Exchange scattering

In the expressions for the BED and BEB cross sections for each orbital the first log term represents large impact parameter collisions dominated by the dipole interaction. The remaining terms represent low-impact parameter collisions, described by the augmented Mott cross section. The second log function describes interference between direct and exchange scattering which is included in the Mott cross section. 

In Eq. (4.10), r = 47ra02R2/T and the second term within the brackets represents interference between direct and exchange scatterings. A corresponding relativistic treatment has been given by Moller (1931). 

The quantity J that should be used in (31) to calculate, for instance, exchange scattering is, according to Schrieffer and Wolff (1966),... 

Fig. 32. The integrated intensity of magnetic reflections of x-ray resonant exchange scattering measured for NdNi2BjC and SmNi2B2C. Dashed line and full line model calculations for a magnetic moment parallel to the tetragonal a-axis and c-axis, respectively (after Detlefs et al. 1997b).

Figure 12. Classical picture of direct and exchange scattering.

Figure 28. Typical deflection functions for energies above ungerade barrier. Dashed lines give contributions from exchange scattering.

It is due to the exchange scattering amplitude Bn0 that the cross section of excitation of a molecule into a triplet excited state is nonzero (see Section IV.B.3). 

If the velocity of the incident electron is comparable with those of molecular electrons, the former can be exchanged for one of the latter. Such processes are described by the exchange scattering amplitude, the form of which in the first Born approximation has been found by Oppenheimer.126 In the Born-Oppenheimer approximation the exchange amplitude (4.11) acquires the form... 

However, this difference in factors is quite important since it leads to a different dependence on the energy E of the incident electron, namely, the exchange cross section rapidly decreases with decrease of E ( 1 IE3). Therefore, for fast electrons the exchange scattering can be disregarded. 

The role of exchange scattering can be observed most clearly when polarised electrons are scattered from a target of polarised light atoms. If one observes a spin-flip process like... 

Pure exchange scattering from spin 112 targets... 

Applying the above formalism for pure exchange scattering from spin 1/2 targets such as the alkali-metal atoms, we obtain for elastic scattering... 

Of the 16 terms in (9.18) for f = jo = 1/2, 10 can be omitted because they violate conservation of total spin angular momentum on the basis of pure exchange scattering, leaving only the above six terms. Recalling the definitions in section 9.1.2 of the direct and exchange amplitudes / and g (equns. (9.4a) and (9.4b) respectively) one has... 

A U(1,2)A with A the product of free positive -energy projection operators, as in (2.9). The operator U(l,2) = u + U must be chosen so that if the external potential is turned off, the one-photon and two-photon exchange scattering amplitudes are reproduced. (I note in passing that if one uses U = Uj-r rather that one must already include U to get the a Ry level shift correctly ) On comparing the eigenvalues of (4.3) with those obtained from,... 

In this article, we shall introduce another physically appealing Fock operator, which is defined with respect to and it includes not only the Fock potential of the doubly occupied active orbitals included in but also—via the blocks involving the direct exchange scattering of the singly occupied active orbitals—stakes care of interaction of electrons in them. This is given by... 

Figure 9 This figure depicts two kinds of semiclassical paths which contribute to the exchange scattering amplitude for a triatomic system ABC. An equipotential energy surface for the ground adiabatic electronic state of H3 is represented. The OXYZ frame is the same as the OXKYZK frame of Fig. 5 with the subscript suppressed. The conical intersection configurations for H, (equilateral triangles) are represented by points on the OY axis. The dashed path partially encircles the conical intersection line, whereas the solid one does not. (From Ref. 36.)...

By the same procedure Campana et al. (1973) have shown the existence of a non-saturated surface sheet at a temperature as far below the ordering temperature of the bulk as 16.75 K. Surface spin-exchange scattering due to 4f-electron excitations explains this result. Bush et al. (1969) observed spin polarization, which can be due to impurities, in semiconducting ferromagnetic EuS films. They proposed this occurs because of an exchange interaction of the impurities with the 4f levels. 

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