2.1 Internal radiation of LaBr₃(Ce) detector

The internal radiation in the LaBr₃(Ce) crystal has two origins: the naturally occurring radioisotope ¹³⁸La and the ²²⁷Ac impurity. Together, they can decrease the detection sensitivity of γ rays with energies up to approximately 2.5 MeV. A better understanding of self-activity is essential for designing experiments.

¹³⁸La is the only naturally occurring radioactive isotope of lanthanum, with 0.09% abundance and a half-life of 1.05 × 10¹¹ years, which affects the energy spectrum below 1.5 MeV. ¹³⁸La decays in two parallel processes, as shown in Fig. 1. 34.4% of the isotope undergoes β^- decay, with a maximum energy of 263 keV, eventually to the first excitation state of ¹³⁸Ce. This process is associated with the emission of a 788.742-keV γ ray. The remaining 65.6% of ¹³⁸La disintegrates by electronic capture (EC). This process results in stable ¹³⁸Ba with the emission of a 1435.795-keV γ ray and the characteristic X-rays of Ba with energies ranging from 31 to 38 keV.

Fig. 1.Full-screen View

Decay scheme of ¹³⁸La. Data are from NNDC [22].

²²⁷Ac is the grand-daughter nuclide in the ²³⁵U decay chain. Because of its similarity in chemistry to lanthanum, it presents as a contaminator with a half-life of 21.77 in LaBr₃(Ce). Fig. 2 shows the decay chain down to the stable ²⁰⁷Pb by emitting α, β, and γ rays. This includes 6 α emitters (²²⁷Ac, ²²⁷Th, ²²³Ra, ²¹⁹Rn, ²¹⁵Po, and ²¹¹Bi) and 4 β emitters (²²⁷Ac, ²¹¹Pb, ²¹¹Bi, and ²⁰⁷Tl). ²²⁷Ac and its daughter nuclei produce a higher energy background by emitting α particles, and they also contribute to the β continuum up to approximately 1400 keV as a result of the β decay of ²¹¹Pb and ²⁰⁷Tl in the decay chain of this nucleus.

Fig. 2.Full-screen View

Actinide decay chain. The half-life, energies of α and characteristic γ rays with relatively high intensities, and β-decay end-point energy for each nuclide. Data are from NNDC [22].

2.2 Experimental setup

Coincidence measurement using an HPGe was conducted in a low-background counting system (LBS). The environmental background counting rate was 58 per second. The LBS is a cylinder with a radius of 64 cm and a height of 66.1 cm, and it consists of four layers: iron, lead, copper, and plexiglass, from the outside to the inside. A schematic diagram of the entire detection system is shown in Fig. 3. The lead layer can shield most of the low-energy environment background, and the purpose of the copper layer is to absorb the characteristic X-rays of lead.

Fig. 3.Full-screen View

(Color online) Schematic diagram of experimental setup. It contains LaBr₃ and Clover crystals and a low-background shielding room. The shielding room is composed of plexiglass, copper, lead, and iron from the inside to the outside. The LaBr₃ detector is supported by a bracket in a shielded room.

The LaBr₃(Ce) detector is the Saint-Gobain B380 with a ϕ3" ×3" crystal. A high-purity germanium (HPGe) Clover detector from Canberra was placed directly facing the LaBr₃(Ce). The high voltage applied to the LaBr₃(Ce) detector was set to 520 V. A higher voltage may cause electron saturation in the photomultiplier, affecting linearity [23] in the energy determination. The Clover consists of four coaxial N-type high-purity germanium detectors, each with a diameter of 60 mm and length of 60 mm. The energy resolutions for the LaBr₃(Ce) and Clover were measured to be 2.1% (FWHM) and 0.166% (FHWM) for a 1.332-MeV γ ray, respectively. The relative efficiency was 38% for each germanium crystal.

The energy and time signals of the two detectors were acquired using the VME data acquisition system and collected for 37,187 s in total. Dead time correction and time stamps were added to the data acquisition software. Standard radioactive sources ⁶⁰Co, ¹³⁷Cs, and ²⁴¹Am were used for the γ-ray energy calibration up to approximately 1.33 MeV. The calibration accuracy was cross-checked using the characteristic γ-rays of ¹³⁸La. Moreover, to calibrate the high-energy spectrum of LaBr₃(Ce), we used the recoil-electron energies from the Compton scattering process of 2.615-MeV γ rays of ²⁰⁸Tl, a naturally radioactive nuclide in an environmental background. Such calibration is only possible using the coincidence measurement with Clover.

