Differential Elastic Scattering Cross Sections Research Articles

A measurement of the total cross section at √s= 1800GeV

The p p differential elastic scattering cross section was measured at √ s =1800 GeV, using an improved accelerator luminosity determination and CDF small angle data in the range of 0.05 ≤ t ≤ 0.2( GeV / c ) 2 . By extrapolating the differential cross sections to t=0 and using the optical theorem we obtain a total cross section of σ tot ( pp ) = 72.0±3.6 mb. This result is preliminary in the sense that we expect to further reduce the systematic error on the optical point.

A measurement of the pp total cross section at √s = 1800 GeV

The pp differential elastic scattering cross section was measured at √s = 1800 GeV, using an improved accelerator luminositydetermination and CDF small angle data in the range of 0.05 ≤ t ≤ 0.2( GeV/c) 2. By extrapolating the differential cross sections to t=0 and using the optical theorem we obtain a total cross section of σ tot(pp) = 72.0±3.6 mb. This result is preliminary in the sense that we expect to further reduce the systematic error on the optical point.

On the attenuation of Auger and photoelectrons in solids with thin overlayers

A systematic study of the depth distribution function (DDF), which in the most general sense describes the attenuation of signal electrons, has been performed by means of a Monte Carlo simulation. The influence of elastic scattering is accounted for in this model by the use of differential elastic scattering cross sections obtained with the partial wave expansion method. The particular features of the Monte Carlo algorithm allow a detailed study of the influence of the substrate-overlayer combination and the overlayer thickness on the DDF. Extensive model calculations were performed for several substrate-overlayer combinations of the elements Be, Al, Si, Ag, In and Au for signal electrons over a wide range of energies (250–1000 eV). No significant effect of backscattering from the interface on the DDF could be observed within the statistical accuracy of the results. The shape of the DDF at the surface shows a strong deviation from exponential behaviour. The extent of this effect depends on the material and the energy. Most importantly, however, the DDF of electrons originating from the substrate, exhibits a significant dependency on the overlayer material. The above effects are due to elastic scattering of the signal electrons by the atoms of the host material.

Cross section for 160° elastic scattering of 1.4–2.4 MeV protons from nitrogen and titanium

Differential elastic scattering cross sections for 1·4–2·4 MeV protons from natural nitrogen and titanium were measured at laboratory scattering angle 160°. The present cross section data are tabulated for later use in backscattering analyses. Our results for nitrogen are in qualitative agreement with previous data taken at slightly different scattering angles. The cross sections of titanium agree with theoretical Rutherford values within experimental errors. Examples of recent analytical applications of proton backscattering are given.

Contribution of exchange on charge-state dependence of large-angle electron-ion elastic scattering

The differential elastic scattering cross sections of electrons from Aq+ ions are calculated incorporating the exchange contribution of the continuum and bound orbitals in addition to the static potential. The effect on the differential cross sections at large angles, in particular for theta =180', is examined for different charges states of carbon, fluorine, and magnesium ions. There is an improved agreement between experiments with Fq+ and theory when the exchange contribution is included.

Electron correlation and charge density study of N2 and O2 by high energy electron scattering

The differential elastic scattering cross sections of N2 and O2 for 29 keV electrons have been measured. The experiment was performed using a Mollenstedt type energy analyzer to isolate the elastically scattered electrons. The difference between the measured results and calculations from molecular Hartree-Fock wave functions reveals the electron correlation in the molecules. Using the previously measured total scattering data, the inelastic scattering cross sections are derived. Several potential energies of the target are evaluated from the cross sections. Results at small angles are analyzed in terms of molecular moments and diamagnetic susceptibilities. The scattering behavior at small angles of the N2 measurement agrees well with several ab initio calculations.

Absolute differential cross section measurements for proton-deuteron elastic scattering at 641.3 and 792.7 MeV.

The absolute p-d elastic-scattering differential cross sections were measured at 641.3 and 792.7 MeV beam energies over a range of c.m. angles from \ensuremath{\sim}35\ifmmode^\circ\else\textdegree\fi{} to \ensuremath{\sim}115\ifmmode^\circ\else\textdegree\fi{} and \ensuremath{\sim}35\ifmmode^\circ\else\textdegree\fi{} to \ensuremath{\sim}140\ifmmode^\circ\else\textdegree\fi{}, respectively. The longitudinally polarized (L-type) proton beam produced by the Lamb-shift ion source at LAMPF was used. The beam intensity was measured to high accuracy (\ensuremath{\sim}0.1%) by a scintillator-beam particle-counting system designed and developed prior to the experiment. Typical uncertainties in the absolute cross sections were about 2--3% total, somewhat larger at back angles. The present results were compared with the existing measurements and the controversy about the previous data at 800 MeV was resolved. The present data can be fit with a relativistic multiple-scattering theory which uses off-mass-shell extrapolations of the nucleon-nucleon amplitudes suggested by the structure of derivative meson-nucleon couplings. Relativistic-impulse-approximation calculations do not fit these data at either energy.

