The Wide-Angle Compton Coincidence Technology

Figure 3 presents the wide-angle Compton coincidence (WACC) experimental setup, which primarily comprises a radioactive source, a high-purity Germanium (HPGe) detector, the scintillation detector under examination, and a subsequent data acquisition system [24, 26-29]. LaBr₃(Ce), LaBr₃(Ce,Sr), and NaI(Tl) cylindrical samples with diameters of 25.4 mm were selected for this study. Silicone oil was used to couple the encapsulated crystals to the PMTs (R6233-100, Hamamatsu Photonics, Japan) [30, 31]. According to the user manual of the BE2020 planar germanium spectrometer manufactured by Canberra, the HPGe crystal had a thickness of 20 mm and a volume of 40,000 mm³, allowing for an energy detection range of 3 keV–3 MeV [32, 33]. Based on the experimental data, the energy resolutions, indicated by the full width at half maximum (FWHM), of the HPGe detector used in this study were determined to be 1.58 keV (⁶⁰Co, 1.33 MeV) and 1.15 keV (¹³⁷Cs, 662 keV).

Fig. 3Full-screen View

Schematic diagram of experimental setup for obtaining Compton electrons with a wide energy range

The experiment involved placing a ¹³⁷Cs radioactive source at a quarter-circle position around the center of the crystal, with a distance of 13 cm between the crystal and source. Gamma photons were emitted by the radioactive source via radioactive decay and underwent Compton scattering when they struck the crystal. Consequently, Compton electrons were generated and absorbed by the crystal, whereas certain scattered photons escaped from the crystal and were absorbed by the nearby HPGe detector. The distance between the tested crystal and HPGe detector was maintained at approximately 15 cm. Lead blocks were positioned between the ¹³⁷Cs source and HPGe detector to provide shielding and minimize the incidence of primary gamma photons directly irradiating the HPGe detector. Coincidence events across a broad energy range were obtained by adjusting the position of the radioactive source and varying the angle between the source, crystal, and HPGe detector.

A desktop waveform acquisition device with a 10 bit @ 2 GS/s (interleaved) or 1 GS/s, which was a DT5751 digitizer [34], was utilized in this experiment to collect signals from the crystal and HPGe detectors (Fig. 4). The HPGe detector signal operating at +3500 V underwent shaping and filtering using an ORTEC 572A amplifier before being sent to channel-0 of DT5751. The output signal from the PMT anode operating at +1300 V was routed to channel-1 of DT5751 after the photoelectrons were multiplied by the dynodes [22]. The signals from the crystal and HPGe detectors successively underwent low-threshold discrimination, delayed stretching, and a logical coincidence. The resulting coincidence output signal was utilized as an external trigger for DT5751, which recorded the corresponding coincidence events and generated two data files when triggered externally. The secondary particles produced by Compton scattering were absorbed by the two detectors in a specific order in the time sequence. For a “true coincidence event” the waveform signal corresponding to the crystal appeared before the HPGe detector.

Fig. 4Full-screen View

Diagram of the data acquisition system for coincidence events

Figure 5 presents the coincidence matrix that represents all the collected data of the events. In Fig. 5 (a), the horizontal axis represents the energy deposited on the HPGe detector, whereas the vertical axis corresponds to the energy deposited on the LaBr₃(Ce,Sr) crystal. As indicated in the Compton scattering formula (Eq. (1)) [24], as the incident angle (θ) of the gamma photon increased, the energy of the Compton electrons in the LaBr₃(Ce,Sr) crystal also increased. $E_{\text{e}}=E_{\gamma }-{E^{\prime }}_{\gamma }=\frac{E_{\gamma }}{1+\frac{m_{\text{e}}{c}^2}{E_{\gamma }\left(1-\text{cos}\theta \right)}}\mathrm{.}$ (1) where Eγ is the energy of the gamma ray radiating from the source, E_e is the energy of the Compton electron, ${E^{\prime }}_{\gamma }$ is the energy of the scattered photon, θ is the Compton scattering angle, and $m_{\text{e}}{c}^2$ is the remaining mass energy of the electron. Five scattering angles of θ were chosen during the experiment to obtain data over a broad energy range.

