Triple Differential Cross Sections Research Articles

Theoretical triple differential cross sections for ionization of N 2 and CH 4 molecules by electron impact

We present the angular distribution of electron emission by calculating the triple differential cross sections for (e, 2e) process on N 2 and CH 4 by using the three-body formalism of molecular first Born approximation (MFBA), two-Coulomb wave (M2CW), and three-Coulomb wave (M3CW) models, respectively. In these models, a Coulomb distorted wave is considered for the motion of the incident electron. We have considered the continuum-continuum correlation effect by choosing the final state as the three-Coulomb and two-Coulomb wave functions in M3CW and M2CW models, whereas the ejected electron is affected by a single centre field of the target in the MFBA model. In the M2CW model, the interaction between scattered electron-residual target ion has been described as a plane wave. The distinguishing feature among the three models has been noted in the TDCS as a strong binary peak with and without a recoil peak for several electron emission energies at fixed scattering angle. In the case of N 2 molecule, the TDCS shows oscillatory behaviour with the variation of the electron emission angle. The positions of the binary peak obtained by our theoretical models are well established by the experimental findings, but a large deviation is found in the region of the recoil peak. The contributions of TDCS for different molecular orbitals of the molecules to the spectrum of angular distributions at different electron emission energies have also been analyzed. Finally, a comparison is made with the measurement in coplanar asymmetry geometry. Overall, good agreement was found between experiments and M3CW theory.

Triple Differential Cross Sections for the Simultaneous Ionization and Excitation of He by Electron and Positron Impact

Triple Differential Cross Sections for the Simultaneous Ionization and Excitation of He by Electron and Positron Impact

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.

Laser-assisted (e,2e) study with twisted electron beam on H-atom

We study the laser-assisted twisted electron beam impact ionization of the hydrogen atom in coplanar asymmetric geometry. We develop the theoretical model in the first Born approximation. In the presence of the laser field, we treat the incident and scattered electrons as Volkov waves; the ejected electron, moving in the combined field of the laser and residual ion H+ , as a Coulomb–Volkov wave function. In this communication, we compare the angular profile of triple differential cross-section (TDCS) for laser-assisted twisted electron beam incidence with the plane-wave, laser-assisted plane wave, and field-free twisted electron beam for (e,2e) processes for different orbital angular momentum (OAM) number (ml ) values. We analyze the effect of impact-parameter b of twisted electron beam and the laser parameters on the angular distribution of the TDCS. We study the (TDCS)av for the macroscopic target to examine the effect of opening angle θ p of the twisted electron beam on the angular profile of TDCS. We also observe the influence of coherent superposition of two Bessel states on the angular profile of TDCS. Our results clearly show the effects of laser parameters (electric field ɛ and number of photon exchanged (l)) and twisted electron beam parameters (OAM number (ml ) and opening angle (θ p )) on the angular distribution of TDCS.

Electron and positron impact differential cross sections for the (e,2e) process on water molecule

We present a theoretical study for electron and positron-impact ionization of water molecule by using the three-body formalism of distorted-wave approximation. In this approximation, the final state contains one-Coulomb, two-Coulomb, and three-Coulomb distortion due to pairwise Coulombic interactions, respectively. In the entrance channel, the initial state is a product of two wavefunctions: the first one for the incident electron/positron described by a Coulomb wave and the second one for the ten bound electrons. The molecular wavefunction for these bound electrons of H2O are described by the linear combination of atomic orbitals. We investigate the angular distribution of the triple differential cross section (TDCS) for single ionization of the outer orbitals 1b1,3a1,1b2, and 2a1. The structure with two peaks around the binary and recoil region are clearly observed for 1b1, 3a1, and 1b2 orbitals. At the same time, a single peak in the binary region with no recoil peak is found for the 2a1 orbital. The present TDCS results are compared with available experimental and theoretical findings. Fair agreement regarding the structure of angular profile of the TDCS is observed for all orbitals except 2a1. Finally, an enhanced TDCS have been found for positron impact compared to the electron impact.

Coincidence measurements of photodouble ionization of benzene and thiophene.

