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Its mandate is to provide the basis for a single, coherent system of measurements throughout the world, traceable to the International System of Units SI. This task takes many forms, from direct dissemination of units as in the case of mass and time to coordination through international comparisons of national measurement standards as in electricity and ionizing radiation. Buy this article in print. Data evaluators, scanning the literature, are faced with bad documentation, lack of traceability, incomplete uncertainty budgets and discrepant .
Poor control of uncertainties has its implications for the end-user community, varying from limitations to the accuracy and reliability of nuclear-based analytical techniques to the fundamental question whether half-lives are invariable or not. This paper addresses some issues from the viewpoints of the user community and of the decay data provider. It addresses the propagation of the uncertainty of the half-life in activity measurements and discusses different types of half-life measurements, typical parameters influencing their uncertainty, a tool to propagate the uncertainties and suggestions for a more complete reporting style.
Problems and solutions are illustrated with striking examples from literature. Content from this work may be used under the terms of the Creative Commons Attribution 3. Any further distribution of this work must maintain attribution to the author s and the title of the work, journal citation and DOI. The exponential decay of radionuclides as a function of time is a cornerstone of nuclear physics and radionuclide metrology. Since its discovery in by Rutherford and Suddy [ 1 ], it has been confirmed in numerous measurements of radioactive decay see e.
Theoretical derivations of the exponential law can be achieved from probabilistic and quantum-mechanical points of view [ 3 ]. Whereas decay constants for spontaneous nuclear decay are considered invariable in time and space, there is an area of research that explores possible violations of the exponential decay law. There is experimental evidence of changes in radioactive decay constants in cases where the nuclear decay is coupled to the atomic environment, i.
In recent years, controversy arose due to claims that half-lives are affected by temperature, conductivity of the hosting material, solar proximity or neutrino flux, which were subsequently refuted by others see [ 7 — 12 ]. At the heart of this controversy are the metrological difficulties inherent to the measurement of half-lives. When based on repeated measurements of activity, the half-life result is strongly influenced by instabilities in the measurement conditions [ 13 — 15 ]. From a metrological point of view it is obvious that instruments, electronics, geometry and background may vary due to external influences such as temperature, pressure, humidity and natural or man-made sources of radioactivity.
Therein lies the problem with half-life measurements: they are undeservedly perceived as easy and the experimental uncertainties are often underestimated, sometimes by an order of magnitude [ 14 , 15 ]. Consequently, nuclear data evaluators are frequently confronted with the problem of deriving a recommended value for half-lives from a discrepant set of data. Evaluations show that, for the majority of the radionuclides, the spread of experimentally determined half-life values is larger than expected from the claimed accuracies [ 16 ].
The published data not being completely reliable, one has to use alternative methods to obtain a mean and associated uncertainty value. The situation is often aggravated by experimenters providing insufficient detail on how the half-life and its uncertainty were determined.
A more comprehensive reporting style, which provides traceability for all major aspects of the measurement that may influence the result and tools that allows assessing the quality of the data, is recommended [ 15 ]. With time, one can expect evaluators to disregard published decay data lacking a sufficient level of traceability when a growing of well-documented experiments become available in the literature. It is of interest to the user community that the quality of decay data, and half-lives in particular, be improved [ 19 , 20 ]. Whether the applications are situated in the field of nuclear medicine, power generation, nuclear forensics, radioactive waste management, analytical techniques, astrophysics, geochronology, basic nuclear research or detector calibration using reference sources, there is generally a half-life correction factor involved for rescaling measured activities to a reference time.
It discusses the propagation of the uncertainty of the half-life in activity measurements and the difficulties with providing an uncertainty budget when measuring half-lives. As the activity in a radioactive sample changes with time, it is appropriate to associate a measured activity with a reference time t 0 , which does not necessarily coincide with the start or stop time of measurement t 1 , t 2. The standard uncertainty of the half-life, , propagates through the decay correction factors as follows.
With every 0. Routine laboratories calibrate their activity detectors by means of secondary standards; calibrated sources with traceable activities of certain radionuclides. These standards are kept and reused for a practical period of time. The standard uncertainty on the calibration factor due to uncertainty on the half-life is then respectively 0. Larger errors can occur for radionuclides with shorter or less reliably known half-life. More intricate rescaling is applied in the field of neutron activation analysis, where the link between elemental concentrations and measured activity of decay products is established through complex activation and decay formulas obtained as solutions of sets of linear first-order differential equations [ 22 ].
