Calculations Of Differential Cross Sections Research Articles

Calculation of the single differential cross section for electron-impact ionization of atoms and molecules

A technique has been developed for calculating the electron-impact ionization single differential cross section directly from the integrated cross sections of positive-energy pseudostates occuring in close-coupling methods. Using the cross sections arising in the convergent close-coupling method, the approach is first tested against the existing benchmark theoretical and experimental data for electron scattering on hydrogen and helium. It is then applied to electron scattering on molecular hydrogen yielding excellent agreement with experimental data when normalized to the total ionization cross section.

Theoretical studies on the elastic scattering of e± off the ions of xenon isonuclear series

This work presents the calculations of differential, integrated elastic and momentum transfer cross sections for the elastic scattering of electrons from the ions of xenon isonuclear series over the incident energy range 1 eV–1000 eV. Coulomb glory, the amplification of elastic backscattering of electrons from positive ions owing to the electrostatic screening of nuclear potential by atomic electrons, is investigated throughout the ionic series of xenon, argon and neon. Cross sections for the angular distribution of elastically scattered positron from selected xenon ions are also calculated. Energy dependency of differential cross sections and Sherman functions are predicted for both the projectiles and a comparison is presented to exhibit the dissimilarity arising out of the difference of the interactions of the projectiles with ions. The theoretical methodology of this work employs the Dirac relativistic partial wave analysis using a complex optical potential, comprising static, exchange, polarization and imaginary components, and a pure Coulomb potential. The results obtained show reasonable agreements with the available experimental data and other theoretical calculations.

Elastic scattering of electrons and positrons from 115In atoms over the energy range 1 eV–0.5 GeV

We present a theoretical study on the calculations of various cross sections related to the scattering of electrons and positrons from indium atoms. Our calculations cover the energy range 1 eV ⩽Ei⩽0.5 GeV. We have employed two approaches, applicable for two domains of energy, based on the Dirac partial-wave analysis. In one approach, we have used both the atomic and nuclear potentials to calculate the cross sections for the low and intermediate energies. The other approach, valid for the high-energy scattering, utilizes only the nuclear potential for the phase-shift analysis, and considers the magnetic scattering from the nucleus too. We report the calculations of differential, integral, momentum-transfer and viscosity cross sections along with the spin asymmetries for the elastic scattering of electrons and positrons. Moreover, we have analyzed the critical minima in the elastic differential cross sections, and also computed the absorption and total cross sections. Our results agree reasonably with the available experimental data and other calculations.

Elastic Scattering of Electrons by Helium Atoms in Born Approximation

Elastic scattering phenomena arising in electron-helium scattering are dominant processes. The determination of accurate elastic differential cross sections for electron-helium scattering has a considerable importance. An accurate calculation of the plane-wave first Born exchange amplitude of electrons elastic scattering by helium atoms is reported. The direct and exchange amplitudes are calculated analytically from the Hartree-Fock orbital wave functions by using a variational method. The forms of these wave functions are very suitable for analytical calculations and powerful to generalize to more complex atomic systems. The interaction potential is modelled by the static Coulomb interaction between the incident electron and the atomic system. The differential cross sections are calculated at intermediate energies taking into account the exchange effects. We have established in the high energies region, by neglecting the exchange effects, the analytical expressions of the total and momentum transport cross sections suitable for the calculation of the plasma transport properties. A very compact form of the Born amplitude has been proposed as a finite series of Gaussian functions, which represents a major tool in the calculations of differential cross sections of two-electron atomic systems. Numerical results are used to analyze the contribution of the exchange amplitude to the differential cross sections at intermediate and high energies. The differential cross sections are calculated for the energy range 30-400 eV. We find good agreement in high energy domain scattering with experimental results and other sophisticated calculations without using any adjustable parameter.

Studying supernova neutrinos through nuclear structure calculations

Differential and integrated cross section calculations are performed in the context of the quasi particle random phase approximation (QRPA) by utilizing realistic two- nucleon forces, for the 64,66 Zn isotopes, contents of the COBRA double beta decay detector. For these isotopes the response to supernova neutrinos is of current inter- est. The response of the 66 Zn isotope to the energy-spectra of supernova neutrinos is also explored by convoluting the original results for the differential cross sections by employing: (i) a two-parameter Fermi-Dirac (FD) and (ii) a Power-Law (PL) neutrino energy distribution. Such folded cross sections are useful in low-energy astrophysical-neutrino detection in underground terrestrial experiments.

