Liquid scintillation counting: A valuable tool to determine half-lives

. In the past two decades, the radionuclide metrology group at PTB has carried out a number of half-life determinations using liquid scintillation counting. The half-lives, which were often determined in collaboration with other institutions, range from a few ten nanoseconds (e.g., 86 keV level of 233 Pa) to several billion years (e.g., 87 Rb). This review aims to give an overview of the various half-life determination techniques that have been used and to demonstrate the great potential of liquid scintillation counting as an experimental tool for such measurements.


Introduction
Half-lives of radionuclides are among the very fundamental data that play an important role in many fields of technology and science. Some examples of how such half-lives are applied include decay corrections for activity determination, activity and dose estimates in nuclear medicine and other fields, radioactive waste management, nuclear forensics and dating terrestrial or extra-terrestrial materials in Earth and astrophysical sciences. The precise knowledge of half-lives can also be of particular importance for radionuclide identifications and for a better understanding of nuclear physics processes. The Physikalisch-Technische Bundesanstalt (PTB) is the national institute for science and technology and the highest technical authority of the Federal Republic of Germany in the field of metrology. One fundamental task of PTB is to realize and maintain the legal units in compliance with the International System of Units (SI); it also disseminates these units. PTB's Radioactivity Department realizes, maintains and disseminates the unit of activity for radionuclides in a wide activity range (from 1 mBq up to several GBq) for more than 50 radionuclides. Among the most important tasks are activity determinations with primary standardization techniques as well as the determination of nuclear decay data such as half-lives. While the determination of several half-lives by means of ionization chambers has a rather long tradition at PTB [1][2][3], the systematic application of liquid scintillation (LS) counting for halflife determinations is rather new. In this review, it will be shown that many new half-life determinations are possible with the LS methods. For example, we gain access to very long or very short half-lives, and the LS methods are an excellent complementary method. In some cases, half-lives could only be measured using the LS methods.

The LS methods for activity determination in radionuclide metrology
The great success of LS counting in radionuclide metrology is mainly based on two methods. These are the CIEMAT/NIST efficiency tracing technique (CNET), which makes use of LS counters with two photomultiplier tubes (PMT), and the triple-to-double coincidence ratio (TDCR) method, which requires counters with three PMTs [4]. In brief, the methods are based on the same free-parameter model [5] and require accurate calculations of the respective electron energy spectra S(E) and the ionization quenching function Q(E) which describes the non-linear response of the scintillator and depends on the sample composition. If we consider a pure beta emitter that emits exactly one beta electron per decay event, the counting efficiency in a system with two PMTs is given by and the counting efficiency for the logical sum of double coincidences is given by Equations 1 to 3 contain an unknown parameter M, which is referred to as the free parameter. For the CIEMAT/NIST method, this free parameter is derived from a tracer measurement using a solution with known activity. In most cases, 3 H is used as the tracer radionuclide. The tracer measurement should be carried out under very similar conditions (e.g., the same type of vials, same sample composition and same geometry).
In the case of the TDCR method, the free parameter M can be derived from the experimental net counting rates for triple (RT) and double coincidences (RD), respectively, since the following equation must be fulfilled With the known free parameter, we can calculate the counting efficiencies applying Eqs. 2 and 3 and, consequently, gain access to the sample activity. Over the past two decades, there has been considerable progress in hardware development -in particular for TDCR counters. Laboratories have developed devices with high counting efficiency and automated sample changers [6] as well as very compact transportable devices [7]. Most electronic modules that process the pulses from a TDCR counter are live-time based with an extending dead time, and traditional modules [8] have often been replaced with FPGA-based devices [9] or even with fast digitizer modules that increase flexibility when applying off-line analyses of data taken in listmode format [10]. The CNET and TDCR methods require several corrections for background, decay, accidental coincidences [11][12] or potential PMT asymmetries [13][14]. However, one of the most challenging parts of the evaluation is usually the calculation of the emission spectrum S(E). For example, the shape of beta spectra can play an extremely important role [15][16][17]. Although radionuclides with electron capture and other complex decays have also been successfully measured, it is important to note that there is still a need to improve computational models. This is especially true of atomic rearrangement as a consequence of electron capture or internal conversion [18]. In some cases, LS counters were complemented with an external solid scintillation detector (e.g., NaI(Tl), CeBr3 or LaBr3) to detect gamma rays or X-rays [19]. In this way, the systems can also be used to apply the 4πβ-γ coincidence counting or anti-coincidence counting techniques. This is an interesting supplement, since the activity determination by means of these techniques does not require information on the emission spectrum S(E). Moreover, the combination of an LS detector and an external gamma-ray detector can provide access to particular half-lives as we will explain below.

