Introduction

Proton-rich nuclei far from stability exhibit a range of unique decay processes, particularly β-delayed charged-particle emissions and direct particle emissions. Spectroscopic studies of β-delayed proton decay and direct proton radioactivity have proven to be powerful tools for investigating the intricate properties of exotic nuclei near and beyond the proton drip line. The resonant proton capture reaction rates of the continuum states in weakly bound nuclei, which play a crucial role in astrophysical processes, can be determined by studying the properties of nuclear states near the proton separation threshold [1-3]. To observe decays from these states, as well as direct proton emissions from the ground state, it is essential to employ a detection system with a low energy threshold and high detection efficiency.

The investigation of β-delayed charged-particle decay in proton-rich nuclei is typically conducted using two principal detection methods: the implantation-decay method with a silicon detector array [1-3] and the time-projection chamber (TPC) detection method [4-8]. The fundamental principles of the implantation-decay method are as follows: The nuclei of interest are implanted and stopped within a detector array. The decay energies of the β-delayed charged particles can then be measured with high accuracy, as the decay occurs directly within the implantation detector.

The correlation between implantation and decay events provides a unique opportunity to derive decay time and decay energy spectra, enabling detailed characterization of the decay properties exhibited by radioactive species. To ensure accurate measurements, the effects of dead layers in silicon detectors must be taken into account when β-delayed charged particles are stopped inside the silicon detector. This capability has driven the development of double-sided silicon strip detectors (DSSDs), which have become cutting-edge instruments for investigating these intriguing decay modes. Additionally, a germanium double-sided strip detector [9] can also serve as an implantation detector in certain experimental setups. A wide range of experiments in β-decay spectroscopy and proton radioactivity have significantly advanced our understanding of exotic nuclei properties. Notable examples include studies on ⁵⁴Zn [10], ⁴⁵Fe [11, 12], ²⁷S [13, 14], ²⁶P [15-17], ²²Si [18, 19], ²²Al [20-22], and ²¹Mg [23]. Compared to silicon detectors, time-projection chamber (TPC) measurements offer direct and comprehensive insights into decay processes. For example, TPCs have facilitated studies of two-proton emissions from ⁴⁵Fe [4] and ⁵⁴Zn [5], as well as β-decay spectroscopy [6, 7]. The TPC detection method can facilitate the establishment of angular and momentum correlations between particles in multiparticle emissions [8]. In contrast, the DSSD-based implantation-decay method provides the precision required for high-resolution spectroscopy measurements [18, 19, 24].

Conventional analog data acquisition systems have been widely employed using various standards, such as Computer-Automated Measurement and Control (CAMAC) and the Versa Module Eurocard (VME) [25-27]. An analog system typically comprises preamplifiers, shaping amplifiers, and analog-to-digital converters (ADCs) for the analog signal channel, and fast amplifiers, discriminators, and time-to-digital converters (TDCs) for timing signals. Trigger signals are generally generated by the coincidence of selected fast signals corresponding to the physical process of interest. In recent years, digital data acquisition systems (DDAQs) have become increasingly prevalent in nuclear physics experiments [28-30], driven by advancements in fast digitizing technologies. In a DDAQ system, signals from preamplifiers are directly sampled and digitized, requiring high sampling frequencies (typically exceeding 100 MHz) and high-resolution sampling (12, 14, or 16 bits) to preserve the original analog signal information [31-34]. Subsequently, energy and timing information from detector outputs can be extracted using advanced numerical algorithms applied to the recorded signal waveforms. The flexibility provided by the wide range of pulse-shape analysis methods is essential for addressing the diverse demands of nuclear physics experiments. This approach offers significant advantages over traditional analog electronics, driving major advancements in data acquisition technology [34, 35, 30]. In decay experiments, DDAQ systems enable processing at higher rates with reduced dead time. Furthermore, digital pulse processing techniques have been employed to record raw signal waveforms, resolve pile-up events [36], and distinguish between different charged particles, such as α particles and protons.

