Lifetime nuclides

Nucleosynthesis is the formation of elements. Hydrogen and helium were produced in the Big Bang all other elements are descended from these two, as a result of nuclear reactions taking place either in stars or in space. Some elements—among them technetium and promethium—are found in only trace amounts on Earth. Although these elements were made in stars, their short lifetimes did not allow them to survive long enough to contribute to the formation of our planet. However, nuclides that are too unstable to be found on Earth can be made by artificial techniques, and scientists have added about 2200 different nuclides to the 300 or so that occur naturally. 

Neutron capture and P emission forms nuclei of ever higher atomic number. Neutron capture and P emission by Co (Z = 27) produces Ni (Z = 28), Ni produces Cu (Z = 29), and so on up the atomic-number ladder Neutron capture and P emission form all possible stable nuclides during the lifetime of a second-generation star. 

If the amount of a radioactive nuclide in a rock sample is N, the sum of this amount plus the amount of its product nuclide is A/q. For argon dating, Nq is the sum of potassium-40 and argon-40 present in a sample of rock. Assuming that Ar gas escapes from molten rock but is trapped when the rock cools and solidifies, the lifetime obtained by substituting these values into Equation is the time since the rock solidified. Such analyses show that the oldest rock samples on Earth are 3.8 X 10 years old. 

The nuclear y-resonance effect in ° Ni was first observed in 1960 by Obenshain and Wegener [2]. However, the practical application to the study of nickel compounds was hampered for several years by (1) the lack of a suitable single-line source, (2) the poor resolution of the overlapping broad hyperfine lines due to the short excited state lifetime, and (3) the difficulties in producing and handling the short-lived Mossbauer sources containing the Co and Cu parent nuclides, respectively. 

The recoilless nuclear resonance absorption of y-radiation (Mossbauer effect) has been verified for more than 40 elements, but only some 15 of them are suitable for practical applications [33, 34]. The limiting factors are the lifetime and the energy of the nuclear excited state involved in the Mossbauer transition. The lifetime determines the spectral line width, which should not exceed the hyperfine interaction energies to be observed. The transition energy of the y-quanta determines the recoil energy and thus the resonance effect [34]. 57Fe is by far the most suited and thus the most widely studied Mossbauer-active nuclide, and 57Fe Mossbauer spectroscopy has become a standard technique for the characterisation of SCO compounds of iron. 

The abundances of radioactive isotopes over time in the galaxy can be modeled based on the above considerations. With an approximately constant production rate, the abundance of a stable nuclide will grow and will be proportional to the time over which it has been produced. In contrast, the abundance of a radionuclide will reach a steady state between production and decay in about eight mean lifetimes. (We will use mean life (t) instead of... 

Cosmic-ray exposure ages are determined from spallation-produced radioactive nuclides. Cosmic-ray irradiation normally occurs while a meteoroid is in space, but surface rocks unshielded by an atmosphere may also have cosmogenic nuclides. These measurements provide information on orbital lifetimes of meteorites and constrain orbital calculations. Terrestrial ages can be estimated from the relative abundances of radioactive cosmogenic nuclides with different half-lives as they decay from the equilibrium values established in space. These ages provide information on meteorite survival relative to weathering. 

Observations of isotopic abundances provides information on the nucleosynthesis operating in the compact core of stars and supernova explosions and on the chemical evolution of the Galaxy. The CNO nuclides in late-type stars are affected by freshly synthesized core material brought up by dredge-up events. On the other hand, the Si isotopes are involved in later phases of nuclear burning, a narrow span of the red giant lifetime before planetary nebulae or supernovae. Therefore relative abundances of Si isotopes we observe remain unchanged from those of interstellar matter from which a star was formed. 

Thus, the deposition temperature and the thermodynamic state function of the adsorption are combined and they can easily be determined from each other. The retention time for a short-lived radioactive species is calculated as the radioactive lifetime of the nuclide ... 

For every atom a random lifetime, which is distributed logarithmically according to the radioactive decay law with the half-life, Ti/2, of the nuclide is calculated ... 

On-line gas chemical studies of dubnium have been mostly performed with Db. This nuclide can be produced in the reaction Bk( 0,5n) at a beam energy of about 100 MeV. It has a half-life of 34 5 s and decays with 67 % by emission of two sequential a particles via 258Lr (T1/2=4.4 s) to the long-lived 254Md (Ti/2=28m). In addition, 262Db has a spontaneous fission decay branch of 33%. Hence, identification of each separated labeled molecule is based on either detection of two characteristic a-particles and their lifetimes or on the detection of a spontaneous fission decay. 

