Differential Elastic Scattering Cross Sections Research Articles

Improvement of Angular Differential Elastic Scattering Cross Sections in Nucleon-meson Transport Code NMTC/JAERI97 for Neutron Transmission Experiment Analysis.

The nucleon-meson transport code NMTC/JAERI97 is revised in the treatment of the angular distribution of the neutron elastic scattering for the energy region from 20 to 100 MeV. The approximation of the angular distribution with the first order Bessel function is changed to the random sampling based on the database evaluated by the optical model potential parameters (OMPs). For 43- and 68-MeV quasi-monoenergetic neutrons through iron, concrete and polyethylene shields, neutron transmission experiments are analyzed with the updated NMTC/JAERI97 code. It is shown that the updated NMTC/JAERI97 calculations agree well with the measured transmission neutron energy spectra and give significantly improved C/E values for the attenuation length in comparison with the results of the original version. It is also notable that the updated calculation represents quite well the measured neutron spectra at the positions of 20 and 40 cm off beam axis of the shields. Moreover, it is found that the cross sections evaluated by an OMP gives a better result than those by the systematics for the transmission calculation of neutrons with energies below 40 MeV.

Three-body approach to proton-hydrogen charge exchange and elastic scattering

The impact-parameter Faddeev approach to atomic three-body collisions which has been developed for, and successfully applied to, ion-atom scattering processes, has now been developed further by including, instead of the Coulomb potentials, the full two-particle off-shell Coulomb T matrices in all ``triangle'' contributions to the effective potentials. Results of calculations of proton-hydrogen collisions with only the ground states of the hydrogen retained in both the direct and the rearrangement channels are presented. Total and differential electron transfer, as well as differential elastic scattering cross sections, are obtained simultaneously in very good agreement with experiment, over a wide range of (nonrelativistic) incident energies.

Fast neutrons incident on titanium

Differential neutron elastic-scattering cross sections of elemental titanium were measured from 4.5 to 10.0 MeV in incident-energy increments of and at forty or more scattering angles distributed between and degrees. Concurrently, differential neutron inelastic-scattering cross sections were measured for observed excitations of , , , , , and . All of the observed inelastic neutron groups were composites of contributions from several isotopes and/or levels. The experimental results were used to develop energy-average optical, statistical and coupled-channels models.

Plasma screening effects on eikonal phase for electron-ion elastic collisions in weakly coupled plasmas

Eikonal approximation is applied to investigate elastic electron-ion collisions in weakly coupled plasmas. Plasma screening effects on eikonal phase are investigated for eikonal differential elastic scattering cross sections. The electron-ion interaction potential in weakly coupled plasmas has been obtained by the introduction of the longitudinal plasma dielectric function. The semiclassical straight-line trajectory method is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase as a function of the impact parameter and the plasma parameters. In the first-order eikonal approximation, the dynamic plasma screening effect is identical to the static screening effect obtained by the Debye–Hückel potential. The eikonal differential elastic cross section substantially decreases with an increase in the projectile energy and increases as the plasma screening effect decreases through the Debye length. The plasma screening effects are more significant for large impact parameters.

Low-velocity elastic scattering of Rb-Rb

With reference to recent progress in preparing slow and intense Rb beams ({ital rubidium atomic funnel} and {ital low-velocity intense source of atoms from a magneto-optical trap}) we have calculated total and differential elastic scattering cross sections and scattering lengths for ground-state collisions of {sup 85}Rb as well as {sup 87}Rb. Our results are based on the state of the art X{sup 1}{Sigma}{sub g}{sup +} and athinsp{sup 3}{Sigma}{sub u}{sup +} potentials. Pronounced resonances in the total scattering cross sections occur for collision velocities below 15 m/s. We propose scattering experiments with slow Rb beams in order to check the currently known singlet and triplet potential-energy curves. {copyright} {ital 1997} {ital The American Physical Society}

Determination of the inelastic mean free path (IMFP) of electrons in germanium and silicon by elastic peak electron spectroscopy (EPES) using an analyser of high resolution

The IMFP of electrons is a fundamental material parameter of surface analysis by AES, XPS, EPES and EELS. In surface analysis calculated IMFP values are used. Their experimental determination is rather difficult. The IMFP of amorphous Ge and polycrystalline Si was determined by comparing the elastic peak intensity ratios with electrolytic Ni reference sample of 1 nm surface roughness, achieved by dedicated Ar + ion bombardment cleaning and examined by STM. Experimental results obtained with a hemispherical analyser type ESA 31 developed by ATOMKI Debrecen have been evaluated by Monte Carlo analysis, based on Jablonski's differential elastic scattering cross sections and elaborated for the HSA analyser angular window. Due to the 5 × 10 −5 energy resolution of the ESA 31 no spectrometer correction was needed. The ratio of the background to the elastic peak was < 1% at 4 keV. The energy range was extended to 5keV using Ashley's IMFP data. Reasonable agreement was found with our previous CMA experimental results in the overlapping energy range and with Ashley. They exhibit systematically higher values by 15–20%. EPES proved to be an efficient tool for IMFP measurements.

