Kinematic factors

To derive the relation for the kinematic factor, it is assumed that the interaction is elastic, projectile energy Eq is much larger than the binding energy of the atom in the target and the nuclear reactions and resonance must be absent. The Kinematic factor K 0, Mi, M2) is given by the relation 

Special cases The kinematic factors for 6 = 180° and 9 = 90° are given by the following relations  

The Kinematic factor for a few target elements (M2) due to He projectile are given in Table 2.1. 

The variation of kinematic factor with mass M2 and scattering angle is as shown in Fig. 2.2. Since the identification of a particular element in the sample 

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For Si atoms the kinematic factor is smaller, fCg, < because of their lower mass. 

Both kinematic factors and fCg functions of the mass ratio Mj/M and the recoil and scattering angle 6. Because the recoil kinematic factor is symmetric in the... 

K denotes the kinematic factor for the elastic scattering process. Thus, in RBS, a projectile of known mass and known energy is employed, and by measuring the... 

The ab initio molecular dynamics study by Hudock et al. discussed above for uracil included thymine as well [126], Similarly to uracil, it was found that the first ultrafast component of the photoelectron spectra corresponds to relaxation on the S2 minimum. Subsequently a barrier exists on the S2 surface leading to the conical intersection between S2 and Si. The barrier involves out-of-plane motion of the methyl group attached to C5 in thymine or out-of-plane motion of H5 in uracil. Because of the difference of masses between these two molecules, kinematic factors will lead to a slower rate (longer lifetime) in thymine compared to uracil. Experimentally there are three components for the lifetimes of these systems, a subpicosecond, a picosecond and a nanosecond component. The picosecond component, which is suggested to correspond to the nonadiabatic S2/S1 transition, is 2.4 ps in uracil and 6.4 ps in thymine. This difference in the lifetimes could be explained by the barrier described above. 

Incorporating the required kinematic factors transforms this transition probability into a cross section,... 

Frequendy, one can display a stopping power formula as shown in Eq. (2.5), in which case the quantity within the parenthesis is called the kinematic factor... 

Figure 4.14 Kinematic factors Ej/E, for He and Ne scattering as a function of scattering angle for the elements present in a hydrotreating catalyst, calculated with (4-4).

The bottom spectrum in Fig. 4.16 is that of the fresh MoCVSi02/Si( 100) model catalyst a part is shown enlarged. The peak at 3.4 MeV has a kinematic factor of about 0.85. As the scattering angle is 170°, the reader can use Fig. 4.14 to verify that this peak belongs to Mo. In the same way one may check that the continuum below E = 2.3 MeV is due to 28Si. Note that small peaks due to the Si isotopes at 29 and 30 amu are just visible as well. The structure around 2 MeV is caused by non-... 

The fact that LEIS provides quantitative information on the outer layer composition of multi-component materials makes this technique an extremely powerful tool for the characterization of catalysts. Figure 4.19 shows the LEIS spectrum of an alumina-supported copper catalyst, taken with an incident beam of 3 keV 4He+ ions. Peaks due to Cu, A1 and O and a fluorine impurity are readily recognized. The high intensity between about 40 and 250 eV is due to secondary (sputtered) ions. The fact that this peak starts at about 40 eV indicates that the sample has charged positively. Of course, the energy scale needs to be corrected for this charge shift before kinematic factors Ef/E-, are determined. 

The basic stopping power formula of Bethe has a structure similar to that of Bohr s classical theory [cf. Eq. (2)]. The kinematic factor remains the same while the stopping number is given hy B = Zln(2mv /7) for incident heavy, nonrelativistic particles. The Bethe... 

Rutherford scattering is an elastic event, that is, no excitation of either the projectile or target nuclei occurs. However, due to conservation of energy and momentum in the interaction, the kinetic energy of the backscattered ion is less than that of the incident ion. The relation between these energies is the kinematic factor, K, which is given by the expression... 

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