The nucleus ³²Ar and its decay [37-43], with an isospin projection of TZ = -2, have been extensively studied, providing a reliable benchmark for testing the performance of the new detection system. An experiment conducted at ISOLDE [40] observed protons emitted from the isobaric analog state (IAS) and verified the isobaric multiplet mass equation (IMME). Another study [41] focused primarily on the giant Gamow–Teller (GT) resonance. Schardt and Riisager [37] examined the limits of exotic currents in weak interactions. The decay strength and ft value for the superallowed β decay of ³²Ar were experimentally determined by Bhattacharya et al. [42], enabling the deduction of the isospin-impurity correction, ${\delta }_{\text{C}}$. Recent work at GANIL [43] further investigated the Fermi strength and GT strength distributions in the decay of ³²Ar, comparing the experimental results with predictions from the shell model.

In this study, we focused on the design and performance evaluation of a detector array comprising DSSDs (Fig. 1), quadrant silicon detectors (QSDs), and germanium detectors for high-precision measurements of β-decay spectroscopy in proton-rich nuclei within the sd-shell region. An advanced DDAQ system, based on the Pixie-16 module developed by XIA LLC [44], was employed during the experiments. Section 2 describes the detector array configuration and the DAQ system, and particle identification capabilities demonstrated in the in-beam test. The detector responses to charged particles and γ-rays obtained during offline testing, are detailed in Sect. 3. Experimental results showcasing high-precision measurements of the β decay of ³²Ar, as an application of the detection system, are presented in Sect. 4. Finally, a summary of the study is provided.

Fig. 1Full-screen View

(Color online) Schematic layout of the detection system (not to scale)

Experimental Setup

2.1

In-beam Test

The performance of the detection system was evaluated using the β-delayed proton emitter ³²Ar at the first Radioactive Ion Beam Line in Lanzhou (RIBLL1) [45]. A K450 separate sector cyclotron (SSC) provided a 69.44 MeV/u primary beam of ³⁶Ar¹⁸⁺ with an intensity of ~87 enA. The secondary beam was generated via projectile fragmentation of the ³⁶Ar primary beam on a 1000 μm thick ⁹Be target. The average intensity and purity of ³²Ar in the secondary beam delivered to the detection chamber had an average intensity of 0.61 particles per second (pps) and a purity of 0.086%. Data collection for ³²Ar spanned 17.8 h. The ³²Ar ions were separated and purified by the RIBLL1 facility and identified through energy loss (ΔE) and time-of-flight (TOF) measurements. The TOF was determined using two plastic scintillation detectors positioned at the two focal planes of RIBLL1. Particle identification and beam optimization were carried out using LISE++ simulations [46] and calibration using secondary beams. Upstream of the detector setup, following the two plastic scintillators (T₁ and T₂), a series of aluminum foils operated by three stepping motors were installed as energy degraders. The thickness of the aluminum degraders could be finely adjusted in small increments of 5 μm, with a full range of 315 μm, enabling precise tuning of the stopping range for ³²Ar ions within the DSSDs. A total of 3.9 × 10^{4 32}Ar ions were implanted into DSSD1 and DSSD2, with implantation proportions of 82.2% and 17.8%, respectively.

A two-dimensional identification plot of ΔE versus TOF for the implanted ions is shown in Fig. 2, demonstrating the system's ability to effectively distinguish among nuclei such as ³²Ar, ³¹Cl, ³⁰S, and ²⁹P.

