Scattering models stretched

Distribution of Rod Lengths. If the distribution of rod lengths shall be studied, the smearing of the equatorial streak by the primary beam profile must be eliminated99. After that the ID scattering intensity is computed by means of Eq. (8.56) and fitted to the respective ID model (e.g., Eq. (8.80)) from Sect. 8.7.1.1. Be careful. The rods may, in fact, not be stretched out perfectly but only resemble long worms instead. 

We now may ask whether the Allegra model can reproduce some of the features experimentally found for the other correlators. The incoherent intermediate scattering fimction can be calculated from an adaptation of Eq. 3.16 to Fig. 3.18 to the results of Allegra et al. We note that in the Q-range where experimental data are available, the line shape deduced from the model is significantly less stretched than the experimental one [ 187]. Therefore, the char-... 

PAMAM dendrimer in methanol[19], and larger also than the 60 A maximum physical radius of a completely stretched structure, but has been employed consistently. In terms of the model, some of the scatter in Figure 4 can be explained by considering that the radius of gyration of this polyelectrolyte is likely to depend on the ionic strength, pH, and even the concentration of borate diesters (internal cycles) none of these factors were systematically controlled in this study. 

Figure 16. Scattering resonances of the full rotational-vibrational Hamiltonian describing the dissociation of CO2 on a LEPS surface obtained by equilibrium point quantization with (2.8). The resonances with 7 = 0,..., 10 are given by dots. Their close vicinity explains the formation of hyphens , i.e., unresolved sequences of dots. Note that rotation is very slightly destabilizing in the present model. The successive hyphens are the bending progressions with V2 = 0,. .. 5. The solid line is given by the Lyapunov exponent of the symmetric-stretch periodic orbit 0 expressed as an imaginary energy.

The stretched helium model can be interpreted as a chaotic scattering system. In order to establish the connection, we first consider the potential (10.2.5) of the Hamiltonian (10.2.4). Some equi-potential lines for V(e xi,X2) are shown in Fig. 10.5 for e = 1/2. This potential is very similar to the potential of elbow scattering systems investigated... 

Fig. 10.6. Distribution of lifetimes for a chaotic scattering experiment with the one-dimensional model. Irregular behaviour and dynamic scattering singularities in the interval 4.7 < 6i < 5.7 indicate the presence of chaotic scattering in the stretched helium atom. (Adapted from Bliimel and Reinhardt (1995).)...

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