They typically contain a saturation factor for the activation during a period t irr , a decay factor and a counting factor C as above. The relative uncertainty of a measured count rate via such factors SDC is. One way of age dating is based on known atomic concentrations P t of the parent nuclide at different times, via. Isochron dating methods use the concentration S of a stable isotope of the daughter element as a reference.
This procedure is routinely used in rubidium-strontium dating, in which the parent 87 Rb and daughter 87 Sr are compared to stable 86 Sr. Ratios are used instead of absolute concentrations because they are conveniently measured with mass spectrometers.
Another application is dating 'young' groundwater, i. The isochron method can also be applied in uranium-lead dating, using Pb as the non-radiogenic isotope. The initial Pb isotopic ratios extracted from meteorites and age of the system are the two factors determining the present day Pb isotopic ratios.
In a closed system, equation 7 represents a linear relationship in which the slope depends on the age. The age of Earth, 4. The dating equations 4 , 5 and 7 are linearly proportional to the half-life of the parent and equation 8 roughly on a ratio of half-lives , which means that the relative uncertainty of the half-life constitutes an upper limit to the attainable accuracy on the age. For several applications, this has become the bottleneck [ 25 ]. Another dating technique, Pb sediment radiochronology [ 26 ], is frequently applied to reconstruct past environmental conditions of ecosystems.
Due to various transport processes, e. The amount of excess Pb in various layers of a sediment core is an indicator of the accumulation rate. Radioactive disequilibrium between parent and daughter arises when both are separated by physicochemical processes, e. Following this separation, the daughter starts to grow in again. Information on the time of separation may be obtained from measuring the ratio of parent to daughter atoms. This property is applied in nuclear forensics, aiming at fingerprinting of nuclear materials [ 23 , 27 , 28 ].
The relative amounts of parent and decay products can be used to identify the age and source of the material. Nuclides of interest are actinides Th, U, Np, Pu, Am with potential applications in improvised nuclear devices or other nuclides that can be applied in radiological dispersion devices Co, Sr, Cs. Age dating of U is more difficult than Pu dating, because their long half-lives lead to minute amounts of ingrowing daughter nuclides. Besides the quality of the separation, the current uncertainties on the relevant half-lives are a major limiting factor on the attainable accuracy.
Consequently, age determinations based on atom ratios are more sensitive to the parent half-life than to the daughter half-life. Similar equations can be derived for cases in which the activity ratio R A of parent and daughter nuclide is measured instead of the atom ratio, with a subtle change in a multiplication factor.
Consequently, age determinations based on activity ratios are more sensitive to the daughter half-life than to the parent half-life, which is the opposite of the effect noticed for atom ratios equation Activity ratio measurements enhance the al of the short-lived nuclide, and may be a good alternative to atom ratio measurements in cases where the atom concentration of the short-lived nuclide is particularly low. The relative uncertainty of the half-lives of the parent via R or the daughter nuclide via R A is of equal importance as the relative uncertainty of the measured ratio R or R A. The principles of radiometric dating can also be applied to fission products created in a nuclear explosion.
Radionuclides may attach to aerosols or be released as noble gases and get collected in air samplers at a remote location. One can distinguish isobaric and non-isobaric clocks [ 30 ]. Non-isobaric clocks start from theoretical cumulative fission yields for the calculation of initial activity ratios and use the current activity ratio of fission products with different half-lives to estimate the time elapsed since the nuclear event.
Isobaric clocks are based on parent—daughter pairs of which the daughter nuclide is not directly produced in the fission reaction. The equations are the same as the equations 9 — 14 applied in nuclear forensics. For example, they are directly applicable to the Ba- La clock [ 31 ], based on progeny of the short-lived noble gas Xe The aerosol-bound 95 Zr- 95 Nb chronometer is another important clock that requires a more elaborate mathematical treatment due the presence of meta-stable 95m Nb in the decay scheme [ 32 ]. Specific equations for time-zero and uncertainty calculation are available to perform bias-free 95 Zr- 95 Nb dating of a nuclear event over a time range of more than a year [ 33 ].
