Recoil factor equation

The first factor, exp( cy/2 gT), is known as the detailed balance factor - it produces an asymmetry in the quantum-mechanical structure factor, whereas the classical one is an even function of co. The second factor, exp(- Q /8M gT), can also be written as exp(- R/4 gT), where r = ffiQVlM is the recoil energy of the target particle. Hence this exponential factor is known as the recoil factor. Equation [56] is exactly true only in the ideal gas case however, it is also approximately valid for other scattering systems as well. 

The very presence of the recoil factor m/M emphasizes that the external field approach is inadequate for calculation of recoil corrections and, in principle, one needs the complete machinery of the two-particle equation in this case. However, many results may be understood without a cumbersome formalism. 

Some of the data used to obtain Equations 1-14 is shown in Figure 7. x is a normalized factor for solute concentration and is equal to a ratio of constants obtained from Table II. The correlation for fission recoils and 7-radiation is very good over the entire concentration range. The curves in Figure 7 are theoretical and represent Equation 8 for fission recoils, Equation 12 for reactor radiation, Equation 13 for 18.9 m.e.v. D+, and Equation 3 for 7-radiation. Figure 7 emphasizes that the... 

While the stress tensor component tfor purely viscous fluids can be determined from the instantaneous values of the rate of deformation tensor 4, the past history of deformation together with the current value of 4, may become an important factor in determining t, for viscoelastic fluids. Constitutive equations to describe stress relaxation and normal stress phenomena are also needed. Unusual effects exhibited by viscoelastic fluids include rod climbing (Weis-senberg effect), die swell, recoil, tubeless siphon, drag, and heat transfer reduction in turbulent flow. 

Several factors decide whether or not the bonds attached to a newly formed atom are sufficiently strong to hold it in place. The impulse is imparted to the newly formed atom in a time that is short compared to the time required for bond dissociation, bond dissociation times being approximately the time for a bond vibration (10 — 10 sec). Consequently the other bonds in the molecule probably do not experience any traumatic change in energy state as the atom recoils. In considering the nuclear transformation of bromine in the HBr molecule, Suess (1940) derived a simple expression, given in equation (1), relating... 

Factorization of the function concentrated polystyrene solution, time-strain factorability is not valid at short times after the imposition of the step shear. An accurate K-BKZ constitutive equation for shearing flows of this material will be much more complex than that for melt I. Furthermore, in strain histories in which a strain reversal takes place, such as constrained recoil (Wagner and Laun, 1978) or double-step strains with the second strain of sign opposite the first (Doi, 1980 Larson and Valesano, 1986), good agreement... 

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