Differential Elastic Scattering Cross Sections Research Articles

Differential elastic scattering and electron-impact ionization cross sections of nitrous oxide

With the aim of providing datasets for simulations of electron transport processes in the upper atmosphere, we measured singly differential elastic electron scattering and doubly differential electron-impact ionization cross sections of nitrous oxide. These measurements were conducted for primary electron energies between 30 eV and 1 keV in the angular range of 20°–150°. Secondary electron energies spanned from 4 eV to approximately half of the primary electron energy. In addition to the measurements, the differential elastic scattering cross sections of nitrous oxide were calculated using the IAM-SCAR + I model. Furthermore, the singly differential and total ionization cross sections of nitrous oxide were obtained by integrating the doubly differential ionization cross sections over emission angle and over both emission angle and secondary electron energy, respectively. These cross sections were compared to calculations performed using the BEB model and to experimental results of other groups, who determined the total ionization cross sections of nitrous oxide by collecting ions generated during electron impact.Graphical abstract

Series representation of differential elastic scattering cross section for electrons: Applications in theoretical models of electron transport in condensed matter

Series representation of differential elastic scattering cross section for electrons: Applications in theoretical models of electron transport in condensed matter

Imprints of α clustering in the density profiles of C12 and O16

The $^{4}$He nucleus is a well bound and highly correlated four-nucleon system that is also found in form of $\alpha$-clusters as substructure in nuclear many-body systems. The standard single-particle shell model cannot represent these four-body correlations. It is highly desirable to find a simple way to identify and distinguish these fundamental structures without large-scale computations. In this paper, we investigate with intrinsic Slater determinants as trial states in how far these two competing pictures prevail in the ground states of $^{12}$C and $^{16}$O. The trial states can describe both the $j$-$j$ coupling shell-model and $\alpha$-cluster configurations in a unified way. One-body density distributions of the trial states are calculated and compared to elastic scattering cross section data. The parameters of the trial state are chosen to reproduce the experimental charge radii. A well developed cluster structure is characterized by an enhancement of the differential elastic scattering cross sections, as well as the elastic charge form factors around the first peak positions. The density profiles of the internal regions can also be probed at higher momentum transfer regions beyond the second minimum. With these trial states one can visualize the competition between cluster and shell structure in an intuitive and simple way.

Annihilation and nuclear elastic scattering of low-energy antiprotons

We perform a fitting procedure to differential elastic scattering cross section data of antiproton at intermediate energy on three different nuclei to evaluate parameters of a six-parameters Woods-Saxon optical potential. Then, with these values, we calculate the reaction cross sections at different momenta and evaluate the differential elastic cross sections for low-momenta antiproton ([Formula: see text]). We find that our analysis underestimates the reaction cross sections for data over the momentum-range 50 MeV/c to 1000 MeV/c. We predict measurable effect for antiprotons with momentum above 50 MeV/c at large angles ([Formula: see text]), in agreement with other recent results. Finally, we consider possible improvements to the model and the analysis.

Multiple elastic scattering of electrons in condensed matter (new version announcement)

Multiple elastic scattering of electrons in condensed matter (new version announcement)

Differential elastic scattering cross-section of spin-polarized electron beams impinging on uranium

We investigate the effects of spin-polarization on the differential elastic scattering cross-section (DESCS) of electrons impinging on uranium atoms using the relativistic partial wave expansion method. The calculations presented here were obtained using the POLARe code. Changes in the shape of the DESCS of keV electron beams due to the transverse spin-polarization of the beam are demonstrated to be particularly intense for specific angles and relatively low energies of the incident beam. They can be used to establish the polarization degree of a given electron beam by comparing the POLARe theoretical calculations with experimental data.

Differential study of proton-helium collisions at intermediate energies: Elastic scattering, excitation, and electron capture

In a series of papers we present a comprehensive investigation of the four-body proton-helium differential scattering problem using the two-center wave-packet convergent close-coupling approach in the intermediate energy region where coupling between various channels is important. The approach uses correlated two-electron wave functions for the helium target. For comparison, a recently developed method that reduces the target to an effective single-electron system is also used. In this paper we present calculations of angular differential cross sections for elastic-scattering, target excitation, and electron-capture processes. The results of the two-electron and effective single-electron methods exhibit a good level of agreement. They also agree well with available experimental data. It is concluded that both versions of the wave-packet convergent close-coupling approach are capable of providing a realistic differential picture of all interdependent and interconnected binary processes taking place in proton-helium collisions at intermediate energies.