A detailed study of the LHC and TEVATRON hadron–hadron prompt-photon pair production experiments in the angular ordering constraint kt-factorization approaches

Based on the kt-factorization framework, it is intended to report a detailed study of the differential cross section of the isolated prompt-photon pairs (IPPP) production in high-energy inelastic hadron–hadron collisions. The two scheme-dependent unintegrated parton distribution functions (UPDF) in which the angular ordering constraints (AOC) are imposed, namely the Kimber–Martin–Ryskin (KMR) and the Martin–Ryskin–Watt (MRW) approaches, in the leading and the next-to-leading orders (LO and NLO) are considered, respectively. These two prescriptions (KMR and MRW) utilize the phenomenological parton distribution function (PDF) libraries of Martin et al, i.e. the MMHT2014. The computations are performed in accordance with the different experimental constraints of the latest existing experiment of the D0, CDF, CMS and ATLAS collaborations. It is shown that the above frameworks are capable of producing acceptable results, compared to the experimental data, the pQCD and some Monte Carlo calculations (i.e. 2γNNLO, SHERPA, DIPHOX and RESBOS). It is also concluded that the KMR framework produces better results in the higher center-of-mass energies, while the same thing can be argued about the LO-MRW prescription in lower energies. Additionally, these two schemes show different behavior in the regions where the fragmentation and higher pQCD effects become important. A clear prediction for the various shoulders and tails, which are detected experimentally, are observed and discussed. The possible double countings between and processes are studied. Finally, in agreement to the work of Golec-Biernat and Stasto, it is shown that there is not any dispute about the application of the AOC and the cut-off, in the above prescriptions, at least in the calculation of the various IPPP differential cross sections. However, mostly the LO and NLO-MRW frameworks are the upper and lower bands of the KMR prescriptions, otherwise they predicate the data.

Classical-trajectory Monte Carlo calculations of differential electron-emission cross sections in fast heavy-ion collisions with water molecules

A classical description of electron emission differential ionization cross sections for highly-charged high-velocity ions ($\sim$ 10 a.u.) impinging on water molecules is presented. We investigate the validity of the classical statistical mechanics description of ionization ($\hbar=0$ limit of quantum mechanics) in different ranges of electron emission energy and solid angle, where mechanisms such as soft and binary collisions are expected to contribute. The classical-trajectory Monte Carlo method is employed to calculate doubly and singly differential cross sections for C$^{6+}$, O$^{8+}$ and Si$^{13+}$ projectiles, and comparisons with Continuum Distorted Wave Eikonal Initial State theoretical results and with experimental data are presented. We implement a time-dependent screening effect in our model, in the spirit of mean-field theory to investigate its effect for highly charged projectiles. We also focus on the role of an accurate description of the molecular target by means of a three-center potential to show its effect on differential cross sections. Very good agreement with experiments is found at medium to high electron emission energies.

Higher-order differential cross section calculation for the associated production ofa W boson and jets in the electron decay channel at a center-of-mass energy of 13TeV in proton-proton collisions

Higher-order cross sections for the production of a W boson in association with jets in the electron decay channel are presented in this study. Cross sections were calculated in a fully differential way using a computational framework based on proton-proton collisions at a center-of-mass energy of 13 TeV. The differential cross section predictions in the fiducial phase-space were compared at next-to-leading order (NLO) and next-to-NLO (NNLO) in perturbative quantum chromodynamics (pQCD). The differential results are reported for the variables including the jet multiplicity, the invariant mass of the W boson, transverse momentum, the jet rapidity, and the electron pseudorapidity that are sensitive to higher-order corrections in pQCD. The presented differential cross sections were generally improved in precision in the NNLO calculation. The total cross sections at NLO and NNLO are also reported in the fiducial phase-space. More accurate results were obtained in the calculation of the total production rates at NNLO. The results in all the calculations are given in the W+ and the W- boson decay channels separately to better assess the impact of the inclusion of higher-order corrections in those processes.

