Energy transferred cross-section

For two local transition dipoles and /<2 ( virtual oscillators ) associated with two atoms or molecules of the gas, the interaction W becomes W 2 R) oc and leads to the following expression for the energy-transfer cross section ... 

In addition to the total cross-section, we also wish to consider the more restrictive types of interactions that can occur between target nuclei and particles with energy E. Consider the condition where we wish to know the probability that a projectile with energy E will transfer an amount of energy between T and T + dT to a target atom. Such a probability function defines the differential energy-transfer cross-section, dcr (E)/dT, and is obtained by differentiating (4.10)... 

This final expression is extremely useful since it allows us to determine the differential energy-transfer cross-section if the angular differential cross-section is known, or if the center-of-mass scattering angle and impact parameter are known. 

Using the power law energy-transfer cross-section, calculate the approximate mean free path, (7.11), between Si recoils for both Si and Sb ions with energy of 1, 10, and 50 keV. 

Studies of collision-induced mode-to-mode energy transfer in the ground electronic states of several small polyatomics reveal two qualitative features of the process. First, the energy-transfer cross-sections are, with only a few exceptions, small compared with the cross-section for collision. Second, there are strong propensity rules governing the pathways of mode-to-mode transfer so that not all levels within the range defined by the distribution of collision energies are equally accessible from the initial level. 

Example 8.1 For saturation of the pump transition even moderate intensities ( p < 10 kW/cm ) are sufficient (Sect. 2.1). Assume an output power of 50 kW of the transfer laser L2 and a beam diameter of 1 mm in the focal plane, which yields /transf = 6.7 MW/cm, energy transfer cross sections of ctt 1.3 X 10 cm, which is about 1000 times larger than the gas-kinetic cross section. The energy transfer Rj = anvhvj, where n is the density of collision partners, colliding with the excited atoms. With n = 10 cm, v = 10 cm/s and hvj = 2 eV, we obtain Rj = l(f eV/s. 

In the remainder of this paper, I will review our understanding of the spatially independent, slow neutron spectrum. In II the general features of the problem will be discussed, independent of the detailed behavior of the actual cross section. In III the energy-transfer cross sections for various moderators will be considered in terms of explicit models, and neutron spectra calculated from these models will be presented. Comparison with... 

In the following section we will consider the experimental and theoretical work that has gone into determining the energy-transfer cross section of Equation (15), and present some of the neutron spectra calculated from these cross sections by solution of Equation (14). 

III. Determination of the energy-transfer cross sections and calculations of infinite medium velocity distributions. 

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