Introduction

The study of exotic shapes of nuclei is an exciting field that has opened new avenues of research in nuclear physics. Understanding the shapes of nuclei is crucial for gaining insight into the underlying physical phenomena governing the nuclear structure and behavior. When nuclei are excited to high energies or exhibit a high angular momentum, they can exhibit a variety of exotic shapes, such as linear-chain, toroid, cylinders, and bubbles, which are not emerge under normal conditions. The toroidal structure of the nucleus was first proposed by Wheeler [1]. Wong systematically studied the conditions for the existence of toroidal nuclei in medium-and heavy-mass regions [2-4] and light-mass regions [5, 6]. Recently, various sophisticated Hartree-Fock (HF) microscopic methods have addressed the issue of light toroidal nuclei [7, 8]. These theoretical studies suggest that these exotic shapes arise because of the interaction between nuclear, centrifugal, and Coulomb forces. Exotic resonance peaks at very high predicted excitation energies in the 7α disassembly of ²⁸Si were recently observed, which matched well with the excitation energy of the toroidal nuclei [9-12], indicating the successful population and detection of toroidal high-spin isomers.

The Hoyle state has important implications for the nuclear reactions and nucleosynthesis processes that occur in stellar environments. ⁸Be and ¹²C nuclei exhibit distinct cluster structures, such as the well-known Hoyle state of ¹²C and the α+²n+²n cluster structure of ⁸He, which closely resemble the 3α-condensate-like structure of the Hoyle state [13]. The Hoyle state is the key to understanding the nature of nuclear forces and nuclear structures. Besides, some studies have demonstrated the emergence of a π-bond linear-chain molecular rotational band in ¹⁴C [14]. Recently, new evidence for a predicted Hoyle-like structure in ¹⁶O was found [15]. Research on multiple clustering configurations in ²⁴Mg yielded significant results [16]. In addition, typical clustering structures in ¹²Be and linear-chain clustering structures in neutron-rich ¹⁶C have been observed [17, 18], indicating that clustering is a general phenomenon observed in light nuclei [19-22]. Therefore, it is plausible to assume that heavier conjugate nuclei have similar cluster states.

The excited states of clustering and toroidal nuclei tend to form exotic shapes that can decay into multiple α clusters. Experimental investigation of nuclei with α-cluster states requires the precise measurement of multiple α particles emitted during the decay process [23, 24]. To study these phenomena, advanced experimental techniques have been developed that can fit the requiement of the measurement of multiple α-particle events with high resolution.

The coincident detection of these particles reveals crucial insights into the fragmentation process of nuclei, which helps in understanding the underlying physics of the nuclear structure and decay mechanism. Several detectors have been specifically developed for measuring multiple α particles and have been used in various research facilities worldwide. One method of studying nuclear reactions involving multiple α particles is to use detectors that can measure the energy and direction of each α particle. The Cylindrical Array for Tracking and Spectroscopy (CATS) in the Grand Accélérateur National d’Ions Lourds (GANIL) consists of two low-pressure multiwire proportional chambers that can detect and identify α particles at a high counting rate [25]. A state-of-the-art 4π array of charged-particle detectors called ChAKRA works at the Variable Energy Cyclotron Center, which facilitates high-resolution charged-particle reactions and spectroscopy studies [26]. The FAZIA can detect the Fermi energy domain of charged particles based on three telescope stages [27]. CSHINE, a detector for studying the state of asymmetrical nuclear matter, can offer opportunities for experimental studies on the collision dynamics and nuclear equations of state in heavy-ion reactions at Fermi energies [28]. Peking University teams performed calibration tests on two annular detector arrays and produced outstanding results in discriminating light-charged particles [29].

The measurement of multiple α particles is a hot topic in nuclear physics because it can provide new insights into the exotic structure and dynamics of the nuclei. Multiple α particles from clustering nuclei decay are challenging to measure owing to the limitations of the solid-angle covering and low reaction cross-section. High-resolution and high-sensitivity detectors are required to reconstruct the breakup process of nuclei that emit multiple α-particles. However, these detectors are rare and expensive, and they must deal with a large amount of background information that can obscure rare events of interest. Therefore, new methods are required to reduce background interference and enhance the signal-to-noise ratio [30-32]. The development of specialized detectors and innovative data analysis techniques is essential for advancing this field of research. Recently, machine learning methods have been used to study and analyze Hoyle states [33, 34] and clustering structures [35], which can be used to classify and predict experimental data. The design of compact and dedicated detectors that can address specific experimental difficulties and challenges, particularly in sophisticated experiments used to explore interesting clustering phenomena in nuclei [36-39]. The following sections introduce the specific structure and detection performance of the detector in terms of design, construction, simulation, and measurement.

