Triply Differential Cross Section Research Articles

Deep Minima in the Triply Differential Cross Section for Ionization of Atomic Hydrogen by Electron and Positron Impact

We investigate ionization of atomic hydrogen by electron- and positron-impact. We apply the Coulomb–Born (CB1) approximation, various modified CB1 approximations, the three body distorted wave (3DW) approximation, and the time-dependent close-coupling (TDCC) method to electron-impact ionization of hydrogen. For electron-impact ionization of hydrogen for an incident energy of approximately 76.45 eV, we obtain a deep minimum in the CB1 triply differential cross section (TDCS). However, the TDCC for 74.45 eV and the 3DW for 74.46 eV gave a dip in the TDCS. For positron-hydrogen ionization (breakup) we apply the CB1 approximation and a modified CB1 approximation. We obtain a deep minimum in the TDCS and a zero in the CB1 transition matrix element for an incident energy of 100 eV with a gun angle of 56.13 ° . Corresponding to a zero in the CB1 transition matrix element, there is a vortex in the velocity field associated with this element. For both electron- and positron-impact ionization of hydrogen the velocity field rotates in the same direction, which is anticlockwise. All calculations are performed for a doubly symmetric geometry; the electron-impact ionization is in-plane and the positron-impact ionization is out-of-plane.

Doubly and Triply Differential Cross Sections for Single Ionization of He by Fast Au53+ Using a Multi-Body Quasiclassical Model

A multi-body multi-center quasiclassical model was used to determine doubly- and triply-differential cross sections following single ionization in 3.6 MeV/amu Au53+ + He collisions. The present model improved recent calculations, in which free electrons were added in the collision to reproduce, at least qualitatively, the experimental binary peak. In the present calculations, the electrons, that were assumed to originate from the collisions of Au53+ with surfaces before colliding with the He target, were now considered to be in the field of the projectile, with nearly the same velocity. The agreement between the calculations and the experiment was improved, for both the doubly- and the triply-differential cross sections and was better than previous calculations based on quantum mechanics.

Deep minima in the Coulomb-Born triply differential cross sections for ionization of helium by electron and positron impact

Previously, a deep minimum in the measurements of the triply differential cross section (TDCS) for electron-helium ionization at an incident energy of 64.6 eV was interpreted in terms of a vortex. We apply the Coulomb-Born (CB1) and modified CB1 approximations to this process at the same incident energy and obtain a deep minimum whose position is in reasonable accord with time-dependent close-coupling results and experimental data. We also obtain the deep minimum in the TDCS that was measured for an energy of 74.6 eV. For both incident energies, but at slightly different gun angles to those used experimentally, we obtain a very deep minimum in the TDCS that is related to a vortex in the velocity field associated with the CB1 transition matrix element. We determine for energies of 44.6 eV–79.6 eV the gun and polar angles for a deep minimum in the CB1 TDCS. We apply both approximations to positron-helium ionization. For an incident energy of 205.25 eV we find a deep minimum in the TDCS that is related to a vortex in the velocity field associated with the CB1 transition matrix element.

Theoretical study of (e, 2e) triple-differential cross sections for DNA component ionization by electrons and positrons

We report in this work a theoretical study of the electron- and positron-induced ionization of DNA components, namely, the thymine and the tetrahydrofuran (THF) molecules. Triply differential cross sections (TDCSs) are calculated in a coplanar geometry by using the second order distorted wave Born approximation (DWBA2). The current calculations exhibit a satisfactory agreement with the experimental measurements performed at a projectile energy E0 = 250 eV for electron impact ionization of specific target orbitals of thymine and THF. Besides, significant differences were observed between electron and positron TDCSs.

Low energy electron and positron impact differential cross sections for the ionization of water molecules in the coplanar and perpendicular kinematics.

We report here triply differential cross sections (TDCSs) for 81 eV electron and positron-impact ionization of the combined (1b1 + 3a1) orbitals of the water molecule by using the second-order distorted wave Born approximation (DWBA2) for ejection electron and positron energies of 5 eV and 10 eV and different momentum transfer conditions. The electron-impact TDCS will be compared with the experimental data measured by Ren et al. [Phys. Rev. A 95, 022701 (2017)] and with the molecular 3-body distorted wave (M3DW) approximation results in the scattering plane as well as the perpendicular plane. The DWBA2 results are in better agreement with the experiment than the M3DW results for the scattering plane, and the M3DW results are somewhat better for the perpendicular plane. This observation is explained in terms of collision interactions. The electron and positron TDCSs are indistinguishable in the scattering plane. In the perpendicular plane, the positron results are similar in shape, but smaller in magnitude. However, the difference reduces with increasing projectile scattering angle and increasing ejected electron energy.

