Introduction

Reactor decay heat refers to the thermal energy released through radioactive decay of fission and neutron transmutation products within a nuclear reactor. Despite the small contribution of decay heat to the thermal output during reactor operation, its role is crucial when the reactor is shut down. Efficient cooling and removal of decay heat are essential for mitigating risks such as overheating or fuel melting. Even after removal from the reactor, spent fuel continues to emit decay heat, which must be adequately cooled during storage and transportation to minimize accidents. Consequently, a comprehensive understanding of the decay heat is essential, which has garnered substantial scientific interest and research efforts [1-3].

Based on abundant nuclear data, the most commonly used method for calculating reactor decay heat is the summation method [4]. Because most fission products are neutron-rich nuclides, β^- decay dominates the radioactive decay within the reactor. The energy released by β^- decay (Q_β) is typically carried by electrons, neutrinos, daughter nuclei, and γ rays. Decay heat is predominantly deposited by electrons and γ rays because the kinetic energy of the daughter nucleus is negligible, and neutrinos easily traverse the reactor without significant energy loss. Consequently, the decay heat contributed by individual radioactive fission products can be estimated using the average γ energy ${\overline{E}}_{\gamma }$ and average β energy ${\overline{E}}_{\beta }$ produced per β decay [5], which can be calculated using the β decay intensity distribution Iβ (Ex) as ${\overline{E}}_{\gamma }={\displaystyle {\int }_0^{Q_{\beta }}}{I}_{\beta }\left(E_x\right)E_x\text{d}{E}_x\mathrm{,}$ (1) ${\overline{E}}_{\beta }={\displaystyle {\int }_0^{Q_{\beta }}}{I}_{\beta }\left(E_x\right)\langle E_{\beta }\left(Q_{\beta }-E_x\right)\rangle \text{d}{E}_x\mathrm{.}$ (2) Here, Ex is the level energy of the daughter nucleus, $\langle E_{\beta }\left(Q_{\beta }-E_x\right)\rangle$ is the average β energy of an individual β feeding. Therefore, Iβ (Ex) is an essential input in the summation method, which must be determined accurately. Additionally, Iβ (Ex) is significant in the study of reactor antineutrino anomalies [6] and the neutrinoless doubleβ decay [7].

In traditional studies, Iβ (Ex) is typically derived from the measurements of β-delayed γ decay using high-purity germanium (HPGe) detectors. However, for β decays with large Q_β values, subsequent γ transitions from high states in the daughter nucleus are typically weak and prone to being overlooked in the measurement owing to the limited detection efficiency of HPGe detectors. This limitation results in an inadequate understanding of Iβ (Ex) as discovered by Hardy et al. [8]. This issue, which is known as the "Pandemonium effect,” is a potential factor contributing to the observed discrepancy between decay heat calculated via summation methods and that measured by calorimetric experiments [9, 10].

A recently developed technique known as total absorption gamma ray spectroscopy (TAGS) [11], provides an effective solution to the Pandemonium effect. TAGS detectors commonly employ scintillators with large volumes as detectors, which significantly enhances the detection efficiency of γ rays. The high efficiency of the TAGS detector allows the detection of the total γ energy emitted during a single β decay event, thereby reducing the risk of overlooking γ rays with low branching ratios. TAGS facilitates multiple measurements to refine Iβ (Ex) of the fission products [12-15], which significantly improves the accuracy of the decay heat summation calculations. In addition, the TAGS technique has been applied in other studies, such as direct measurements of the cross sections of radioactive capture reactions [16-19] and the β-Oslo method [20, 21] developed to indirectly investigate the (n,γ) reaction cross sections.

However, because TAGS detectors cannot attain the desired detection efficiency of 100% and the resolution is limited, the measured total energy γ spectrum of β decay cannot directly represent the β intensity distribution. Further analysis is required by utilizing the response functions for individual β feeding. If the excited state decays directly to the ground state, Monte Carlo simulation can be used to construct the response function. However, when feeding is followed by multiple-cascade γ transitions, the response function is highly correlated with the multiplicity and energy assignment of the cascade [22]. These factors are often ambiguous, particularly for nuclides far from the stability valley, which leads to significant uncertainties in deriving the β intensity distribution.