Nucleus-nucleus elastic scattering at intermediate energies: Glauber model approach

The differential elastic scattering cross section of a few heavy-ion systems, in the energy range 8{endash}100 MeV/nucleon, has been studied in the framework of the Coulomb-modified Glauber model. Ingredients in this formalism are the densities of the colliding ions and the elementary nucleon-nucleon scattering amplitude. The only free parameter {alpha}{sub NN}, the ratio of the real to imaginary part of the forward nucleon-nucleon scattering amplitude, is varied to fit the data. Elastic scattering angular distributions using the realistic two-parameter Fermi densities and the surface-matched Gaussian densities agree reasonably well with each other. {copyright} {ital 1997} {ital The American Physical Society}

Neutron scattering from elemental silver

Differential neutron elastic-scattering cross sections of elemental silver were measured from 1.5 → 10 MeV at scattering angles distributed between ≈17° and 160°. Cross sections for ten inelastically scattered neutron groups were determined, corresponding to observed excitations of 328 ± 13, 419 ± 50, 748 ± 25, 908 ± 26, 1150 ± 38, 1286 ± 25, 1507 ± 20, 1623 ± 30, 1835 ± 20, and 1944 ± 26 keV, all of which were composites of contributions from the two isotopes 107Ag and 109Ag. The experimental results were interpreted in terms of the spherical-optical and rotational and vibrational coupled-channels models.

Elastic scattering and the associated anomalous dispersion in the atomic region 13 ⩽ Z ⩽ 82 at 30.85 keV

We have measured the differential elastic scattering cross sections in the atomic region 13 ⩽ Z ⩽ 82 using nearly monoenergetic unpolarised Cs Kα (30.85 keV) radiation at a scattering angle of 90°. Experimental elastic scattering cross sections are compared with the theoretical estimates based on form factor formalisms (relativistic, non-relativistic and relativistic modified form factors). Good agreement is observed between the experimental results and the theoretical estimates. Form factors were deduced using experimental elastic scattering cross sections. Real (f') and imaginary (if") parts of the anomalous dispersion correction components have been calculated relativistically. Experimental nonanomalous form factors were corrected for anomalous dispersion. Experimental results were compared with the theoretical estimates and discussed in order to reflect the data on the current knowledge. Deviation of the experimental form factors above and below the absorption edges, and also nearer to the edges clearly indicates the need of dispersion corrections.

Elastic scattering and the associated anomalous dispersion in the vicinity of Cd, In, Sn and Sb, K-absorption edges

Using nearly monoenergetic unpolarized Kα X-rays with energies E = 17.44-42.75 keV, differential elastic scattering cross sections for Cd, In, Sn and Sb were measured at an angle of 90° to assess the contribution of anomalous dispersion in the vicinity of K-absorption edges. An X-ray tube with a secondary target arrangement was used to obtain the monoenergetic radiation. A new method is developed to estimate the degree of monochromaticity, geometrical effects of the measuring system, solid angle correction and some considerations which are necessary in experiments using an X-ray tube with secondary target arrangement. Experimental results are compared with theoretical elastic scattering cross sections calculated using relativistic form factors (RFFs), relativistic modified form factors (RMFs), a combination of RFFs, RMFs and angle-independent “anomalous” scattering factors (ASFs), and relativistic numerical calculations based on multipole expansion of the second order S-matrix approach. Fairly good correspondence is observed between the experimental results and a combination of RFFs with ASFs above and below the edges. The experimental results are in excellent agreement with S-matrix values and a combination of RMFs with ASFs above and below the edges of Cd, In, Sn and Sb. However, the differences are larger nearer to the edges indicating the importance of anomalous terms in reproducing “anomalous” behaviour of the K-threshold regions.

Eikonal differential scattering cross sections for elastic electron–ion collisions in strongly coupled plasmas

The eikonal approximation is applied to investigate the elastic electron–ion collision processes in strongly coupled plasmas. Plasma-screening effects are investigated for the eikonal differential elastic scattering cross sections. The electron–ion interaction potential in strongly coupled plasmas has been approximated by the ion-sphere model potential. The classical straight-line trajectory approximation is applied to the motion of the projectile electron in order to investigate the variation of the eikonal differential elastic scattering cross section as a function of the impact parameter and ion-sphere radius. A modified eikonal approximation called the Wallace correction is also considered. The eikonal differential elastic scattering cross sections substantially decrease with an increase of the energy of the projectile electron and increase as the plasma-screening effect decreases through the ion-sphere radius.

