Recoil effects

Hand M R and Harris J 1990 Recoil effects in surface dissociation J. Chem. Phys. 92 7610... 

The Mossbauer effect can only be detected in the solid state because the absorption and emission events must occur without energy losses due to recoil effects. The fraction of the absorption and emission events without exchange of recoil energy is called the recoilless fraction, f. It depends on temperature and on the energy of the lattice vibrations /is high for a rigid lattice, but low for surface atoms. 

The recoil effect causes an energy shift of the emission line from Eq to smaller energies by an amount r, whereby the y-photon carries an energy of only Ey = Eq — Ep. However, a recoil effect also occurs in the absorption process so that the photon, in order to be absorbed by a nucleus, requires the total energy Ey = Eq+ r to make up for the transition from the ground to the excited state and the recoil effect (for which and Py will have the same direction). 

Secondly, fractionation can also take place as a result of radioactive decay, especially in the low-temperature environment, and these effects are generally described as recoil effects. To illustrate the physics of recoil, we choose for example the decay of... 

Seawater interaction is a potential source of several U-series nuclides, and is strongly enriched in B, Cl and Sr. Thus, abundances of these elements and/or their isotopes can often be used to test for seawater contamination (e.g.. Turner et al. 2000a). Because will be located in mineral sites that have been damaged by recoil effects, " U is likely to... 

Dran J-C, Langevin Y, Petit J-C (1988) Uraruum isotopic disequilibrium reappraisal of the alpha-recoil effect. Chem Geol 70 126... 

Figure 20. Secular variation in 5 U(0) for Bahamas flowstone sequence. Changes in 5 U(0) are related to uranium-series disequilibrium conditions in host limestone, periodic addition of new material with elevated (marine) 5 U(0), alpha recoil effects and variation in recharge, and hence water-rock interaction times (see text for details).

Figure 5.1 Resonant absorption of y-radiation by a nucleus can only take place in the solid state because of recoil effects. The excited nucleus of a free atom emits a y-photon with an energy EirER, whereas the nucleus in the ground slate of a free atom can only absorb a photon if it has an energy equal to Eo+ER. As the linewidth of nuclear transitions is extremely narrow, the emission spectrum does not overlap with the absorption spectrum. In a solid, a considerable fraction of events occurs recoil free (ER=0), and here the emission spectrum overlaps completely with the absorption spectrum (provided source and absorber have the same chemical environment).

Radiative Corrections to Nuclear Size and Recoil Effects... 

Calculations for Figure 14 illustrate a recoil source with the same parameters as those used in the study depicted by Figure 11, except that a buffer carbon layer 0.0006 cm. thick with a diffusion coefficient of 10"6 cm.2/sec. was placed between the coating and the kernel. Distribution coefficients were taken as unity. A recoil range of 0.0006 cm. was assumed in both the kernel and coating materials. Results of this calculation differ considerably from those for experiments with no recoil. These differences are consistent with. —4.5% release from the kernel during irradiation. After release of this quantity of fission product from the particle, the releases begin to approach those of the bare kernel. The recoil effects were unimportant after releases of 7 to 8%. 

Pulse Dampeners—Device used to control pump pulsing. Usually a tight coil of metal tubing in a metal container that acts as a baffle and counters pulsing by a spring recoil effect. 

In actual experiments, of course, things are not quite so simple. In the first place, one does not observe the instantaneous release but only its integration in discrete temperature steps. Problems also arise because of the recoil effect mentioned earlier and various interferences and other uncertainties arising in the neutron irradiation. 

The recoil effect mentioned above is due to the impact of the gamma-photon on the sample nucleus. The nucleus thereby takes some of the photon energy so that insufficient remains to match the required transition energy. It is therefore necessary to bind the nucleus (and its atom) into a solid matrix. Under these circumstances, the recoil energy can be... 

In order to avoid recoil effects all samples must be solid but, since measurements are made at 4.2 K, samples which are fluid at room temperature can be measured without difficulty. The amounts required are relatively small, typically 20-30 mg for 127I and 2-20 mg for 129I these amounts refer to the mass of iodine contained in the sample. Samples are usually pressed into discs or mulled with grease, and can often be recovered unharmed. In the case of 129I this is essential, as the expensive isotope must be recycled. 

The terminal iodine atoms of I5 have a unique subspectrum, enabling the intensity of the two other subspectra for this anion to be estimated the remaining intensity of these two subspectra represent the I3. When account is taken of the different intensities expected for the different sites due to recoil effects, reasonable estimates of the ratio of the two ions can be made (Table 10). 

The hyperfine structure interval in hydrogen is known experimentally on a level of accuracy of one part in 1012, while the theory is of only the 10 ppm level [9]. In contrast to this, the muonium hfs interval [12] is measured and calculated for the ground state with about the same precision and the crucial comparison between theory and experiment is on a level of accuracy of few parts in 107. Recoil effects are more important in muonium (the electron to nucleus mass ratio m/M is about 1/200 in muonium, while it is 1/2000 in hydrogen) and they are clearly seen experimentally. A crucial experimental problem is an accurate determination of the muon mass (magnetic moment) [12], while the theoretical problem is a calculation of fourth order corrections (a(Za)2m/M and (Za)3m/M) [11]. 

The higher-order two-loop corrections are to be calculated within the so-called external filed approximation (i. e. neglecting by the nuclear motion), while the recoil effects require an essential two-body treatment. There are a few approaches to solve the two-body problem (see e.g. [31]). Most start with the Green function of the two-body system which has to have a pole at the energy of the bound state... 

We will review here experimental tests of quantum electrodynamics (QED) and relativistic bound-state formalism in the positron-electron (e+,e ) system, positronium (Ps). Ps is an attractive atom for such tests because it is purely leptonic (i.e. without the complicating effects of nuclear structure as in normal atoms), and because the e and e+ are antiparticles, and thus the unique effects of annihilation (decay into photons) on the real and imaginary (related to decay) energy levels of Ps can be tested to high precision. In addition, positronium constitutes an equal-mass, two-body system in which recoil effects are very important. 

In contrast to normal atoms this calculation is not accurate enough because of essential recoil effects. The leading relativistic recoil term for the Is state is of order (Za)2m/M and it depends on the nuclear structure. The difference is free of nuclear influence and the result is [16]... 

A very important point is the overall uncertainty of our calculations and we consider here particularly the contribution of the QED part to the uncertainty. The second order vacuum polarization effects (<5VP2) are of order (rx2/tt2)Ef (cf. relativistic corrections are of order (Za)2Ep))- Another source of uncertainty arises from higher order recoil effects (<5rec2) which can be estimated as <5rec2 = m/M ATec. ... 

Abstract. The quantum electrodynamic theory of the nuclear recoil effect in atoms to all orders in aZ and to first order in m/M is considered. The complete aZ-dependence formulas for the relativistic recoil corrections to the atomic energy levels are derived in a simple way. The results of numerical calculations of the recoil effect to all orders in aZ are presented for hydrogenlike and lithiumlike atoms. These results are compared with analytical results obtained to lowest orders in aZ. It is shown that even for hydrogen the numerical calculations to all orders in aZ provide most precise theoretical predictions for the relativistic recoil correction of first order in m/M. 

In the non-relativistic quantum mechanics the nuclear recoil effect for a hydrogenlike atom is easily taken into account by using the reduced mass p = mM/(m + M) instead of the electron mass m (M is the nuclear mass). It means that to account for the nuclear recoil effect to first order in m/M we must simply replace the binding energy E by E(1 — m/M). 

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