Determination of intermediate halflives
In principle, several half-lives can simply be determined by means of long-term measurements following the exponential decay. Such measurements are often carried out using ionization chambers or solid scintillation detectors. Great care is required for the measurements and the subsequent analysis. This is to allow for potential variations of background, system non-linearity (e.g., for current measurement devices), sample instability, detector instability as well as for potential changes of the source-detector geometry that may influence the detection efficiency. In addition, potential radioactive impurities must be taken into account. LS counters can be quite powerful for certain half-life determinations, and it was shown that excellent results can be obtained, in particular, when the counting efficiencies are high [20][21][22][23][24]. It should be noted that the counting efficiencies of many beta emitters are often higher if 4π LS counting is used instead of other conventional detectors. The counting efficiency of alpha emitters in LS counters can even be virtually 1. An almost ideal half-life determination by means of a TDCR counter was realized for 225 Ac in equilibrium with its progeny [10]. At PTB, a long-term measurement was carried out, and data were continuously taken for about 111 days, which corresponds to more than 11 halflives of 225 Ac. To this end, an LS sample was prepared using an 225 Ac solution with outstandingly high radionuclidic purity. The sample was placed in a TDCR counter, and the source-detector system was kept constant during the entire period of observation. The counting efficiency of 225 Ac (in equilibrium with its progeny) is very high, and consequently low variations of the counting efficiency are expected. An interesting feature of the TDCR method is that the TDCR parameter itself provides valuable information about the counting efficiency that might change over time. In the case of 225 Ac, the TDCR parameter was found to be very stable. The half-life can either be determined using the double counting rates or the triple counting rates as a function of time. In the case of 225 Ac, both types gave the same half-life, which was finally determined to be 9.9179 (30) d. Note that the stability monitoring via the TDCR parameter can be superior to methods where only the stability of the measuring system is checked by means of a few measurements with a long-lived reference source. The latter method can usually not indicate potential problems with sample instability, which might occur due to chemical and/or physical effects (e.g., precipitation, sorption, temperature effects). The LS method has also been successfully used to determine the half-life of other radionuclides like 90 Y [20], 113m Cd [21], 177 Lu [22], 223 Ra [23] and 18 F [24]. We cannot discuss all these cases within the scope of this paper. However, we would like to highlight a few rather exotic examples. In the case of 227 Th, we have to deal with the fact that the radionuclide under study is not in radioactive equilibrium with its progeny. Hence, the counting rates can even increase at the beginning of a measurement campaign, and the determined half-life can depend on the half-life of the longest-lived progeny, 223 Ra. A new methodology with an innovative correction for the decays during the measurement was developed and then applied to a primary activity standardization of 227 Th and the determination of its half-life [25]. In a few cases, the measurements were only possible because of sophisticated sample preparation. For the half-life determination of 211 Pb, LS samples were obtained by using a mineral-oil-based scintillator as a trap for 219 Rn that escaped from a solid 223 Ra source [26]. A similar experiment was carried out using 228 Th sources that emanate 220 Rn. In this way, LS samples with 212 Pb could be obtained, and the half-life of 212 Pb was determined with high precision [27]. Again, the TDCR parameter was found to be useful for judging whether the samples are stable or not. Interestingly, it was found that the samples were unstable when using glass vials, whereas good stability was found with polyethylene vials. The measurements could also be supplemented by Cherenkov counting, which confirmed the results. The examples were also noteworthy since the production of radionuclidic pure 211 Pb or 212 Pb samples was achieved without any radiochemical efforts.
In another experiment, we demonstrated that recoil atoms from alpha decay can be collected on a plexiglass backing which can then be measured as a Cherenkov sample. In this way, we gained access to the half-lives of 213 Bi and 209 Pb [28]. Such experiments might be improved when using other backing materials such as plastic scintillators, and they show the large potential of LS counting for half-life determinations.

