Fully Differential Cross Sections Research Articles

A fresh look at the nested soft-collinear subtraction scheme: NNLO QCD corrections to N-gluon final states in qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} annihilation

We describe how the nested soft-collinear subtraction scheme [1] can be used to compute the next-to-next-to-leading order (NNLO) QCD corrections to the production of an arbitrary number of gluonic jets in hadron collisions. We show that the infrared subtraction terms can be combined into recurring structures that in many cases are simple iterations of those terms known from next-to-leading order. The way that these recurring structures are identified and computed is fairly general, and can be applied to any partonic process. As an example, we explicitly demonstrate the cancellation of all singularities in the fully-differential cross section for the qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ q\\overline{q} $$\\end{document} → X + Ng process at NNLO in QCD. The finite remainder of the NNLO QCD contribution, which arises upon cancellation of all ϵ-poles, is expressed via relatively simple formulas, which can be implemented in a numerical code in a straightforward way. Our approach can be extended to describe arbitrary processes at NNLO in QCD; the largest remaining challenge at this point is the combinatorics of quark and gluon collinear limits.

Bessel beam double ionisation (e, 3e) of Helium atoms

We present the results of previous plane wave and current twisted wave electron double ionisation (e, 3e) near the threshold energy using the second Born approximation to calculate the fully differential cross section (FDCS)T-SBA and also calculate the fully differential cross section for plane wave using the second Born approximation (SBA) and including post-collision interactions (FDCS) PW+PCI of the He atom. We investigate the effect of different “m” parameters on orbital angular momentum (OAM) using the second Born approximation for both twisted and plane waves incident and scattered electrons. We compare our theoretical twisted wave results with experimental non-twisted results (i.e., plane wave); we found that the theoretical twisted wave results are in good agreement with experimental non-twisted (i.e., plane wave) results of He atoms.

Cluster approach to scattering in MoS2 photoemission

We examine the photoemission cross sections and Wigner time delays from MoS 2 core-level orbitals Mo4s, Mo4p, S3s. We employ a cluster approach and study the photoemission process for progressively larger model clusters, in order to assess the scattering effects by neighboring atoms. First we explore how the fully differential cross section (FDCS) from the localized orbitals evolves as we increase the cluster size. In order to establish the underlying scattering mechanics that are mapped into the FDCS and Wigner time delays, we jointly analyze them in terms of the polar emission angle and photoemission energy for fixed azimuthal angles. The Wigner-time-delay scale goes from a few tens up into the hundreds of attoseconds when increasingly large clusters are considered, indicating the presence of high order scattering processes and interference. We find that, for the largest clusters, some internal propagation pathways start taking shape, which in an infinite system would amount to band structure positive energy states. We conclude that second- or higher-order neighbors around the main emitter strongly affect the photoelectron propagation and yield, therefore supporting their importance for models that aim for quantitative descriptions.

Projectile transverse momentum controls emission in electron vortex ionization collisions

The realization of electron vortex (EV) beams in the past decade has led to numerous proposed applications in fields from electron microscopy to control and manipulation of individual molecules. Yet despite the many unique characteristics and promising advantages of EV beams, such as transverse momentum and quantized orbital angular momentum, there remains a limited understanding of their fundamental interactions with matter at the atomic scale. Collisions between EV projectiles and atomic targets can provide some insight into these interactions and we present here fully differential cross sections (FDCS) for ionization of excited state atomic hydrogen targets using EV projectiles. We show that the projectile’s transverse momentum causes the ionized electron angular distributions to be altered compared to non-vortex projectiles and that the ionized electron’s ejection angle can be controlled by adjustment of the vortex opening angle, a feature unique to vortex projectiles. Additionally, an inherent uncertainty in the projectile’s momentum transfer leads to a broadening of the classical binary peak, making signatures of the target electron density more readily observable. FDCS for aligned 2p targets exhibit structures can be used to determine the alignment.

