Measurement of the shape-factor functions of the long-lived radionuclides 87Rb, 40K and 10Be

doi:10.1016/j.nima.2006.11.064

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment

Volume 572, Issue 2, 11 March 2007, Pages 760-767

https://doi.org/10.1016/j.nima.2006.11.064 Get rights and content

Abstract

Accurate half-life values for both ⁸⁷Rb and ⁴⁰K are essential for geochronological purposes. In another context, the activity determination of the cosmogenic radioisotope ¹⁰Be requires a better accuracy, too, so that the records of this radioisotope on the Earth's surface and inside meteorites can be interpreted. Liquid-scintillation counting is an excellent tool for carrying out precise $β$ -ray nuclide standardizations. However, the accuracy of the current standardization methods is frequently limited by the presence of inaccuracies in the shape-factor function. In this work, the shape-factor functions of ⁸⁷Rb, ⁴⁰K and ¹⁰Be are determined by experiment and compared with theoretical predictions. The measured shape-factor functions of ⁸⁷Rb and ¹⁰Be were in good agreement with theory, but for ⁴⁰K, some unexpected deviations were detected which make further investigations necessary.

Introduction

Among geologists, there is a general consensus that the accuracy of radioisotopic age determinations is limited by the uncertainty in the decay constants of the long-lived nuclides [1]. Especially the disagreement which has been observed for ⁸⁷Rb between the absolute counting measurements and the age comparisons makes a joint effort necessary to improve the accuracy of this nuclide's decay constant in the near future. The situation is similar for ⁴⁰K, but here not only the half-life, but also the uncertainty in the beta-to-capture-branching ratio plays a role.

The radionuclide ¹⁰Be is produced, together with other long-lived nuclides (e.g., ¹⁴C and ³⁶Cl), by the continuous interaction of the cosmic radiation with the upper atmosphere. The subsequent precipitation of the meteoric ¹⁰Be, in rainfall or snow, spreads ¹⁰Be on the Earth's surface. The records of the long-lived isotopes of cosmogenic origin such as ¹⁰Be are valuable aids for studying Pleistocene and Holocene processes by accelerator mass spectrometry (AMS) [2], [3].

In last few years, a substantial improvement has been achieved in activity determinations by including the CIEMAT/NIST (Centro de Investigaciones Energéticas Medioambientales y Tecnológicas/National Institute of Standards and Technology) method [4], [5], [6], [7] in the analyses of liquid-scintillation counting measurements. This method is now used extensively by many reference laboratories for the standardization of solutions of $β$ - and $β$ - $γ$ -ray nuclides with uncertainties of less than 0.5% [8], [9], [10]. One of the steps of the CIEMAT/NIST method is the computation of the theoretical Fermi distribution of the nuclide. The shape of the Fermi distribution is modified by the shape-factor function for the forbidden $β$ transitions of ⁸⁷Rb, ⁴⁰K and ¹⁰Be. The shape-factor functions of ⁴⁰K and ¹⁰Be induce shifts to higher energies in their respective Fermi distributions. For ⁸⁷Rb, the spectrum is shifted by the shape-factor function into the opposite direction, i.e., to the low-energy part. For the activity standardization of the long-lived nuclides the shape-factor functions must therefore be exactly known [11], [12], [13]. In particular for ⁸⁷Rb with its comparatively low endpoint energy, the dependence on the beta spectrum computation is considerable.

A proof of disagreements in several of the shape-factor functions being available in the literature became possible when standardization methods based on Cherenkov counting were developed [14], [15]. Especially the first standardizations performed by Cherenkov counting, i.e., the standardization of the radionuclide ${}^{210}{Bi}$ had not been possible with sufficient accuracy with the shape-factor functions available until then [16], [17], [18]. The influence of the shape-factor function on the Cherenkov counting efficiency for ${}^{210}{Bi}$ motivated the development of a shape-factor measuring method based on Cherenkov counting [19]. Although the method was applied successfully to some high-energy $β$ -ray emitters such as ${}^{234 m}{Pa}$ [20], its applicability could not be extended to other interesting $β$ -particle emitters with endpoint energies below 500 keV since the accessible Cherenkov counting rates in water are too low. Thus, for ⁸⁷Rb with its endpoint energy of about $E_{0} = 283 keV$ , another method is needed.

One possibility of avoiding the limitations imposed by the Cherenkov threshold energy consisted in replacing the Cherenkov detection yield with another observable which combines not only the characteristics of the Cherenkov counting efficiency but is also related to the liquid-scintillation pulse-height spectra. In this way, the observable cutoff energy yield could be defined analogous to the Cherenkov detection yield, as the $β$ -particle emission yield over a certain cutoff energy [21].