Determination of (very) long half-lives
Very long half-lives (> 90 years) are typically determined using the following expression where A is the activity. In a few initial experiments carried out at PTB, the number of nuclei N was determined by means of a stochiometric approach that requires careful weighing of (dry) salts with natural isotopic abundance [29][30] [29] and 147 Sm [41]. Further halflife determinations are moreover in progress (e.g., 53 Mn, 32 Si) or planned ( 157 Tb, 137 La).
A prerequisite for such half-life determinations is always the availability of a suitable base material, which must, in addition to sufficient activity, have a high radionuclide purity and a suitable chemical structure.
Thus, PTB often cooperates with other partners like the Paul Scherrer Institute (PSI) in Villigen (Switzerland) that have the required expertise in radiochemical work. In addition, many partners with expertise in the field of mass spectrometry contributed to the above-mentioned determinations of long half-lives. If we look back at Eq. 5, we still have the activity whose determination is the main task of PTB's Radioactivity Department. It should be noted that this task can be very challenging since the required nuclear and atomic data for the efficiency computations are often unknown or at least uncertain. Sample preparation can also be difficult. Exotic radionuclides are often investigated, and in many cases, the available activity is limited. We cannot discuss all these examples here and therefore refer to the numerous references listed. A recent and very comprehensive work on the determination of the halflife and other decay parameters of 40 K could be suitable material for interested readers, as it describes many of the previously mentioned difficulties and their solutions [39].

Determination of very short half-lives
It was also demonstrated that digital LS-γ coincidence systems can be used to determine very short half-lives. The detector systems comprise a fast digitizer with a high sampling rate (e.g., 1 GHz), and the detector signals of the LS counter and a gamma-ray detector are recorded in listmode format with a timestamp for each event. The data can then be processed in an off-line analysis. This enables detector settings (e.g., the energy range of the gamma-ray detector) to be changed even after the actual measurement. The analysis then yields time difference spectra which are finally used for a fit procedure to determine the half-life. Time differences are measured between specific start and stop signals. For example, the 514 keV level half-life of 85m Rb can be measured using the detected 85 Sr electron-capture events in the LS channel as the start signal and the detected 514 keV gamma rays in a CeBr3 detector as the stop signal [19]. In some cases, it was found that also LS-LS time differences can be used for half-life determinations. In particular when studying decay chains, the measurements can be prone to errors due to possible premature stopping of the clock by events from uncorrelated decays [42]. Methodologies were, however, proposed to overcome such obstacles [42][43]. At PTB, we have successfully applied LS-γ and LS-LS measurements to determine the half-lives of 213 Po [10], 215 Po [44] and various level half-lives [19,45].

Other cases
In Section 3, we introduced half-life determination by means of long-term measurements. This method often works well if the counting efficiency of the radionuclide under study is high and if the overall observation time is short. However, these conditions are often not met. Considering 55 Fe, the efficiency is too low (about 50%) and the half-life of about 1000 days would require measurements over several years. However, LS samples are seldom stable over such long periods of time. Thus, we proposed repetitive primary activity measurements as a further method for half-life determination. The advantage is that measurement results of various fresh LS samples can be used for the analysis, even if the time difference between the sample preparations and measurements is a few years. This method was successfully applied to determine the halflife of 55 Fe [46] using custom-built TDCR counters. It was additionally ensured that all data were evaluated using the same model assumptions.

Concluding remarks
The examples shown above indicate that LS counting is a very powerful tool for half-life determinations. Figure 1 contains the half-lives that have been measured by means of LS counting at PTB since 2003. The halflives in Fig. 1 cover an impressive range of about 25 orders of magnitude.
In this paper, we have mainly given references from our institution that are related to LS counting methods. In fairness, however, we must point out that other groups also follow similar LS-based approaches, and that for some radionuclides, there are of course other methods that have already been used successfully. It is not only in radionuclide metrology that the determination of uncertainties is particularly important. In this short review, we cannot discuss this subject in much detail, and we again refer to the various references given. In addition, we would like to point out that Stefaan Pommé et al. have performed some fundamental and very useful work on uncertainties in half-life determination (see, [47][48][49] and references therein). Finally, it should be noted that there is a continuing need for further very precise half-life determinations. About 20 years ago an enormous need for more precise decay constants was identified for several radionuclides of importance in geochronology [50]. Since then, several new measurements have been carried out, but our knowledge of half-lives of a few isotopes used in geochronology still lags behind the constantly improving analytical precision. Also, for other longlived radionuclides, a very large need for new measurements was identified [51]. It is astonishing that in the 21st century some half-lives have never been measured directly or are being measured for the first time [32]. It is therefore to be expected that the research area for the determination of half-lives will continue to play a major role in the future.