Triply differential measurements of single ionization of argon by 1-keV positron and electron impact

By establishing coincidences between target ions and scattered projectiles, and coincidences between target ions, scattered projectiles, and ejected electrons, triply differential cross-section (TDCS) information was generated in terms of projectile energy loss and scattering angles for interactions between 1-keV positrons and electrons and Ar atoms. The conversion of the raw experimental information to the TDCS is discussed. The single-ionization TDCS exhibits two distinguishable regions (lobes) where binary and recoil interactions can be described by two peaks. A comparison of the positron and electron impact data shows that the relative intensity of both binary and recoil interactions decreases exponentially as a function of the momentum transfer and is larger when ionization is induced by positron impact, when compared with electron impact.

Differential Cross Sections for Ionization of Argon by 1 keV Positron and Electron Impact

Differential information was generated by establishing coincidences and imposing conditions on data recorded for target ions, scattered projectiles, and ejected electrons, as a function of projectile energy loss and scattering angles; in order to describe the interaction between a positron (electron) 1 keV beam and a simple Ar jet. Single ionization triply differential cross section (TDCS) results exhibit two distinct regions (lobes) for which binary (events arising from 2-body interaction) and recoil (events which can only be produced by many-body interactions) interactions are associated. Results indicate that binary events are significantly larger for positron impact, in accordance with theoretical predictions. A similar feature is found for different energy losses and scattering angles. Intensity of the recoil lobe for both projectiles, positron and electron, is observed to depend on the energy loss and scattering angle. Also, it can be noticed that for positron impact the recoil interactions intensity is larger than that observed for electron impact.

A four-body approach to electron-impact single ionization of helium atoms

A four-body approach based on the three-Coulomb distorted wave (3CDW) model is applied to study of the electron-impact single ionization of helium atoms. Triply differential cross sections (TDCS) are calculated for different values of the incident and ejection energies and various amounts of the scattering angles. The ejection angular distribution of the TDCS in general exhibits two peaks, binary and recoil peaks. The obtained results are compared with the available experimental data as well as other theoretical predictions. The comparison shows a good agreement between the present calculations and the measurements. Also, the obtained results are compatible with the other theories.

(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.

Two-photon double ionization of the H2molecule: Cross sections and amplitude analysis

We perform time-dependent calculations of triply differential cross sections (TDCS) of two-photon double-electron ionization of the aligned H${}_{2}$ molecule. Our TDCS results for equal energy sharing between photoelectrons agree quite well with a recent time-dependent calculation by Guan et al. [X. Guan, K. Bartschat, and B. I. Schneider, Phys. Rev. A 77, 043421 (2008)] who employed a slightly different numerical technique. We supplement these studies by calculating TDCS at an unequal energy sharing and by generating symmetrized ionization amplitudes.

Differential cross sections for single ionization of H2 by 75keV proton impact

We have calculated Triply differential cross sections (TDCS) and doubly differential cross sections (DDCS) for single ionization of H2 by 75 keV proton impact using the molecular 3 body distorted wave Eikonal initial state (M3DW-EIS) approach. Previously published measured DDCS-P (differential in the projectile scattering angle and integrated over the ejected electron angles) found pronounced structures at relatively large angles which were interpreted as an interference resulting from the two-centered potential of the molecule.

Comparison of Experiment and Theory for Electron Impact Ionization of Isoelectronic Atoms and Molecules

Experimental and Theoretical Triply Differential Cross sections will be presented for low energy electron impact ionization of Ne, CH4, and NH3. The collision mechanisms responsible for the various structures found in the cross sections will be discussed.

Effects of photon momentum in nonrelativistic(γ,2e)processes

We study the effects of nonzero photon momentum on the triply differential cross section (TDCS) for ($\ensuremath{\gamma},2e$) processes. Due to the low value of the photon momentum, these effects are weak and manifest only in special kinematical conditions such as the back-to-back emission of the electrons with equal energy sharing. Helium and a few light heliumlike ions are treated in detail. Quite unexpectedly, the magnitude of these effects is maximal for relatively small photon energies. However, although this effect on the TDCS remains rather small, of the order of a few mb eV${}^{\ensuremath{-}1}$ sr${}^{\ensuremath{-}2}$, it is sufficient to be observed experimentally.

Second-Order Born Effect in Single Ionization of Argon by Electron Impact

We extend the standard distorted wave Born approximation (DWBA) to include the second-order Born amplitude in order to describe the multiple interactions between a projectile and an atomic target. Both the first- and second- order DWBA models are used to calculate triply differential cross sections (TDCS) of coplanar (e, 2e) on atomic argon with the scattered electron energy fixed at 500 eV, the scattering angle at 6° and the ejected electron energies at 37, 74 and 205 eV. Overall agreements with experimental measurements have been obtained in shape, and the second-order DWBA model improves the calculations as expected, especially for recoil peak of TDCS.

