Cross section, differential orientation dependence

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. 

The differential cross-section L (q) calculated above depends on the initial spin state i of the neutron-nuclei system. Let us average over these initial states i. We allow, that the spin states of the nuclei j (j = 1,. . ., AO are distributed at random and that these states and the initial state of the incident neutron are totally uncorrelated. In such a condition, the distribution of spin states for the incident neutron has no effect on the cross-section it will be assumed here that the orientation of these spins is at random (non-polarized incident beam). The total number of spin states is... 

Fig. 8.31 (a) Differential cross sections for collision-induced notational transitions J" J" AJ for different values of AJ, as a function of the scattering angle in the center of mass system (b, c) dependence of interaction potential in the orientation of the molecule against the line between atom and molecule... 

Note that the projection mt in Equations 4.16 and 4.17 vanishes because we require that the wavevector of the incident plane wave be parallel to the space-fixed quantization axis. The same choice is adopted in the conventional theory of atom-molecule collisions in the absence of fields [45]. Generally, the initial collision flux may not be parallel to the quantization axis (defined by the direction of the external field), and the differential cross-section Equation 4.13 must depend on both the orientation of the incoming flux and the direction of the outgoing flux. In this section, we restrict the discussion to the particular case of the DCS evaluated at fixed. Ri = 0 (Equation 4.17). 

The anisotropy in N0( n)-rare gasgsystems was firstly investigated by Reuss and coworkers analyzing, with the sudden approximation, the orientational dependence of the glory structure of the integral cross section (ICS) in experiments with state selection and without state selection of NO. An estimate of the anisotropy for NO-He was also reported from low resolution total differential cross section (DCS) measurements. 

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