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Angular distribution of electrons elastically scattered from N2.

Measurement of the angular distribution of electrons elastically scattered from N2 as a function of energy, utilizing a crossed-beam technique. Measurements have been made of monoenergetic electrons with energies between 5 and 90 eV scattered from a collimated beam of N2 at angles from -114 to +160 deg. The wide angular range of the measurements has enabled the determination of the total elastic-scattering and momentum-transfer cross sections. The measurements are relative and have been normalized to Fisk's (1936) theoretical calculation at 5 eV. The results generally agree well with other published measurements and with theory.

Shyn, T. W.↗

Angular Distribution of Elastically Scattered Electrons Determined and Its Effect on Collector Performance Computed

It has been demonstrated that the suppression of secondary electron emission significantly improves the performance of electron beam collectors (ref. 1). However, a complete analysis of the effects of secondary electron emission with respect to collector performance has not been possible because of the lack of quantitative data on angular distributions of secondary electrons. Secondary electrons are emitted with energies ranging from near zero to the energy of the incident primary. For our purposes, we define elastically scattered electrons as secondary electrons within 20 percent of the incident energy. Elastically scattered electrons are of great concern because their energy allows them to follow trajectories that can carry them almost anywhere within the vacuum envelope. If these secondaries leave the collector and reenter the slow wave circuit, they can produce undesired signal distortion and oscillation.This apparatus, which was built by Krainsky (ref. 2), was used at the NASA Lewis Research Center to obtain detailed measurements of the angular distributions of elastically scattered secondaries. Data were obtained for three surfaces of significant interest to collector applications: highly polished copper, copper roughened by ion sputtering, and isotropic graphite. Lewis researchers discovered that elastically scattered electrons have a complex angular distribution that is strongly dependent on the atomic number and surface morphology of the target material, as well as the energy and angle of incidence of the primary beam. At low energies, secondary emission from polished copper in the chosen energy range is primarily directed back to the source of primary electrons (backscattering). Forward scattering increases with primary energy until, at high energies, forward scattering dominates the angular distribution. Although back-scattered secondaries dominate the distributions of the textured copper surface, the yield is substantially lower. From the standpoint of secondary emission, isotropic graphite is the most attractive material because it exhibits low yield and little back scattering.

Krainsky, Isay L.↗

Close-coupling calculations with an INDOX/1s static potential, semiclassical exchange, and a semi-empirical polarisation potential for electron-CO2 elastic scattering and rotational excitation

A semiempirical molecular-orbital method for modelling the effective potential for electron-molecule scattering is applied to elastic scattering and rotational excitation of CO2 at 20 eV impact energy. Agreement with experiment is reasonably good. The calculated rotationally summed integral cross section is 67.8 a sub 0 squared.

Onda, K.↗

Measurement of the total cross section and $\rho$-parameter from elastic scattering in pp collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

In a special run of the LHC with β* = 2.5 km, proton–proton elastic-scattering events were recorded at $\sqrt{s}=13$ TeV with an integrated luminosity of $340$ μb -1 using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam t variable in the range from - t = 2.5 · 10 -4 GeV 2 to - t = 0.46 GeV 2 using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section σ tot , parameters of the nuclear slope, and the p -parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit t → 0. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the t-dependence. The results for σ tot and p are σ tot (pp → X) = 104.7 ± 1.1 mb, p = 0.098 ± 0.011. The uncertainty in σ tot is dominated by the luminosity measurement, and in p by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Angular distribution of electrons elastically scattered from CH4

Differential elastic (vibrationally) scattering cross sections of CH4 by electron impact have been measured using a modulated crossed-beam method. The energy and angular range covered were from 5 to 50 eV and from 12 to 156 deg, respectively. The integrated and momentum transfer cross sections were obtained from the differential cross sections. The present results are compared with earlier data. Some discrepancies were found in the measurements and theoretical results.

