Recoil calculations

As a second example, results from a TOP ERDA measurement for a multi-element sample are shown in Fig. 3.65 [3.171]. The sample consists of different metal-metal oxide layers on a boron silicate glass. The projectiles are 120-MeV Kr ions. It can be seen that many different recoil ions can be separated from the most intense line, produced by the scattered projectiles. Figure 3.66 shows the energy spectra for O and Al recoils calculated from the measured TOF spectra, together with simulated spectra using the SIMNRA code. The concentration and thickness of the O and Al layers are obtained from the simulations. 

In the case of the polarization insertions the calculations may be simplified by simultaneous consideration of the insertions of both the electron and muon polarization loops [18, 19]. In such an approach one explicitly takes into account internal symmetry of the problem at hand with respect to both particles. So, let us preserve the factor 1/(1 - - m/M) in (9.9), even in calculation of the nonrecoil polarization operator contribution. Then we will obtain an extra factor m /m on the right hand side in (9.12). To facilitate further recoil calculations we could simply declare that the polarization operator contribution with this extra factor m /m is the result of the nonrecoil calculation but there exists a better choice. Insertion in the external photon lines of the polarization loop of a heavy particle with mass M generates correction to HFS suppressed by an extra recoil factor m/M in comparison with the electron loop contribution. Corrections induced by such heavy particles polarization loop insertions clearly should be discussed together with other radiative-recoil... 

There are quite a few web sites that offer approximate recoil calculators and I used the one at www.10xshooters.com/calculators/Shotgun Recoil Calculator.htm although www.gunnersden.com/index. htm.shotgun-recoil.html uses the same formula it just makes you do the calculations yourself ... 

For accurate ion trajectory calculation in the solid, it is necessary to evaluate the exact positions of the intersections of the asymptotes (A A2) of the incoming trajectory and that of the outgoing trajectories of both the scattered and recoiled particles in a collision. The evaluation of these values requires time integrals and the following transfonnation equations ... 

Theorists calculate cross sections in the CM frame while experimentalists usually measure cross sections in the laboratory frame of reference. The laboratory (Lab) system is the coordinate frame in which the target particle B is at rest before the collision i.e. Vg = 0. The centre of mass (CM) system (or barycentric system) is the coordinate frame in which the CM is at rest, i.e. v = 0. Since each scattering of projectile A into (v[i, (ji) is accompanied by a recoil of target B into (it - i[/, ([) + n) in the CM frame, the cross sections for scattering of A and B are related by... 

The recoiler is driven by motor M - that adjusts its speed and tension as calculated for the whole process line. It is this drive and the bridles that maintain the required tension throughout the process and make the pay-off reel drives operate as regenerative units. 

Chemical effects of nuclear decay have been studied in Germanium through the use of Ge and Ge. Ge decays to Ga with a 275 day half-life by 100% electron capture with no y quanta emitted. Ge is a P emitter which decays to As with a 11.3 h half-life, by three jS transitions having maximum energies of 710 keV (23%), 1379 keV (35%) and 2196 keV (42%). From this are calculated maximum recoil energies of 1.7 eV, 4.5 eV and 10.2 eV, respectively. 

When a single y-ray of known energy is emitted, the recoil energy given to the atom is calculated from the conservation of energy and momentum. The result is... 

Attempts have been made to calculate the recoil energy spectrum using an assumed statistical distribution of y-energies and direction. Notably, Hsiung et al. (39) have done this calculation for C1 produced by CCI4 (n,y). While the results of the calculation were in reasonble agreement with experimental data, the complexity of the necessary assumptions makes the agreement seem perhaps fortuitous. 

As a noble gas, Rn in groundwater does not react with host aquifer surfaces and is present as uncharged single atoms. The radionuclide Rn typically has the highest activities in groundwater (Fig. 1). Krishnaswami et al. (1982) argued that Rn and all of the other isotopes produced by a decay are supplied at similar rates by recoil, so that the differences in concentrations are related to the more reactive nature of the other nuclides. Therefore, the concentration of Rn could be used to calculate the recoil rate for all U-series nuclides produced by a recoil. The only output of Rn is by decay, and with a 3.8 day half-life it is expected to readily reach steady state concentrations at each location. Each measured activity (i.e., the decay or removal rate) can therefore be equated with the input rate. In this case, the fraction released, or emanation efficiency, can be calculated from the bulk rock Ra activity per unit mass ... 

Since Ra and " Ra are both produced by recoil from the host mineral, it might be assumed that the production rates are equal. However, the relative recoil rates can be adjusted by considering that the parent nuclides near the mineral surface may not be in secular equilibrium due to ejection losses i.e., the activity of Th may be lower than that of Th due to recoil into groundwater of the intermediate nuclide Ra. Krisnaswami et al. (1982) calculated that the recoil rate of " Ra is 70% that of Ra if radionuclides are depleted along the decay chain in this way. 

The Ra isotopes in the other decay series can be evaluated similarly. Ra in the series (Table 1) is the product of the third a decay, and so the effects of near-surface deletion or decay of recoiled precursors must be calculated accordingly. Ra in the series is also the product of the third a decay. Further processes that may be considered where circumstances warrant include nonsteady state conditions or removal by precipitation at rates that are fast compared to the decay rate of the Ra nuclides. 

The distribution of Th is not controlled by decay processes that can be used to constrain its supply rate, but the Th- Ra pair can be used to provide some constraints on Th adsorption. In an area where Ra concentrations are constant, mobile Ra is supplied by only recoil and decay of mobile Th. The amount of Th that is absorbed on surfaces can be obtained if the amount of mobile Ra is constrained (i.e., the Ra partition coefficient and the groundwater concentration are known) and can be compared to an estimate of the recoil rate of Ra (using the measured Rn activity in the groundwater) from the host rock. In this way, Luo et al. (2000) calculated that recoil from the host rock was insufficient to explain the amount of mobile Ra, and argued that adsorbed Th provided much of the mobile Ra then Th partition coefficients can... 

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