design and construction

The detector consists of two layers of double-sided silicon strip detectors (DSSDs) and CsI detectors with a frame arranged to maximize the sensitive area for particle collection and detection. Frame design is crucial, as shown in Fig. 1. Telescope arrays are built with aluminum frames because aluminum is low-cost, lightweight, and the reaction and activation cross sections of aluminum are low, the impact on detection is small. Therefore, the front frame of the cesium iodide is made of high-purity aluminum.

Fig. 1Full-screen View

(Color online) Exploded view of the charged particle detector and the view of the telescope array

The overall detector structure can be broadly divided into four parts. As shown in Fig. 1, the gap between the two DSSDs of type BB7 is 10 mm. To prevent the DSSDs from being damaged by the tension of the Kapton cables, four aluminum pads are attached to secure the Kapton cables.

A custom-made frame fits the trapezoidal CsI tightly and protects it from damage. The frame also contains a slot for the signal wire of the DSSDs. The cesium iodide crystal is sandwiched between a reflective layer and an aluminized film on the front surface to collect light.

The optoelectronic conversion readout model consists of 25 silicon photomultipliers (SiPMs) and their power supply and control circuits. Each SiPM is attached to a CsI crystal. The frames ensure that the SiPM and CsI are well aligned so that the scintillation from the CsI can be collected and converted into a charge signal by the SiPM as much as possible. The frames also provide mechanical support and stability to the module and prevent the CsI from sliding out of position. The SiPM signal readout model incorporates a temperature feedback circuit that can correct the signal changes due to the temperature.

The signals from the four 34-channel signal cables from DSSDs and 25-channel signal lines from SiPMs are collected using a circuit board connected to the electronics analysis module. The 25-channel signal lines are split into common 16-channel signal cables that can match various data acquisition modules.

In particular, a Si-CsI combination detector for multiple α particle coincidence measurements can detect the energy and position of multiple α particles with high precision [40-42]. This can help to explore the fundamental laws of nature governing the interactions of these particles. This design utilizes 25 CsI crystals, each of which is an oblique prism with a hypotenuse pointing towards the collision center, causing the α particles to deposit energy in only one crystal. The front and rear sides of each crystal measured 12.96 mm×12.96 mm and 15.16 mm × 15.16 mm, respectively, at a height of 50 mm. The 5×5 CsI crystals were sandwiched between TiO₂ for good reflection and combined into the frustum of a square pyramid with dimensions of 66 mm × 66 mm on the front side and 77 mm × 77 mm on the rear side. An array of 25 CsI crystals was machined from a large piece of crystal to ensure that their physical properties were similar, and TiO₂ was sandwiched between the crystals to act as a reflection layer and glue them together. This design renders the telescope array robust and compact.

The detector consists of three layers: two DSSDs and a CsI scintillator. The BB7-type DSSD from Micron Semiconductor Ltd was used to measure the position and energy loss of the incident particles. BB7 type DSSD, which has a larger sensitive area and narrower strips than the W1 type, has an active area of 63.96 × 63.96 mm, which consists of 32 strips, approximately 2 mm wide, on each side. DSSDs with thicknesses of 300 mm, 500 mm, and 1000 mm were purchased depending on the experimental requirements. This type of detector is suitable for high-resolution measurement of charged particles. Heavy ions deposit full energy in the DSSDs, whereas lighter particles such as α punch through the DSSDs and hit the CsI, where the residual energy is deposited. This configuration allows the detector to identify and locate multiple α particles simultaneously, which is suitable for various applications that require a high angular resolution for charge particle detection.

The semiconductor material of the Si detector forms a p-n junction, which makes it highly sensitive to charged particles. The detector can also locate the position of the particle interaction within the detector with a high spatial resolution, which is essential for accurately distinguishing multiple hit events. Moreover, the detector has a low threshold level that allows the detection of very low-energy particles.

