Differential Crossed Section measurements

By careful inspection of the relationships of the semiclassical close collision approximations and Bethe formula, one can obtain simple and accurate information on ionization cross sections. By the method first proposed by Platzman, and used extensively by others, it is instructive to form the ratio of the differential cross sections [measured c(W,T) or calculated da(W,T)ldW)] to the Rutherford cross section. This ratio, called Y, is mathematically defined as... 

III. EXPERIMENTAL DIFFERENTIAL CROSS-SECTION MEASUREMENTS AND INTERPRETATION... 

Figure 18 shows differential cross sections measured using the helium plasma jet described in Section III.A.6. It is surprising that so much structure is still resolved, even though the velocity resolution of the beam is only 30%. No fit has so far been attempted for these data. 

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. 

Finch, R.M., Kover, A., Charlton, M. and Laricchia, G. (1996b). Differential cross-section measurements in positron-argon collisions. Can. J. Phys. 74... 

We cannot in this chapter make a comprehensive coverage of all of the experimental procedures presently being utilised. We will give a brief overview of the major modern techniques. The emphasis will be on differential cross-section measurements using single-collision beam—beam scattering geometry, since these are the most widely used techniques. They are versatile and also demonstrate most of the basic techniques involved in cross-section measurements. 

Static gas targets such as those used by Wagenaar and de Heer (1985) are usually unsuitable for differential cross-section measurements. These days scattering experiments are carried out in a crossed-beam arrangement. A large variety of beam sources are used. These range from effusion from simple orifices or capillary arrays to supersonic nozzles, from ovens... 

Fig. 2.5. Double tandem electron spectrometer for low energy electron—atom differential cross-section measurements (Weyhreter et al, 1988).

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 status for inelastic collisions is a little less satisfactory than for elastic collisions. CoIIisional excitation of atoms involves excited states with several magnetic substates. Standard total or differential cross section measurements sum over the magnetic substates, and thus give no information on the shape of the excited state and direction of the angular momentum transferred to the excited atom. These can be determined in... 

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... 

As discussed in the last chapter, electron—photon (e, e y) measurements yield much more information on the scattering process than simple inelastic differential cross section measurements. In particular the population of magnetic sublevels can be obtained, which can be visualised by the corresponding charge-cloud probability distribution (fig. 8.1). The set of parameters discussed in the last chapter must be enlarged when polarised... 

Figure 2 shows the three different final total, T contributions to the total alt-sorption cross section of HOBr(X A —t 2 A ) for HOBr initicilly in two different K states of its J = 1 ground dbrational state [43] (note that K is used merely as a formal label, it is not a valid quantum number). In a differential cross section measurement the cunplitudes associated with the different J contributions shown would interfere and might lead to characteristic angular distribution patterns. 

The velocity dependence of the total collision cross section is a restricted source of information regarding the intermolecular potential (IP), Bernstein (1973). Much more information is contained in differential cross section measurements which therefore form a great challenge for future scattering experiments with oriented molecules. 

In Table II the results obtained by Schwartz (1973), Moerkerken (1973) and Moerkerken (1974) are collected, together with the products eRm which were assumed in the determination of q2.12/q2.6. Concerning the NO results two choices were made for eRm, the upper one based on the differential cross section measurements by Tully (1972) on the systems N2-Ar, N2-Kr,... 

Ar and Oz-Kr the other one based on combination rules and the potential parameters found in Hirschfelder (1965). Although the first choice is the only one based upon experiments on related systems one has to keep in mind that differential cross section measurements explore a different region of the IP than do the total collision cross section measurements. In other cases (Butz, 1971 and Kupperman, 1973) differences of about 30% were... 

The HD2 system is computationally a much more difficult one than the isotopically reversed DH2 one. The reason is that, at a given total energy, there are many more accessible D2 rovibrational states than there are H2 ones, requiring therefore a much larger number of channels (i.e., terms) in the LHSF expansion of (174). Recent differential cross-section measurements for the H + D2 reaction [67, 68] have stimulated accurate... 

Li so that the incident /-value must be between 1 and 4. The observed width suggests that / = . Differential cross section measurements (Willard et a/. )... 

We have carried out reactive differential cross section measurements in CMB experiments [21,22] and determined the spatial distribution and energy distribution of the products from reaction (1) and (2). The results are compared with those of quasiclassical and quantum mechanical (approximate) dynamical computations on ab initio surfaces, which have been carried out by Schatz [13,25,26] and by Clary [12,26,27] at the experimental energies. 

Molecular beam experiments are performed in a laboratory frame of reference but the chemically interesting events take place with respect to the center of mass of the colliding species. In order to interpret the data, differential cross sections measured in the laboratory (LAB) coordinate system must be transformed to reflect events which took place in the center-of-mass (CM) coordinate system. To effect this transformation the invariant motion of the center of mass must be subtracted from the scattering data obtained in the LAB system. A simple example which illustrates the difference between LAB and CM kinematics is shown, for an elastic collision, in Fig. 8.6. In CM the particles always move directly toward one another before interaction and directly apart afterwards. This condition is a consequence of momentum conservation in a system with a stationary center of mass. The interaction causes each particle to be deflected through... 

Mark S, Gerlich D. (1996) Differential cross sections, measured with guided-ion-beams. Applications to N+ -f- N2 and C2HJ - - C2D4 Collisions. Chem. Phys. 209 235-258. 

The objective of cross-section adjustment is to reduce the fi ctional discrepancy between the measured value, Ek, and calculated value, Ck, of integral property k taking into account the uncertainties in the cross-section data and the integral measurements. For a review of recent work in the subject see [4.41]. The assumption is made that the difference between C k, the value calculated using the adjusted cross-sections, and Ck can be approximated as linearly dependent on the fractional adjustments to the nuclear data parameters, Xi. The values of Xi are found by a least squares fit to the integral and differential cross-section measurements, relative to the uncertainties. The procedure produces the covariance matrix of the adjusted cross-sections from which the fractional accuracy of reactor... 

Instead of carrying out an adjustment of cross sections to obtain a simultaneous best fit to both the integral and differential cross-sections, the integral measurements can be used to guide the choice of differential cross-section measurements to be included in an evaluation. This approach is valuable when there are sets of discrepant measurements and it is evident that one or the other set contains an error larger than the estimated uncertainties. This approach has been adopted, for example, in evaluations for Am-241 and Am-243 to choose between different measurements of the fission cross-sections. Benchmark testing has also been applied in the development of Evaluated Nuclear Data Libraries. 

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