A is the mass number of the nuclide. The sign denotes an unstable nuclide (for elements without naturally occurring isotopes it is the most stable nuclide) and the sign a nuclide of sufficiently long lifetime to enable the determination of its isotopic abundance. 

With respect to the lifetime of the excited states resulting from changes in the atomic number, isothermal and adiabatic decay may be discussed. All the experimental results indicate an adiabatic decay, which means transfer of the excitation energy to all the electrons, resulting in a certain lifetime of the excited state of the daughter nuclide of the order of about 1 ps. 

Mdssbauer spectrometry gives information about the chemical environment of the Mdssbauer nuclide in the excited state at the instant of emission of the photon. It does not necessarily reflect the normal chemical state of the daughter nuclide, because of the after-effects that follow the decay of the mother nuclide (recoil and excitation effects, including emission of Auger electrons). At very short lifetimes of the excited state, ionization and excitation effects may not have attained relaxation at the instant of emission of the y-ray photon this results in a time-dependent pattern of the Mdssbauer spectrum. 

The short lifetimes of A1 and, especially, " Ca, coupled with the evidence for an external origin of these nuclides, have important implications for the origin of the solar system. Based on estimated production rates and isotope mixing during interstellar transit and injection into the solar system, a duration of at most 1 Myr can be... 

Any disturbance from secular equilibrium decays back toward secular equilibrium through the decay of the shorter-lived supported chains. If the chains have significantly different decay rates, they are reasonably well decoupled and can be used to date processes comparable to the lifetimes of each chain (e.g., Condomines et al., 1988 Rubin et al., 1994 Thompson et al., 2003). As a useful rule of thumb, the time taken for a parent-daughter pair to return to approximate secular equilibrium, is about five half-lives of the shorter lived nuclide. In five half-lives, —97% of initial disequilibrium has decayed. Whether any detectable disequilibrium actually remains depends on the precision of measurements and degree of initial disequilibrium. 

A principal advantage of working with the short-lived nuclides in gaseous phase is a safe upper limit for the permissible concentration of any chemically active contamination. Indeed, the chemical fate of the recoil atom cannot be affected when its collisions with the contaminations are improbable because of the short lifetime. Equation 3.4 shows that the safe concentrations are smaller than about 109/fi/2 cm-3. 

Fig. 3.9 Comparison of the transportation efficiencies (including the survival yields), measured at the exit of a straight open cylindrical tube, for relatively short-lived tracers, which are carried either as gaseous molecules or as aerosols. The values are plotted versus the hold-up time of the gas divided by the mean lifetime of the particular nuclide.

When simulating the molecular histories, especially for the experiments with shortlived nuclides, it is necessary to note that the actual processing time is a random variable with an individual value for each molecule. It is so not only because of the individual lifetimes of the involved nuclei, but also due to some external factors. These are, for example, the nominal t c and the temporal profile of injection. However, equally important is the temporal regime of detection of the decay events — whether they are registered in the course of the run or after its end. 

A concrete example comes from the experimental works with the radionuclides characterized by lx, much shorter than t c. A long continuous on-line experiment formally looks like the frontal chromatography of the products. However, when the decay events of such nuclides are registered immediately by the material of the column, the resulting internal chromatogram is the same as it would be in the elution regime. The random processing time tf equals the random individual lifetime of the nucleus. 

In the meantime, a reasonably fast radioactive decay makes a different technique for obtaining data on fjp feasible, even with rather low activities. One can measure the fraction r]c of the nuclei introduced into the IC column which survives at its exit. This principle can be used in on-line experiments with the nuclides which have mean lifetimes much less than the nominal duration of the run in practice, it means the range from seconds to hours. For a nuclide with the particular tx, two or more measurements at different temperatures must be done. At least one at a temperature when t -C tx to find the production rate of the detectable activity, as well as one when r c is of the order of lx and so the surviving fraction is in the range 0 < rf < 1. From the point of view of the statistics, most desirable is to aim at rjc near 0.5. Obviously, r = exp -t r/tx), hence ... 

Finally we pay attention to the ideal frontal TC (cf. Fig. 4.1). The high temperature front of the zone profile is obviously proportional to the adsorption isobar and so, at least for the localized adsorption model, to the adsorption constant. As such, it would obey Eq. 5.14. It holds for the activities which do not appreciably decay in the course of run. As for the shorter-lived nuclides, both the elution and the formally frontal TC result in non-ideal frontal chromatograms. Their shapes are close to what would arise from ideal processing during t . but they are smeared due to the random lifetimes of nuclei. Still the initial part of the thermochromatogram might be useful for evaluation of the required quantity, provided that the statistics of detected decay events is good. 

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