Elastic scattering of intermediate energy hadrons from 12C

The elastic-scattering differential cross sections for protons (150-1040 MeV), antiproton (46.8 and 179.7 MeV) and pions (180 and 260 MeV) on 12C are analysed within the framework of Glauber multiple scattering theory up to the third-order term. Pauli, short-range dynamical and centre-of-mass correlations besides the Coulomb effect are considered. It is found that nucleon-nucleon correlations may play an important role in describing the experimental data in cases of proton scattering at 1.04 GeV and antiproton scattering at 179.7 MeV. The range of applicability of the Glauber multiple scattering theory is discussed.

Dispersive versus constant-geometry models of the neutron- 208Pb mean field

Phenomenological optical-model analyses of differential elastic scattering cross sections of neutrons by 208Pb indicate that the radius of the real part of the potential decreases with increasing energy in the domain 4 < E < 40 MeV. On the other hand, the experimental total cross section is compatible with a real potential whose radial shape is energy independent. In order to clarify this situation, we compare a “constant geometry” model whose real part has an energy-independent radial shape with a “dispersive model” whose real part has an energy-dependent radial shape calculated from the dispersion relation which connects the real and imaginary parts of the field. The following three main features are considered, (i) The junction of the optical-model potential with the shell-model potential at negative energy, (ii) The agreement between the calculated total and differential cross sections and their experimental values, (iii) The extent to which the real part of the optical-model potential can be accurately determined by analyzing the total cross section only. It is concluded that the presently available experimental data support the existence of an energy dependence of the radial shape of the real potential, in keeping with the dispersion relation. A new parametrization of a “dispersive” mean field is also presented. It does not involve more parameters than the previously published one but takes better account of the physical properties of the spectral functions; it is shown to improve the agreement between predicted and experimental scattering data.

Selection of measured points in elastic cross section

On the basis of Gauss-Legendre quadrature the authors suggest the selection of measurement angles in the elastic differential scattering cross section which should minimise measurement time in experiments to determine the angle-integrated elastic cross section.

Corrections to tabulated anomalous-scattering factors

Z-dependent energy-independent corrections to the relativistic anomalous-scattering factors tabulated by a number of workers are given. These corrections are most significant for medium-Z and high-Z atoms, but are experimentally observable even in low-Z elements. Examples of use of the correction factors are provided for the real anomalous-scattering factor f' and for the differential elastic scattering cross section do'/dO.

Algebraic scattering theory for heavy ions.

Algebraic potentials from SO(3,1) and SO(3,2) representations of scattering functions are deduced by matching to scattering functions obtained by fitting $^{12}\mathrm{\ensuremath{-}}^{12}$C elastic-scattering differential cross sections. Their variations with energy suggest a simple mapping between algebriac and coordinate-space interactions.

High energy predictions for ¯pp andpp elastic scattering and total cross sections

Predictions for thes behavior at high energies are made for¯pp andpp: the differential elastic scattering cross section dσ/dt vs.t, the squared 4-momentum transfer; the total elastic cross sectionσel; the nuclear slope parameterB; the curvature parameterC; ϱ, the ratio of the real to the imaginary portion of the forward scattering amplitude; and the total cross sectionσtot. A hybrid approach is employed in order to gain reliable predictions. The energy dependence ofϱ andσtot is fixed by fittingpp and¯pp experimental data forϱ andσtot from 15 GeV toS¯ppS energies, using analytic amplitudes. The other quantities are found using the Chou-Yang model, where the total, cross section is fixed from the fit.

Absolute elastic differential scattering cross sections for electron impact on carbon dioxide in the intermediate energy region

Absolute elastic differential scattering cross sections (DCS) for electron impact on carbon dioxide in the electron impact range 20-100 eV and angular range 20-120' are reported. The results are obtained using a relative flow technique in which the DCS of CO2 is compared with that of helium at each energy and angle. The authors present both the absolute values of the DCS of CO2 and the ratios DCS(CO2)/DCS(He).

Absolute elastic differential electron scattering cross sections for carbon monoxide and molecular nitrogen in the intermediate energy region

This paper reports absolute elastic differential scattering cross sections (DCS) for electron impact on CO and N2 in the energy range 20-100 eV and angular range 20-120'. The results are obtained using a relative flow technique in which the DCS of CO is compared with that of helium at each angle and energy and the DCS of N2 is compared directly with the DCS of CO. The results of elastic DCS of neon are presented as a check on the experimental procedure.