Photodouble ionization (PDI) triple-differential cross sections (TDCSs) of benzene and thiophene have been measured in electron-electron coincidence experiments under 10-10 eV and 20-20 eV equal energy sharing conditions. A multi-Gaussian fit method has been employed to characterize the TDCSs. The trends and features observed for benzene and thiophene do highlight differences with helium most likely from molecular PDI contributions to the TDCS. A comparison with the well-known helium PDI TDCS for equal energy sharing conditions [Avaldi and Huetz J. Phys. B: At. Mol. Opt. Phys., 2005, 38, S861-S891] supported the validity of the multi-Gaussian fitting method and contextualized the benzene and thiophene fits. The molecular targets and energy sharing conditions were chosen to provide insight into the unexpected resonances observed in aromatic hydrocarbons but not aromatic heterocyclic molecules [Wehlitz et al., Phys. Rev. Lett., 2012, 109, 193001]. Contrary to the work of [Wehlitz et al., Phys. Rev. Lett., 2012, 109, 193001], no significant differences between benzene and thiophene were found.

Electron impact single ionization TDCS of H2O at 81 eV for coplanar asymmetric emission of electrons

We report the results of triple differential cross section (TDCS) for the electron impact single ionization of water molecules at incident electron energy 81 eV for coplanar asymmetric emission of electrons. The TDCS results have been obtained in distorted wave second Born approximation using orientation averaged molecular orbital (OAMO) approximation. The TDCS results have been calculated for the ionization of 1b1 and 3a1 molecular orbital of water molecules for the coplanar asymmetric emission of electrons. The obtained theoretical TDCSs are compared with the available measurements as well as with the first Born results. The second Born results are found to be significant by improving agreement with the measurements particularly in the binary peak region.

Electron impact triple differential cross sections of Xe atoms for coplanar to perpendicular plane single ionisation at 60 eV, 80 eV and 100 eV above ionisation

The evolution of the triple differential cross section (TDCS) for the electron impact ionisation of xenon atoms is reported for the variation of momentum of the projectile electron from a coplanar geometry to a perpendicular plane through intermediate angles with the detection plane. The TDCSs have been calculated for the Xe atoms at 60 eV, 80 eV and 100 eV above the ionisation potential. We have calculated the TDCS using distorted wave Born approximation, utilising both the first and second Born terms. Effects of target polarisation and post-collision interaction have also been included in the complete description of the collision dynamics. The TDCS results are compared with recent measurements by Patel et al (2022 Phys. Rev. A 105 032818) showing a dependence between the TDCS and the scattering geometry and kinematics of the collision. Second-order effects have been found significant, particularly in the description of perpendicular plane ionisation at a low energy and the effect of target polarisation has been found important in describing the coplanar ionisation of the xenon target. With an overall good agreement with the recent measurements, there are points of disagreement which are the motivation for further theoretical effort in the near future, as the present attempt is the first of its kind to analyse these measurements.

Theoretical study of (e,2e) triple differential cross section of 1b3g orbital of ethylene by vibrational multi-center distorted-wave method

The vibrational motions are usually neglected when calculating (e,2e) triple differential cross sections (TDCSs) of molecules. Here, multi-center distorted-wave method (MCDW) has been modified by including molecular vibrations. This vibrational MCDW method is employed to calculate the TDCSs of 1b3g orbital of ethylene at low (100 eV) and medium (250 eV) incident electron energies in coplanar asymmetric kinematic condition. The results show that molecular vibrations significantly influence the angular distributions of the TDCSs, especially in the binary region along momentum transfer near the Bethe ridge.

Triple differential cross sections for single ionization of an atom by bare ion impact

We present triple differential cross sections (TDCSs) for single ionization of atoms by proton and highly charged bare ions impact by means of the three-body formalism of the first Born, two-Coulomb wave and three-Coulomb (3C) wave (3CW) methods, respectively. The TDCS has been calculated both in the scattering and perpendicular planes. The purpose of this work is to investigate the validity of different methods as well as the role of interaction between projectile and residual-target-ion in the final state for weak perturbation strength with low electron emission energy at several momentum transfers. By comparing our calculations with experimental data, overall, the 3CW predicts better agreement with experiments than other calculations in the scattering plane. In the perpendicular plane, all calculations deviate from experimental data with increasing transverse momentum transfer for p − He collision. At low momentum transfer, the location of binary peak obtained by the first Born approximation calculation is well established with the experiment for proton impact. On the other hand, the 3CW model is in much better agreement with experiments, both in absolute values and peak position for highly charged impact. Finally, the strong influence of the internuclear Coulomb distortion on TDCS has been observed at low and intermediate momentum transfer.