Fig. 5Full-screen View

(Color online) Two-dimensional spectrum of coincidence events in both HPGe and (a) LaBr₃(Ce,Sr), (b) LaBr₃(Ce), (c) NaI(Tl) with the ¹³⁷Cs source, that is, the coincidence matrix

The diagonal points presented in Fig. 5 demonstrate the "true coincidence events" of interest. Each point corresponds to a specific scattering angle, and the combined deposited energies in both the crystal and HPGe detector are constant at 661.6 keV. The uneven "spread" among the diagonal at different energy levels is owing to the diverse energy resolutions of the crystal for Compton electrons. Furthermore, the non-linear response of the crystal determines the “linearity” of the diagonal. An analysis of the coincidence matrix enabled the extraction of the energy resolution and non-linear response of the crystal for Compton electrons.

Figure 5 presents the horizontal and vertical lines indicating the accidental coincidence events simultaneously detected by both detectors. The horizontal line represents the finite resolution of the crystal and the vertical line represents the excellent resolution of the HPGe detector. The other points on the graph denote events in which partial energy was deposited in the detector or where detection occurred after scattering through the surrounding materials.

The WACC method accurately measures the energy response and resolution of the crystal detector to the Compton electrons. Before the Compton experiments, it was necessary to calibrate the E–C relationship of the HPGe detector, which can be obtained from the energy spectra of multiple radioactive sources or directly using the vertical lines in the coincidence matrix.

The HPGe detector offers an outstanding energy resolution, making it an excellent standard detector. The energy deposited in the crystal was calculated by subtracting the scattered photon energy in the HPGe detector from the known gamma-ray source energy. In actual data processing, the cut width of the HPGe energy axis must be determined based on the statistics of the Compton scattering event. Within this range, the central value is considered to be the energy deposited in the HPGe detector, and Eq. (2) is used to calculate the energy deposited in the crystal. In this study, cutting was performed along the HPGe energy axis and projected onto the crystal axis. $\langle E_{\text{scin}}\rangle =E_{\gamma }-\langle E_{\text{HPGe}}\rangle \mathrm{.}$ (2) where Eγ is the known gamma-ray source energy, $\langle E_{\text{HPGe}}\rangle$ is the deposited energy in the HPGe detector, and $\langle E_{\text{scin}}\rangle$ is the deposited energy in the crystal.

To understand the effect of the cut width or energy window width, we measured the energy resolution of the LaBr₃(Ce,Sr) crystal to 46.6 keV Compton electrons for different cut widths. The results indicated that the energy resolution remained reasonably stable until a cut width of 4 keV was reached (Fig. 6). Wider cut widths led to a broadened scattering angle range of relevant valid events and an increase in the FWHM of the Compton electron spectrum. Subsequently, the resolution deteriorated. The energy resolution of the HPGe detector was within 1–2 keV, which must be considered when determining a reasonable cut width. It is also essential to ensure a sufficient number of events. Therefore, a cutoff width of 4 keV was used when the energy deposited in the HPGe detector was less than 615 keV. When the deposited energy was within 615–661.6 keV, a cutoff width of 2 keV was selected.

Fig. 6Full-screen View

Resolution of Compton electrons in LaBr₃(Ce,Sr) versus the cut width in HPGe for a ¹³⁷Cs source

Multiple truncations of the HPGe energy axis were performed to obtain the crystal spectra for various Compton electron energies. Figure 7 illustrates an example of this approach, in which a data range of events from 614 to 616 keV was considered at an HPGe energy of 615 keV with a cut width of 2 keV to produce the Compton electron spectrum (Fig. 7 (b)). A Gaussian-shaped, single-energy electron peak was visible and fitted with a Gaussian function, returning an energy resolution of 15.81 ± 0.25% for the 46.6 keV Compton electrons in the LaBr₃(Ce,Sr) crystal.