Studying multi-nucleon transfer reaction in a recoil mass spectrometer

We present simulation of a recoil mass spectrometer for measurement of multi-nucleon transfer reactions, based on Monte Carlo techniques. Target-like ions are generated event by event and transported to the focal plane of the spectrometer by the method of transfer matrices. Measured focal plane spectra for the elastic and six transfer channels of the reaction $$^{28}$$ Si+ $$^{94}$$ Zr are reproduced at two projectile energies near the Coulomb barrier. Excellent reproduction is achieved even with first-order ion-optical calculations, indicating not so significant role of higher order aberrations in conventional recoil separators with smaller acceptance. This is in striking contrast with the large acceptance magnetic separators used for studying transfer reactions, for which complex trajectory reconstruction algorithms involving higher order aberrations are essential. Transmission efficiency of the spectrometer, calculated by the reported code, is crucial to convert measured transfer probabilities to differential and integral transfer cross sections for each channel. We show effectiveness of the proposed methodology by extracting differential elastic scattering cross sections from measured yields for the reaction $$^{28}$$ Si+ $$^{94}$$ Zr. Besides being useful for other recoil mass spectrometers, our methodology can be employed for measurement of quasi-elastic reaction cross sections in velocity filters and gas-filled separators.

Neutron elastic scattering on calcium isotopes from chiral nuclear optical potentials

We formulate microscopic neutron-nucleus optical potentials from many-body perturbation theory based on chiral two- and three-body forces. The neutron self energy is first calculated in homogeneous matter to second order in perturbation theory, which gives the central real and imaginary terms of the optical potential. The real spin-orbit term is calculated separately from the density matrix expansion using the same chiral interaction as in the self energy. Finally, the full neutron-nucleus optical potential is derived within the improved local density approximation utilizing mean field models consistent with the chiral nuclear force employed. We compare the results of the microscopic calculations to phenomenological models and experimental data up to projectile energies of $E = 200$ MeV. Experimental elastic differential scattering cross sections and vector analyzing powers are generally well reproduced by the chiral optical potential, but we find that total cross sections are overestimated at high energies.

Low energy elastic electron scattering from benzonitrile (C6H5CN)

SynopsisWe present experimental differential elastic scattering cross sections (DCSs) for low energy electron scattering from benzonitrile along with integral and momentum-transfer cross sections that are determined from these DCSs. The measurements of DCSs are obtained using the relative flow method with helium as the standard gas, in a crossed electron-molecular gas beam arrangement. Our measurements are made at incident electron energies in the range of 1 – 30 eV and scattering angles in the range of (10°-130°).

A Dispersive Optical Model Analysis of the Alpha Particles Scattering by Titanium Element Nucleus and Its Natural Isotopes

A dispersive optical model analysis of the alpha particles scattering by titanium element nucleus and its natural isotopes has been applied for a new scattering potential within the energy range (1-100) MeV which has contained the range of the Coulomb barrier, and for constant input values of the parameters of this potential. This potential is extent of the mean field potential and is called by (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations have been compared with these resulting from global parameterizations of the alpha particles scattering potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section and polarization resulted only from the Coulomb spin-orbit term that has been appeared characteristically for selected energy and for selected center-of-mass scattering angle within the energy range (1-100) MeV, showed the excellent agreement with available experimental data and better than these resulted from global parameterizations of the alpha particles scattering potential.

Analytical Expressions for the Differential Elastic Scattering Cross Sections of Nonidentical Nuclear Particles with Channel Spin 1 and 2

In this paper, general analytical expressions are obtained for the differential elastic scattering cross sections of two nuclear particles with allowance for spin-orbit splitting for channels with the half-integer spins 3/2 and 5/2, which are parameterized with respect to the orbital quantum number l. This representation makes it possible to take into account explicitly a definite, energy-dependent number of scattering partial waves and to consider the relative contribution of each partial wave. The obtained expressions can be used when performing phase shift analysis in elastic scattering of nonidentical particles, for example, N2H, N6Li, 2H7Li, and 2H9Be at low energies.

Differential elastic scattering cross sections for deuterons on 9Be, at energies and angles suitable for elastic backscattering spectroscopy

The differential cross sections of the 9Be(d,d0) elastic scattering were determined in the present work in the energy range of Ed,lab = 1600–2200 keV in variable steps, mainly 20 keV at five backscattering angles (120°, 140°, 150°, 160° and 170°). The measurements were performed at the 5.5 MV TN11 HV Tandem Accelerator of the N.C.S.R. “Demokritos” implementing a high precision goniometer. The target used was a thin Si3N4 substrate with a beryllium layer on top. The obtained differential cross section values are compared to the ones existing in literature and the observed similarities and discrepancies are discussed.