Shyn, T. W.↗

Nuclear spin features relevant to ab initio nucleon-nucleus elastic scattering

Effective interactions for elastic nucleon-nucleus scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations, as well as a consistent treatment of the relevant operators at each order. Previous work using these interactions has shown good agreement with available data. Here, we study the physical relevance of one of these operators, which involves the spin of the struck nucleon, and examine the interpretation of this quantity in a nuclear structure context. Using the framework of the spectator expansion and the underlying framework of the no-core shell model, we calculate and examine spin-projected, one-body momentum distributions required for effective nucleon-nucleus interactions in $J=0$ nuclear states. The calculated spin-projected, one-body momentum distributions for $^4$He, $^6$He, and $^8$He display characteristic behavior based on the occupation of protons and neutrons in single particle levels, with more nucleons of one type yielding momentum distributions with larger values. Additionally, we find this quantity is strongly correlated to the magnetic moment of the $2^+$ excited state in the ground state rotational band for each nucleus considered. In conclusion, we find that spin-projected, one-body momentum distributions can probe the spin content of a $J=0$ wave function. This feature may allow future ab initio nucleon-nucleus scattering studies to inform spin properties of the underlying nucleon-nucleon interactions. The observed correlation to the magnetic moment of excited states illustrates a previously unknown connection between reaction observables such as the analyzing power and structure observables like the magnetic moment.

6 ≤ A ≤ 19↗

Electron-H Elastic Scattering

Precision calculations for e^{-}-H and e^{-}-He^{+} for S-wave scattering in the elastic region have been carried out using the optical potential approach. This formalism is now extended to e^{-}-H P-wave scattering in the elastic region. The scattering equations are solved by the non-iterative method. Phase shifts are calculated using Hylleraas-type correlation functions up to 84 terms. Results are rigorous lower bounds to the exact phase shifts and they are compared to those obtained in previous calculations.

Bhatia, A. K.↗

P(P bar)P elastic scattering and cosmic ray data

It is shown that the total cross section for pp elastic scattering at cosmic ray energies, as well as the total cross section, the slope parameter b(s,t) and the differential cross section for small momentum transfer at ISR and collider energies for p(p)p elastic scattering can be simultaneously fitted by using a simple Regge pole model. The results of this theory is discussed in detail.

FAZAL-E-ALEEM↗

Elastic scattering of 600-MeV protons from H, D, He-3, and He-4.

Study of the elastic scattering of 600-MeV protons from light nuclei. Differential cross sections have been obtained for the scattering of protons from hydrogen, deuterium, helium-3, and helium-4. Polarization was measured for deuterium and He-4 nuclei. The p-p cross-section data are in excellent agreement with the predictions from the Livermore phase shifts. Small-angle p-D, p-He-3 elastic scattering data are compared with calculations based on the multiple-scattering theories of Watson and Glauber.

Boschitz, E. T.↗

Elastic scattering and rotational excitation of a polyatomic molecule by electron impact - Acetylene

Differential, integral, momentum transfer, and partial cross sections have been calculated for elastic scattering and rotational excitation of C2H2 by 10-eV electrons. The effective potential includes static, exchange, and polarization interactions calculated by the INDOX/1s method and the semiclassical exchange approximation with adiabatic polarization at large electron-molecule distances. The scattering is treated by well converged rotational close coupling using the centrifugal dominant scheme to select the channels included and including up to 32 coupled channels for a given total angular momentum. The calculated integral cross sections for pure elastic scattering and rotation excitation are 54.5 and 41.4 a(0)squared, respectively. These are much larger than the values (34.4 and 18.6 a(0)squared) previously (Onda and Truhlar, 1979) calculated for the isoelectronic molecule N2, at this energy. This illustrates how the greater spatial extent of C2H2 greatly increases the cross sections for pure elastic and rotationally inelastic scattering.

Thirumalai, D.↗

Electron-Hydrogen Elastic Scattering

Scattering by single-electron systems is always of interest because the wave function of the target is known exactly. Various approximations have been employed to take into account distortion produced in the target. Among them are the method of polarized orbitals and the close coupling approximation. Recently, e-H and e-He+ S-wave scattering in the elastic region has been studied using the Feshbach projection operator formalism. In this approach, the usual Hartree-Fock and exchange potentials are augmented by an optical potential and the resulting phase shifts have rigorous lower bounds. Now this method is being applied to the e-H P-wave scattering in the elastic region. The number of terms in the Hylleraas-type wave function for the 1,3 P phase shifts is 84 and the resulting phase shifts (preliminary) are given. The results have been given up to five digits because to that accuracy they are rigorous lower bounds. They are in general agreement with the variational (VAR) results of Armstead, and those obtained from the intermediate energy R-matrix method (RM) of Scholz et al., and the finite element method (FEM) of Botero and Shertzer. The later two methods do not provide any bounds on phase shifts.

Bhatia, A. K.↗