Dynamics of Twisted Electron Impact Ionization of CH4 and NH3 Molecule

Electron vortex beams (EVBs, also known as twisted electron beams) possess an intrinsic orbital angular momentum (OAM) with respect to their propagation direction. This intrinsic OAM represents a new degree of freedom that provides new insights into investigating the dynamics of electron impact ionization. In this communication, we present, in the first Born approximation (FBA), the angular profiles of the triple differential cross section (TDCS) for the (e, 2e) process on CH4 and NH3 molecular targets in the coplanar asymmetric geometry. We compare the TDCS of the EVB for different values of OAM number m with that of the plane wave. For a more realistic scenario, we investigate the average TDCS for macroscopic targets to explore the influence of the opening angle θp of the twisted electron beam on the TDCS. In addition, we also present the TDCS for the coherent superposition of two EVBs. The results demonstrate that the twisted (e, 2e) process retrieves the p-type character of the molecular orbitals, which is absent in the plane wave TDCS for the given kinematics. The results for the coherent superposition of two Bessel beams show the sensitivity of TDCS toward the OAM number m.

Projectile Coherence Effects in Twisted Electron Ionization of Helium

Over the last decade, it has become clear that for heavy ion projectiles, the projectile’s transverse coherence length must be considered in theoretical models. While traditional scattering theory often assumes that the projectile has an infinite coherence length, many studies have demonstrated that the effect of projectile coherence cannot be ignored, even when the projectile-target interaction is within the perturbative regime. This has led to a surge in studies that examine the effects of the projectile’s coherence length. Heavy-ion collisions are particularly well-suited to this because the projectile’s momentum can be large, leading to a small deBroglie wavelength. In contrast, electron projectiles that have larger deBroglie wavelengths and coherence effects can usually be safely ignored. However, the recent demonstration of sculpted electron wave packets opens the door to studying projectile coherence effects in electron-impact collisions. We report here theoretical triple differential cross-sections (TDCSs) for the electron-impact ionization of helium using Bessel and Laguerre-Gauss projectiles. We show that the projectile’s transverse coherence length affects the shape and magnitude of the TDCSs and that the atomic target’s position within the projectile beam plays a significant role in the probability of ionization. We also demonstrate that projectiles with large coherence lengths result in cross-sections that more closely resemble their fully coherent counterparts.

Differential toverline{t} cross-section measurements using boosted top quarks in the all-hadronic final state with 139 fb−1 of ATLAS data

Measurements of single-, double-, and triple-differential cross-sections are presented for boosted top-quark pair-production in 13 TeV proton–proton collisions recorded by the ATLAS detector at the LHC. The top quarks are observed through their hadronic decay and reconstructed as large-radius jets with the leading jet having transverse momentum (pT) greater than 500 GeV. The observed data are unfolded to remove detector effects. The particle-level cross-section, multiplied by the toverline{t}to WWboverline{b} branching fraction and measured in a fiducial phase space defined by requiring the leading and second-leading jets to have pT> 500 GeV and pT> 350 GeV, respectively, is 331 ± 3(stat.) ± 39(syst.) fb. This is approximately 20% lower than the prediction of {398}_{-49}^{+48} fb by Powheg+Pythia 8 with next-to-leading-order (NLO) accuracy but consistent within the theoretical uncertainties. Results are also presented at the parton level, where the effects of top-quark decay, parton showering, and hadronization are removed such that they can be compared with fixed-order next-to-next-to-leading-order (NNLO) calculations. The parton-level cross-section, measured in a fiducial phase space similar to that at particle level, is 1.94 ± 0.02(stat.) ± 0.25(syst.) pb. This agrees with the NNLO prediction of {1.96}_{-0.17}^{+0.02} pb. Reasonable agreement with the differential cross-sections is found for most NLO models, while the NNLO calculations are generally in better agreement with the data. The differential cross-sections are interpreted using a Standard Model effective field-theory formalism and limits are set on Wilson coefficients of several four-fermion operators.