Several state-of-the-art TAGS detectors have been developed in recent years to improve the precision of the β intensity distribution, such as SuN [23], DTAS [24], and MTAS [25-27]. These new TAGS detector devices feature improved detection efficiencies compared with their predecessors, effectively minimizing the impact of cascade modes on the response function. Moreover, the use of detector arrays instead of a single detector enables γ–γ coincidence analysis, facilitating a deeper investigation into the cascade modes involved in the de-excitation of the daughter nucleus.

In this work, we introduce a new TAGS detector called the large-scale odular BGO detection array (LAMBDA), which is specifically designed to measure β decay intensity distributions of fission products. Section 2 details the design features of LAMBDA. Section 3 presents the property tests of the completed modules with standard γ-ray sources. Section 4 introduces the assembly and testing of the prototype LAMBDA-I. Section 5 presents the commissioning measurement of LAMBDA-I utilizing ¹⁵²Eu source.

Design of LAMBDA

Selecting an appropriate scintillator is crucial for achieving high detection efficiency. In most TAGS detector designs, NaI(Tl) scintillators are selected owing to their moderate detection efficiency, energy resolution, and cost-effectiveness. However, the limited attenuation capacity of NaI(Tl) for γ rays with energies in the MeV range necessitates the use of large crystals to achieve high efficiency. For example, approximately one ton of NaI(Tl) crystals was used to construct MTAS [25, 26]. The increase in crystal size compromises the energy resolution and introduces several experimental challenges, such as the need for larger shields.

In the design of LAMBDA, the BGO scintillator was selected because of its high attenuation capacity for γ rays [28]. Compared to NaI(Tl), the BGO material exhibits higher density and effective atomic number. To achieve an equivalent efficiency for 4 MeV γ rays, the volume of the BGO crystal should be approximately 15% that of NaI(Tl). Additionally, less encapsulation material is required for manufacturing BGO detectors, reducing γ-ray attenuation within the noncrystal material because the BGO crystal is non-hygroscopic in air.

As shown in Fig. 1, LAMBDA comprises of 102 identical modules arranged in rectangular shapes. The primary component of each module is a BGO crystal with dimensions of 60 mm×60 mm×120 mm. The thickness of 120 mm ensures high attenuation capacity for γ rays in the MeV range. The central hole in the LAMBDA, whose cross-sectional area is120 mm×120 mm, provides adequate space for accommodating the vacuum chamber, silicon detector, and moving tape collector in β decay measurements. Furthermore, six additional modules placed on the two sides of the central hole increase the solid-angle coverage.

Fig. 1Full-screen View

(Color online) LAMBDA design scheme consisting of 102 modules. Each module has a BGO crystal with dimensions of 60 mm×60 mm×120 mm coupled to a 2 inch photomultiplier tube (PMT)

The detection efficiencies of LAMBDA were estimated using Monte Carlo simulations with GEANT4 code [29]. In the simulation, only the BGO detector modules were involved with a gap of 3 mm between them. Figure 2 shows the simulated total and full-energy peak efficiencies for single γ rays in the range of 0.5 MeV to 8 MeV, assuming a point source positioned at the center of LAMBDA. The total efficiencies remain flat and exceed 93% across the entire energy range. The full-energy efficiencies decrease rapidly with increasing γ energy from 0.5 MeV to 3 MeV and stabilize at approximately 84% at higher energies.

Fig. 2Full-screen View

(Color online) Monte Carlo simulated efficiency of the LAMBDA in the 0∼8 MeV energy range. The upper (blue) and lower (red) curves present the total and full-energy peak efficiencies, respectively

In the actual β-decay measurements, the position of γ emitter is not confined to a single point. To investigate the influence of the source position on the detection efficiency, the efficiencies of 4 MeV γ rays emitted from various positions along the Y axis shown in Fig. 1 were simulated using GEANT4. As shown in Fig. 3, the variation in the efficiency within ±5 cm is less than 2%. The dip observed around the central position originates from the gap between the BGO modules. The typical beam spot size in the decay experiment is approximately ±2 cm, leading to an uncertainty of ~1% in the efficiency.

