of Ar(3p) by electron impact in coplanar doubly symmetric geometry from near threshold to intermediate energies. Theoretical triple differential cross sections (TDCS) are compared with the latest experimental data. It is found that when the incident electron energies are 40 eV higher than the ionization threshold, for argon, the binary and recoil collision mechanism will dominat as the energies increase, but not in the near threshold energy regime, where the distortion effects are of great significance. In order to completely describe the electron impact ionization of argon, it is imperative that more scattering mechanisms should be considered in the theoretical models.

Ionization of Metastable 2P-State Hydrogen Atoms by Electron Impact for Coplanar Asymmetric Geometry

The triple differential cross-sections of First Born approximation have been calculated for ionization of metastable 2P-state hydrogen atoms by electron impact in the asymmetric coplanar geometry. In this study a multiple scattering theory of ionization of hydrogen atoms is used. The latest results of the present method are compared with other calculations. It will be added for new experimental study of ionization of hydrogen atoms in their metastable states.

One-photon double ionization of H2with arbitrary orientation

We investigate the one-photon double ionization of H${}_{2}$ by numerically solving the time-dependent Schr\"odinger equation (TDSE) in the prolate spheroidal coordinates. The triple differential cross sections (TDCS) are extracted from the differential probability by three different methods. The dependence of the TDCS on the orientation of H${}_{2}$ is analyzed by a configuration interference model. The model perfectly reproduces the TDSE results. The obvious interference patterns are observed when the angle between the laser polarization and the molecular axis is properly small. In addition, we revisit the heliumlike model by including the phase difference, which gives a much better fitting of the TDSE results than the previous model without the phase difference taken into account.

Measurement of the differential cross section of photon plus jet production inpp¯collisions ats=1.96 TeV

We study the process of associated photon and jet production, p (p) over bar -> gamma + jet + X, using 8.7 fb(-1) of integrated luminosity collected by the D0 detector at the Fermilab Tevatron Collider at a center-of-mass energy root s = 1.96 TeV. Photons are reconstructed with rapidity vertical bar y(gamma)vertical bar 20 GeV. The highest-p(T) jet is required to be in one of four rapidity regions up to vertical bar y(jet)vertical bar 0) and opposite signs (y(gamma)y(jet) <= 0) of photon and jet rapidities. We compare the measured triple-differential cross sections, d(3)sigma/dp(T)(gamma)dy(gamma)dy(jet), to next-to-leading order (NLO) perturbative QCD calculations using different sets of parton distribution functions, and to predictions from the SHERPA and PYTHIA Monte Carlo event generators. The NLO calculations are found to be in general agreement with the data but do not describe all kinematic regions.

The effect of wave function orthogonality on the simultaneous ionization and excitation of helium

Within the framework of the first-order Born approximation, the triple differential cross sections (TDCSs) for simultaneous ionization and excitation of helium are calculated. The wave function of the ejected electron is chosen to be orthogonal or non-orthogonal to the wave function of the bound electron before ionization. It is found that the orthogonality has a strong effect on the TDCS, especially when plane waves and Coulomb waves are used to describe the projectile and the ejected electron.

(e, 2e) Investigations of the Simultaneous Ionization and Excitation of Helium to He+(n=2)

Three‐Coulomb‐wave method is employed to treat the process of (e, 2e) simultaneous ionization and excitation to the n=2 state of helium, with radial and angular correlated wave‐function of He target. The triple differential cross sections are calculated and analyzed in very asymmetric coplanar geometry at incident energies of 5.50, 1.50 and 0.57 keV. Results are compared with the absolute measurements and the theoretical first and second Born approximation. The present triply differential cross section (TDCS) is found to be in good agreement with experimental data qualitatively. The distinguishing feature noted in TDCS structure is the presence of intense recoil peak that for certain parameters is even larger than the binary peak, an unusual feature for the single‐ionization process at high and intermediate energies.