Fig. 7Full-screen View

Projected spectra of the LaBr₃(Ce,Sr) crystal with the HPGe energy gated at (a) 605 keV, (b) 615 keV, (c) 625 keV, and (d) 635 keV, respectively; that is, the (a) 56.6 keV, (b) 46.6 keV, (c) 36.6 keV, and (d) 26.6 keV Compton electron energy spectrum

Atoms or molecules are excited when incident particles deposit energy in a crystal, leading to the emission of scintillation photons with wavelengths similar to those of visible light [30]. The light yield, defined as the number of scintillation photons per unit of energy deposited in the crystal, is described by Eq. (3). $S=\frac{ADC}{AD{C}_{\text{spe}}\cdot E}\mathrm{.}$ (3) where S is the light yield of the crystal, ADC represents the peak position of the spectrum after deducting the baseline, E is the deposited energy in the crystal, and the ADC_spe = 8.0321 channels denote the single-photoelectron response of the Hamamatsu R6233-100 PMT at a high voltage of +1300 V. The response was calibrated using the LED-triggered charge method[36].

Measured by Radioactive Sources

Radioactive sources of ¹³³Ba, ¹³⁷Cs, ²⁴¹Am, ¹⁵²Eu, and ²⁰⁷Bi were employed across a range of γ-ray energies from 30.85 keV to 1063.7 keV to investigate the gamma-ray responses. The tested crystal was coupled to a Hamamatsu R6233-100 PMT via silicon oil, and the digitizer DT5751 acquired the signal waveforms in the self-triggering mode. ROOT, a data analysis framework conceived by the European Organization for Nuclear Research (CERN)[37], was used to analyze the experimental data, including baseline subtraction, fitting of the full-energy peak, and analysis of the peak position and FWHM.

Single Energy X-ray Measurements Using the Hard X-ray Calibration Facility

We employed two sets of hard X-ray calibration facilities (HXCF, Fig. 8) established by the National Institute of Metrology (NIM) in Beijing Changping, China[38-40] to investigate the energy responses of the three aforementioned crystals to X-rays in the 8–120 keV range. The HXCF, which plays a substantial role in the calibration of gamma-ray detectors on GECAM, CubeSats, and SVOM satellites[41-43], was first built for the high-energy telescope of the HXMT as a calibration facility[44] and comprises four primary components: X-ray generator, monochromator, collimator, and standard detector. To shield stray light from the X-ray generator, the collimator features apertures of various sizes at the entrance and exit. A low-energy HPGe detector (Canberra Industries) was used as a standard. Before testing, we calibrated the HPGe detector for energy linearity, resolution, and detection efficiency using various standard radioactive sources[45].

Fig. 8Full-screen View

(Color online) Hard X-ray Calibration Facility. Both the HPGe and crystal detectors were placed on a displacement platform and maintained on the same horizontal line

The entire set of testing equipment, including the data-acquisition system, was placed inside an X-ray testing chamber (Fig. 9), and remotely controlled for data retrieval in a control room. The energy and flux of the X-rays were determined using an HPGe detector. The testing procedures are shown in Fig. 10. We used GENIE 2000, which is a spectroscopic data acquisition and analysis software, to record the spectral data from the HPGe detector. The crystal detector was coupled to a PMT (Hamamatsu Model CR160) using silicone oil. The signals from the crystal detector were collected using a digitizer (DT5751) and analyzed using computer software for the corresponding spectra.

Fig. 9Full-screen View

Data acquisition system diagram for single-energy X-ray detection

Fig. 10Full-screen View

Test procedure for the non-linear response of the crystals to X-rays

The range of X-ray testing was between 8–120 keV in this study, with fine measurements of the absorption edge of the crystal at a step size of 0.1 keV. The performance of the crystal detector gradually changed as the X-ray energy increased, allowing for a reduced number of test energy points. Owing to testing at room temperature (22–23 ℃), the detector noise was slightly higher, limiting the starting test energy points to the range of 8–10 keV. For the two LaBr₃ crystals, the PMTs coupled to them operated at -800 V, whereas that for the NaI(Tl) crystal operated at -1000 V.