Triply differential cross-sections for single ionization of sodium by electron impact in doubly symmetric geometry

Dynamically screened three-Coulomb-wave model (DS3C) is used to study the single ionization of the 3S orbital of sodium by electron impact. Triply differential cross-sections (TDCSs) are calculated in doubly symmetric geometry at excess energies of 6, 10, 15, 20, 30, 40, 50 and 60 eV using a parameterized optimized effective potential. Comparisons are made between recently experimental data and theoretical predictions of the three-Coulomb wave function (3C) approach and distorted-wave Born approximation (DWBA). The angular distribution of the present TDCS is found to qualitatively reproduce the reported experimental data. It is shown that dynamically screened effects are important in this geometry.

Electron-impact ionization of atomic hydrogen: dynamical variational treatment

A simple and straightforward calculating scheme is proposed for electron-impact single and multiple ionization of atoms. The method is based on the application of the Hulthen-Kohn dynamical variational principle. An effective charge seen by the scattered electron is determined for a certain type of trial wave functions mathematically in a rigorous way excluding any empirical assumptions. Validity of the elaborated approach is assessed by calculating triply differential cross section (TDCS) for electron-impact ionization of hydrogen. It is shown that, inclusion of the effective charge into the calculation reduces height of a “binary peak” in comparison with the first Born approximation result. The height of a “recoil peak” depends on the sign of the effective charge. The calculated TDCS are compared with the available experimental data and with the results of sophisticated theories and agreement is found.

Effects of dynamical screening on single ionization of sodium by electron impact in doubly symmetric geometry

A dynamically screened three-Coulomb-wave model (DS3C) is applied to study the single ionization of sodium by electron impact. Triply differential cross sections (TDCS) are calculated in doubly symmetric geometry at excess energies of 6, 10, 15, 20, 30, 40, 50, and 60 eV. Comparisons are made among DS3C and the latest experimental data and such theoretical predictions as the three--Coulomb--wave function approach, the distorted-wave Born approximation, and the nonperturbative convergent close-coupling method. The angular distribution and relative magnitude of the present TDCS are found to qualitatively reproduce the reported experimental data. It is shown that dynamically screened effects are important in the geometries studied here.

Differential cross sections for single ionization of H2by 75-keV proton impact

We have calculated triply differential cross sections (TDCS) and doubly differential cross sections (DDCS) for single ionization of H{sub 2} by 75-keV proton impact using the molecular three-body distorted-wave-eikonal initial-state (M3DW-EIS) approach. Previously published measured DDCS (differential in the projectile scattering angle and integrated over the ejected electron angles) found pronounced structures at relatively large angles that were interpreted as an interference resulting from the two-centered potential of the molecule. Theory treating H{sub 2} as atomic H multiplied by a molecular interference factor only predicts the observed structure when assumptions are made about the molecular orientation. Here we apply the M3DW-EIS method, which does not rely on such an ad hoc approach, but rather treats the interference from first principles.

The role of projectile interactions in triply differential cross sections for excitation–ionization of helium

We report triply differential cross section (TDCS) for the simultaneous excitation–ionization of helium by electron impact for both coplanar and non-coplanar geometry. In the coplanar case, calculations have been performed for an incident energy of 500 eV and low ejection energies (3 and 10 eV), whereas in the noncoplanar case we have considered impact energies in the range 1240–4260 eV for a symmetric geometry. The present calculation is based on the eikonal approximation due to Glauber. We have incorporated the effect of post-collision interaction in the Glauber approximation. A comparison is made of the present calculations with the results of other theoretical methods and recent experiments. The Glauber results are in reasonably good agreement with the experiment for small scattering angles.

Hybrid orbital and numerical grid representation for electronic continuum processes: Double photoionization of atomic beryllium

A general approach for ab initio calculations of electronic continuum processes is described in which the many-electron wave function is expanded using a combination of orbitals at short range and the finite-element discrete-variable representation (FEM-DVR) at larger distances. The orbital portion of the basis allows efficient construction of many-electron configurations in which some of the electrons are bound, but because the orbitals are constructed from an underlying FEM-DVR grid, the calculation of two-electron integrals retains the efficiency of the primitive FEM-DVR approach. As an example, double photoionization of beryllium is treated in a calculation in which the $1{s}^{2}$ core is frozen. This approach extends the use of exterior complex scaling (ECS), successfully applied to helium and ${\mathrm{H}}_{2}$, to calculations with two active electrons on more complicated targets. Integrated, energy-differential and triply-differential cross sections are exhibited, and the results agree well with other theoretical investigations.