Fig. 2Full-screen View

(Color online) Two-dimensional identification plot of ΔE versus TOF for the ions in the secondary beam is shown. The horizontal axis represents the time difference between scintillators T1 and T2, while the vertical axis corresponds to the energy loss in the SDΔE2 detector. An additional coincidence gating condition based on the energy loss in the QSDΔE1 detector is applied to enhance the identification

2.3

Digital data acquisition system

The DDAQ system consists of a crate, several Pixie-16 modules from XIA LLC [44], a crate controller module, and a trigger module. The primary component is the Pixie-16 6U CompactPCI/PXI crate, which accommodates additional plug-in units, provides localized power, and facilitates communication of digital signals between units. Additionally, a PCI-8366/PXI-8368 crate controller is included, serving as the commander for the other modules and enabling communication with the computer via fiber optic cable. The computer sends commands to the DAQ system and retrieves data from the memory of the modules through the crate controller, at a rate of up to 109 MByte/s.

The Pixie-16 modules serve as digitizers, converting analog signals into digital data using a 12/14/16-bit ADC at sampling rates of 100/250/500 MHz. Seven 250 MHz Pixie-16 modules with 14-bit ADCs were employed in this experiment. The ohmic and junction sides of two 16×16 DSSDs were connected to four modules with 64 channels, while the remaining detectors were connected to the other three modules. These modules derive energy and time information from the input signal based on a predefined algebraic formula [50]. The Pixie-16 module combines the functions of a shaping amplifier, discriminator, ADC, and TDC, typically found in traditional DAQ systems. The programmable MicroZed-based trigger I/O (MZTIO) [51] module acts as the logic trigger component, routing signals between the PXI backplane and crate front panel and creating logical combinations within a field-programmable gate array (FPGA) chip. Synchronization of different crates is achieved using the Pixie-16 clock and the trigger I/O module. Further details on the technical implementation, including clock synchronization and trigger distribution between separate crates, can be found in [52, 53]. Figure 3 shows a photo of a typical digital data acquisition system.

Fig. 3Full-screen View

(Color online) Depiction of the data acquisition system

Detector signals were initially digitized using the Pixie-16, with subsequent signal processing performed by a set of real-time algorithms in the firmware. When a physical event is detected via local or external triggers, its data are first saved in the FPGA's local memory and then transferred to an external first-in, first-out (FIFO) memory [54]. Data in the FIFO are sent to the host computer via a fiber optic cable and then transmitted to the data storage center. Parameters such as the rise and flat-top times of the trapezoidal filter are set through a graphical user interface (GUI) using specific algorithms derived from digital signal processing (DSP). The trigger and energy filter parameters for the rise and flat-top times in the present experiment are listed in Table 1. An internal or external trigger can be selected from the DDAQ system. For the internal trigger, a specific threshold was established for the Pixie-16 modules. The multiplicity and/or coincidence in each Pixie-16 module or between modules were determined using the system FPGA [34]. A programmable MZTIO module was used to implement efficient and flexible trigger patterns for external triggers. The MZTIO module is based on a custom carrier board and a commercial MicroZed Zynq processor module, which combines an FPGA fabric (for trigger logic) and an ARM processor (running Linux) on the same chip. All Zynq firmware and software packages were customized for DDAQ [55]. The external triggering mechanism was implemented as follows: The multiplicity triggers extracted from each selected channel in the immediately neighboring Pixie-16 modules were sent to the low-voltage differential signaling (LVDS) inputs of the MZTIO through the RJ45 connectors. Subsequently, a corresponding trigger signal, called a "valid trigger," based on user-defined logic, was generated and sent back as a module validation trigger for the Pixie-16 modules.

Table 1Full-screen View

Trigger and energy filter parameter settings for the rise and flat-top times of this experiment

Parameter	Detector type
	Silicon	HPGe
Trigger Trise (μs)	0.104	0.104
Trigger Tflat (μs)	0	0.104
Energy Trise (μs)	3.040	5.506
Energy Tflat (μs)	0.256	1.600
τ (μs)	150	50

Show more

With the powerful trigger logic system of DDAQ [56], complex logic operations of signals from different detectors can be easily implemented. An example of trigger generation is provided in the literature [55]. The trigger system used in the experiment is shown in Fig. 4. The logic trigger signals for the two DSSDs were generated by the coincident signals between the junction and the ohmic sides. After passing through the analog constant-fraction discriminator (CFD) module ORTEC 935 [57], the signals from the two plastic scintillator detectors were converted using a time-to-amplitude converter (TAC) to obtain the TOF signal. The ΔE detectors were triggered by a logical OR operation between the QSDΔE1 and SDΔE2 detectors. The trigger signal was delayed to align with the TOF signal and stretched to a width of approximately 500 ns.