Momentum mappings for subtractions at higher orders in QCD

Subtraction schemes provide a systematic way to compute fully-differential cross sections beyond the leading order in the strong coupling constant. These methods make singular real-emission corrections integrable in phase space by the addition of suitable counterterms. Such counterterms may be defined using momentum mappings, which are parametrisations of the phase space that factorise the variables that describe the particles becoming unresolved in some infrared or collinear limit from the variables that describe an on-shell phase space for the resolved particles. In this work, we review existing momentum mappings in a unified framework and introduce new ones for final-collinear and soft counterterms. The new mappings work in the presence of massive particles and with an arbitrary number of soft particles or of clusters of collinear particles, making them fit for subtraction methods at any order in perturbation theory. The new mapping for final-collinear counterterms is also used to elucidate relations among existing final-collinear mappings.

Target dependence of postcollision interaction effects on fully differential ionization cross sections

We have measured and calculated fully differential cross sections (FDCS) for ionization of helium by 75-keV proton impact. Ejected electrons with a speed close to and above the projectile speed were investigated. This range of kinematics represents a largely unexplored regime. A high sensitivity of the FDCS to the details of the description of the few-body dynamics, reported earlier for ionization of ${\mathrm{H}}_{2}$, was confirmed. A peak structure was found in an electron angular range between the regions where the so-called binary and recoil peaks are usually observed. The need for nonperturbative calculations using a two-center basis set is demonstrated.

Few-body dynamics underlying postcollision effects in the ionization of H2 by 75-keV proton impact

We have measured fully differential cross sections (FDCS) for ionization in $75\text{\ensuremath{-}}\mathrm{keV}p+{\mathrm{H}}_{2}$ collisions for ejected electron speeds close to the projectile speed. The data were analyzed in dependence on both the electron emission angle and the projectile scattering angle. Pronounced postcollisional effects between the projectile and the ejected electrons were observed. Significant differences between experiment and theory and between two conceptually very similar theoretical models were found. This shows that in the region of electron-projectile velocity-matching the FDCS is very sensitive to the details of the underlying few-body dynamics.

Theoretical investigation of the fully differential cross sections for single ionization of He in collisions with 75-keV protons

We present a theoretical investigation of the single ionization of He in collisions with ${\mathrm{H}}^{+}$ projectile ions at 75-keV impact energy. Using the frameworks of the independent-electron model and the impact parameter picture, fully differential cross sections (FDCS) are evaluated in the continuum distorted-wave with eikonal initial-state approximation (CDW-EIS). Comparisons are made to the recent measurements of Schulz et al. [Phys. Rev. A 73, 062704 (2006)] and Arthanayaka et al. [J. Phys. B: At. Mol. Opt. Phys. 49, 13LT02 (2016)]. Strong influence of the internuclear interaction and effects of target core polarization due to the presence of the projectile ion are observed. Comparing the present results to experimental data and other theoretical predictions, it has been found that the CDW-EIS method qualitatively reproduces structures in the FDCS. Projectile coherence effects are investigated by representing the projectile beam as a Gaussian wave packet. Evidence of interference effects due to projectile-electron and projectile-target core interactions are discussed and the need for further theoretical investigations is proposed.

Fully differential cross-sections for single ionization of helium by AuQ+ impact

We present fully differential cross-sections (FDCS) within the four-body formalism using the three-body Coulomb wave (4B-3C) for the single ionization of He by 3.6 Mev/amu AuQ+ ions. The purpose of this work is to investigate the validity of the 4B-3C model for more highly charged ions. By comparing our calculations with experimental data and the three-distorted-wave eikonal-initial-state (3DW-EIS) approximation, we find the 4B-3C predict unique forward peak structures in the FDCS and broadly reproduce the experimental data over the entire angular range in a satisfactory manner for Au24+. Clear discrepancies are found between both theories and with experiment for Au53+.

Fully differential cross sections for the single ionization of helium by fast ions: Classical model calculations