Light Yield Non-linearity to Compton Electrons

The light yields of the LaBr₃(Ce), LaBr₃(Ce,Sr), and NaI(Tl) crystals were normalized to "1" at an energy of 662 keV. Figure 11 demonstrates the non-linearity of the light output of the LaBr₃(Ce), LaBr₃(Ce,Sr), and NaI(Tl) crystals to the Compton electrons within the energy range 3–400 keV. To better quantify the non-linearity of these crystals, we introduced a metric known as the non-linearity standard deviation (NLSD), denoted by Eq. (4), where x_i represents the relative light yield at each energy point. The NLSD values for the LaBr₃(Ce), LaBr₃(Ce,Sr), and NaI(Tl) crystals were 0.11, 0.03, and 0.06, respectively. A larger NLSD value indicates a more significant non-linearity of the crystal. $NLSD=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left(x_i-1\right)}^2}}\left(n=\mathrm{1,2,3...}\right)\mathrm{.}$ (4) For both types of LaBr₃ crystals, as the energy of the Compton electrons decreased, the non-linearity of the light yield gradually increased. Within the measured electron energy range, the LaBr₃(Ce,Sr) crystal exhibited a better linearity than that of the LaBr₃(Ce) crystal, particularly at energies below 20 keV. We hypothesized that the doping of Sr²⁺ may have improved the internal energy transfer mechanism within the LaBr₃(Ce,Sr) crystal, enhancing the energy transfer efficiency in the low-energy region, thereby ameliorating non-linearity. Both crystals exhibited a 10% “defect” light output at approximately 5 and 20 keV, respectively. The minimum measurable energy point using WACC was 3.1 keV, at which the LaBr₃(Ce,Sr) crystal exhibited a “defect” of approximately 24%, whereas that of the LaBr₃(Ce) crystal exhibited 35%. This experiment validated the simulation results presented by C. Zheng et al.[17], which demonstrated the non-linearity of the electrons, while also affirming the accuracy and rationality of both the model and experimental work conducted by the GECAM research team.

Fig. 11Full-screen View

Comparison of the light yield non-linearity of LaBr₃(Ce), LaBr₃(Ce,Sr), and NaI(Tl) crystals for the 3–400 keV Compton electrons

In comparison to the two LaBr₃ crystals, the NaI(Tl) crystal did not exhibit the monotonic "defect" of the luminescence phenomenon as the energy of the Compton electrons decreased. At approximately 14 keV, the NaI(Tl) crystal reached its maximum light yield, exhibiting an "excess" light output of approximately 15.5%. Beyond 14 keV, the light yield gradually decreased as the energy increased. Conversely, as the energy decreased to below 14 keV, the light yield decreased. The lowest test energy point was 4.1 keV, at which the NaI(Tl) crystal demonstrated a luminosity non-linearity “defect” of approximately 14%.

The Absolute Light Yield of Crystals

The three crystals were irradiated using multiple radioactive sources to obtain the energy spectra of each crystal for different sources. The single-photoelectron responses of the Hamamatsu R6233-100 PMT used in the measurements were calibrated using the LED-triggered charge method at various voltages, enabling the calculation of the absolute light yields of the three crystals. The absolute light yields and energy resolutions of the samples tested at 661.6 keV are listed in Table 2.

Energy Resolution

Figure 12 illustrates the energy resolution of the LaBr₃(Ce), LaBr₃(Ce,Sr), and NaI(Tl) crystals for the Compton electrons in the 3–400 keV range. The energy resolution of the NaI(Tl) crystal was comparable to that of the LaBr₃ crystals at 16–30 keV (Fig. 12).

Fig. 12Full-screen View

Comparison of the energy resolution of the LaBr₃(Ce), LaBr₃(Ce,Sr), and NaI(Tl) crystals for the Compton electrons in the 3–400 keV range

The energy resolution of the crystals was expressed using the FWHM of the full-energy peak of the X-ray. Figure 13 presents the energy resolution of the LaBr₃(Ce,Sr), LaBr₃(Ce), and NaI(Tl) crystals for X-rays in the 8–100 keV range, as measured by HXCF. The LaBr₃(Ce,Sr) crystal exhibited the best energy resolution within this energy range. At 100 keV, the resolution of the LaBr₃(Ce,Sr) crystal was 8.74 ± 0.0681%, whereas those of the LaBr₃(Ce) and NaI(Tl) crystals were 9.41±0.0976% and 10.39 ± 0.1168%, respectively. Furthermore, a slight degradation in the energy resolution, less than 1%, was observed near the binding energy of the K-shell electrons.

