Space inelastic scattering

To generalize what we have just done to reactive and inelastic scattering, one needs to calculate numerically integrated trajectories for motions in many degrees of freedom. This is most convenient to develop in space-fixed Cartesian coordinates. In this case, the classical equations of motion (Hamilton s equations) are given... 

The dynamic calculations include all beams with interplanar distances dhki larger than 0.75 A at 120 kV acceleration voltage and thickness between 100 A and 300 A for the different zones. The structure factors have been calculated on the basis of the relativistic Hartree - Fock electron scattering factors [14]. The thermal difiuse scattering is calculated with the Debye temperature of a-PbO 481 K [15] at 293 K with mean-square vibrational amplitude

= 0.0013 A following the techniques of Radi [16]. The inelastic scattering due to single-electron excitation (SEE) is introduced on the base of real space SEE atomic absorption potentials [17]. All calculations are carried out in zero order Laue zone approximation (ZOLZ). 

W. Coene, D. Van Dyck, Inelastic Scattering of High-Energy Electrons in Real Space, Ultramicroscopy, 33,261-267,1990. 

Time- and space-resolved fluctuation data for flame gas temperature and major species densities have been obtained from Raman scattering and from stronger inelastic scattering processes. When combined with information about velocity from laser velocimetry, these data and their correlations provide key new information for flow field and combustion field modeling. 

Fig 7 a-f. Shake-up and shake-off processes in photoionization (a) Real space picture illustrating contraction of the atomic charge density in response to the creation of a core hole (b, d) Shake-up (c, f) Conjugate shake-up and (e) inelastic scattering... 

Scattered quantum states SQs,(R), i = 1,2, have localized sources (origin) in real space. The principle of linear superposition works for these states. These functions carry information on interactions of the internal ingoing state I (x) with the slits V(x R0i) I/(x)) see Scully et al. case, Section 5.1. In what follows, both elastic and inelastic scattering situations are examined. Here, we hint at general cases emphasizing what differs from the standard models. 

One can, in principle, perform what are necessarily inelastic scattering experiments which would determine the probability of finding an electron in some relatively small region of space, small relative to the dimensions of the system to which the electron is bound. This must result in the excitation or loss of the electron as a consequence of the uncertainty principle and the electronic state of the system is thus changed. Such experiments, leading to a change in state of the system under observation, are probabilistic in their outcome and p in this case is justifiably interpreted as a probability distribution function. 



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