Fully differential cross sections (FDCSs) have been calculated for the single ionization of helium by 1- and 3-MeV proton and 100-MeV/u ${\mathrm{C}}^{6+}$ ion impact using the classical trajectory Monte Carlo (CTMC) method in the nonrelativistic, three-body approximation. The calculations were made employing a Wigner-type model in which the quantum-mechanical position distribution of the electron is approximated by a weighted integral of the microcanonical distribution over a range of the binding energy of the electron. In the scattering plane, the model satisfactorily reproduces the observed shape of the binary peak. In the region of the peak the calculated FDCSs agree well with the results of continuum-distorted-wave calculations for all the investigated collisions. For 1-MeV proton impact the experimentally observed shift of the binary peak with respect to the first Born approximation is compared with the shifts obtained by different higher-order quantum-mechanical theories and the present CTMC method. The best result was achieved by CTMC, but still a large part of the shift remained unexplained. Furthermore, it was found that the classical theory failed to reproduce the shape of the recoil peak observed in the experiments, it predicts a much narrower peak. This indicates that the formation of the recoil peak is dominated by quantum-mechanical effects. For 100-MeV/u ${\mathrm{C}}^{6+}$ ion impact the present CTMC calculations confirmed the existence of the ``double-peak'' structure of the angular distribution of the electron in the plane perpendicular to the momentum transfer, in accordance with the observation, the prediction of an incoherent semiclassical model, and previous CTMC results. This finding together with wave-packet calculations suggests that the ``${\mathrm{C}}^{6+}$ puzzle'' may be solved by considering the loss of the projectile coherence. Experiments to be conducted using ion beams of anisotropic coherence are proposed for a more differential investigation of the ionization dynamics.

Electron capture to the continuum manifestation in fully differential cross sections for ion impact single ionization

We present theoretical calculations of single ionization of He atoms by protons and multiply charged ions. The kinematical conditions are deliberately chosen in such a way that the ejected electron velocity matches the projectile impact velocity. The computed fully differential cross sections (FDCS) in the scattering plane using the continuum-distorted wave-eikonal initial state show a distinct peaked structure for a polar electron emission angle θk = 0°. This element is absent when a first order theory is employed. Consequently, we can argue that this peak is a clear manifestation of a three-body effect, not observed before in FDCS. We discuss a possible interpretation of this new feature.

Differential cross sections for ionizations of H and H2 by 75 keV proton impact

We have calculated total, partial and fully differential cross sections (FDCSs) for ionizations of H and H2 by 75 keV proton impact within the framework of the continuum-distorted-wave-eikonal-initial-state (CDW-EIS) approximation. Applying the single active electron model, the interaction between the projectile and the target ion is taken into account in the impact parameter picture. Extension of the CDW-EIS model to the molecular target is performed using the two-effective center approximation. The obtained results are compared with those of experimental and other theoretical data when available. The agreements between the theories and the experimental data are generally reasonable except for some cases of the FDCSs.

Large discrepancies observed in theoretical studies of ion-impact ionization of the atomic targets at large momentum transfer

A full quantum mechanical version of the three-body distorted wave-eikonal initial state (3DW-EIS) theory is developed to study of the single ionization of the atomic targets by ion impact at different momentum transfers. The calculations are performed both with and without including the internuclear interaction in the transition amplitude. For and collisions, the emission of the active electron into the scattering plane is considered and the fully differential cross-sections (FDCSs) are calculated for a fixed value of the ejected electron energy and a variety of momentum transfers. For both the specified collision systems, the obtained results are compared with the experimental data and with the cross-sections obtained using the semi-classical continuum distorted wave-eikonal initial state (CDW-EIS) approach. For , we also compared the results with those of a four-body three-Coulomb-wave (3CW) model. In general, we find some large discrepancies between the results obtained by different theories. These discrepancies are much more significant at larger momentum transfers. Also, for some ranges of the electron emission angles the results are much more sensitive to the internuclear interaction to be either turned on or off.

Partial wave analysis of oriented collisions

We present fully differential cross sections (FDCSs) for two collision processes with oriented atoms. The first collision is electron-impact ionization of oriented Mg (3p), and the second collision is electron-impact excitation-ionization (EI) of helium with an oriented final state He+(2p0) ion. Surprisingly, the theoretical functional form of the FDCS is the same for both processes, despite the fact that the only physical similarity is an oriented excited state in both processes. We present FDCS as a function of orientation angle and ejected electron angle for both ionization of oriented Mg(3p) and EI of helium in order to explore possible physical similarities between the two processes. We examine the contributions to the FDCS of individual partial waves of the ionized electron and projectile. For the ionization of oriented Mg, we show that the FDCS are dominated by larger partial waves of the ejected electron, with the dominant partial waves having a dependence on scattering angle and outgoing electron energy sharing. For the EI process, the FDCS is dominated by the L = 2 partial wave, independent of scattering angle or energy sharing. Also, for EI it is possible to have angular momentum transferred from either the target helium atom or the incident projectile.