Fig. 13Full-screen View

Energy resolution of the LaBr₃(Ce,Sr), LaBr₃(Ce), and NaI(Tl) crystals varies with the X-ray energy

Comparison of the X/γ-Ray and Compton Electron Responses

All the data in this study were standardized by setting the full-energy peak response of the 662 keV gamma rays from a ¹³⁷Cs source as the normalization factor. The non-linearity of the LaBr₃(Ce,Sr) crystal light yield for the Compton electrons and gamma rays in the 3–1000 keV range is shown in Fig. 14. Note, the response of the Compton electrons exhibited an excellent linearity at approximately 70 keV, with a non-linearity of less than 2%. However, a "deficiency" in the light output occurred when the energy of the Compton electrons was below 70 keV, whereas substantial non-linearity was observed in the response to gamma rays below approximately 200 keV.

Fig. 14Full-screen View

Light yield non-linearity of the LaBr₃(Ce,Sr) crystal for Compton electrons, gamma rays, and X-rays

A more detailed test was conducted on the photon response below 120 keV using HXCF. Figure 14 presents the non-linear light yield response curve of the LaBr₃(Ce,Sr) crystal to X-rays in the energy range of 8–120 keV. Because the error bars are similar in size to the data point symbols, they are not visible in the figure. Ideally, the relative light yield should be "1" at all energy points. However, this was not the case and varying degrees of light-yield deficiencies were observed within the tested energy range. Below 40 keV, the LaBr₃(Ce,Sr) crystal exhibited substantial non-linearity in the relative light yield response to X-rays, with the non-linearity exceeding 10%. As the energy decreased, the slope of the curve increased, reaching a non-linearity of 36% at 8 keV. When the X-ray energy exceeded 40 keV, the non-linear curve approached the ideal state and the slope became milder, indicating that the fluctuation in the number of photons generated per unit energy absorbed by the LaBr₃(Ce,Sr) crystal was small within the energy range of 40–120 keV. The LaBr₃(Ce,Sr) crystal exhibited absorption edges at 13–15 keV and 38–40 keV, and a slight reduction in the relative light yield was observed within these two energy intervals.

The NLSD values for testing the LaBr₃(Ce,Sr) crystal with X-rays and Compton electrons were 0.17 and 0.03, respectively. The light output of the LaBr₃(Ce,Sr) crystal exhibited a greater non-linearity in response to the X-rays than to the Compton electrons. This can be attributed to the different mechanisms by which these particles interact with atoms in matter. For X/γ-rays ranging from a few keV to several hundred keV, there are two possible interaction processes with the crystal: (1) a direct photoelectric cascade sequence or (2) Compton scattering followed by a photoelectric cascade sequence. These processes generate several primary electrons (e.g., Compton electrons and primary photoelectrons) and multiple secondary electrons (e.g., Auger electrons and secondary photoelectrons), with the final light emission being the sum of the contributions from secondary electrons with different energies. Notably, these electrons are the products of the interaction between the incident photons and matter, and their energies cannot exceed those of the incident particles. Therefore, the light output induced by the photons in the LaBr₃(Ce,Sr) crystal was always lower than that caused by the Compton electrons with equivalent energies.

We conducted detailed testing of the LaBr₃(Ce) crystal using the same experimental procedures and data processing methods. Figure 15 illustrates the non-linear light-yield response of the LaBr₃(Ce) crystal to Compton electrons and gamma rays in the 3–1000 keV energy range. The non-linear curves tended to be flat, and the results were similar for the Compton electrons and gamma rays when the energy was above 200 keV; however, significant differences were observed below 200 keV. As the energy decreased, the LaBr₃(Ce) crystal exhibited a lower response to the full-energy peak of the gamma rays than to the Compton electrons of the same energy. This finding is consistent with the test results for the LaBr₃(Ce,Sr) crystal, indicating that the manner in which the particles interact with the matter directly affects the light output of the crystal. For gamma rays in the energy range of several hundred kiloelectronvolts, Compton scattering is most likely the initial interaction, and most gamma rays require multiple interactions for full absorption. The high-energy primary and secondary electrons resulting from these interactions exhibited good linear responses, reflecting the excellent linearity of the response to high-energy gamma rays.

