Recoil factor

The paper summerizes the experimental data on the equilibrium factor, F, the free fraction, fp, the attachment rate to the room air aerosol, X, the recoil factor,, and the plateout rates of the free, qf, and the attached, q3, radon daughters, determined in eight rooms of different houses. In each room several measurements were carried out at different times, with different aerosol sources (cigarette smoke, stove heating etc.) and under low (v<0.3 It1) and moderate (0.3[Pg.288]

The recoil factors r define the probability of whether an attached radioactive atom desorbs from the particle surface in consequence of an alpha decay or not. Mercer and Strowe (1971) found a recoil factor = 0.81 in their chamber studies in contradiction to the value of ri 0.4 measured by Kolerski et al. (1973). No other results about the recoil factor are available in the literature. 

This paper will summerize our experimental data on the equilibrium factor (F), the free fraction (f ), the attachment rate to the room air aerosol (X), the recoil factor r and the plateout... 

Finally with the measured values of c a, cja and cj- the recoil factor rx can be calculated ... 

The calculated recoil factor r had an average value of about 0.50 0.15, including the results with particles of cigarette smoke, stove heating etc. In spite of an error for the determination of about 30 %, this value is significantly lower than determined by Mercer (Mercer and Stowe, 1971 Mercer, 1976). 

Table lb. The equilibrium factor (F), the free fraction (fp), the attachment parameters (X,0,d), the plateout rates (qf, qa) and the recoil factor (r ), calculated from the measured data of Table la (lo i/ ventilation). 

Figure 5. Relative standard deviation on the fitting of the deposition rate of the unattached daughters (Xun) and on the fitting of the ventilation rate (Xvent)> calculated by means of a Monte- Carlo simulation model. The lower curve is obtained with counting statistics alone. The upper curve includes one hour time fluctuations on the input parameters, with 10% rel. stand, dev. on X, un (15/h), a(.35/h), Vent(.45/h) and radon cone. (50 bq/m ) and 2% on recoil factor (.83), penetration unattached (.78) and flow rate (28 1/min).

Contributions to the energy which depend only on the small parameters a. and Za. are called radiative corrections. Powers of a arise only from the quantum electrodynamics loops, and all associated corrections have a quantum field theory nature. Radiative corrections do not depend on the recoil factor m/M and thus may be calculated in the framework of QED for a bound electron in an external field. In respective calculations one deals only with the complications connected with the presence of quantized fields, but the two-particle nature of the bound state and all problems connected with the description of the bound states in relativistic quantum field theory still may be ignored. 

This momentum space potential is similar to the momentum space potential corresponding to insertion of the electron-loop polarization in the Coulomb photon, considered in Subsubsect. 7.1.1.1. The only difference is in the overall multiplicative constant, and that the respective expression in the case of the one electron polarization insertion contains in the denominator instead of k in (7.46). This means that the mixed loop contribution is suppressed in comparison with the purely electron loops by an additional recoil factor... 

Due to the additional recoil factor (mg/m) this contribution is suppressed by four orders of magnitude in comparison with the nonrecoil corrections generated by insertion of two electron loops in the Coulomb photon (compare (7.12)). Numerically, for the 2P — 2S interval we obtain... 

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... 

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. 

To summarize, the p + NR elastic scattering amplitude is conveniently calculated using the relativistic DWBA formalism, where the following dianges from the procedure desoibed in ref. [Ra 88b] are carried out (1) NR distorted waves and bound state wave functions are used for the upper components (2) the lower components are set to the NR or free partide limit [i.e., no potential terms included in (a k)/ E + m)] (3) ) corresponds to the dioice of t according to eq. (6.5) and may include density dependence (4) the pA recoil factor, EJ E + ), is included. 

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. 

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