Neutron scattering and reactions on93Nb from 1 to 20 MeV

The cross sections of all the more important reactions of neutrons on 93Nb are calculated and the results compared with the experimental data. The optical model is used to obtain the differential elastic scattering cross section and the Weisskopf-Ewing, Hauser-Feshbach and Feshback-Kerman-Koonin (1980) theories are used for the compound and statistical multistep compound contributions to the neutron and proton emission cross sections. Several other reaction channels in particular the (n,2n), (n,p) and (n, alpha ) are also studied using one or more of these theories.

Skyrmions and meson-baryon reactions.

Mattis, using a Skyrmion model for the baryons, has expressed the s-channel isospin partial-wave amplitudes for the reaction \ensuremath{\varphi}+B\ensuremath{\rightarrow}\ensuremath{\psi}+B', where \ensuremath{\varphi} and \ensuremath{\psi} represent arbitrary, nonstrange mesons and B, B' denote either the nucleon or \ensuremath{\Delta}, in terms of a set of reduced partial-wave amplitudes. Using the expression proposed by Mattis, I show that if one crosses to t-channel isospin amplitudes, the partial-wave sums may be carried out explicitly. The result is that the spin-projection amplitudes for given ${I}_{t}$ may be written as linear combinations of unknown reduced amplitudes which depend upon the mesons, but not upon whether the pair (B,B') is (N,N), (N,\ensuremath{\Delta}), or (\ensuremath{\Delta},\ensuremath{\Delta}). There are, in general, fewer reduced amplitudes than spin-projection amplitudes, leading to linear relations among the latter, as well as linear relations among amplitudes involving (N,N), (N,\ensuremath{\Delta}), and (\ensuremath{\Delta},\ensuremath{\Delta}). From these relations I extract a considerable number of observable consequences, among them the predictions that the ${\ensuremath{\pi}}^{+}$p and ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$p elastic-scattering differential cross sections are identical at all energies and angles, that the polarization asymmetries are equal but opposite, and that there is no polarization in ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$p\ensuremath{\rightarrow}${\ensuremath{\pi}}^{0}$n. While these and many other such predictions are not strictly true, the model offers a picture of two-body reactions which often coincides with much of the Regge phenomenology of the recent past. It may represent ultimately a viable link between the fundamental theory of strong interactions, QCD, and the enormous amount of data on two-body hadron reactions.

Complex microscopic optical potential and medium energy elastic scattering of 12C on 12C and 208Pb

Differential elastic scattering cross sections of 12C on 12C and on 208Pb at laboratory energies 1440 and 2400 MeV are calculated with microscopically determined complex optical potentials. The complex optical potentials are derived in the energy density formalism from the potential energy density generated by solving the Bethe-Goldstone equation with the Reid soft core NN interaction. Effects of the excitation of the low-lying collective states are taken into account explicitly by the coupled channel formalism. Considering that there is no adjustable parameter to fit the cross section in the calculations, the results are in reasonable agreement with recent experimental data.

A spectrometer for double-differential neutron-emission cross section measurements in the energy range 1.6 to 16 MeV

A neutron spectrometer for the measurement of double-differential neutron-emission cross sections has been set up. An electron linac (GELINA) is used as a pulsed white neutron source. The energy of the incident neutrons is determined by the time-of-flight method. The secondary neutron spectra are determined by unfolding the pulse-height distributions observed in eight NE213-scintillators surrounding the sample. The measured spectra are normalised to the shape of the incident neutron flux measured with a 235U-fission chamber, and afterwards converted to absolute cross sections using as standard the carbon differential elastic scattering cross section below 2 MeV.

Role of electron-molecule angular scattering in shaping the electron-velocity distribution.

Five models has been studied to elucidate the role of electron-molecule angular scattering in shaping the velocity distribution for electrons in nitrogen at E/N values of 300 and 1500 Td. The angular dependence of the differential scattering cross sections for elastic and inelastic collisions has been observed to have significant effects on the shape of the velocity distribution, the rate coefficients, and the transport parameters. The velocity distribution is most sensitive to the angular dependence of elastic scattering. Moreover, for a given elastic differential scattering cross section, variations in the angular dependence of inelastic scattering cause significant changes in the distribution. The magnitude of these changes depends on the relative action of the inelastic collisions with respect to the elastic collisions for a given energy interval, i.e., whether the scattering by the inelastic collisions is isotropic, forward, or backward in a given energy interval.