A dynamical (e,2e) investigation of the structurally related cyclic ethers tetrahydrofuran, tetrahydropyran, and 1,4-dioxane

Triple differential cross section measurements for the electron-impact ionization of the highest occupied molecular orbitals of tetrahydropyran and 1,4-dioxane are presented. For each molecule, experimental measurements were performed using the (e,2e) technique in asymmetric coplanar kinematics with an incident electron energy of 250 eV and an ejected electron energy of 20 eV. With the scattered electrons being detected at -5°, the angular distributions of the ejected electrons in the binary and recoil regions were observed. These measurements are compared with calculations performed within the molecular 3-body distorted wave model. Here, reasonable agreement was observed between the theoretical model and the experimental measurements. These measurements are compared with results from a recent study on tetrahydrofuran [D. B. Jones, J. D. Builth-Williams, S. M. Bellm, L. Chiari, C. G. Ning, H. Chaluvadi, B. Lohmann, O. Ingolfsson, D. Madison, and M. J. Brunger, Chem. Phys. Lett. 572, 32 (2013)] in order to evaluate the influence of structure on the dynamics of the ionization process across this series of cyclic ethers.

Triple-differential cross section for single ionization of H2 by electron impact

The triple-differential cross section (TDCS) for the (e, 2e) ionization of a hydrogen molecule is calculated using the molecule distorted-wave Born approximation (MDWBA). Distorted waves are obtained by solving momentum-space coupled-channel Lippmann—Schwinger equations, including the ground state and the lowest-lying electronic state of b3Σu. TDCSs at the incident energy 100 eV in coplanar asymmetric geometry are reported. The present calculations are compared with the available experimental measurements and the theoretical results.

Nuclear-recoil differential cross sections for the two-photon double ionization of helium

The time-dependent close-coupling method is used to calculate fully differential cross sections for the two-photon double ionization of the He($1{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}^{e}$) ground state at a photon energy of 44 eV and the He($1s2s{\phantom{\rule{0.16em}{0ex}}}^{1,3}{S}^{e}$) excited states at a photon energy of 34 eV. The total and triple-differential cross sections for the ground state are in good agreement with available calculations. We also used the time-dependent close-coupling method to calculate fully differential nuclear-recoil cross sections of He${}^{2+}$ for the two-photon double ionization of He in the ground and excited states at the same photon energies. The nuclear-recoil differential cross sections of He${}^{2+}$ for the ground state are in good agreement with the measurements recorded with a reaction microscope at the free-electron laser facility in Hamburg (FLASH).

Second-order Born effects in the coplanar to perpendicular plane single ionization of Xe (5p)

Differential cross section results for the coplanar to perpendicular plane ionization of xenon atoms at incident electron energies of 40 and 20 eV above ionization potential are reported. The cross sections have been calculated in the modified distorted wave Born approximation (DWBA) formalism including the second-order Born amplitude. Our present attempt verifies the role of second-order processes in the ionization of xenon atoms at low and intermediate energy ranges. We compare the (e, 2e) triple differential cross section results of our calculation with the very recent measurements of Nixon and Murray (2012 Phys. Rev. A 85 022716) and relativistic DWBA-G results of Illarionov and Stauffer (2012 J. Phys. B: At. Mol. Opt. Phys. 45 225202). Overall agreement with measurements has been improved by inclusion of a second-order term in the description of the collision process.

Ionization of a water molecule by electron impact in coplanar symmetric and asymmetric geometries

Our previous analytical formalism developed in the second Born approximation is completed by the exchange effect between the free outgoing electrons. This formalism is used to predict the triple differential cross sections for the single ionization of a water molecule by electron impact. The results are compared to previous experimental and theoretical findings given in coplanar symmetric and asymmetric geometries. Good agreement with the experiment is given by the present formalism. The discussion of the present results can be used to improve the different models used to study the ionization of a water molecule by charged particles.

Experimental and theoretical investigation of (e, 2e) ionization of Ar(3p) in asymmetric kinematics at 200 eV

Experimental and theoretical studies of electron impact ionization of the 3p orbital of argon are reported. The relative triple-differential cross sections were measured in the coplanar asymmetric geometry. The experimental data at an incident electron energy of 200 eV, ejected electron energies of 15 and 20 eV, and scattering angles of −10°, −15°, and −20° were obtained using a conventional crossed-beam (e, 2e) spectrometer. The experimental data are compared with predictions from first- and second-order hybrid distorted-wave plus R-matrix models, as well as a fully nonperturbative B-spline R-matrix approach.

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.

Dynamical (e,2e) investigations of tetrahydrofuran and tetrahydrofurfuryl alcohol as DNA analogues

Triple differential cross section measurements for the electron-impact ionization of the highest occupied molecular orbital of tetrahydrofuran (THF) are reported. Experimental measurements were performed using the (e,2e) technique in asymmetric coplanar kinematics with an incident electron energy of 250eV and an ejected electron energy of 20eV. With the scattered electrons being detected at −5°, the angular distribution of the ejected electrons was observed. These measurements are compared with calculations performed within the molecular 3-body distorted wave (M3DW) model, and against previous measurements on THF and tetrahydrofurfuryl alcohol to further understand the role that kinematics and structure play in electron-impact ionization.

