Scattering processes, typical cross section

Table V Typical Cross Section Values for Scattering Processes...

It can be seen from Eq. (7.11) that o has the dimensions of area. The magnitude of b is typically of the order of 10 cm, and this gives rise to the usual unit for a cross section which is called a bam (10 " cm = 10 m ). To a first approximation the cross section may be regarded as the effective area which the target nucleus presents to the incident beam of neutrons for the process of elastic scattering. The above cross section (Eq. (7.11)) is usually called the bound-atom cross section because the nucleus was considered fixed at the origin. Where the atom is free to recoil, however (e.g. in the gaseous state), the cross section applicable to this condition is called the free-atom cross section [3,37]. The bound-atom cross section... 

The total positron scattering cross section, erT, is the sum of the partial cross sections for all the scattering channels available to the projectile, which may include elastic scattering, positronium formation, excitation, ionization and positron-electron annihilation. Elastic scattering and annihilation are always possible, but the cross section for the latter process is typically 10-2O-10-22 cm2, so that its contribution to erT is negligible except in the limit of zero positron energy. All these processes are discussed in greater detail in Chapters 3-6. 

There are several ways in which a femtosecond laser pulse can nigger chemical transformations at a surface. Direct optical excitation of the adsorbates is a process of very low probability, owing to the generally small cross section for such processes. The laser pulse can, however, efficiently create excited elecnons in the metal near the surface (the optical penettation depth is typically -10 nm), which rapidly thermalize to a hot Fermi-Dirac distribution by electton-elecnon scattering... 

However in most processes of practical relevance such as electron-molecule collisions in industrial plasmas and upper atmosphere, orientations of the molecules seem to be not fixed. On another hand typical interaction times for 1-30 eV of collision energy is 10 14-10 15 s. Timescale for the rotations of the polyatomic molecules at room temperature is 10 12 s and longer. This comparison allows us to assume that scattered electron responds adiabatically to the rotations of the molecules and validates the fixed-nuclei approximation19,20 implicitly assumed in equations (14) and (15). Nevertheless orientation of the molecule with respect to the incoming electron is random and therefore cross sections must be averaged over all the orientations of the molecule. This is carried out by the following technique. Inelastic differential cross sections are obtained from (11) as... 

Irradiation of adsorbate-covered surfaces with higher energy photons (typically up to 6.4 eV) with lower intensities opens the possibility of direct valence excitation. Since the lifetimes of electronic excitations at metal surfaces are much shorter than those for nuclear motion, photochemical reactions appear rather improbable. Surprisingly, however, the cross sections determined for photodesorption were found to be comparable to those found for reactions with free molecules, mainly because the short lifetime of the excited state is compensated by a much larger cross section for absorption of the light [32,62-64]. This process takes place in the near-surface region of the metal (within about 10 nm), where relaxation of the photoexcited electrons leads to rapid establishment of a transient energy distribution. As depicted in Fig. 4.11, these hot electrons may scatter at the surface or are resonantly attached to an empty level of the adsorbate. 

Our model implies independent scattering (the assumption that we share with the great majority of photobioreactor researchers). Indeed, typical biomass concentrations within the process are low enough to reasonably assume that each microbial ceU interacts with radiation independently. We can therefore define particle cross sections a that characterize the radiative properties of microbial cells independently of their concentration Q and keM.p = where... 

The S AXS pattern of uniaxial extruded PBT films revealed a network of oriented fibrils with irregular cross sections, very similar to the structure found in fibers of the aramids [131], The diffuse equatorial scattering, also observed for example in cellulose fibers, is typical of fibers manufactured by wet-spinning and air-gap spinning processes. 

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