Fig. 3Full-screen View

(Color online) Full-energy peak efficiency of the LAMBDA detector obtained for 4 MeV γ rays vs the position of the source along the Y axis shown in Fig. 1

Fabrication and test of the modules

To date, 60 BGO crystals have been fabricated at the Shanghai Institute of Ceramics, Chinese Academy of Sciences (SICCAS) [30]. The following process was adopted while fabricating the crystals into modules. One of the 60 mm×60 mm surfaces of the BGO crystal was polished to serve as the light output end, whereas the other sides were frosted to enhance photon diffuse reflection. A 2-inch PMT (CR173-1) was coupled to the BGO crystal using EJ-550 silicone grease to collect and convert the scintillation photons. Except for the light output area, the surfaces of the BGO crystals were coated using a 65 μm enhanced specular reflector (ESR) foil (3M Corporation) to increase light reflection efficiency. The BGO crystal was then installed within a 1 mm-thick carbon fiber housing that served as a light shield and provided mechanical protection. Furthermore, the low atomic number of carbon helped minimize the γ attenuation effect of the housing.

To examine the performance of the modules and evaluate their consistency, an initial batch of 50 modules was tested using the ¹³⁷Cs γ source. As illustrated in Fig. 4, at room temperature, the energy resolutions of the modules at 662 keV range from 9.3% to 10.3%, with an average value of 9.8%, which is worse than the typical value of 7~8% for 3 inch NaI(Tl) detectors. Because the light yield of BGO crystals increases with decreasing temperature [31-33], we employed a cooling method to improve the energy resolution of the BGO modules. This cooling method has been successfully used in a previous study [16]. Consequently, 30 modules were cooled to -20 °C, yielding an improved average energy resolution of 8.3%, as shown in Fig. 4. This energy resolution is comparable to the typical value for NaI(Tl) of a similar size.

Fig. 4Full-screen View

(Color online) Energy resolutions of BGO modules measured at 25 °C (black squares) and -20 °C (red circles) for the 662 keV γ ray

The detection efficiency of each detector module was evaluated using a ¹³⁷Cs γ source as shown in Fig. 5. The average full-energy peak efficiencies are 1.45% and 0.69% at distances of 100 mm and 200 mm between the source and detector modules, respectively. The results are consistent with the values of 1.46% and 0.69% obtained from the GEANT4 simulations. Furthermore, the standard deviations of the efficiency for the 50 modules were 0.014% and 0.008% at distances of 100 mm and 200 mm, respectively, exhibiting good consistency in the full-energy peak efficiency across all modules.

Fig. 5Full-screen View

(Color online) Full-energy peak efficiency of the BGO module for 662 keV γ rays at 100 mm (black squares) and 200 mm (black circles) distances. The solid and dashed red curves indicate the corresponding simulated results

The energy non-linearity effect [34] of the module within the 1∼12 MeV range was evaluated using γ rays emitted by both natural radioactive isotopes (1.46 MeV from ⁴⁰K and 2.61 MeV from ²⁰⁸Tl) and nuclear reactions (1.78 MeV, 4.50 MeV, 10.02 MeV, and 11.80 MeV from ²⁷Al(p,γ)²⁸Si and 6.13 MeV from ¹⁹F(p,αγ)¹⁶O). A linear fit yielded a goodness-of-fit value of R²=0.99998, indicating a maximum deviation of 30 keV in the 1~12 MeV range.

Assembly and test of LAMBDA-I

Owing to the limited number of modules currently available, a simplified version of LAMBDA, referred to as LAMBDA-I, was proposed. Figure 6 illustrates the configuration of LAMBDA-I, which comprises 48 BGO modules. LAMBDA-I preserves the essential detection components of LAMBDA, maintaining solid angle coverage of nearly 4π.

Fig. 6Full-screen View

(Color online) LAMBDA-I structure scheme consisting of 48 completed modules

The data acquisition system of LAMBDA-I utilized Pixie-16 modules from XIA Inc. [35] to record the experimental data. These modules operated at a sampling frequency of 100 MHz with 14-bit precision. Data were acquired through independent self-triggered channels with timestamps, enabling event reconstruction using software based on preset coincidence windows. EHS F060p modules (ISEG Inc.) were used to supply high voltage to the 48 PMTs. Fine adjustments of the high voltage of each channel aligned the characteristic γ peaks of the spectrum from each BGO module, thus minimizing discrepancies in the energy calibrations.

The performance of LAMBDA-I was evaluated by measuring the γ rays emitted from ¹³⁷Cs and ⁶⁰Co point sources positioned at the central position. Figure 7 shows the obtained sum spectra representing the sum energy of all triggered modules. The 2505 keV sum peak of ⁶⁰Co β decay, which corresponds to the total energy released by the de-excitation of the 2505 keV level in ⁶⁰Ni, is observed. The presence of weak γ peaks at 1173 keV and 1332 keV indicates the insufficient detection efficiency of LAMBDA-I, corresponding to the escape of one of the two γ rays from LAMBDA-I without any energy deposit. The energy resolutions of LAMBDA-I are 10.1%, 7.3%, 6.9%, and 5.2% at 662 keV, 1173 keV, 1332 keV, and 2505 keV, respectively. The full-energy peak efficiencies are (82.5±1.5)% and (50.6±1.2)% for the 662 keV sum peak of ¹³⁷Cs and 2505 keV sum peak of ⁶⁰Co, respectively.