2.3 Coincidence measurement

The intrinsic radiation of the LaBr₃(Ce) scintillator was identified by coincidence measurement using the LaBr₃(Ce) and Clover detectors. The relevant background spectra after energy calibration are shown in Fig. 4. In the self-counting spectrum of LaBr₃(Ce), we first see a low-energy peak centered at approximately 35.5 keV. This is attributed to the sum of 95.6% of the 31.83 keV K_α X-ray response and 90 % of the 5.6 keV Auger electron response in the EC decay process, by referring to the theoretical calculation [20]. The energy shift is due to the non-proportional response of the LaBr₃(Ce) crystal. Then, we see a β continuum with an end point of 263 keV mixed with the Compton continua, primarily from the 788.7 and 1435.8 keV of ¹³⁸La and the 1460.8 keV of ⁴⁰K. With increasing energy, the 788.7 keV bump is shown to extend to higher energies and end at approximately 1 MeV. This is due to the coincidence of the 788.7-keV γ with the β^- continuum. The 1435.8-keV γ-rays produced by the EC of ¹³⁸La coincided with the 32-keV X-rays of ¹³⁸Ba and the 1460.8-keV γ-rays of ⁴⁰K, resulting in a double peak near 1461 keV, as shown in Fig. 4(a).

Fig. 4.Full-screen View

(Color online) Background radiation spectra measured for 37,187 s by the LaBr₃(Ce) detector (a) and the Clover (b). The coincidence β spectrum (red) and X-ray spectrum (green) in the LaBr₃(Ce) detector are shown in (a). The coincidence spectrum (red) and environmental background spectrum (black) of the Clover are shown in (b). For details, refer to the text.

The spectrum above 1.8 MeV shows a three-peak structure, revealing the presence of α emitter contaminants. Although the α energies from ²²⁷Ac and its daughter nuclei are as high as 5.0∼7.4 MeV (see Fig. 2), the energies are read out in the spectrum calibrated with γ-rays to be in the energy range of 1.5 and 2.5 MeV because of the well-known light quenching effect (see, for example Ref. [18]).

The energy spectrum of the Clover detector, as well as the coincidence spectrum, are shown in Fig. 4(b). It is clear that the characteristic γ-rays of 788.7 keV and 1435.8 keV of ¹³⁸La decays were enhanced and the environmental background was further reduced in the coincidence spectrum. Setting gates in the Clover spectrum at 788.7 keV and 1435.8 keV of ¹³⁸Ba decays allows us to pick up the β spectrum and the X-ray spectrum in the LaBr₃(Ce) detector, as shown in Fig. 4(a)].The coincidence β spectrum has triggered a precise study of ¹³⁸La decay [20, 24-27], which is a second forbidden unique decay. The β and X-ray distributions are shown for comparison in the LaBr₃(Ce) spectrum.

Part of the coincidence events in the Clover and LaBr₃(Ce) detectors are displayed in Fig. 5, while the projection to the Clover is shown in Fig. 6. The horizontal bands in Fig. 5 are traced back to the α-γ cascades. The correlated γ ray energies and their relative intensities are key to identifying the α emitters.

Fig. 5.Full-screen View

(Color online) Matrix of the LaBr₃(Ce) vs. Clover. Listed are also the events of α-γ correlations and the identified radioactive isotopes. Both detectors were calibrated with characteristic γ-rays. The events between 1.5 and 2.4 MeV for LaBr₃3(Ce) correspond to 5-7.4 MeV α particles of the ²²⁷Ac decay chain. See the text for details.

Fig. 6.Full-screen View

Projected γ-ray energy spectrum of Fig. 5 in the Clover. Labeled are the identified nuclei.

The α emitters identified by the γ-α coincidence are ²²⁷Th, ²²³Ra, ²¹⁹Rn, and ²¹¹Bi. This is consistent with previous investigations of LaBr₃(Ce) with a size of ϕ1" ×1" [9] and LaCl₃(Ce) with a size of ϕ25mm × 25mm) [17]. The main γ-rays and α emitted by ²²⁷Th, ²²³Ra, ²¹⁹Rn, and ²¹¹Bi are shown in Table 1. Some α values listed in the table cannot be seen in Fig. 5 because their branches are relatively low. The α (6.038 MeV from ²²⁷Th, 6.62 MeV from ²¹¹Bi, and 6.82 MeV from ²¹⁹Rn) with relatively high intensity cannot be seen in Fig. 5 because the parent nucleus decays to the ground state of the daughter nucleus. The third peak in the single spectrum of LaBr₃(Ce) in Fig. 4(a) is the 7.386 MeV α line from the ground state of ²¹⁵Po to the ground state of ²¹¹Pb, in which there is no cascade γ-ray.