The advantage of liquid-scintillation spectrometers over other types of detectors is obvious. Since for $β$ -particle energies higher than 60 keV, all $β$ -decay events are detected with 100% efficiency, the cutoff energy yields can be obtained directly from liquid-scintillation pulse-height spectra, without any corrections. The only restriction is that the cutoff energy has to be set to a value above 60 keV. The successful application of the cutoff energy yield method to ⁸⁷Rb was demonstrated in a previous work [22]. In this paper, the application is extended to the long-lived nuclides ⁴⁰K and ¹⁰Be.

The $β$ transitions are unique for both ⁴⁰K and ¹⁰Be and in principle, the shape-factor functions should be predictable by means of theoretical arguments [23], [24], [25]. In fact, in the case of the ¹⁰Be shape-factor function, the experimental results were found to be consistent with theory. In contrast to ¹⁰Be, however, unexpected results were obtained for ⁴⁰K and there is thus a need for further investigation for this nuclide.

Section snippets

Samples and equipment

Apart from the radionuclides which are directly involved in this study (i.e., ⁸⁷Rb, ⁴⁰K and ¹⁰Be), radionuclide solutions of ¹⁴C, ¹⁴⁷Pm, ³⁶Cl, ²⁰⁴Tl, ³²P, ⁸⁹Sr and ⁹⁰Y were prepared for calibrating the spectrometer in energy. To avoid adsorption and precipitation problems within the samples, specific amounts of carrier and acid were incorporated in the radionuclide solutions (Table 1). The solution of ⁹⁰Y was eluted from a solution of ⁹⁰Sr in equilibrium with ⁹⁰Y by using an Eichrom column with

Method and results

To compare different radionuclide pulse-height spectra, the preparation of the samples with an identical chemical quench is required. To obtain one specific value of SQP(E) by successively adding increasing amounts of a chemical quenching agent can be time- and labor-consuming. Another—more feasible—possibility is to apply the Spectral Interpolation Method [26], where the spectral shape of the radionuclide is computed from neighboring SQP(E) pulse-height spectra.

Fig. 1 shows the spectral shapes

Analysis of the results

The transition energy $E_{0}$ listed in Table 2 is generally in very good agreement either with the endpoint energy obtained by extrapolation of the Kurie plots or with the energy value extracted from the analysis of nuclear data. However, the two nuclides ⁸⁷Rb and ⁴⁰K are an exception. Table 3 lists the measured endpoint energy values for these two long-lived radionuclides. The first four values correspond to Kurie plot extrapolations which were carried out with different types of spectrometers.

Conclusions

The shape-factor functions of the three long-lived nuclides ⁸⁷Rb, ⁴⁰K and ¹⁰Be were determined and compared with theory. The cutoff energy yields and the maximum-point energies of ⁸⁷Rb and ¹⁰Be were extracted from the liquid-scintillation pulse-height spectra and found to be in good agreement with their theoretical predictions. However, this does not apply to ⁴⁰K, for which the shape-factor function $C (W) = p^{6} + 7 (q^{4} p^{2} + q^{2} p^{4}) + q^{6}$ , together with the endpoint energy of 1311 keV, indicates considerable

Acknowledgements

We wish to thank A. Remmert et al. from the TU Munich and I. Villa et al. from the University of Bern for providing us with solutions of ¹⁰Be and ⁴⁰K, respectively. The first author would like to acknowledge the financial support of the Education and Science Ministry of Spain through the Ramón y Cajal Programme.

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Measurement of the shape-factor functions of the long-lived radionuclides 87Rb, 40K and 10Be

Abstract

Introduction

Section snippets

Samples and equipment

Method and results

Analysis of the results

Conclusions

Acknowledgements

Cosmochim. Acta

Nucl. Instr. and Meth. A

Appl. Radiat. Isot.

Comput. Phys. Commun.

Nucl. Instr. and Meth. A

Appl. Radiat. Isot.

Appl. Radiat. Isot.

Appl. Radiat. Isot.

Appl. Radiat. Isot.

Comput. Phys. Commun.

Nucl. Phys.

Appl. Radiat. Isot.

Nucl. Instr. and Meth. A

Nucl. Phys. A

Appl. Radiat. Isot.

At. Data Nucl. Data Tables

Nucl. Data Sheets

Nucl. Data Sheets

Nucl. Phys. A

Nucl. Phys. A

Nucl. Phys.

Nucl. Data Sheets

Measurement of the shape-factor functions of the long-lived radionuclides ⁸⁷Rb, ⁴⁰K and ¹⁰Be