Fig. 4Full-screen View

Schematic of the main logic trigger generation for detectors is shown. A and B represent the ohmic and junction sides of the DSSD, respectively. For further details, refer to the text

To better suppress the trigger rate, the ΔE detectors can also be triggered by the valid coincidence signals between the ΔE-TOF and DSSD signals (yellow line). All trigger signals were sent to and configured in the MZTIO module. The other QSDs and Ge detectors used in this experiment were self-triggered to capture the signals.

offline and in-beam performance

A ²³⁹Pu-²⁴¹Am-²⁴⁴Cm triple-α source was used for preliminary energy calibration of the DSSDs and QSDs. The primary peak energies of the triple-α source were 5157, 5486, and 5805 keV. Energy calibration was conducted independently for each strip before analysis. Using a linear calibration model, $E(x)=ax+b$, where x represents the ADC channel number, the coefficient a exhibited fluctuations of less than 5% across all strips, while b shifted by less than 1% of the full energy range (10 MeV). The energy spectra obtained from the pixels of the 10th junction strip and the 10th ohmic strip in DSSD2 are shown in Fig. 5. Constrained by the energy resolution of the detector, a low-energy tail emerges due to contamination of the primary peak by non-primary peaks. For example, the principal α-decay paths of ²³⁹Pu are 5157 keV (71%), 5144 keV (17%), and 5106 keV (12%) [58]. The results obtained from the Gaussian fit indicate that for the 5157 keV energy peak, the energy resolutions of both the junction and the ohmic strips are approximately 70 keV (FWHM). The formal energy calibration of the DSSDs was performed using known β-delayed protons from ²⁵Si [59] and ²⁹S [60] decay during the experiment. This calibration provides more reliable energy measurements as it does not require additional corrections, such as for the incident angle of the particle or the thickness of the dead layer.

Fig. 5Full-screen View

α energy spectrum for the pixel in the 10th junction strip and the 10th ohmic strip is presented. By applying a Gaussian fit to the 5157 keV peak, the junction strip yields an energy resolution of 71 keV (FWHM)

To evaluate the detection efficiency of the DSSDs for β-delayed protons in the decay process, the Monte Carlo simulation was applied. In the simulation, protons were set to be emitted isotropically from various random positions given by the distributions of the ion stopping positions. The peak area of each proton group in the β-delayed proton spectra can be corrected according to the efficiency distributions to extract the true count for the intensity determination. The distribution of the implantation depth (z distribution) can be deduced from the SRIM calculation [61] using the energy-loss distributions. The detection efficiencies of the DSSDs were experimentally determined based on the known intensities of β-delayed protons from ²⁹S, which were found to be in good agreement with the simulation results shown in Fig. 6.

Fig. 6Full-screen View

Simulated and experimental detection efficiencies for β-delayed protons as a function of the proton energy in DSSD2

Energy and efficiency calibrations of the HPGe detectors were performed using ¹⁵²Eu [62] and ¹³³Ba [63] sources. The detection efficiencies of the standard sources are as follows: $\epsilon =\frac{N_{\text{det}}}{N}\mathrm{,}$ (1) where $N_{\text{det}}$ is the count of γ rays with a certain energy measured by the HPGe detectors and N is the count of γ rays emitted by the standard γ source. N can be calculated using the following expression: $N=N_0{e}^{-\lambda T}\cdot \text{d}t\cdot I_{\gamma }\mathrm{,}$ (2) where $N_0{e}^{-\lambda T}$ is the activity of the standard γ source, T is the time from the production of the source to the experiment, dt is the counting time, and $I_{\gamma }$ is the branching ratio of the standard γ sources, as shown in Table 2 extracted from Ref. [62, 63]. The activities $N_0{e}^{-\lambda T}$ of ¹⁵²Eu and ¹³³Ba sources were 181 ± 10% kBq and 120 ± 10% kBq, respectively.

