Angular scattering calculations

An example of practical importance in atmospheric physics is the inference of effective optical constants for atmospheric aerosols composed of various kinds of particles and the subsequent use of these optical constants in other ways. One might infer effective n and k from measurements—made either in the laboratory or remotely by, for example, using bistatic lidar—of angular scattering fitting the experimental data with Mie theory would give effective optical constants. But how effectual would they be Would they have more than a limited applicability Would they be more than merely consistent with an experiment of limited scope It is by no means certain that they would lead to correct calculations of extinction or backscattering or absorption. We shall return to these questions in Section 14.2. 

For rotational excitation of HC1 by Ar at room temperature, the maximum rotational angular momentum quantum number coupled during collision is about 12. The maximum number of coupled j,m states is Nc = (jmax + 1)(jmax + 2)/2 = since HC1 is a heterodiatomic molecule, and thus all states of the same total parity are coupled. With 91 channels, the quantum scattering calculations are feasible, but rather expensive. A further complication of the... 

As can be expected, the angular scattering intensity distribution has become anisotropic. From the data obtained, two values of the average correlation distance between neighboring nodules can be calculated, parallel and perpendicular to the deformation direction respectively. Although the accuracy of the data is not outstanding, it can be seen that d increases with the macroscopic extension ratio, Ax, whereas dx decreases only slightly (Fig. 10). It is not possible to ascertain experimentally whether dL is proportional to AJ1/2 as it should be if the deformation proceeded at constant volume L e., if the network could be considered incompressible. 

The positron-trap technique has been used by Surko and coworkers to measure the Doppler broadening of the 511 keV line for positrons in helium gas. This method does not have the drawback of the experiment described above, in which both positronium and free-positron events overlap on the angular distribution curves here the positrons are thermalized prior to the introduction of the gas and therefore cannot form positronium. A comparison of the theoretically predicted and experimentally measured Doppler spectra (Van Reeth et al., 1996) is shown in Figure 6.16. The theoretical results were obtained from the variational wave functions for low energy positron-helium scattering calculated by Van Reeth and Humberston (1995b) see equations (3.75) and (3.77). 

Model calculations usually divide the reaction into two parts and make various assumptions about the nature of the entrance channel (or reactant) and exit channel (or product) interactions. In some models, these interactions are treated independently and in others some degree of coupling is introduced. Not all reaction models are capable of describing the nature of the product energy disposal many are concerned only with the total reaction cross section or the product angular scattering distributions. 

J.D. Kress, R.T. Pack, and G.A. Parker, Accurate 3-dimensional quantum scattering calculations for F+H2 - HF+H with total angular-momentum J = 1. Chem. Phys. Lett., 170 306-310, 1990. 

Fig. 19. The theoretical angular resolved multiple scattering calculation for a square bipyramid with a short double V—O bond (d = 1,58 A) and with a long V—O bond (d = 2.6 A) along the z axis due to the oxygen of a water molecule and four oxygens on the xy plane at 2.0 A. The upper curves show calculated polarized curves with the V atom out of plane by 0.5 A and the lower curves are the same for a similar cluster with the same distances but with the V atom in the plane...

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