Unified treatment of scattering and cluster structure in alpha +closed shell nuclei: 20Ne and 44Ti.

The model of an \ensuremath{\alpha} cluster orbiting a closed shell core provides a highly successful description of low lying bound and resonant states of $^{20}\mathrm{Ne}$ and has been successfully extended to $^{44}\mathrm{Ti}$ by various authors. This description is closely related to \ensuremath{\alpha} scattering from the relevant closed shell core, and although the scattering has previously been reasonably well reproduced with a local optical model potential, few attempts have been made to link the two phenomena. In this paper, a universal \ensuremath{\alpha}-core interaction is given which describes the spectra, B(E2\ensuremath{\downarrow}) transition strengths, \ensuremath{\alpha}-decay widths, and differential elastic scattering cross sections for the systems corresponding to $^{20}\mathrm{Ne}$${=}^{16}$O+\ensuremath{\alpha} and $^{44}\mathrm{Ti}$${=}^{40}$Ca+\ensuremath{\alpha}. This potential has only a single free parameter, the radius, whose value is kept fixed for each nucleus.

Path-length distribution of photoelectrons emitted from homogeneous noncrystalline solids: Consequences for inelastic-background analysis.

The path-length distribution function characterizing the probability for a photoelectron to escape from a homogeneous solid after traveling a certain path length R has been found analytically by solving a Boltzmann-type kinetic equation with appropriate boundary condition. The solution is obtained in the transport approximation and is valid for an arbitrary geometry and under the condition that the typical angular spectrum of photoelectrons is a smooth function of the angular variable. It is shown that, depending on the initial anisotropy of the photoelectron emission, the path-length distribution may either reach a maximum value at a certain path length or be a monotonically decreasing function. The path-length distribution has also been calculated by the Monte Carlo technique employing realistic Mott differential elastic-scattering cross sections. The theoretical results were obtained for a number of photoelectron lines in Al, Cu, and Au with different asymmetry parameters and photoelectron energies. It was shown that within about 10% accuracy the path-length distribution function is a universal function of the path length divided by the transport mean free path. This conclusion is in full accordance with the prediction of the transport approximation. The consequences and implications of elastic-scattering effects for the inelastic background analysis of Auger electron spectroscopy and x-ray photoemission spectroscopy energy spectra are discussed.

A theory of quantitative angle-resolved X-ray photoelectron spectroscopy

The theoretical approach, based on solving the kinetic equation in the transport approximation, to describe photoemission, has been verified by comparison with Monte Carlo calculations. The analytical expression for the photoelectron distribution with respect to both azimuthal and polar angles has been derived. The angular spectrum of signal photoelectrons has been found to consist of three terms. One of the terms corresponds to the particles escaping from the sample without being scattered elastically and coincides with the initial angular distribution of photoelectrons ejected from atoms, the other terms describe the partly and fully randomized fractions of the photoelectron current. The mean escape depth of signal electrons leaving the target in a narrow solid angle has been calculated analytically. This escape depth generally depends on the azimuthal and polar emission angles as well as on the asymmetry parameter. It is shown that, in the case of heavy elements, the elastic collisions affect noticeably the mean escape depth. The sampling depth differs significantly from the value found in the straight line approximation. The analytical results are in good agreement with the corresponding Monte Carlo data obtained by making use of a realistic differential elastic scattering cross section.

Influence of surface excitations on electrons elastically backscattered from copper and silver surfaces.

The influence of surface excitations on electrons elastically backscattered from solid surfaces is investigated. Elastic-scattering differential cross sections are calculated using the partial-wave expansion method and the finite difference techique for solid atoms with the Hartree-Fock-Wigner-Seitz potential. An extended Drude dielectric function which allows the characteristic oscillator strength, damping constant, and critical-point energy for each subband of valence electrons is employed to estimate electron inelastic mean free paths for volume excitations. The same dielectric function is applied to evaluate the probability of surface excitations for incident and escape electrons by including the recoil effect without the small-angle approximation. Results of Monte Carlo simulations on the elastic reflection coefficient and the angular distribution of electrons elastically backscattered from Cu and Ag surfaces are presented. It is revealed that surface excitations significantly reduce the elastic reflection coefficient for low-energy electrons, but less significantly influence the angular distribution for large escape angles. Our results agree very well with experimental data.