By combining the signals from both layers of DSSD and applying kinematic judgments, the particle momentum can be accurately determined. The hit position can also be used in conjunction with the final CsI scintillator array to reduce uncertainty in the direction of the particle momentum. This can significantly improve the accuracy of particle momentum determination by reducing the effects of multiple hits and detector resolution.

The design of two layers DSSDs allowed us to obtain more values of energy or energy loss for each particle combined with the CsI array. This enables us to identify the type of particle using the ΔE - E method.

The Si-CsI detector is a versatile device that can be used for multi-alpha-particle detection. It combines the advantages of a Si detector, which can determine the position and energy of the particles with high precision, and a CsI scintillator. The SiPM is a key component of the detector, as it has high sensitivity and a fast response time, allowing for accurate detection and measurement of low-energy particles [43-45]. SiPMs coupled with scintillator crystals such as lutetium–yttrium oxyorthosilicate and LaBr₃(Ce) crystals have been highly sought after in various fields [46, 47]. The combination of SiPMs and CsI exhibits favorable characteristics in terms of detection performance. The high sensitivity and small size of SiPMs enable detectors to achieve high spatial resolution and precise energy measurements. In addition, SiPMs have good single-photon resolution, providing high-precision photon counting and particle identification capabilities.

One challenge in using DSSD is the possibility of multiple α particles simultaneously hitting the DSSD. The combination of the X position from the front side and Y position from the back side will lead to a multi-value for position measurement if more than one particle hits the DSSD, which makes it difficult to accurately calculate the momentum of the particle. To overcome this issue, an additional layer of DSSD can be used to obtain multi-channel signals and striking positions. Using two layers DSSDs provides an additional set of positional information (other X and Y positions). The real hit position should be on the same line as the reaction center, which is the target. Based on this, we can determine the real positions of double-hit events.

SiPMs are ideal for compact detectors owing to their high integration and small size. Previous studies have indicated that the spectral response of SiPMs is compatible with their CsI emission spectra. Because the SiPM+CsI can detect γ, it can be used as a portable dosimeter for environmental dose equivalent and environmental dose rate equivalent measurements [45]. The combination used for proton detection consists of well-separated protons and deuterons at energies below 12 MeV. [48]. Using the Pulse Shape Discrimination (PSD) method, α particles can be easily separated from β-γ [52, 51]. In addition, the CsI crystal coupled to the SiPM was used to detect α particles and low-energy protons and was tested using the Tandem Van-der-Graff of the INFN-Laboratori Nazionali del Sud (LNS) [49]. Thus, it can be inferred that the CsI-SiPM combination can also be applied in heavy-ion collision experiments. SiPMs are high-performance detectors that detect and amplify single-photon signals. The advantages of SiPMs over conventional photomultiplier tubes (PMTs) are manifold, such as high photon detection efficiency, single photon sensitivity, fast response time, low operating voltage, low power consumption, and small size. They also have good radiation and magnetic resistance, which make them adaptable to various environments and conditions. Therefore, using SiPMs as back-end photoelectric signal conversion devices for CsI can enhance detection capabilities by enabling efficient light signal readout and processing.

Simulation

Geant4 provides a toolkit to simulate the detection process, which offers various models for physical processes such as elastic scattering, inelastic scattering, ionization, and trajectory refinement. These models are essential for studying the interactions between particles and different materials in a detection design. Geant4 also allowed us to define the complex detector geometries in detail. This enabled us to accurately model the detector and evaluate its performance.

The experimental results showed that the kinetic energy of α from the ²⁸Si breakup was lower than 300 MeV [10]. α particles with energies below 520 MeV can be fully stopped in a 50 mm CsI crystal. Therefore, the energy of α particles can be measured using a CsI crystal. Furthermore, α-conjugate nuclei with higher masses, such as ¹²C, ¹⁶O, ²⁰Ne, and ²⁴Mg, are mostly stopped in DSSDs. Therefore, the experiment can detect the light and heavy particles of interest simultaneously.

3.1

Angular Resolution

The DSSDs can provide the position information of the particle hitting the detector, and the θ and ϕ values of the particle emissions can be calculated using this position information. Assuming that the Z-axis is the direction of the incident particle beam, θ and ϕ can be obtained as follows: $\theta =\arctan \left(\frac{\sqrt{x^2+y^2}}{z}\right),$ (1) $\varphi =\arctan \left(\frac{y}{x}\right),$ (2) where x, y, and z are the position information obtained from the DSSDs.