The intrinsic detection efficiency of the Ge detectors can be expressed using the following equation [64]: $\text{ln}(\epsilon )={\left\{{\left(A+Bx+C{x}^2\right)}^{-G}+{\left(D+Ey+F{y}^2\right)}^{-G}\right\}}^{-\frac{1}{G}}\mathrm{,}$ (3) where $x=\text{ln}\left(E_{\gamma }/100\left[\text{keV}\right]\right)$, $A+Bx+C{x}^2$ is applicable to the low-energy region; $y=\text{ln}\left(E_{\gamma }/1000\left[\text{keV}\right]\right)$, $D+Ey+F{y}^2$ is applicable to the high-energy region; G represents the interaction parameter between the high and low-energy components. The uncertainty in the full-energy peak efficiency shown in Fig. 7 was calculated by considering the peak fitting uncertainty and activity uncertainties of the sources. The total efficiency and energy resolution for registering γ rays at 1112 keV were estimated to be 1.52(15)% and 3.3 keV (FWHM), respectively.

Fig. 7Full-screen View

Absolute detection efficiency of the HPGe detectors for γ rays from standard sources as a function of energy. Details are provided in the text

Results and discussion

The detection of β-delayed proton decay events required a signal above the fast trigger threshold in the two DSSDs while simultaneously rejecting coincidence signals within the ΔE-TOF gate. To further suppress noise and background, the energy difference between decay signals from the junction side strips and the ohmic side strips was constrained to within ±10% of the signal value or no more than ±100 keV. Additionally, x–y pixel position information from the DSSDs was utilized to correlate ion implantation events with subsequent decay events. Each x–y pixel of the DSSD effectively acts as an independent detector, enabling the implantation rate per pixel to remain low. This design allows for a higher overall implantation rate in the DSSD, even in continuous-beam mode.

The time difference between an implantation event and all subsequent decay events occurring in the same x–y pixel of the DSSD is defined as the correlation time. As shown in Fig. 8, the decay-time spectrum of ³²Ar is obtained by summing the correlation times from all pixels in DSSD2. To reduce the influence of background at low energies, only decay events with energies above 800 keV in the DSSDs are considered. The decay-time spectrum includes a small number of random correlations, where implantation events are accidentally paired with decay events from other implantations or background disturbances. True correlated implantation-decay event pairs follow an exponential distribution, while uncorrelated pairs contribute a constant background. The fitting expression is as follows: $N(t)=H{e}^{-\frac{t\text{ln2}}{T_{1/2}}}+I\mathrm{,}$ (4) where $N(t)$ represents the total number of ions decaying as a function of time t, H is the number of ions decaying initially, I is the constant background, and T_1/2 is the half-life of the isotope. From the fit to the decay-time spectrum, the half-life of ³²Ar was determined to be T_1/2 = 99.6 ± 1.5 ms, where the uncertainty includes both statistical errors and the fitting uncertainty. This result is in excellent agreement with previous measurements, as summarized in Table 3.

Fig. 8Full-screen View

Decay-time spectrum of ³²Ar is shown at the top and residuals between experimental data and the fitting curve are shown at the bottom

The β-delayed proton spectrum from the decay of ³²Ar, measured by DSSD2, is shown in Fig. 9. Each proton peak in the spectrum is labeled with a letter "P" followed by a number, corresponding to distinct proton emission events from the β-delayed proton decay of ³²Ar. To ensure accurate decay event detection, the time difference between an implantation event and subsequent decay events was limited to approximately six half-lives (600 ms). Disturbances from penetrating heavy ions and light particles were effectively eliminated through anticoincidence with veto detectors QSD1, QSD2, and QSD3. The origin of each proton peak was identified through half-life analysis. Three distinct proton peaks were observed, and the corresponding peak intensities are summarized in Table 4.