Radial: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations

The Fortran subroutine package radial for the numerical solution of the Schrödinger and Dirac wave equations of electrons in central potentials V(r) is described. The considered potentials are such that the function V(r)≡rV(r) is finite for all r and tends to constant values when r→0 and r→∞. This includes finite-range potentials as well as combinations of Coulomb and finite-range potentials. The function V(r) used in the numerical calculation is the natural cubic spline that interpolates a table of values provided by the user. The radial wave equations are solved by using piecewise exact power series expansions of the radial functions, which are summed up to the prescribed accuracy so that truncation errors can be completely avoided. The radial subroutines compute radial wave functions, eigenvalues for bound states and phase shifts for free states. Specific subroutines are also provided for computing the radial functions and phase shifts for free states of complex optical potentials having a finite-range absorptive imaginary part. The solution subroutines are accompanied by example main programs, as well as with specific programs that perform calculations relevant in atomic, nuclear, and radiation physics (the self-consistent solution of the Dirac–Hartee–Fock–Slater equations for neutral atoms and positive ions, and the calculation of cross sections for elastic scattering of high-energy electrons and positrons by atoms and of nucleons by nuclei). The distribution package includes a detailed manual with a description of the basic physics and the mathematical formulas implemented in the subroutines. Program summaryProgram Title:radialProgram Files doi:http://dx.doi.org/10.17632/h6nbws5h6s.1Licensing provisions: CC by NC 3.0Programming language: Fortran 90/95Supplementary material: Manual in pdf format. Includes a description of the basic physics, and the complete set of formulas implemented in the program.Journal reference of previous version: Comput. Phys. Commun. 90 (1995) 151–168.Does the new version supersede the previous version?: YesReasons for the new version: The present subroutine package contains a revision and extension of the radial subroutines [1], which have been recoded. The new subroutines implement a more accurate normalisation of bound states; the phase convention of Dirac’s central-field orbitals has been replaced with that of Rose [2]. Subroutines for computing free states of complex optical-model potentials with an absorptive imaginary part have been added to the package. Subroutines giving the coefficients of asymptotic power-series expansions of radial functions for bound and free orbitals are also included. Finally, the present package contains complementary programs that use the radial subroutines for solving generic problems of interest in atomic and nuclear physics, namely, the self-consistent solution of the Dirac–Hartree–Fock–Slater equations for free neutral atoms and positive ions, and the calculation of differential cross sections for elastic collisions of electrons and positrons with atoms, and the scattering of nucleons by nuclei. The package also includes a manual in pdf format with a summary of the underlying physics and a detailed description of the formulas and numerical algorithms implemented in the programs, as well as derivations of the most relevant components.Summary of revisions: The original subroutines have been recoded and extended to include 1) a more accurate normalisation of bound states, 2) the calculation of free states of complex optical-model potentials, 3) asymptotic power-series expansions of radial functions, and 4) three practical applications.Nature of problem: The radial subroutines solve the radial Schrödinger and Dirac wave equations for a particle in a central potential V(r). They deliver the radial function(s), the energy eigenvalue for bound orbitals, and the phase shift for free orbitals.Solution method: The potential function V(r)≡rV(r) is defined by a table of values for a grid of radii that is dense enough to allow accurate natural cubic spline interpolation. The radial function is calculated for the potential defined by the interpolating cubic spline by means of exact power-series expansions, which are summed up to the desired accuracy.Additional comments including restrictions and unusual features: The subroutines are not capable of computing either bound or free states with energies very close to zero. Since the power-series expansions of the radial functions define exact piecewise solutions of the radial wave equations, they can be summed up to the accuracy required by the user. Truncation errors are controlled by the tolerance parameter ϵ, which determines the accuracy of the series summations. With double-precision arithmetic and ϵ∼10−15 the results are affected by only round-off errors. The subroutines deliver the values of the radial functions on a grid of radii defined by the user, which may be different from the grid used to specify the potential.[1] Salvat, F., J.M. Fernández-Varea, and W. Williamson, Jr. (1995), “Accurate numerical solution of the radial Schrödinger and Dirac wave equations.” Comput. Phys. Commun. 90, 151–168.[2] Rose, M.E. (1961), Relativistic Electron Theory (John Wiley and Sons, New York).

Charged-current neutrino-nucleus scattering off Xe isotopes

Xenon detectors are used in the search for dark matter and neutrinoless double-beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta})$. As the next-generation detectors reach masses in the ton scale, neutrinos from astrophysical sources are soon predicted to become background in such detectors. Theoretical predictions of neutrino scattering cross sections and information of nuclear structure effects therein are crucial in accounting for the background. We perform calculations for differential and total cross sections of charged-current neutrino scattering off the most abundant xenon isotopes. The nuclear-structure calculations are made in the proton-neutron quasiparticle random-phase approximation and the microscopic quasiparticle phonon model for even-mass and odd-mass nuclei, respectively. We compute total cross sections as a function of the neutrino energy, and also give estimates of total averaged cross sections for $^{8}\mathrm{B}$ solar neutrinos and supernova neutrinos using realistic energy distributions.