Analytical Expressions for the Differential Elastic Scattering Cross Sections of Nonidentical Nuclear Particles with Channel Spins 3/2 and 5/2

Analytical Expressions for the Differential Elastic Scattering Cross Sections of Nonidentical Nuclear Particles with Channel Spins 3/2 and 5/2

A Dispersive Optical Model Analysis of the Protons Scattering by Titanium Element Nucleus and Its Natural Isotopes

A dispersive optical model analysis of the proton scattering by titanium element nucleus and its natural isotopes is applied to the construction of the complex single-particle mean field starting from Fermi energy value to the energy value 100MeV and for constant input values of the parameters of this mean field. This mean field is called (coulomb-nuclear) interference potential, that contains (spin-orbit) coulomb term. The results according to DOMACNIP program that has been designed for that purpose would contain: continuous energy variation of the depths of the real and imaginary parts of the mean field, which are connected by dispersion relations were compared with these resulting from global parameterization of the optical model potential. In addition to continuous energy variation of the real radius parameter of the Wood-Saxon approximation to the mean field potential with its Hatree-Fock approximation of the nonlocal potential. Consequently, our results for the continuous energy variations of the predicted total reaction cross section within the energy range (1-100) MeV, and with calculation step of the pervious range whose magnitude (1 MeV), differential cross sections, Ratio of the differential elastic scattering cross section to Rutherford cross section, polarization for selected energy showed the excellent agreement with available experimental data and with these resulted from global parameterization of the optical model potential.

Covariance Matrices for Differential and Angle-Integrated Neutron-Induced Elastic and Inelastic Scattering Cross Sections of 56Fe

Correlations between neutron inelastic scatterings angular distributions are not included in the Joint Evaluated Fission and Fusion (JEFF) nuclear data library, while they are key quantities for uncertainty propagation of nuclear data. By reproducing the angle-integrated cross sections and uncertainties of JEFF-3.1.1, the present work obtains covariance matrix between high energy model parameters using the least square method implemented in the CONRAD code. With this matrix, it is possible to generate correlations between angle-integrated cross sections and angular distributions, which are usually presented by Legendre coefficients. As expected, strong correlations are found, for example, between the Legendre coefficients of elastic and first-level-inelastic scatterings and the angle-integrated total, elastic, total inelastic cross sections.

Measurements of elastic scattering cross sections for 25.2, 28.5, 37.4, 36.8, and 42.2 keV X‐ray photons in elements with 22 ≤ Z ≤ 83

The differential elastic scattering cross sections were measured for 25.2 (Sn‐Kα), 28.5 (Sn‐Kβ1,3), 37.4 (Nd‐Kα1), 36.8 (Nd‐Kα2), and 42.2 (Nd‐Kα1,3) keV X‐ray photons at 139° scattering angle in elements with 22 ≤ Z ≤ 83. The measurement was done in reflection mode experimental setup involving 50Sn/60Nd secondary targets excited with 241Am radioisotope. The scattered X‐ray photons were detected using a high‐resolution low energy germanium detector (horizontal configuration, FWHM = 300 eV at 59.5 keV) coupled with computerized multichannel analyzer. The intensity of X‐ray photons along with geometrical factors were calculated from the theoretical knowledge of K X‐ray fluorescence cross sections and measured K X‐ray yields from excited targets. The measured values of differential cross sections were compared with the theoretical available values based on form factor and second‐order S‐matrix (SM) approaches. The experimental values of cross sections exhibit a large deviation from modified form (MF) values for the elements with BK/Ein ≈1, where BK is the K‐shell binding energy of electrons and Ein is the energy of incident photon. These deviations in experiment results were smooth out by the inclusion of anomalous scattering factors (ASFs) to the MF values. The measured elastic cross sections were found to be ~7% lower than MFASF values and agree with SM values for all elements under investigation.

High-Resolution Measurements of e^{+}+H_{2}O Total Cross Section.

Using a purely electrostatic positron beam, the total cross section of positrons scattering from H_{2}O has been measured for the first time with a high angular discrimination (≃1°) against forward scattered projectiles. Results are presented in the energy range (10-300)eV. Significant deviations from previous measurements are found which are, if ascribed entirely to the angular acceptances of various experimental systems, in quantitative accord with abinitio theoretical predictions of the differential elastic scattering cross section.