Fig. 9Full-screen View

β-delayed proton spectrum from the β decay of ³²Ar, measured by DSSD2, is shown in the figure. Each proton peak originating from the β-delayed proton decay of ³²Ar is labeled with a letter "P" followed by a number. The black line represents the raw spectrum measured by DSSD2, while the red line indicates the energy spectrum vetoed by QSD1

The intensities of β-delayed protons can be determined using the following equation: $I_{\beta p}=\frac{N_{\text{p}}}{{\epsilon }_{\beta p}\cdot N_{\text{imp}}}\mathrm{,}$ (5) where $I_{\beta p}$ is the intensity of the decay branch, N_p represents the number of β-delayed proton decay events measured by the DSSD, ${\epsilon }_{\beta p}$ is the β-delayed proton detection efficiency, calibrated using β-delayed protons from ²⁹S in the subsequent stage of the experiment, and N_imp is the total number of implanted ³²Ar ions. Background correction is performed using the correlation time to remove background contributions from β-particles or other accidental disturbances. Thanks to the waveform digitization capability and the trigger rate employed in this experiment, it is reasonable to assume that all triggered events were successfully recorded. Consequently, unlike traditional data acquisition systems, dead-time correction was not necessary in this experiment. The intensities of each proton group obtained in the present study are in good agreement with those from previous work [43]. The overall uncertainties include both calibration parameter uncertainties and peak-energy Gaussian fitting uncertainties.

Due to the relatively low statistics, no β-delayed γ rays from the decay of ³²Ar were observed in the present experiment. However, the β-delayed γ rays from the decay of ³⁰S, which had higher implantation counts, are shown in Fig. 10 to demonstrate the measurement capability of the system. Statistically, the significant peak in the spectrum is the well-known 511-keV γ ray, originating from positron-electron annihilation. The 677-keV γ ray is assigned to the de-excitation from the first 0⁺ excited state to the ground state of ³⁰P. Its intensity was determined to be 74(5)%, which is in good agreement with the literature value of 78.4(4)% [65]. After a γ-γ coincidence check, the 1368-keV and 2754-keV γ rays were likely due to ²⁴Mg contaminants from the decay of ²⁴Al. The inset of Fig. 10 shows the two γ rays from the β decay of ³¹Cl, despite the low implantation counts. The 1248-keV and 2234-keV γ rays are assigned to the de-excitation from the two lowest excited states to the ground state of ³¹S.

Fig. 10Full-screen View

Cumulative γ-ray spectrum measured by the HPGe detectors in coincidence with the β particles from the decay of ³⁰S, as recorded by DSSD2, is shown. The inset displays the partial γ-ray spectrum in coincidence with the β particles from the decay of ³¹Cl. The γ-ray peaks are labeled with their respective energies

Additionally, the proposed detection system can be applied to measure other exotic decay modes. Further improvements and methods are under consideration, including the use of pulse shape discrimination (PSD) for silicon detectors, which can be applied to identify different charged particles using the DDAQ system.

Conclusion

A novel decay detection system utilizing an implantation method with a digital data acquisition system was developed and commissioned for the experiment on β-delayed proton decay of ³²Ar in continuous-beam mode. This setup enabled accurate identification of the implanted nuclei and subsequent decays through energy, time, and position measurements. Although the collection time in our experiment was much shorter than in previous studies of ³²Ar, a relatively high number of decay events were accumulated, and reliable results were obtained due to our enhanced experimental techniques. It would be beneficial to extract more information from future experiments with improved statistics. The detection system demonstrated its effectiveness in measuring β-delayed proton decay, and further research can be extended to studying more exotic decay modes.