Precise calculation of differential cross sections for the Z boson plus jets production in proton-proton collisions at a center-of-mass energy of 13 TeV

The differential cross section predictions for the associated production of a Z boson and jets are presented in proton-proton collisions at a center-of-mass energy of 13 TeV. The differential cross sections are calculated by using a computational framework for the dielectron decay mode of the Z boson. Higher-order differential cross section predictions are obtained in the fiducial phase space and are compared at next-to-leading order (NLO) and next-to-NLO (NNLO) in perturbative quantum chromodynamics (pQCD). The predicted results are reported as functions of the variables including the jet multiplicity, the invariant mass of the Z boson, and transverse momenta of the Z boson and of the decay products. The predicted results are also reported for the angular correlation variables for the final state decay products. The differential results are generally improved in precision upon inclusion of the NNLO corrections. The total cross sections are calculated in the fiducial phase space at different orders in pQCD up to NNLO. The total production rates are predicted more accurately by the NNLO calculation.

Discrepancy of Astrophysical S-Factor.

Optical potential parameters have been discussed as an art more than physics. The effects of optical model parameters (OMPs) on differential cross section calculations and hence extraction of spectroscopic factor has been discussed. Optical model parameters have been expected especially for charged particles with light nuclei. The ambiguity of the optical potential parameters has been solved. Global optical potential parameters have been explained as not the best choice for extraction spectroscopic factor and hence calculate astrophysical S-factor. The measurements of experimental data have been discussed as the most important parameter that produces discrepancy in the astrophysical S-factor. The models used to extract spectroscopic factor is briefly discussed where examples are discussed. The importance of astrophysical s-factor has been explained under nuclear models. Few models have been chosen as just examples of discrepancy of astrophysical S-factor in spite of there are many models deal with such point of view. The discussion has neglected some effects of extraction astrophysical S-factor as coulomb barrier and electron screening.

Ionization and electron capture in collisions of bare carbon ions with hydrogen

Ionization and electron capture in collisions of bare carbon ions with atomic hydrogen has been studied using the wave-packet continuum discretization approach. The three-body Schr\odinger equation governing the collision process is solved using the two-center expansion of the total scattering wave function. Calculations have been performed for the projectile energy range from 1 keV/amu to 10 MeV/amu. While there is excellent agreement with experimental data for the total electron-capture cross section over the entire energy range, the calculated total ionization cross section slightly overestimates the only available measured point. The singly and doubly differential ionization cross sections at 1 and 2.5 MeV/amu are in good agreement with experiment. The differential cross section calculations are extended to lower energies where perturbative methods are expected to fail. At 100 keV/amu impact energy the present singly differential cross section in the ejected angle of the electron shows a pronounced peak in the forward direction. It is concluded that at low incident energies electron capture into the continuum of the projectile strongly enhances electron ejection in the forward direction.

Low-energy electron scattering from molecular hydrogen: Excitation of the X1Σg+ to b3Σu+ transition

We present time-of-flight differential cross-section measurements and convergent close-coupling calculations of differential cross sections for the electron-impact excitation of the $X\phantom{\rule{0.16em}{0ex}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}\ensuremath{\rightarrow}b\phantom{\rule{0.16em}{0ex}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ transition in molecular hydrogen. A part of this work was recently published [M. Zawadzki et al., Phys. Rev. A 97, 050702(R) (2018)]. In this work, agreement between theory and experiment is excellent overall, and marks a transition in electron-molecule scattering where differential scattering of excitation is found to be in such precise agreement. We also present total electron-impact excitation differential cross sections for ${\mathrm{H}}_{2}$ for which agreement between theory and experiment is found to be excellent.

Neutral-Current Neutrino-Nucleus Scattering off Xe Isotopes

Large liquid xenon detectors aiming for dark matter direct detection will soon become viable tools also for investigating neutrino physics. Information on the effects of nuclear structure in neutrino-nucleus scattering can be important in distinguishing neutrino backgrounds in such detectors. We perform calculations for differential and total cross sections of neutral-current neutrino scattering off the most abundant xenon isotopes. The nuclear-structure calculations are made in the nuclear shell model for elastic scattering and also in the quasiparticle random-phase approximation (QRPA) and microscopic quasiparticle-phonon model (MQPM) for both elastic and inelastic scattering. Using suitable neutrino energy distributions, we compute estimates of total averaged cross sections for ​8B solar neutrinos and supernova neutrinos.

Calculations of Differential Cross Sections Using Mixed Quantum/Classical Theory of Inelastic Scattering.