Fig. 7Full-screen View

(Color online) Comparison of the sum γ spectra of ¹³⁷Cs and ⁶⁰Co sources measured by LAMBDA-I (black circles) with GEANT4 simulations (red curves)

The determination of the response function of LAMBDA-I is crucial for deconvolving the γ spectrum, and is typically achieved through Monte Carlo simulations. As shown in Fig. 7, the GEANT4 simulations accurately reproduce the experimental results. The full-energy peak efficiencies obtained from the GEANT4 simulation were 82.8% and 50.9% for the sum peaks of ¹³⁷Cs and ⁶⁰Co, respectively, which are consistent with the measured values.

The γ–γ coincidence method is a promising technique for resolving unknown cascade transitions in the β decay daughter nucleus. Figure 8 presents a two-dimensional plot of the total energy versus the single-module energy measured using the ⁶⁰Co source. A 1332 keV-1173 keV cascade transition is identified, indicating that LAMBDA-I is capable of cascade transition analysis. As the 1332 keV-1173 keV cascade transition accounts for 99.9% of the de-excitation of the 2505 keV state in ⁶⁰Ni, events falling below the line with a total energy of 2505 keV are primarily caused by incomplete measurement of the total energy. Such tailing effects originating from high levels introduce a remarkable background to the data analysis of lower levels, particularly when the β feedings to high-energy levels are strong. Therefore, further improvements in both the detection efficiency and energy resolution are desired.

Fig. 8Full-screen View

(Color online) Two-dimensional spectra of the sum energy vs single energy of ⁶⁰Co source from LAMBDA-I. The 1332 keV-1173 keV cascade transition is indicated

Gamma source commissioning of LAMDBA-I

To estimate the accuracy and uncertainty of LAMBDA-I during measurement of the complex β-delayed γ decay, a commissioning experiment was performed using the ¹⁵²Eu source. ¹⁵²Eu has two decay modes [36]: electron capture (EC) to ¹⁵²Sm with a branching ratio of 72.08% and β^- decay to ¹⁵²Gd with a branching ratio of 27.92%. The β⁺ decay of ¹⁵²Eu is very weak (0.03%) and can be neglected in the analysis. According to the ENSDF database [37], EC and β^- decay of ¹⁵²Eu can feed 12 states in ¹⁵²Gd and 21 states in ¹⁵²Sm, respectively. The complexity of ¹⁵²Eu decay is comparable to that of fission products.

In the measurement, the ¹⁵²Eu source was positioned at the center of LAMBDA-I. The activity of the source was approximately $3.7\times {10}^4$ Bq. To analyze the obtained data, the coincidence window was set to ±300 ns. Fig. 9 shows the sum and single spectra of ¹⁵²Eu measured using LAMBDA-I. The rapid decline observed at approximately 1.7 MeV in the sum spectrum is caused by the decay energy of EC ($Q_{\text{EC}}=1.874$ MeV) and β^- decay ($Q_{{\beta }^{-}}=1.819$ MeV). Counts in the higher-energy region mainly arise from the natural background and pile-up effects. Unlike the sum spectrum, the single spectrum is the superposition of the γ spectra measured by each detector module.

Fig. 9Full-screen View

(Color online) Spectra of ¹⁵²Eu decay obtained by LAMBDA-I, including (a) sum spectrum, (b) single spectrum gated with nhit=1, and (c) single spectrum gated with nhit=2. The dark and light grey shadows indicate the natural background and pileup part, respectively. The rainbow palette shadow represents the fitted response function of each branch of ¹⁵²Eu decay. The red curve represents the total contribution of all the branches, natural background, and pileup effect

The branching ratio of βfeeding to each state in the daughter nucleus can be extracted using its relation with the TAGS-measured total energy spectrum: $D_i=N{\displaystyle \sum _{k=0}^{k_{\text{max}}}{b}_k}{R}_{ik}\mathrm{,}$ (3) where Di represents the count of the ith channel in the measured spectrum; N is the total number of decays; bk is the branching ratio of β-feeding to the kth level in the daughter nucleus; and Rik is the response function of TAGS to the kth β-feeding.