Angle resolution is crucial for the performance of the system. To evaluate the desired angular resolution, we select several discrete values of θ and ϕ. The distance between the target and the detectors, which was 150 mm, was chosen to cover a forward angle of up to ± 25. The distribution of θ without ϕ restriction is shown in Fig. 2(a). The detectors can cover a ϕ angle from 0 to 360, except for the gaps between the telescope arrays. The ϕ-distribution is shown in Fig. 2(b).

Fig. 2Full-screen View

(Color online) Distribution of α particles. Panels (a) and (b) show the θ and ϕ resolutions of the telescope array, which is placed 15 cm away from the target. Black curve represents the input value of the simulation, and the red and green curves represent the angular distribution calculated with single DSSD and double layer DSSDs, respectively

As Fig. 2 shows, the FHWM of angular resolution for θ ranges from 0.2 to 0.4, whereas the FHWM of angular resolution for ϕ is approximately 2.2. The measurements of θ and ϕ show a noticeable difference in the angular resolution capability between the single DSSD and double-layer DSSD. The double-layer DSSD performs better in terms of angular resolution capability. These angular-resolution capabilities affect the reconstruction of fragmented nuclei during multiple α events. Hence, the use of two layers of DSSDs enables more precise event reconstruction. The next section illustrates the differences in the reconstruction of the particle excited states between single- and double-layer DSSDs.

3.2

Event Reconstruction

By collecting and analyzing the data of the particles emitted from the nuclear collision process, we can infer the dynamics and nuclear state of the collision event. Event reconstruction is a crucial technique that allows physical information to be drawn from data. The performance and accuracy of event reconstruction are essential parameters affecting the performance of charged-particle telescope arrays.

The outcome of low-energy particle collisions can be characterized by several parameters, such as the excitation energy of the fragment before it decays and the angular distribution of the fragment. These parameters provide valuable information on the dynamics and mechanisms of the collision process, as well as the properties and structures of the particles and fragments involved. Therefore, it is essential to measure and analyze the experimental parameters of low-energy particle collisions. Important and interesting physical parameters, such as Ex denote the excitation energy of the projectile nuclei, and E_tot denotes the total kinetic energy of all fragments in the laboratory frame. $E_x={\displaystyle \sum }{K}_{\text{c}\text{.m}\text{.}}-Q$ (3) and $E_{\text{tot}}={\displaystyle \sum }{K}_{\text{lab}}+K_{\text{recoil}}$ (4) where K_c.m. denotes the kinetic energy in the center-of-mass frame of the summed particles. Q is the Q-value of a nuclear reaction, which represents the difference between the masses of the initial reactants and final products. K_lab denotes the kinetic energy in the laboratory frame, and K_recoil represents the kinetics of the recoil nuclear energy calculated by the conservation of energy and momentum.

This information is crucial for gaining a more comprehensive understanding of the physical processes underlying an experiment. By combining the cascade decay process, we can gain insights into the fundamental properties of the particles involved as well as the energy distribution and dynamics of the system as a whole. In addition, according to the charge multiplicity distribution, the temperature of the heavy-ion collisions can be determined, which can be applied to analyze the reaction dynamics [50].

This spectrum from ²⁸Si fragmented into 7α particles [10] was used as an input for Geant4 simulation to model the detection process, and the α particles hit the detectors event-by-event. Such simulations are more realistic and allow for better evaluation and analysis of the performance of the detector under experimental conditions. However, based on these data, it is estimated that approximately 20% of the 7α events may be lost because of the detection geometry efficiency.

Figure 3 shows the excitation energy distribution of ²⁸Si reconstruction from 7α. It is evident that the calculated result with double DSSDs matches the simulated input. A single DSSD shows poor performance for the 7α events. Because some events respond simultaneously on multiple silicon strips, this can interfere with the position resolution of a single DSSD, whereas double DSSDs can eliminate such effects through momentum analysis.

Fig. 3Full-screen View

(Color online) Panel (a) shows the excitation energy distribution of ²⁸Si reconstructed by 7α particles. The panel (b) shows the distribution with a restriction on the input value between 83 MeV and 85 MeV

This array of charged-particle detectors was specially designed and optimized for α particle detection. It can detect the 7α particle events that occurred in the experiment, as well as the fragmentation of α-conjugated nuclei into Nα events. By analyzing the data from these events, we can reconstruct the excitation energies of the nuclei.

