Scattering cross-section length

In Eq. (7.21) the normalization to the scattering cross-section r2 leads to the definition of absolute intensity in electron units which is common in materials science. If omitted [90,91], the fundamental definition based on scattering length density is obtained (cf. Sect. 7.10.1). 

In the scattering theory approach, the stopping power, or energy loss per unit length for a projectile of energy Ep, can be written in terms of a differential scattering cross section da/dQ as... 

Table 1 Coherent Scattering Lengths, Incoherent Scattering Cross Sections, and Absorption Cross Sections for Some Elements...

Element Coherent scattering length (cm X 10 ) Incoherent scattering cross section (cm x 10 ) Absorption cross section (cm X 1024)... 

To examine the role of the LDOS modification near a metal nanobody and to look for a rationale for single molecule detection by means of SERS, Raman scattering cross-sections have been calculated for a hypothetical molecule with polarizability 10 placed in a close vicinity near a silver prolate spheroid with the length of 80 nm and diameter of 50 nm and near a silver spherical particle with the same volume. Polarization of incident light has been chosen so as the electric field vector is parallel to the axis connecting a molecule and the center of the silver particle. Maximal enhancement has been found to occur for molecule dipole moment oriented along electric field vector of Incident light. The position of maximal values of Raman cross-section is approximately by the position of maximal absolute value of nanoparticle s polarizability. For selected silver nanoparticles it corresponds to 83.5 nm and 347.8 nm for spheroid, and 354.9 nm for sphere. To account for local incident field enhancement factor the approach described by M. Stockman in [4] has been applied. To account for the local density of states enhancement factor, the approach used for calculation of a radiative decay rate of an excited atom near a metal body [9] was used. We... 

Both classical and quantum mechanical treatments of Raman scattering are based on Eq. (2.1), and such treatments are very valuable in understanding the effect and interpreting spectra (1-5). One of the more analytically important results of Raman theory is the Raman scattering cross section, aj, which will be discussed at some length below. Before considering the factors that affect CT, it is useful to review several aspects of Raman theory. 

Figure 2. Suppression of identical particle collisions. Full squares measured scattering cross-section for Beliaev damping as a function of the excitation wavenumber in units of the inverse healing length. The assumptions of our analysis are tested using hydrodynamic simulations (dashed line), and found to agree with Beliaev damping theory (solid line) and the experimental data. Corrections observed in the hydrodynamic simulation take into account the full inhomogeneity and finite size of the experimental system, and validate the approximations of our analysis.

Consider first of all the scattering of neutrons by the nuclei in a monoatomic liquid. This process is characterized by a scattering cross-section, Qq, which, in turn, is related to Z>d, the bound atom scattering length. For slow neutrons. 

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