Differential cross sections elastic scattering

Elastic scattering of neutrons. The absence of Coulomb scattering simplifies formula (16.1) in which fc d) and may be put equal to zero. The differential cross section for scattering near a resonance formed by the partial wave of orbital momentum 1% reduces to... 

Fig. 2 Elastic differential cross section for scattering of electrons by cyclopropane panel) and helium atom (right panel). Collision energies are 2.6 eV (left panel) and 10 eV (right panel). Present calculations with exact exchange interaction are displayed by red curves while the local AAFEGE exchange model is shown by green curves. The results are compared to experimental data for cyclopropane [22] and helium [23], both displayed as circles in respective panels...

Since this agrees with the first Bom differential cross section for (in)elastic scattering, Femii s Rule 2 is therefore valid to first order in the interaction F. 

Figure 8.3 The vibrational elastic and inelastic differential cross sections for electron scattering off LiF at = 5.44 eV (Alhassid and Shao, 1992b, where the source of the data is given). Solid lines with an improved dipole interaction [which breaks the 0(4) symmetry]. Long dashed lines the calculations by Bijker and Amado (1986). The short dashed lines are the Bom approximation.

Elastic scattering cross sections were caleulated using the Rutherford formula, taking into account the screening parameter given by Moliere [187], The differential cross section (dc/ df2)ei and total cross sections cTei for each molecule are represented by... 

Figure 2. Central part of apparatus used for measurement of differential elastic cross sections for scattering of helium metastables from ground-state atoms (reproduced from Brutschy et al.30)... 

The elastic scattering of electrons by COz, OCS, and CS2 molecules has been studied theoretically.238 The authors of Ref. 239 have calculated the differential and the total cross sections of scattering of 10-eV electrons by an acetylene molecule. The total cross section proved to be 54.5, which is greater than that for a N2 molecule (34.4a ). The authors believe this to be an illustration of how larger geometrical size of a molecule results in a greater scattering cross section. 

In this chapter we describe the elastic scattering of positrons by atoms and molecules over the kinetic energy range from zero to several keV, concentrating mainly on the angle-integrated cross section, crei- However, reference is also made to differential cross sections, dae /dQ, which have recently become amenable to experimental measurement using crossed gas and positron beams. 

Fig. 3.14. Differential cross sections for positron-argon elastic scattering at the following energies (a) , 2.2 eV (b) , 3.4 eV (a) o, 6.7 eV (b) o, 8.7 eV. (The corresponding fc-values are respectively 0.4, 0.5, 0.7 and 0.8 a.u.) The solid curves give the theory of Schrader (1979) whilst the broken curves are the scaled results of McEachran, Ryman and Stauffer (1979).

Fig. 3.16. Elastic differential cross sections for positrons and electrons scattering from argon, (a) Electrons at 100 eV o, Hyder et al. (1986) , Srivastava...

The positron impact data at 30° and 45° are presented in Figure 5.21. The absolute scale was derived, as described by Kover, Laricchia and Charlton (1994), by comparison with electron data and positron elastic differential cross sections, and results for both the scattered positrons and the ejected electrons are displayed. Again, the ejected electrons, which... 

Coleman, P.G. and McNutt, J.D. (1979). Measurement of differential cross sections for the elastic scattering of positrons by argon atoms. Phys. Rev. Lett. 42 1130-1133. 

DuBois, R.D. and Rudd, M.E. (1975). Absolute differential cross sections for 20-800 eV electrons elastically scattered from argon. J. Phys. B At. Mol. Phys. 8 1474-1483. 

McAlinden, M.T. and Walters, H.R.J. (1994). Differential cross sections for elastic scattering and positronium formation for positron collisions with Ne, Ar, Kr and Xe. Hyperfine Interactions 89 407-418. 

Gianturco, FA. and Stoecklin, T. (1996). Hie elastic scattering of electrons from CO2 molecules I. Close coupling calculations of integral and differential cross sections, J. Phys. B 29, 3933-3954. 

Differential cross sections for elastic scattering of electrons from THF have been determined together with vibrational and electronic energy loss spectra. Band assignments were verified by Cl calculations <2005MI411>. 

For atomic targets a convenient way of determining the average target density and C( ,) is to carry out a low-energy elastic scattering differential cross-section measurement and to use a phase-shift analysis to determine the absolute cross section. 

Another commonly-used normalisation procedure is to use the relative flow technique. In this method the elastic differential cross section for a particular species may be obtained by comparing the scattered intensity under the same conditions with that from another target with a known cross section. It is important to ensure, for both the gas under study and the reference gas, that the electron flux density and distribution, the detector efficiency, and the target beam flux distribution are the same for both gases during the measurement. 

The differential cross section at 33° near an elastic resonance is illustrated in fig. 4.5 for a calculation of electron scattering by the hydrogen atom. This resonance has L = 1 with the electrons in a state of total spin S = 1. 

Fig. 4.5. The differential cross section at 33° near a resonance Eo=9J7 eV, F=8.9 X 10 eV, L = 1, S = 1 in a calculation of electron—hydrogen elastic scattering.

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