Fast-neutron scattering from vibrational palladium nuclei

Differential neutron elastic-scattering cross sections are measured from ≈ 1.5 to 10 MeV in sufficient energy and angle detail to define the energy-average behavior. Concurrently, neutron inelastic-scattering cross sections are measured from ≈ 1.5 to 8 MeV. Inelastically-scattered neutron groups are observed corresponding to excitations of: 306 ± 14, 411 ± 47, ≈ 494, 791 ± 20, 924 ± 20, 1156 ± 24, 1358 ± 35, 1554 ± 47 and 1706 ± 59 keV, with additional tentative groups at 1938 and 2059 keV. Particular attention is given to the inelastic excitation of the 2 + yrast states of the even isotopes. This broad data base is examined in the context of optical-statistical and coupled-channels models. The resulting model parameters are consistent with systematic trends in this vibrational mass region and provide a suitable vehicle for many applications.

Non-Rutherford elastic scattering cross sections for 170° backscattering of 0.15–3.00 MeV protons from beryllium

Differential elastic scattering cross sections of 0.15–3.00 MeV protons for beryllium have been measured at a laboratory scattering angle of 170°. The values of the cross sections are presented in graphical and tabular form and compared with previous graphical data. The interferences from other nuclear reactions in the experiment are discussed.

Empirical forms for the electron/atom elastic scattering cross sections from 0.1 to 30 keV

Empirical forms have been found for the total and differential elastic scattering cross sections for electron/atom scattering. The cross sections are valid over the range 0.1–30 keV and across the periodic table. The empirical forms of the cross sections are derived from trends in tabulated Mott scattering cross sections. The form of the total cross section is similar to a previously published cross section and is based on the screened Rutherford cross section. The fit to the differential Mott cross sections is decomposed into two parts, one part being of the same mathematical form as the screened Rutherford cross section σR, and the second part being an isotropic distribution σI. These two mathematical forms were chosen because they give a straightforward generation of random scattering angles. The screened Rutherford part of the differential scattering cross section is first fitted to the half-angle of the Mott cross sections. This fit of the differential screened Rutherford is in turn reduced to a fit of the screening parameter alone over energy and atomic number. The screened Rutherford part of the cross section is highly peaked in the forward scattering direction and needs to be balanced by the isotropic distribution. The ratio of the total cross sections (σR/σI) between the screened Rutherford part of the differential scattering cross section and the isotropic part of the distribution is then fitted to give the same ratio of forward to backscattered currents as the tabulated Mott differential cross sections. Using this dual form of the scattering cross section for the differential cross section, and the previously (independently) fitted total cross section, the backscattering coefficients for normal incidence are calculated. The two equations describing the differential cross section, one for the Rutherford screening parameter and one for the ratio σR/σI, are simplified to remove redundant parameters, and then fitted to the backscattering coefficients calculated directly from the tabulated Mott cross sections. A straightforward expression for the differential cross section was found to give backscattering results covering all the major trends with energy and atomic number compared to the backscattering coefficients calculated using tabulated Mott cross sections.

Ab initio potential energy surface for H–H2

Ab initio calculations employing large basis sets are performed to determine an accurate potential energy surface for H–H2 interactions for a broad range of separation distances. At large distances, the spherically averaged potential determined from the calculated energies agrees well with the corresponding results determined from dispersion coefficients; the van der Waals well depth is predicted to be 75±3μEh. Large basis sets have also been applied to reexamine the accuracy of theoretical repulsive potential energy surfaces (25–70 kcal/mol above the H–H2 asymptote) at small interatomic separations; the Boothroyd, Keogh, Martin, and Peterson (BKMP) potential energy surface is found to agree with results of the present calculations to within the expected uncertainty (±1 kcal/mol) of the fit. Multipolar expansions of the computed H–H2 potential energy surface are reported for four internuclear separation distances (1.2, 1.401, 1.449, and 1.7a0) of the hydrogen molecule. The differential elastic scattering cross section calculated from the present results is compared with the measurements from a crossed beam experiment.

Angular distribution of electrons elastically scattered from ozone.

We have measured differential elastic-scattering cross sections of ozone by electron impact. A crossed-beam method was used. The energy and angular range measured were from 3.0 to 20 eV and from 12\ifmmode^\circ\else\textdegree\fi{} to 156\ifmmode^\circ\else\textdegree\fi{}, respectively. Strong forward and backward scattering was observed as the incident energy increased. Integrated and momentum-transfer cross sections have been obtained from the differential cross sections. The integrated cross sections over this energy range were found to be almost constant in magnitude.