3.1 Simulation of the self-counting LaBr₃(Ce)

We compare the simulation with the experimental data acquired at the same measurement time, that is, 37,187 s. The best fit to the experimental spectrum is found using the least squares method when the activity of ¹³⁸La 482(19) Bq corresponds to 1.396 (55) Bq/cm³. This corresponds to 180,030,639 decays of ¹³⁸La over 37,187 s in total. The uncertainty quoted here is due to the experimental statistics, detection efficiency, and branching ratio of the γ-rays. The experimental and simulated spectra are plotted in Fig. 7. Good agreement is seen, except for the low-energy part up to approximately 150 keV. To reproduce the experimental spectrum, we adopted the following function [31] for the γ-ray energy (Eγ) resolution (η):

Fig. 7.Full-screen View

(Color online) Comparison of experimental (black line) and simulated (red line) self-counting energy spectra in the LaBr₃ detector. The sampling of simulation was scaled to the experimental data collected for 37,187 s.

It should be noted that in the above simulation, we did not consider the contribution from ²²⁷Ac and its daughter nuclei. This may partially account for the difference between the simulation and experimental spectra. Another possible reason for the low-energy deficiency in the simulation could be insufficient understanding of the β decay of ¹³⁸La. This has been discussed in Ref. [24-27].

3.2 Activities determined using the Clover data

An alternative way to deduce the ¹³⁸La activity is to use the coincidence γ ray information at 788.7 and 1435.8 keV in Clover. This would require an accurate efficiency calibration of the Clover detector using a volume source of the same volume as the LaBr₃(Ce) detector, which is practically impossible.

In reality, we performed a two-step optimization of the calibration [32]. In step one, we followed the standard routine for efficiency calibration using the standard radioactive point sources ¹³⁷Cs, ²⁴¹Am, ⁵⁴Mn, ⁸⁸Y, ¹⁰⁹Cd, ⁶⁵Zn, and ¹⁵²Eu. These sources are selected to avoid a possible true summing effect. The point source was placed 3 cm from the front surface of the Clover detector. We used the EFFIT program in the software package [33] to describe the efficiency curve for the low-energy and high-energy regions separately.

In this step, we optimized the thickness of the dead layer encapsulating the crystal by the least squares method to best reproduce the Clover spectrum of ¹⁵²Eu. The best simulation results of the ¹⁵²Eu spectrum together with the experimental data are presented in Fig. 8(a). The simulated detection efficiency curve was compared with the experimental results using a standard point source, as shown in Fig. 9.

Fig. 8.Full-screen View

(Color online) Comparison of Clover spectrum (black line) with simulation (red line) for a ¹⁵²Eu source (a) and LaBr₃(Ce) crystals (b). The sampling of the simulation for LaBr₃(Ce) was scaled to the experimental data collected for 37,187 s

Fig. 9.Full-screen View

(Color online) γ-ray detection efficiencies of Clover. The red dashed line is the fitting curve for the experimental data (solid triangle) from the standard point source, while the black dashed line is the simulation efficiency under the same detection configuration. The black solid line represents the detection efficiency when the source is evenly distributed in the LaBr₃(Ce) crystal.

In step two, we modeled the detection efficiency of the Clover with sources evenly distributed in the LaBr₃(Ce) crystal, instead of point sources. The simulated efficiency curve is shown in Fig. 9. The efficiency of 788.7 keV and 1435.8 keV γ-rays were determined to be 0.00347(11) and 0.00257(10), respectively. In the simulation, the interaction of characteristic γ-rays with both the LaBr₃(Ce) and Clover detectors and even the shielding material were taken into account.

As a result, we found that the Clover spectrum collected for 37,187 s is best reproduced when the total count of the 788.7-keV γ-ray is 22,423 (164). The simulation and experimental data are shown in Fig. 8(b). The activity of ¹³⁸La is thus extracted to be 504 (16) Bq, corresponding to 1.451 (58) Bq/cm³. The uncertainty takes into account the contributions from the statistics, detection efficiency, and branching ratio of the γ-rays in the decay of ¹³⁸La. In the same way, the activity of ¹³⁸La was also deduced from the 1435.8-keV γ-ray to be 500 (20) Bq, corresponding to 1.437 (63) Bq/cm³. Both are consistent with those determined from the self-counting of the LaBr₃(Ce) detector, as shown in Table 3. In fact, the activity of ¹³⁸La in the LaBr₃(Ce) B380 detector can be estimated according to the natural abundance of ¹³⁸La, 0.08881(71)% [22], and its half-life T_1/2=1.0510¹¹a. The activity amounts to 1.456 (40) Bq/cm³. This is in good agreement with our measurements.