Extension of the multiconfiguration Hartree-Fock method to allow double photoionization of atoms

Very recently we were successful in extending the multiconfiguration Hartree-Fock (MCHF) method for electron-impact ionization of atoms to allow double photoionization of atoms. We report, as a test case, the results of our calculation of the triple differential cross section (TDCS) for double photoionization of helium. We have calculated the initial state in the Hartree-Fock and the MCHF approximations and the final state in the Coulomb approximation and the screening potential approximation in order to compare with previously published works. We compare the present results calculated at 30-eV excess photon energy shared equally by two final-state continuum electrons, with other similar theoretical calculations. Finally, we also calculate the TDCS at 20-eV excess photon energy to compare with experimental observation.

Electron-impact ionization of neon at low projectile energy: an internormalized experiment and theory for a complex target.

As a fundamental test for state-of-the-art theoretical approaches, we have studied the single ionization (2p) of neon at a projectile energy of 100eV. The experimental data were acquired using an advanced reaction microscope that benefits from high efficiency and a large solid-angle acceptance of almost 4π. We put special emphasis on the ability to measure internormalized triple-differential cross sections over a large part of the phase space. The data are compared to predictions from a second-order hybrid distorted-wave plus R-matrix model and a fully nonperturbative B-spline R-matrix (BSR) with pseudostates approach. For a target of this complexity and the low-energy regime, unprecedented agreement between experiment and the BSR model is found. This represents a significant step forward in the investigation of complex targets.

Ab initio calculation of double ionization of atoms

The Solov’ev-Vinitsky method was used to perform an ab initio calculation of the triple-differential cross section for the double single-photon photoionization of helium for the case of equal emitted-electron energies. A Gaussian width γ describing angular electron-electron correlations at the total electron energy E taking values in range between 0.1 and 100 eV was obtained for this cross section. The results agree with available experimental data, but they raise a doubt as to whether the well-known Wannier law γ ∝ E1/4 is applicable at experimentally accessible energies. The Gaussian width γ was investigated as a function of the total emitted-electron energy for targets that have a strongly asymmetric configuration of the initial state—specifically, a negative atomic-hydrogen ion H− and heliumin the 1s2s1S and 1s3s1S excited states. It was found that this function, γ(E), had a maximum at low energies. It was also shown that, at low energies, the dependence of the double-differential cross section on the angle between the emitted-electron momenta for the targets indicated above differed substantially from the Gaussian dependence, featuring maxima whose number was equal to the number of radial nodes in the initial state. This opens new possibilities for a qualitative analysis of the electron structure of targets.

A theoretical study on impulse approximation of (e, 2e) reactions

The triple differential cross sections for electron impact ionization hydrogen (e, 2e) reactions are calculated as an example by use of the impulse approximation and Born approximation model at different coplanar asymmetric geometries. The results of the present work are compared with experimental data. The structures of the cross sections and the physical nature of these structures are discussed in detail. Moreover, the exchange effect contribution to the cross section is also discussed, which supports our earlier conclusions.

Triple differential cross section for the ionization of Ar(3p) by low-energy electron impact in the coplanar asymmetric geometry

(e, 2e) triple differential cross sections for the ionization of Ar (3p) by 70.8 eV electron impact are calculated in the coplanar asymmetric geometry using the modified distorted-wave Born approximation, and compared with the recent experimental data of Ren et al. [Ren et al. 2012 Phys. Rev. A 85 032702]. The results show that electron exchange effect and post-collision interaction play an important role in the (e, 2e) process of low-energy electron impact.

TDCS calculations for the ionization of H2 by electron impact

Triple differential cross sections (TDCSs) are calculated for the ionization of the hydrogen molecule by electron impact with asymmetric and symmetric kinematical configuration, respectively in coplanar arrangement and in the plane perpendicular to the incident direction. In the scattering plane we explore the angular distribution of the TDCS as well as the dependence of the cross section on the internuclear separation. In the perpendicular plane the TDCSs are investigated as a function of the angular separation between the outgoing electrons and for an equal energy sharing between them.