Double Differential Cross-sections for Ionization of Metastable 2P-state Hydrogen Atoms by Electrons at Intermediate Energies with Exchange Effects

Double differential cross sections were obtained from the triple differential cross sections. The present calculations are compared with the hydrogenic ground-state experimental data, theoretical results, and DDCS first Born results. Discrepancies have been found between the present results and those measurements and theoretical results and also qualitative agreement with those of compared theories. The exchange effect results give an enormous prospect for experimental outcomes in the field of ionization problems. We are expecting that the present study makes more significant contribution to the study of atomic scattering problems using the multiple scattering theories. In the future calculations, other kinematic conditions or other atomic species will also be interesting and significant.

Importance of deuteron breakup in the deuteron knockout reaction

Background: An isoscalar $pn$ pair is expected to emerge in nuclei that have similar proton and neutron numbers and it may be a candidate for a deuteron ``cluster.'' There is, however, no experimental evidence for it.Purpose: The purpose of this paper is to construct a new reaction model for the $(p,pd)$ reaction including the deuteron breakup in the elementary process and the deuteron reformation by the final-state interactions. How these processes contribute to the observables of the reaction is investigated.Methods: The distorted wave impulse approximation is extended twofold. The elementary processes of the $(p,pd)$, i.e., the $p\text{\ensuremath{-}}d$ elastic scattering and the $d(p,p)pn$ reaction, are described with an impulse picture employing a nucleon-nucleon effective interaction. The three-body scattering waves in the final state of the $(p,pd)$ reaction are calculated with the continuum-discretized coupled-channels method. The triple-differential cross section (TDX) of the $(p,pd)$ reaction is calculated with the new model.Results: The elementary processes are described reasonably well with the present model. As for the $(p,pd)$ reaction, the deuteron reformation can either increase or decrease the TDX height depending on the interference between the elastic and breakup channels of deuteron, while the back-coupling effect always decreases it.Conclusions: It is shown that the deuteron reformation significantly changes the TDX of the $(p,pd)$ reaction through the interference. It is important to include this process to quantitatively discuss the $(p,pd)$ cross sections in view of the deuteron formation in nuclei. For more quantitative discussion regarding the experimental data, further improvement will be necessary.

Effects of environment on the electron-impact ionization dynamics of argon clusters

Ionization of the $3p$ orbital of argon (Ar) monomers, dimers (${\mathrm{Ar}}_{2}$), and small-size Ar clusters (${\mathrm{Ar}}_{n},\phantom{\rule{0.16em}{0ex}}\ensuremath{\langle}n\ensuremath{\rangle}\ensuremath{\approx}15$) is investigated for 90-eV electron impact. Experimentally, the three-dimensional momentum vectors of the two outgoing electrons and the residual ion are measured in triple coincidence, as is the mass-over-charge ratio of the ion, using a reaction microscope that covers a large part of the final-state phase space. The triple-differential cross sections (TDCS) are obtained for almost the full solid angle of the ejected electron, in which the data for Ar monomers are well reproduced by $B$-spline $R$-matrix calculations for ejected electron energies of 3 eV, 5 eV, and 10 eV, and projectile scattering angles of ${10}^{\ensuremath{\circ}}$ and ${20}^{\ensuremath{\circ}}$. Compared to the Ar monomer, the cross sections for ${\mathrm{Ar}}_{2}$ and ${\mathrm{Ar}}_{n}$ exhibit effects due to the neighboring atoms by the suppression of binary and recoil lobes and the enhanced electron emission out of the projectile scattering plane. These environmental effects are further investigated using a multicenter three-distorted-wave theory, which can generate the TDCSs for electron-impact ionization of ${\mathrm{Ar}}_{2}$. These studies reveal an important role of multicenter scattering reactions on the ionization dynamics of Ar clusters. Moreover, a two-center interference is not found in the TDCS of ${\mathrm{Ar}}_{2}$. This is interpreted as due to the involvement of orbitals with both gerade and ungerade symmetries in the ionization process.

