Differential scattering cross-section definition

In view of (8.28) and from the definition of Gs(r,f) in Section 8.1.2, we find the incoherent component of the double differential scattering cross section to be... 

In the next section (Sec. 2), we will develop the theory of the BCRLM. We discuss the solution of the coupled-channel equations in both natural collision coordinates " and hyperspherical coordinates. " Both coordinate systems are widely used to treat collinear reactive scattering processes. We will discuss the projection " of the hyperspherical equations on coordinate surfaces appropriate for applying scattering boundary conditions and review the definition of integral and differential scattering cross sections in this model. 

All of the effective collision cross sections introduced above can, in principle, be evaluated from a knowledge of the intermolecular pair potential by means of equation (4.17) and the definition of the collision operator (4.5). This process would then make it possible to predict the transport properties of dilute gases from first principles. However, such a procedure would require that it is possible to evaluate the inelastic differential scattering cross section ajj or an equivalent to it which enters (4.5). Until very recently this could only be accomplished for dilute monatomic gases. There were two reasons for this first, only for such systems are accurate intermolecular potentials available (Aziz 1984 Maitland et al. 1987 van der Avoird 1992) second, only for such systems was the... 

In the early days of chemical dynamics (the 1960 s) the study of elastic scattering was an important project, both experimentally and theoretically, for developing the tools to be used to study more interesting processes, e.g., elastic scattering of the rare gas atoms. Y.T.Lee s (1986 Nobel Prize with M. Polanyi and D. Herschbach) measurements of the differential scattering cross sections allowed the definitive determination of the intermolecular potential energy function V(r) of essentially all the rare gas atoms with each other... 

A definite but small anisotropy of the differential quenching cross section is observed when the electric vector EA of the exciting laser light is rotated in the scattering plane. It follows equation (VI. 1), where 9n has to be replaced by ip + (w/2). 

The gamma function F is used in the definition of the Coulomb phase shift.) There are three potential observables for elastic scattering. The first is the differential (elastic) scattering cross section,... 

To illustrate these definitions, we consider a collision between two hard spheres (HS) with radii ri and T2, yielding a total hard sphere radius r = ri -f T2. The HS differential reaction cross section is r /4, independent of scattering angle. The HS integral reaction cross section is Trr, consistent with circular area of radius... 

The definition of the final quantum state [see Eqs. (4.3) and (4.4)] of the system includes the direction k into which the separating fragments are scattered. If we omit the integrals over all final scattering directions in Eqs. (4.1) and (4.10), we obtain a cross section for scattering into a specific final direction. These are called differential cross sections. Below 1 will briefly outline the definition and properties of the partial differential cross section, which is the probability of producing a specific final quantum state of the system scattered into a well-specified direction. 

The first part of the review deals with aspects of photodissociation theory and the second, with reactive scattering theory. Three appendix sections are devoted to important technical details of photodissociation theory, namely, the detailed form of the parity-adapted body-fixed scattering wavefunction needed to analyze the asymptotic wavefunction in photodissociation theory, the definition of the initial wavepacket in photodissociation theory and its relationship to the initial bound-state wavepacket, and finally the theory of differential state-specific photo-fragmentation cross sections. Many of the details developed in these appendix sections are also relevant to the theory of reactive scattering. 

In the case of scattering the channel states of relative motion are defined by the momentum of one electron relative to the collision centre of mass, which is at the nucleus if we neglect the kinetic energy of the nucleus. To obtain the differential cross section we use the form (6.40) for w,o in the definition (6.41). 

The experiment measures the rate of transition into a solid angle dSl subtended by the detector at scattering angles 9, energy channels i, 0 are defined by energy resolution. In atomic units the relative velocity V is ko. We use the notation dai 9,4>) for the differential cross section in this experiment. The definition (6.41) becomes... 

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