Practical Qβ analysis method based on the Fermi–Kurie plot for spectra measured with total absorption BGO detector
Introduction
Measurement of β-decay energies (Qβ) is one of the precise methods of atomic mass determination. Systematic measurements of Qβ, especially those of unstable nuclei far from the β-stability line such as new isotopes, are expected to extend our knowledge of nuclear structures. It is difficult to use the traditional β–γ coincidence method to measure Qβ of these nuclei because they do not have well-established decay schemes owing to their low production yields, high Qβ, and short half-lives. In order to measure these Qβ, we have developed two types of total absorption detectors: one is composed of large BGO scintillation detectors [1], [2], [3], [4], and another is made up of an HPGe detector and an anti-Compton BGO detector [5]. It is a significant advancement to obtain Qβ with accuracies of 100 keV for nuclei far from the β-stability line because theoretical values and even reliable systematic values have uncertainties of about 500 keV.
The basic concept of a total absorption detector is that it absorbs all energies of radiations emitted from radio isotopes. We explain this using a decay scheme having two β-feedings as shown in Fig. 1(a). One of the β-rays (β1) feeds to an excited state (Eγ1), and then a single γ-ray (γ1) is emitted, and another β-ray (β2) feeds to the ground state; β1 is absorbed by the detector simultaneously with the γ1 as shown by the dashed line (β1+γ1) in Fig. 1(b); endpoint energy of the spectrum becomes the Qβ, and the β2 indicates a normal β-ray spectrum. The solid line in Fig. 1(b) shows the expected total absorption spectrum, which is the sum of these two β-feedings (β1+γ1 and β2). The endpoint energy of the total absorption spectrum directly shows the Qβ; it is expected that the Qβ can be deduced with no dependence on, and no need for information about the, decay scheme. Another advantage of this detector is its approximately 100% efficiency. The efficiency is about 100 times larger than that of the traditional β–γ coincidence method [6], [7], [8], [9], [10], [11]. Therefore, the total absorption detector can measure Qβ of lower-production-yield nuclei.
In order to analyze the Qβ of a total absorption spectrum based on Fermi–Kurie (F–K) plot method in practice, we noted the following phenomena:
- (i)
superimpositions of β-rays having different maximum β-ray energies (Eβ,max) and
- (ii)
superimpositions of -rays having different forbiddennesses.
We proposed a simplified decay scheme that is composed of a one-component β-ray, as shown in Fig. 2. The decay scheme in Fig. 2(a) is approximated as Fig. 2(b), and this simplified decay scheme features the introduction of Eγ and α as approximations of (i) and (ii), respectively. The purpose of this study is to describe the practical Qβ-analyzing method based on the F–K plot by means of these approximations and to clarify its limitations for applications. These issues were not detailed in our previous papers. In particular, parameter α is newly considered in this work.
At the beginning of our research, the conventional root plot method was applied and an uncertainty of approximately 100 keV was obtained [1]. As described later, it was found that the Qβ deduced by this method depends slightly on the type of decay schemes. Therefore, we considered that the F–K plot method with an assumed decay scheme has an advantage for a precise Qβ determination. In the most recent paper, an earlier version of an F–K plot method was investigated [2]. In the last method, a simplified decay scheme than the present one (Fig. 2(b)) was used; only the parameter Eγ was introduced, and α was not considered. Even so, the previous method could deduce Qβ with an uncertainty of 60 keV.
In this paper, we demonstrate that the present analyzing method gives more reliable Qβ with an uncertainty of 60 keV using longer straight lines. First, we propose the physical basis of our method using theoretically calculated spectra, and evaluate the uncertainties of this method. Next, we introduce our actual total absorption BGO detector, and evaluate the performance of the analyzing method by measuring nuclei that have well-evaluated Qβ. We argue for the superiority of this method by comparing results with those from previous analyzing methods. Finally, this method is applied to re-analysis of the Qβ of fission products produced with 238U(p, f) reactions [12].
Section snippets
Property of β-ray spectra
The idea of the present analyzing method is to approximate different β-ray feedings that have the same endpoint energy in the total absorption spectrum as a single-component β-ray (see Fig. 2). Here, focusing attention to a limited region (∼1 MeV) around the endpoint energy of the spectrum, we applied this approximation using the Fermi–Kurie (F–K) plot method.
In the actual case, most β-rays have forbiddenness of either allowed or first-forbidden transitions, and the first-forbidden transition is
Measurements and Qβ analyses using the present method
In order to check reliability of the present method, measured spectra for 12 nuclei of 91−94Rb, 139−143Cs, 142Ba and 142,144La having well-evaluated Qβ were analyzed. These nuclei have Qβ of 3–11 MeV, and 80–90% of the β-rays feed to the energy level below Qβ/2 [14]. Radioactive sources were produced with 238U(p, f) reactions using an on-line mass separator (Tokai-ISOL) [12]. They were collected on an aluminized Mylar tape at a beam collection port, and were periodically transported to the center
Source preparations
Using the present method, the previously measured Qβ [2] were re-analyzed. In Ref. [2], the Qβ were analyzed using the previous version of the one-component approximation method. Nuclei of 158,159Pm, 159,161Sm, 160−165Eu, 163Gd and 166Tb were prepared by 238U(p, f) reactions using the Tokai-ISOL (on-line mass separator) [12]. Under low background conditions (40 cps) in the measurement room, our detector could measure nuclei with emissions as little as one particle per second. These nuclei have a
Conclusion
A practical Qβ-analyzing method based on the F–K plot for spectra measured with total absorption BGO detector was proposed. In this method, we assumed a single β-feeding to a pseudo-level Eγ (0≤Eγ≤Qβ/2) having mixed-type forbiddenness of the allowed and unique-type first-forbidden transitions with a ratio of α (0≤α≤1). The F–K plot that showed the longest straight line was adopted based on the chi-square test. We confirmed that the present method is proper when the analyzing regions are limited
Acknowledgements
The authors thank the Japan Atomic Energy Agency (JAEA) tandem accelerator crew for providing intense, stable beams. Many thanks are due to all ISOL staff members for collaboration in our experiments and discussions. The authors are also grateful to Mr. I. Miyazaki and Mr. O. Suematsu for valuable discussions and to Mr. T. Shindo for his help in the early stage of the experiments.
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2014, Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated EquipmentCitation Excerpt :In our previous measurement using the total absorption BGO detector, the isomeric state was not identified because the detector׳s energy resolution was insufficient. The difference between the present Qβ and the previous value of 4690(70) [8] was consistent with the energy of the isomeric state. It is important to identify isomeric states because β-rays fed to isomeric states are not simultaneously absorbed with succeeding γ-rays (isomeric transitions).
Mathematical physics for nuclear experiments
2022, Mathematical Physics for Nuclear Experiments