Multiple elastic scattering of electrons in condensed matter

Since the 1940s, much attention has been devoted to the problem of accurate theoretical description of electron transport in condensed matter. The needed information for describing different aspects of the electron transport is the angular distribution of electron directions after multiple elastic collisions. This distribution can be expanded into a series of Legendre polynomials with coefficients, Al. In the present work, a database of these coefficients for all elements up to uranium (Z=92) and a dense grid of electron energies varying from 50 to 5000 eV has been created. The database makes possible the following applications: (i) accurate interpolation of coefficients Al for any element and any energy from the above range, (ii) fast calculations of the differential and total elastic-scattering cross sections, (iii) determination of the angular distribution of directions after multiple collisions, (iv) calculations of the probability of elastic backscattering from solids, and (v) calculations of the calibration curves for determination of the inelastic mean free paths of electrons. The last two applications provide data with comparable accuracy to Monte Carlo simulations, yet the running time is decreased by several orders of magnitude. All of the above applications are implemented in the Fortran program MULTI_SCATT. Numerous illustrative runs of this program are described. Despite a relatively large volume of the database of coefficients Al, the program MULTI_SCATT can be readily run on personal computers. Program summaryProgram title: MULTI_SCATTProgram Files doi:http://dx.doi.org/10.17632/cvt9yz9gj8.1Licensing provisions: GNU General Public License 3 (GPL)Programming language: Fortran 90Nature of problem: Typically, elastic electron backscattering probabilities are estimated from results of Monte Carlo simulations of electron trajectories in a solid. This approach, although very convenient for a programmer, has major drawbacks: (i) the solid acceptance angles of analyzers are rather small, thus a large number of electron trajectories must be generated to obtain reasonable statistics; (ii) large running times are needed to reach an acceptable precision; (iii) results are always burdened with a statistical error. In the program MULTI_SCATT, an analytical formalism is implemented which leads to an accuracy comparable with Monte Carlo simulations, however it is faster by several orders of magnitude.Solution method: The program MULTI_SCATT requires presence of the database containing the coefficients Al for the series expansion of the differential elastic-scattering cross section. This database has a large volume of 96.2 Mb; a major computer effort is needed to complete these. This database has a large volume of 96.2 Mb; a major computer effort is needed to complete these calculations, and it has been decided to avoid this stage by providing the precalculated Al data. To obtain the Al value for a selected energy, the data from the database are interpolated in logarithmic coordinates. The elastic electron scattering probability is calculated from a slowly convergent series. Acceleration of the series convergence was found to be effective in the considered range of electron energies. Consequently, the running times of the program MULTI_SCATT are considerably decreased.Additional comments:(i) Restrictions: The program MULTI_SCATT can be used for electron energies between 100 and 5000 eV. Calculations of the elastic-backscattering probability and the calibration curve are performed under the assumption of normal incidence of the primary beam. This program is designed for applications in elemental solids, however, it can also be generalized to compounds (see text).(ii) Unusual features: To facilitate the use of the program MULTI_SCATT, several additional databases of parameters needed for the calculations are implemented using the DATA statement: inelastic mean free paths for different classes of materials, number of electrons in the valence band, atomic masses, densities, etc.Running time: Depending on the option selected, the running time is typically of the order of tens of milliseconds. For example, for tungsten and an electron energy of 500 eV, the running time varies from 12.8 milliseconds (angular distribution of electron directions after two collisions) to 60.2 milliseconds (calibration curve).

Carrier-envelope phase mapping in laser-induced electron diffraction

We present laser-induced electron diffraction measurements of elastic differential scattering cross sections (DCSs) of a photoelectron on the parent ion for argon, krypton, and xenon, using waveform-controlled few-cycle pulses. Considering only cutoff electrons and employing the adiabatic theory for the analysis enables us to eliminate ambiguities in extracting the DCSs from experimental spectra. Contrary to previous works, which mainly focused on the angular dependence of the DCS, our method allows us to extract also its dependence on the scattering momentum. In the case of xenon, we demonstrate how this method can be used to obtain the complete angular and momentum dependence of the DCS in a range of these variables determined by the pulse. The obtained results are compared to theoretical calculations based on the single-active-electron approximation, which shows a high level of agreement. Further investigations may provide opportunities to study multielectron effects when more advanced theoretical models become available.