The above procedure can also be applied to evaluate the activities of the ²²⁷Ac decay chain contaminators. In Fig. 6, we identified the characteristic γ-rays at 351.1 keV (²¹¹Bi), 271.2 keV and 401.8 keV (²¹⁹Rn), 269.5 keV and 445.0 keV (²²³Ra), and 236.0 keV (²²⁷Th). The activities of ²¹¹Bi, ²¹⁹Rn, ²²³Ra, and ²²⁷Th are 0.0136 (15) Bq/cm³, 0.0125 (12) Bq/cm³, 0.0127 (10) Bq/cm³, and 0.0158 (22) Bq/cm³, respectively.

The half-life of the parent radionuclide ²²⁷Ac is much longer than the half-life of the daughter radionuclide in the Ac-decay chain. In principle, secular equilibrium should occur, namely, the activities A of each emitter should be equal:

where λi and Ni are the decay constant and the number of nuclear species i, respectively. Indeed, as shown in Fig. 10, the activities of ²¹¹Bi, ²¹⁹Rn, ²²³Ra, and ²²⁷Th agree well within the error bars. Here, the decay branchings of the ²²⁷Ac and ²¹¹Bi decay were taken into account. The average activity was computed to be 0.0135(13) Bq/cm³. The secular equilibrium allows us to determine the activities of all nuclei in the decay chain, namely, ²⁰⁷Tl, ²¹¹Po, ²¹⁵Po, ²²³Fr, and ²²⁷Ac as 1.3510^-2(13), 3.7910^-5(36), 1.3510^-2(13), 1.910^-4(11), and 1.3510^-2(13), respectively. The results are summarized in Table 3.

Fig. 10.Full-screen View

Activities of ²²¹Bi, ²¹⁹Rn, ²²³Ra, and ²²⁷Th deduced from the α-γ coincidence experiment. The average value and relevant uncertainty are indicated by the shaded area.

We included all of the α emitters in the decay chain, as discussed above, into the Geant4 code, and simulated the 37,187-s energy spectrum. The quenching effect of the α particles and recoil nuclei in the scintillator is not included because of the lack of precise calibration. The results are shown in Fig. 11. The energy resolution of each alpha particle was assumed to be 6%.

Fig. 11.Full-screen View

(Color line) (a) Simulated alpha energy spectrum of the LaBr₃(Ce) detector. The contributions from each isotope are labeled. (b) High-energy part of the experimental spectrum. The simulation was scaled to an experimental duration of 37,187 s.

One can easily identify a similar pattern of simulations for the experimental high-energy spectrum. This verifies the ²²⁷Ac contribution to the energy spectrum of 4.5 MeV to 5.2 MeV, ²²³Ra and ²²⁷Th to the spectrum of 5.2 MeV to 6.5 MeV, ²¹¹Bi and ²¹⁹Rn to the spectrum of 6.5 MeV to 7.2 MeV, and ²¹¹Po and ²¹⁵Po to the spectrum of 7.2 MeV to 8.5 MeV. The sum activity of α contaminators is 0.095(4) Bq/cm³, which is smaller by a factor of 14 than that of ¹³⁸La.

A similar intrinsic background exists in all of the La-containing crystals. A pioneering study [17] of the LaCl₃(Ce) detector with a crystal size of ϕ25 mm ×25 mm identified the total α activity of ²²⁷Th, ²²¹Bi, ²¹⁹Rn, and ²²³Ra as 0.126 Bq/cm³, and each contribution is summarized in Table 3. In the present study of the B380 type, the ²²⁷Ac atom/La atom amounts to 2.0× 10^-12. The sum activities of ²²⁷Th, ²²¹Bi, ²¹⁹Rn, and ²²³Ra are typically 40% of that in Ref. [17]. This indicates that the actinium impurity has been significantly reduced in the last decade.

¹³⁸La and ²²⁷Ac impurities resulted in a counting rate (including environmental background) of 237 counts/s for γ-ray energies between 20 and 500 keV, 182 counts/s between 500 and 1.5 MeV, and 27 counts/s above 1.5 MeV in our LaBr₃(Ce) detector. Self-irradiation affects its application to low-production experiments, in particular for potential cases with a count rate of less than 450 counts/s.