Fig. 15Full-screen View

Light yield non-linearity of the LaBr₃(Ce) crystal for Compton electrons, gamma rays, and X-rays

Figure 15 demonstrates the non-linearity curve of the LaBr₃(Ce) crystal to X-rays in the 8–120 keV energy range. Compared to the LaBr₃(Ce,Sr) crystal, this response curve deviated from the ideal state more significantly, and nearly all the measured energy points exhibited scintillation responses below 90%. The light output sharply decreased near the K-shell binding energies (13–15 keV and 38–40 keV) of Br and La, leading to a greater non-linearity of the LaBr₃(Ce) crystal response curve to the X-rays. The data points below 28 keV exhibited a non-linearity greater than 20%, and the light output at 8 keV was only 58% of the ideal state.

As the X-ray energy decreased, the induced secondary electron energies in the crystal decreased, thereby resulting in more significant light "defects". The NLSD values obtained by testing the LaBr₃(Ce) crystal with the X-rays and Compton electrons were 0.22 and 0.11, respectively. The LaBr₃(Ce) crystal exhibited a greater non-linearity toward the X-rays and Compton electrons compared to the LaBr₃(Ce,Sr) crystal, particularly at energies below 100 keV. This may be attributed to the doping process, indicating that doping with Sr²⁺ ions can improve the non-linearity of LaBr₃ crystals.

To better understand the differences in non-linearity among the different types of crystals, the NaI(Tl) crystal was chosen as the third test subject (Fig. 16). Unlike the two LaBr₃ crystals, the NaI(Tl) crystal exhibited a pronounced "excess" response to the Compton electrons in the 8–80 keV energy range, with a non-linearity exceeding 4%. At electron energies lower than 6 keV, the crystal displayed slight "defects" in the light output, whereas above 80 keV, the curve tended to flatten, indicating a good linear response of this sodium iodide compound to high-energy electrons.

Fig. 16Full-screen View

Light yield non-linearity of the NaI(Tl) crystal for Compton electrons, gamma rays, and X-rays

Figure 16 also demonstrates the non-linearity of the light yield of the NaI (Tl) crystal to X-rays in the 8–120 keV energy range. Compared with the response to the Compton electrons, the X-ray test results exhibited a similar trend, with NLSD values of 0.06 for both. However, there were differences in the slopes of the curves. Direct photoelectric interactions with matter are most likely to occur for photons in the tens-of-keV range. Assuming this photoelectric absorption occurs with iodine K-shell electrons (probability of 83% when the photon energy is greater than 33.17 keV), the resulting photoelectrons have energies within the range, with a substantial "excess" light output. The total light emission induced by all secondary electrons generated from the photons exceeded that caused by Compton electrons with equivalent energies. Therefore, when the energy was within the 40–70 keV range, the NaI(Tl) crystal exhibited a higher relative light output to the X-rays, producing a greater number of photons per unit of X-ray-deposited energy compared to the case of the Compton electron incidence.

The response of the NaI (Tl) crystal to the X-rays was similar to that of the Compton electrons at approximately 33 keV, is related to the binding energy (33.17 keV) of the iodine K-shell electrons, as photons with energies lower than this cannot excite K-shell electrons from the iodine atoms. Nearly all of the photon energy was transferred to electrons, and only a small fraction of low-energy photons interacted with an iodine L-shell electron (with a binding energy of 5.19 keV) to produce lower-energy X-rays through the photoelectric effect.

Within the measured X-ray energy range, the NaI(Tl) crystal exhibited varying degrees of "excess" light output, which can also be explained by the sequence of the photoelectric effect cascade. The low-energy electron response demonstrated an "excess" and reached its maximum value at ~14 keV, as shown in Fig. 16. Therefore, when photons undergo a series of interactions to produce multiple low-energy secondary electrons, a "burst" phenomenon occurs in the light output, which also explains why the photon response reached a maximum value at approximately 30 keV instead of 14 keV. As the incident photon energy increased, the light output gradually decreased but remained above 100%, which was owing to the more complex distribution of secondary electron energies, resulting in numerous secondary electrons with energies lower than 6 keV. The electron response below 6 keV exhibited a "deficient" luminous response, which formed a so-called "compensation" effect with the "excess" phenomenon observed in the tens of keV range.