Effects of Nuclear Recoil

In interpreting the experimental results, a major difiSculty arises. This is the question of the possible alteration of the original distribution of radioactive atoms among the various species present in the crystals by the particular method of analysis employed. This difficulty may be illustrated by considering potassium chromate. If chromium recoil leads to species such as Cr04 , CrOs, Cr02 +, CrO +, and Cr + in the crystal (SI), dissolution of the sample in water will result in the production of chromate by all but the last two, at least, since chromic anhydride and 

These ideas have been extended by Green, Harbottle, and Maddock (IS) to cases where oxide ions are lost. They supposed that the important reaction of the recoil species at the end of its track was the loss of one or more oxide ions, or conversely, incomplete readdition of oxide ions to the recoil atom. Then each partially-reconstituted species (for example, MnOr, MnOs+, Mn02+ +, etc.) will suffer either hydration (which will reconstitute the parent) or reduction on dissolution in water. The argument runs that the greater the oxidation potential of the parent anion, the sooner will a species be reached (through successive loss of oxide ions) which will inevitably oxidize water on dissolution, and consequently the lower the retention. This rough relationship is indicated by Fig. 1 in 

The foregoing considerations show that it is possible to explain many of the observations on the oxyanions in terms of recombination reactions between the recoil atom and oxygen atoms or ions produced in collisions. 

Although the activation energy for the recombination of fragments is fairly low, the fragments may not be nearest neighbors and the activation energy for diffusion may be a few electron volts (80). 

The theory that the oxygenated recoil species are formed in reactions between recoil atoms and surrounding oxyanions or dislodged oxygens is supported by the results of mixed crystal experiments. Mixed crystals (solid solutions) of potassium chromate in potassium sulfate [35) and fluoberyllate (50), and potassium permanganate in potassium perchlorate (67) have been investigated. The results are given in Table II. These 

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The two-time Green s function method has the advantage of being applicable to many atomic physics problems, such as the recombination of an electron with an ion [20], the shape of spectral lines [21] and the effect of nuclear recoil on atomic energy levels [22,23]. 

Following the above mechanical use of nuclear recoil, purely chemical effects of nuclear recoil were observed by Szilard and Chalmers (1934a, b) in 1934. They used (n,y) reaction of iodine in ethyl iodide. The product of neutron capture, I, could be chemically extracted into an aqueous phase after mixing ethyl iodide with water. 

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. 

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. 

Chemical effects of nuclear reactions do not only cause rupture of chemical bonds, they also lead to formation of new chemical bonds, a result that may be used for preparation of labelled compounds. Recoil labelling and self-labelling both involve radiation-induced reactions and also belong to the field of radiation chemistry. 

Chemical effects of nuclear transformations (hot atom chemistry) have been extensively studied in connection with induced nuclear transformations, both in the gas phase, in solution and in the solid state. In the latter cases the dissipation of the kinetic ergy and neutralization of the charge within a small volume produces a high concentration of radicals, ions, and excited molecules in the region where the recoiling atom is slowed to energies where it can form stable bonds. Usually the product molecule is labeled neither very specifically nor conq>letely randomly. The topic of hot atom behavior is also treated in Ch. 7. 

Nuclear transitions involve energies which are orders of magnitude larger than those associated with the excitation of vibrational or electronic states. It thus becomes necessary to account for the effects of mechanical recoil in the emission and absorption of such high-energy radiation in order to interpret the results of resonance-type measurements. 

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).

The Mossbauer effect involves the resonance fluorescence of nuclear gamma radiation and can be observed during recoilless emission and absorption of radiation in solids. It can be exploited as a spectroscopic method by observing chemically dependent hyperfine interactions. The recent determination of the nuclear radius term in the isomer shift equation for shows that the isomer shift becomes more positive with increasing s electron density at the nucleus. Detailed studies of the temperature dependence of the recoil-free fraction in and labeled Sn/ show that the characteristic Mossbauer temperatures Om, are different for the two atoms. These results are typical of the kind of chemical information which can be obtained from Mossbauer spectra. 

This paper describes a new reaction which may yield useful amounts of the product isotope following neutron capture by lanthanide or actinide elements. The trivalent target ion is exchanged into Linde X or Y zeolite, fixed in the structure by appropriate heat treatment, and irradiated in a nuclear realtor. The (n, y) product isotope, one mass unit heavier than the target, is ejected from its exchange site location by y recoil. It may then be selectively eluted from the zeolite. The reaction has been demonstrated with several rare earths, and with americium and curium. Products typically contain about 50% of the neutron capture isotope, accompanied by about 1% of the target isotope. The effect of experimental variables on enrichment is discussed. 

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]... 

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). 

As it follows from Ref. [13], the formulas (3)- (5) will incorporate partially the nuclear size corrections to the recoil effect if Vib(r) is taken to be the potential of an extended nucleus. In particular, this replacement allows one to account for the nuclear size corrections to the Coulomb part of the recoil effect. In Ref. [33], where the calculations of the recoil effect for extended nuclei were performed, it was found that, in the case of hydrogen, the leading relativistic nuclear size correction to the Coulomb low-order part is comparable with the total value of the (aZ)em2/M correction but is cancelled by the nuclear size correction to the Coulomb higher-order part. 

For low Z, in addition to the corrections considered here, the Coulomb inter-electronic interaction effect on the non-relativistic nuclear recoil correction must be taken into account. It contributes on the level of order (1 /Z)(aZ)2m2/M. 

In 1S-2S spectra of hydrogen and deuterium, recorded by C. WIEMAN [16] in this way, the observed linewidth remained as large as 100 MHz. Nonetheless, the isotope shift could be measured well enough to yield first experimental evidence for a relativistic correction to the nuclear recoil effect This correction was known theoretically, but was considered too small to be observable. 

The term Mossbauer effect describes the recoil-free resonant absorption of y quanta by nuclei of the same kind as the emitters. If a free nucleus undergoes a transition from an excited state by emission of a y quantum, it suffers a recoil. The energy of this quantum in the laboratory frame is given as = E — E/j, where E is the nuclear transition energy and Er is the recoil energy of the nucleus after the emission of the y quantum. It can be expressed as... 

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