Triple-differential cross sections in three-dimensional kinematics for electron-impact-ionization dynamics of tetrahydrofuran at 250-eV projectile energy

We report a combined experimental and theoretical study of the ionization dynamics of tetrahydrofuran induced by 250 eV electron impact in which the highest occupied molecular orbital is ionized leading to the stable parent ion. Experimentally a reaction microscope was used, covering nearly the entire $4\ensuremath{\pi}$ solid angle for the ejected slow electron. We present the triple-differential cross sections for the projectile scattering angles of ${\ensuremath{\theta}}_{1}$ = $\ensuremath{-}{10}^{\ensuremath{\circ}}$ as a function of the emission angle of the ejected electrons with energies of ${E}_{2}=10$, 15, and 20 eV, i.e., for asymmetric energy sharing between the scattered and ejected electrons. The measured triple-differential cross sections are internormalized across the three ejected energies. The experimental data are compared with predictions from the molecular three-body distorted-wave (M3DW), the multicenter distorted-wave (MCDW) approaches, and a modified MCDW-WM method which includes the postcollision interaction using the Ward-Macek approximation. Generally, the M3DW cross sections show better agreement with experiment than the MCDW calculations except for the emission angles near the projectile forward direction. The MCDW and MCDW-WM calculations do not reproduce the recoil lobes and show very small intensity for the cross sections outside the scattering plane.

Dressing effects in the laser-assisted ( e,2e ) process in fast-electron–hydrogen-atom collisions in an asymmetric coplanar scattering geometry

We present the theoretical treatment of laser-assisted $(e,2e)$ ionizing collisions in hydrogen for fast electrons, in the framework of the first-order Born approximation at moderate laser intensities and photon energies beyond the soft-photon approximation. The interaction of the laser field with the incident, scattered, and ejected electrons is treated nonperturbatively by using Gordon-Volkov wave functions, while the atomic dressing is treated by using first-order perturbation theory. Within this semiperturbative formalism, we obtain a closed-form formula for the nonlinear triple differential cross section (TDCS), which is valid for linear as well circular polarizations. Analytical simple expressions of TDCS are derived in the weak field domain and low-photon energy limit. It was found that for nonresonant $(e,2e)$ reactions, the analytical formulas obtained for the atomic matrix element in the low-photon energy limit give a good agreement, qualitative and quantitative, with the numerical semiperturbative model calculations. We study the influence of the photon energy as well of the kinetic energy of the ejected electron on the TDCS, in the asymmetric coplanar geometry, and show that the dressing of the atomic target strongly influences the $(e,2e)$ ionization process. We discuss the exchange effects between the ejected and scattered electrons in the TDCS.

Twisted-electron-impact single ionization of an H2O molecule by multicenter distorted-wave calculations

We report theoretical investigation of the twisted-electron-impact single-ionization dynamics of an ${\mathrm{H}}_{2}\mathrm{O}$ molecule. The triple-differential cross sections for $1{b}_{1}$, $3{a}_{1}$, $1{b}_{2}$, and $2{a}_{1}$ orbitals are obtained by a twisted-electron-impact multicenter distorted-wave method. The coplanar asymmetric kinematic condition is adopted at incident electron energy ${E}_{i}=250$ eV and ejected electron energy ${E}_{e}=10$ eV. By integrating the impact parameter, all possible rotation angles ${\ensuremath{\varphi}}_{k}$ of the projectile are averaged for the triple-differential cross section, which is independent of the orbital angular momentum and varies as a function of opening angle ${\ensuremath{\theta}}_{k}$. The results show that the ionization by a plane-wave projectile is more likely than by a twisted-electron projectile if the scattering angle is smaller than a critical value. However, when the scattering angle exceeds the critical point, the twisted-electron projectile can possess higher ionization probability, which will reach a maximum when the opening angle numerically approaches the scattering angle.

Twisted electron impact single ionization coincidence cross-sections for noble gas atoms

We present the angular profiles of the triple differential cross-section (TDCS) for the (e, 2e) process on the noble gas atoms, namely He (1s), Ne (2s and 2p), and Ar (3p), for the plane wave and the twisted electron impact. We develop the theoretical formalism in the first Born approximation (FBA). The present study compares the TDCS for different values of orbital angular momentum number m and opening angles θ p of the twisted electron beam with that of the plane wave beam in co-planar asymmetric geometry. In addition, we also investigate the TDCS for macroscopic targets to explore the influence of the opening angle θ p of the twisted electron beam on the TDCS. Our results show that the peaks in binary and recoil regions shift from the momentum transfer direction. The results also show that for larger opening angles, the peaks for p-type orbitals split into double-peak structures, which are not observed in the plane wave results for the given kinematics. The angular profiles for averaged cross-section show the dependence of TDCS on the opening angles, especially for the larger opening angles, which are significantly different from the plane wave TDCS.