Scattering cross section total

A particle is subdivided into a small number of identical elements, perhaps 100 or more, each of which contains many atoms but is still sufficiently small to be represented as a dipole oscillator. These elements are arranged on a cubic lattice and their polarizability is such that when inserted into the Clausius-Mossotti relation the bulk dielectric function of the particle material is obtained. The vector amplitude of the field scattered by each dipole oscillator, driven by the incident field and that of all the other oscillators, is determined iteratively. The total scattered field, from which cross sections and scattering diagrams can be calculated, is the sum of all these dipolar fields. 

The elastic scattering of electrons by COz, OCS, and CS2 molecules has been studied theoretically.238 The authors of Ref. 239 have calculated the differential and the total cross sections of scattering of 10-eV electrons by an acetylene molecule. The total cross section proved to be 54.5, which is greater than that for a N2 molecule (34.4a ). The authors believe this to be an illustration of how larger geometrical size of a molecule results in a greater scattering cross section. 

If k is in atomic units ap1. the differential cross section is in units per steradian. Differential and total cross sections for multichannel scattering by an atomic target can be derived from general formulas [27, 184], The partial cross section for scattering from channel q to channel p is... 

Here E, q, n ) denotes the incoming scattering solutions associated with the product in state E, q1, n 0), and Vq is the component of the total potential that vanishes as the A to B distance becomes arbitrarily large. The cross section for scattering into arrangement q, independent of the product internal state n, is then... 

Consider an atom-diatom A + BCiE J ) collision at total energy E with AB(EAg,jAg) + C as one possible product. Here EBC,jgC are the internal energy and rotational angular momentum of the BC diatom and EAB,jAB are the analogous AB variables. The differential cross section for scattering into dEAB djAB (other cross sections have analogous formulations) is given by... 

In both cases, la and lb, the total photodissociation cross section is completely determined by the short-time dynamics in the Franck-Condon region. In contrast, the partial cross sections, which determine the vibrational, rotational, and electronic-state distributions of the products, involves longer time dynamics. To obtain all of the relevant information about the reaction, the wavepacket evolution must be followed out into the product region of the potential energy surface and projected onto the various different vibrational and rotational states of the fragments. The partial cross section for scattering... 

In QENS experimenis, one measures the double-differential cross-section, d cr/ df2 dE, which represents the number of neutrons scattered into the sohd angle df2 with energy in the range dE. The amphtude of the scattered wave varies between nuclei (because of different isotopes or spins), so that averages have to be performed for each element. The total cross-section per scatterer is obtained by integrating over energies and sohd angles... 

Accordingly, the total cross section for scattering o can be written as the sum of two components ... 

It is interesting to find that a combination of elastic and reactive scattering results in additional information concerning the probability of reaction under certain conditions. In Chapter 2, where an expression was derived for the frequency per unit volume of binary collisions, we found that the total elastic cross section for scattering was given as db for... 

Hssion cross section, absorbtion cross section, self-scatter cross section, capture cross section, removal cross section, number of upscatter groups, number of downscatter groups, and where USCAT, DSC AT, FISS, and REM represent the cumulative probabilities, obtained by dividing the appropriate cross sections by the total cross section. 

However, the main reaction for X -mesons is nuclear absorption resulting in stars or hyperons they also elastically and charge exchange scatter. The total cross-section for X"-meson interactions is commensurate with the geometrical size of the nucleus. The cross-section for scattering of X -mesons seems to be about one order of magnitude smaller than the K total cross-section. 

As to the total cross-section of scattering by free electron irradiated by unpolarized light, it is described by the same Thomson formula (5.7) that is easy to check by integrating (5.8) over 20 (from 0 to Jt) and over (p (from 0 to 27t). 

Version 1.3 of the NIST Database for SESSA [95, 99, 100] can be used for two main purposes. First, data are provided for the many parameters needed by a user to derive quantitative information from AES and XPS spectra (differential inverse IMFPs, total IMFPs, differential elastic-scattering cross sections, total elastic-scattering cross sections, transport cross sections, photoionization cross... 

Experimentally, it is these invariants (equation (B 1.3.17), equation (B 1.3.18) and equation (B 1.3.19)) that can be obtained by scattering intensity measurements, though clearly not by measuring the total cross-section only. 

Measurement of the total Raman cross-section is an experimental challenge. More connnon are reports of the differential Raman cross-section, doj /dQ, which is proportional to the intensity of the scattered radiation that falls within the element of solid angle dQ when viewing along a direction that is to be specified [H]. Its value depends on the design of the Raman scattering experiment. 

Parker G A and Pack R T 1978 Rotationally and vibrationally inelastic scattering in the rotational lOS approximation. Ultra-simple calculation of total (differential, integral and transport) cross sections for nonspherical molecules J. Chem. Phys. 68 1585... 

Figure 2. Total differential cross-section versus laboratory scattering angle for vibrational ground state of hydrogen molecules in single collisioins with 30-eV protons.

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