Fully differential cross-sections in single ionization of helium by 2 MeV/amu C6+ impact: The role of correlated wave functions

We study the effect of final-state dynamic correlation in single ionization of helium atom by 2 MeV/amu C6+ impact analyzing the fully differential cross-sections (FDCS). The transition matrix is introduced using a correlated continuum wave (CCW) and that for the initial state by an undistorted Born-approximation. The final state is modeled by the CCW function so that both the correlation and the interaction between the projectile and the residual target ion (PT interaction) are treated. The analytical expression of the transition matrix has been obtained through a series representation of the CCW function. Illustrative computations are performed in the scattering plane. A comparison of fully differential results using the present model with other theories and experimental data reveals that the dynamic correlation is responsible for the enhancement of the FDCS structure. The PT interaction is also checked in our model. We observe a satisfactory, although not perfect, agreement of the CCW calculations with experimental findings. Large discrepancies between the experimental data and theoretical predictions are found, which can at least be partly attributed to the inclusion of dynamic correlation effects.

Angular momentum and orientation effects in excitation-ionization collisions

We present theoretical fully differential cross sections (FDCS) for electron-impact excitation-ionization of helium in which the final state He+ ion is oriented in a particular direction. Specifically, we study the process for He+ ions in the 2p0 state. Using our 4-body distorted wave model, we show a strong dependence of the FDCS on the ion’s orientation and trace some unexpected structures in the FDCS to the L = 2 term in the partial wave expansion for the ionized electron. A comparison is drawn to the ionization of oriented Mg (3p0) atoms, and unlike that process, we find that for excitation-ionization angular momentum must be transferred from either the projectile or the target atom.

Coulomb three-body effects in the single ionization of helium by 16MeV O <sup>7+</sup> impact

Three-Coulomb-wave (3C)model is applied to study the single ionization of helium by 16MeV O7+ impact in the scattering plane. Fully differential cross sections (FDCS) is presented for the different momentum transfers. Our theoretical results are compared with the recent experimental data and the results of continuum distortedwave eikonal-initial-state (CDW-EIS). It is shown that the 3C calculations qualitatively reproduce the experimental peak structure, especially at smaller momentum transfers. PACS: 34.80.Dp

Calculation of fully differential cross sections for the near threshold double ionization of helium atoms

Fully differential cross sectional (FDCS) results are reported for the electron-impact double ionization of helium atoms at 5 and 27 eV excess energy. The present attempt to calculate the FDCS in the second Born approximation and treating the postcollision interaction is helpful to analyze the measurements of Ren et al (2008 Phys. Rev. Lett. 101 093201) and Durr et al (2007 Phys. Rev. Lett. 98 193201). The second-order processes and postcollision interaction have been found to be significant in describing the trends of the FDCS. More theoretical effort is required to describe the collision dynamics of electron-impact double ionization of helium atoms at near threshold.

Fully Differential Cross Sections for Single Ionization of Helium by AuQ+ Impact

We present fully differential cross sections (FDCS) within three-body distorted wave (3DW) for the single ionization of He by 3.6 MeV/amu AuQ+ (Q=24, 53) ions. By comparing our calculations with experimental data and other theoretical predictions, we find the cross sections are strongly influenced by highly charged projectile, ejected electron would be “pulled” along in the forward direction. However, all of the theoretical approaches can not display experimental unique forward peak structures in the FDCS.

Nucleus–Nucleus Effects in Fully Differential Cross Sections for Energetic C6+ +He Collisions with Small Momentum Transfer**Supported by the National Natural Science Foundation of China under Grant No 11274215, and the Natural Science Foundation of Shanxi Province under Grant No 2010011009.

The modified Coulomb–Born approximation with and without the internuclear interaction (MCB-NN and MCB) is used to calculate the fully differential cross sections (FDCS) for the single ionization of helium by 100 MeV/amu C6+ impact. The effects of the internuclear interaction on the FDCS are examined in geometries. The results are compared with experimental data and theoretical predictions from a three-body distorted-wave (3DW) model and a time-dependent close-coupling model. It is shown that the present MCB-NN results are in good agreement with the experiments in the scattering plane and the MCB results qualitatively reproduce the experimental structure outside the scattering plane. In particular, the MCB theory predicts the ‘double-peak’ structure in the perpendicular plane.