Differential cross section absolute

Differential cross-sections for particular final rotational states (f) of a particular vibrational state (v ) are usually smoothened by the moment expansion (M) in cosine functions mentioned in Eq, (38). Rotational state distributions for the final vibrational state v = 0 and 1 are presented in [88]. In each case, with or without GP results are shown. The peak position of the rotational state distribution for v = 0 is slightly left shifted due to the GP effect, on the contrary for v = 1, these peaks are at the same position. But both these figures clearly indicate that the absolute numbers in each case (with or without GP) are different. 

All the values of dae /dd described here so far have been relative, the absolute scale usually having been obtained by normalization to theory. Efforts have been made by the Detroit group to make direct absolute differential cross section measurements for positrons, where the only comparison was between the positron data and their own normalized electron data. Absolute values of dae /dO for positrons were reported by Dou et al. (1992a, b), but Kauppila et al. (1996) were subsequently unable to reproduce these data. Clearly, the unambiguous determination of absolute positron differential cross sections remains a task for the future. 

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... 

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. 

L. Malegat, P. Selles, A.K. Kazansky, Absolute differential cross sections for photo double ionization of helium from the ab initio hyperspherical R-matrix method with semiclassical outgoing waves, Phys. Rev. Lett. 85 (2000) 4450. 

J. R. Grover, D. E. Malloy and J. B. A. Mitchell, Applications of Radioactive Molecular Beams (1) The Chemistry of Astatine (2) The Measurement of Absolute Differential Cross Sections, Brookhaven National Laboratory (U.S.) report 25416 (1979). 

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. 

The differential cross section is given by the absolute square of this amplitude (4.48). Trial values of the phase shifts Sl are then varied to give... 

Accurate absolute measurements of double-differential cross sections are quite difficult to make. Measurements carefully taken by competent investigators often differ significantly. Kim (1983) gave a recommended... 

The measurement of absolute multidimensional cross sections, such as (e,2e), is usually difficult to achieve with high accuracy due to the various experimental difficulties associated with low pressure gas targets and electron optics. Relative cross sections to different ion states can be obtained with much greater accuracy than the absolute values. The relationship between the (e,2e) differential cross section and the experimentally observable parameters is given by (see section 2.3.3)... 

To understand an electron—atom collision means to be able to calculate correctly the T-matrix elements for excitations from a completely-specified entrance channel to a completely-specified exit channel. Quantities that can be observed experimentally depend on bilinear combinations of T-matrix elements. For example the differential cross section (6.55) is given by the absolute squares of T-matrix elements summed and averaged over magnetic quantum numbers that are not observed in the final and initial states respectively. This chapter is concerned with differential and total cross sections and with quantities related to selected magnetic substates of the atom. 

There are only isolated measurements of integrated cross sections, but there are absolute measurements of differential cross sections. We adopt the procedure of using the coupled-channels-optical calculation of Bray et al. (1991c) to interpolate and extrapolate these measurements, since it agrees quite well with differential cross sections in figs. 8.4 and 8.5. 

Experimental differential cross sections are put on an absolute scale by first normalising to the differential cross section for the first dipole transition (3p). The integrated cross section for this transition is determined by numerical integration using differential cross sections measured as close to 0 = 0 as possible, supplemented by shape extrapolation based on a calculation. Integrated cross sections are determined in ways that ultimately depend on measurements of the optical oscillator strength (5.84). They... 

Fig. 9.6. Angular distribution of S, T and U and the derived moduli and relative phases of the scattering parameters for elastic scattering from Xe at 60 eV. Experiment o, Berger and Kessler (1986) Mollenkamp et al. (1984) and Wiibker, Mollenkamp and Kessler (1982). Absolute measured differential cross sections used in the derivation of the moduli / and g , Register et al. (1986) g, Williams and Crowe (1975). Theory —, McEachran and Stauffer (1986) ., Haberland et al. (1986) -----, Awe et al. (1983).

Since the absolute differential cross section for scattering by unpolarised electrons was not determined by Sohn and Hanne, they analysed their results using normalised state multipoles defined by... 

Up to now there has been no calculation of differential cross sections by a method that is generally valid. We use a formulation due to Konovalov (1993). Understanding of ionisation has advanced by an iterative process involving experiments and calculations that emphasise different aspects of the reaction. Kinematic regions have been found that are completely understood in the sense that absolute differential cross sections in detailed agreement with experiment can be calculated. These form the basis of a structure probe, electron momentum spectroscopy, that is extremely sensitive to one-electron and electron-correlation properties of the target ground state and observed states of the residual ion. It forms a test of unprecedented scope and sensitivity for structure calculations that is described in chapter 11. 

Fig. 10.2 shows that the plane-wave impulse approximation is as good for relative helium differential cross sections at different energies as it is for hydrogen. Here p) is the Hartree—Fock orbital. For helium there is an absolute experiment by van Wingerden et al. (1979) for 0 = 0 in symmetric kinematics at different total energies. Fig. 10.3 shows that the plane-wave impulse approximation using the Ford T-matrix element is consistent with the experiment. 

Chemical dynamics experiments in which OH product quantum state distributions and an absolute reaction cross section for reaction (1) could be measured were reported in 1984. Subsequent experiments revealed additional details about the reaction dynamics, including nascent OH( H) spin-orbit and A-doublet rotational fine structure state distributions, Oi P) product fine structure state distributions, and OH angular momentum polarization distributions,as well as differential cross sections. The experimental results indicate that depending on the reagent collision energy... 

The intensities of the scattered neutrons on the detector are then radially averaged, if the scattering unit is an isotropic scatterer, after normalization and subtraction of solvent and background, converted to absolute differential cross sections per unit sample volume, (5E/5Q) (0, in rmits of cm and plotted on a 1-D plot as a function of the scattering vector, Q. 

The square of the absolute value of the scattering amplitude /(0) is the differential cross section. f(9) is given by... 

Symbols EA electron affinity thr threshold energy Q total cross sections a differential cross section. Specification parameters a absolute value of cross section E energy dependence m mass selection of negative ions T temperature dependence. 

The differential cross sections reported in this paper are absolute measurements for an apparatus having our geometry and resolution. The geometrical and resolution corrections are dependent, to some extent, on knowledge of an intermolecular potential and are included in the theoretical calculations. The largest corrections are for the finite resolution of the detector. 

As an example, in Fig. 3 we show the result for the semiclassical absolute direct differential cross section for neutral helium atoms colliding with neon targets at projectile energies of 0.5, 1.5, and 5.0 keV [12]. Also, for comparison we present the experimental data of Gao et al. [23]. 

The advantage of semiclassical corrections is the inclusion of quantum effects to the differential cross section in the small scattering angle, the so-called forward peak character of the differential cross section. Furthermore, in the particular case of the Schiff approximation, the glory and rainbow angle effects in the interference are accurately represented. This behavior can be observed in Fig. 3, where the absolute direct differential cross section obtained with ENDyne goes through the experimentally determined absolute cross sections. 

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