It is shown that the mixed quantum/classical theory (MQCT) for the description of molecular scattering is considerably improved by using integer values of orbital angular momentum l, just like in quantum theory, instead of treating it as a continuous classical variable related to the impact parameter. This conclusion is justified by the excellent accuracy of the modified theory for prediction of the differential cross sections, at various values of collision energy and in both forward and backward scattering regimes. This approach requires fewer trajectories, compared to the random Monte Carlo sampling, and the only convergence parameter is lmax (maximum orbital angular momentum) similar to Jmax in the full quantum theory (maximum total angular momentum). Calculations of differential and integral cross sections for elastic and inelastic channels are presented, and the role of the scattering phase is discussed. The low-energy range is analyzed in detail to obtain insight into how the mixed quantum/classical treatment works in the scattering regime dominated by resonances. The differential cross section for rotationally inelastic scattering, computed by MQCT approach, is presented for the first time.

Polarization and exchange effects in elastic scattering of electron with atoms and ions**Project supported by the National Natural Science Foundation of China (Grant No. 11274219) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China.

Laser-induced electron diffraction (LIED), in which elastic scattering of the returning electron with the parent ion takes place, has been used to extract atomic potential and image molecular structures with sub-Å precision and exposure time of a few femtoseconds. So far, the polarization and exchange effects have not been taken into account in the theoretical calculation of differential cross section (DCS) for the laser-induced rescattering processes. However, the validity of this theoretical treatment has never been verified. In this work, we investigate the polarization and exchange effects on electron impact elastic scattering with rare gas atoms and ions. It is found that, while the exchange effect generally plays a more important role than the polarization effect in the elastic scattering process, the exchange effect is less important on electron–ion collisions than on electron–atom collisions, especially for scattering in backward direction. In addition, our calculations show that, for electron–atom collisions at incident energies above 50 eV, both the polarization and exchange effects can be safely neglected, while for electron–ion collisions, both the polarization and exchange potentials do not make substantial contributions to the DCS at incident energies above 20 eV and scattering angles larger than 90°. Our investigation confirms the validity of the current LIED method.

Double differential cross section calculations for 16O and 90Zr elements

Double differential cross sections in proton induced reactions on 90Zr and O2 (inert matrix fuel) is calculated at the bombarding energies between 29 and 300 MeV. The proton-induced nuclear reaction cross section data can be used in technical applications such as the isotope production alternatives, spallation reactions for production of neutrons in spallation neutron source, etc. In this study, the cascade excition model including the effect of preequilibrium is used to calculate the differential cross section. Then, the obtained results are discussed and compared with available experimental data.

Laser-modified Coulomb scattering states of an electron in the parabolic quasi-Sturmian-Floquet approach

Electron scattering states in combined Coulomb and laser fields are investigated with a nonperturbative approach based on the Hermitian Floquet theory. Taking into account the Coulomb-specific asymptotic behavior of the electron wave functions at large distances, a Lippmann-Schwinger-Floquet equation is derived in the Kramers-Henneberger frame. Such a scattering-state equation is solved numerically employing a set of parabolic quasi-Sturmian functions which have the great advantage of possessing, by construction, adequately chosen incoming or outgoing Coulomb asymptotic behaviors. Our quasi-Sturmian-Floquet approach is tested with a calculation of triple differential cross sections for a laser-assisted $(e,2e)$ process on atomic hydrogen within a first-order Born treatment of the projectile-atom interaction. Convergence with respect to the number of Floquet-Fourier expansion terms is numerically demonstrated. The illustration shows that the developed method is very efficient for the computation of light-dressed states of an electron moving in a Coulomb potential in the presence of laser radiation.

Elastic electron differential cross sections for argon atom in the intermediate energy range from 40 eV to 300 eV

Measurements and calculations for electron elastic differential cross sections (DCS) of argon atom in the energy range from 40 to 300 eV are presented. DCS have been measured in the crossed beam arrangement of the electron spectrometer with an energy resolution of 0.5 eV and angular resolution of 1.5∘ in the range of scattering angles from 20∘ to 126∘. Both angular behaviour and energy dependence of DCS are obtained in a separate sets of experiments, while the absolute scale is achieved via relative flow method, using helium as a reference gas. All data is corrected for the energy transmission function, changes of primary electron beam current and target pressure, and effective path length (volume correction). DCSs are calculated in relativistic framework by expressing the Mott’s cross sections in partial wave expansion. Our results are compared with other available data.