Starting from an initial activity A , the accumulated dose is proportional to the of atoms that decay in the body:. The relative uncertainty of the effective half-life propagates linearly to the dose. The biological half-life cannot be determined as precisely as the physical half-life, and the dominance of either rate differs from one radionuclide to another. The latter are the only cases in which the dose calculation depends ificantly on the accuracy of the physical half-life.
The bone seekers 90 Sr, Ra and Pu have extremely long effective half-lives 18— a [ 34 ] , which reduces their uncertainty propagation towards the accumulated dose during a person's lifetime. Half-lives of excited nuclear states, giving access to transition probabilities, provide direct insight into the structure of the nucleus and offer one of the most stringent tests of nuclear models. Different measurement techniques are applied to cover half-life ranges between picoseconds and seconds. In this method, nuclei produced by a beam-induced nuclear reaction in a thin target are allowed to fly freely in vacuum over variable distances from the target to a stopper 'plunger'.
Gamma-spectroscopy measurements are performed with a single off-axis HPGe detector, preferably at extreme forward or backward angles, or by a cluster of detectors arranged at the same polar angle to increase sensitivity. Gamma rays emitted in flight are distinguished from those emitted after the nucleus has come to rest in the stopper, due to their Doppler shift. The mean life of a given level and the accumulated time delay from higher lying states that feed it can be deduced from the relative intensities of the shifted and unshifted peaks at different target-to-stopper distances.
In principle all the effects which should be considered when applying the RDDS method were known right from the beginning when the method was developed, but from time to time some of these effects were underestimated or invalid assumptions were made. In some cases the reasons for failures could be identified later but for other cases the situation remained unclear. Typical sources of uncertainty mentioned in the review paper by Dewald et al [ 35 ] are:.
These problems stimulated efforts to improve the technique with respect to higher reliability and to make it more transparent so that the presence of possible systematic errors is revealed more easily. Some of these improvements are [ 35 , 36 ]:. Nano- and microsecond nuclear states are mostly measured electronically in delayed coincidence experiments or alternatively by time interval analysis. The radiation yielding the state of interest is detected to provide a start pulse for an electronic clock, and the radiation by which the state decays is detected in the same or another device to provide a stop pulse.
The half-life is derived from the analysis of the time difference between both als. Using ultrafast scintillators plastic scintillator, LaBr 3 Ce , BaF 2 , the applicability range of the method has been extended down to picoseconds [ 37 ]. Also states of tens of milliseconds or even seconds are within reach, provided that the count rate is sufficiently low.
Conventional experimental set-ups contain electronic modules, such as delay line amplifiers, timing single channel analysers TSCA , time-to-amplitude converters TAC and multi-channel analysers ADC , but they can also be replaced by programmable processors FPGA or software performing off-line data analysis of digitally acquired data saved in list files [ 38 ]. Common features of the delayed coincidence method are that time differences are stored in a spectrum, that the decay constant is derived from the slope of an exponential function fitted to a part of the spectrum and that has to be taken for data not due to the intended parent—daughter pairs.
Random coincidences may be recorded due to background als, decays from other states or closely spaced but unrelated parent and daughter events. The first two interferences can be ificantly reduced if the experiment allows for energy selectivity, e. By means of energy selection, multiple half-lives can be derived from one experiment. There exist different variants of how the data are recorded, each requiring a specific mathematical basis for the functional shape of the time spectrum.
Two options are discussed below, based on different manners to collect and interpret time differences. In a classical set-up, a timer is started whenever a parent decay is detected and stopped when a daughter decay is detected. Then the system is made sensitive again for parent decays.
In doing so, all the parent events arriving before the first daughter event are ignored. In this type of experiment, the time spectrum theoretically takes the following shape: [ 39 ]. In that case, systematic errors are to be expected from using equation This can be solved by means of an alternative time analysing circuit in which a parent decay starts the timer and not a single but multiple delayed coincidences are added to the time spectrum, one time value for every recorded daughter decay over a long period of time [ 40 ].
Theoretical analysis [ 39 ] predicts that time spectra obtained by this approach are represented by the sum of a constant term and an exponential function with the time constant of the radioactive decay of the daughter, exactly as in equation Using multiple delayed coincidences eliminates the spectral distortion effect, but at the price of an increased of random coincidences.Absolute dating half life problems
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RADIOMETRIC TIME SCALE