Among the levels in ¹⁵²Sm and ¹⁵²Gd fed by the β decay of ¹⁵²Eu, several exhibit similar excited energies, such as the 1023 keV, 1085 keV, 1109 keV, and 1123 keV states. The feeding of these adjacent states cannot be distinguished in the sum spectrum because of the limited energy resolution of LAMBDA-I, which results in significant uncertainties in the branching ratio analysis. Fortunately, the multiplicities and individual γ energies of the transitions from these levels to the ground state are often different. Therefore, these adjacent levels may be separated using the number of triggered modules in LAMBDA-I (nhit) and the corresponding single spectrum. In this approach, the experimental data were classified into three types of spectra [38], the sum spectrum ($D_{ik}^{\text{sum}}$), single spectrum gated with nhit=1 ($D_{ik}^{\text{single,nhit=1}}$), and single spectrum gated with nhit=2 ($D_{ik}^{\text{single,nhit=2}}$), as shown in Fig. 9.

The response function Rik was extracted from the GEANT4 simulation for each β-feeding. In the simulation, the β energy spectrum and subsequent γ transitions for each β-feeding were generated using the Radioactive-Decay-5.6 library [39] within the GEANT4 code. The number of simulated events for each branch was set to 10⁶. The simulated data were then convoluted using the experimental energy resolution and used for constructing the corresponding Rik. Consistent with the analysis of the experimental spectra, the corresponding response functions $R_{ik}^{\text{sum}}$, $R_{ik}^{\text{single,nhit=1}}$, and $R_{ik}^{\text{single,nhit=2}}$ were constructed.

The Bayesian Analysis Toolkit [40] (BAT), which is based on Bayesian theory and executed via Markov Chain Monte Carlo (MCMC) simulations, was adopted to solve Eq. 3. In the analysis, feedings with branching ratios below 0.05% were omitted because of their negligible impact on the data analysis. The natural background and pile-up effects were introduced into the analysis as individual and fixed components. The background spectrum was obtained under the same conditions but without the ¹⁵²Eu source and was normalized according to the measurement time. The pileup spectrum was constructed by convolving the sum spectrum with itself, based on the count rate and coincidence window width. Owing to the small likelihood of two γ rays simultaneously hitting the same module, the pileup effects in the single spectra were minimal and therefore neglected, as shown in Fig. 9(b) and (c).

The fitting results for BAT are shown in Fig. 9, in which the contribution of each feeding branch is indicated by a rainbow shadow. The combined contributions from all the branches, the natural background, and the pile-up (red curve) are consistent with the experimental data. Table 1 lists the branching ratios of ¹⁵²Eu decay obtained, comparing with those recommended in ENSDF [37]. The sources of uncertainty include a simulation of the LAMBDA response function of 3%, an experimental coincidence window width of 1%, a pileup effect of 2%, and the statistical error of the BAT code. The present results are consistent with the ENSDF data within the uncertainties, except for a few levels.

The average γ energy of the ¹⁵²Eu decay is derived as (1178±22) keV using the branching ratios obtained in the present work, which is in good agreement with the value (1177±3) keV calculated using the ENSDF data [37]. The 22 keV uncertainty mostly arises from the error in the branching ratio owing to the small uncertainty in the level energy, which is in the current state of the art [3]. The consistency of the present results and ENSDF data demonstrates the capability of LAMBDA-I to study the β intensity and decay heat.

Summary

This study introduces a novel design for a TAGS detector, named LAMBDA, for measuring the β decay intensity distributions of fission products. The final version of LAMBDA, comprising 102 BGO modules, achieved full-energy peak efficiency in the current state-of-the-art. LAMBDA-I, which consisted of 48 completed modules, was tested using a ¹⁵²Eu source. The β intensities of ¹⁵²Eu decay were derived using the BAT code with response functions constructed through GEANT4 simulations. The obtained average γ energy was consistent with the value derived from the ENSDF data, demonstrating the capability of LAMBDA-I to study β intensity and decay heat. Currently, LAMBDA-I is installed at the Beijing Radioactive Ion-beam Facility (BRIF) [41, 42] and is used to measure the β decay intensity of fission products. To provide advanced instrumentation for future research on decay heat, future efforts will focus on producing the remaining BGO modules and assembling the final version of the LAMBDA.