One possible explanation for the occurrence of 7α particles might be the cascade decay of ²⁸Si, which means that the decay product may contain other α-conjugated nuclei, such as ⁸Be and ¹²C. To investigate this hypothesis, the data from the α-conjugated nuclei should be analyzed. Reconstructing the cascade decay process of ²⁸Si to understand how it produces 7α particles is a novel approach for studying the nuclear structure and dynamics of ²⁸Si and its decay products.

The excitation energy of ⁸Be is low, and the 2α particles from the decay have a very small emission angle in collisions, which requires a high angular resolution to detect the 2α event. ⁸Be nuclei will be produced in large numbers in the reaction, indicating that there is a high rate of double-alpha hit events in the experiment. Therefore, it is important to simulate how the detector responds to the fragmentation events of ⁸Be.

Figure 4(a) depicts the excitation energy spectra of ⁸Be reconstructed using 2α-particles. When 2α hit the detector simultaneously, two sets of X-Y values are obtained, corresponding to two sets of spatial positions. The single-layer DSSD cannot distinguish the real position of α hit, which causes the result to deviate from the input value. Double-layer DSSDs provide another set of spatial positions from which the hit position can be determined through momentum analysis.

Fig. 4Full-screen View

(Color online) Excitation energy distribution of ⁸Be breaks up to 2α particles and ¹²C breaks up to 3α particles

In addition to ⁸Be, ¹²C can also be produced during the reaction. The production of ¹²C in stars via the triple-alpha process depends on a specific resonance of ¹²C, called the Hoyle state. This resonance has important implications for nuclear structure theory and nuclear astrophysics applications. It is essential to evaluate the ability of the detectors to reconstruct the ¹²C fragmentation events that occur in the Hoyle state. The simulation results are presented in Fig. 4(b). In the simulation for reconstructing ¹²C, the double-layer DSSDs outperformed the single-layer DSSD.

As shown in Fig. 4, the charged-particle telescope array reconstructs the excitation energies of ⁸Be and ¹²C with reasonable accuracy. The α particles derived from the double-layer DSSD provided more accurate excitation energies than those derived from the single-layer DSSD. Therefore, a double-layer DSSD design is required for this purpose.

Moreover, the results demonstrate that the telescope array is versatile and suitable for various experiments, in addition to those involving the disintegration of ²⁸Si into 7α particles. It can also achieve good performance in experiments that generate multiple α particles or multiple fragments of different masses, owing to its high-angle resolution.

The telescope array exhibited remarkable performance and accuracy in the excitation energy spectra of the reconstructed nuclei. Thus, it is a vital tool for studies involving these processes.

measurement

The simulation results indicate that the detector meets the performance requirements of the experiment; however, further validation is necessary to assess its actual performance. At present, the evaluation of the capability of the detector to detect charged particles is limited to the use of an ²⁴¹Am source. The decay of ²⁴¹Am primarily produces α particles with an energy of 5.486 MeV. These α particles with the low penetration depth can be blocked using a single-layer DSSD. Therefore, the energy resolution can be determined separately for the DSSD and CsI components. The energy resolution of the cesium-iodide scintillation detector was test.

The energy spectrum of the telescope array consists of 25 CsI crystals coupled to 25 SiPMs with a 30 V voltage and gain of 20 on the operation amplifier circuit, as shown in Fig. 5. It can be seen that there are small differences in performance for CsI crystals. This may be due to the variation in the α spectra because of the heterogeneity of the CsI crystals, although they are from one large block of CsI. In addition, the position of the radioactive source during the measurement may influence the results.

Fig. 5Full-screen View

(Color online) Test results of 25 CsI+SiPM detectors with the ²⁴¹Am α source. The data points are fitted with a Gaussian function

Figure 6 shows that the energy resolution is approximately 9%. Compared with the traditional CsI and PMT coupling design, coupled with SiPM can achieve comparable energy resolution [52, 51].

Fig. 6Full-screen View

(Color online) Test results of 25 CsI+SiPM detectors. Channel number is the readout

According to Fig. 7, the energy resolution of the CsI+SiPM composite detector depends on the voltage applied to SiPM. A higher voltage results in a higher gain, a smaller dynamic range, and better energy resolution. However, when detecting a particle with high energy, the increased noise and saturation effects caused by high voltage can affect the detector resolution. To detect high-energy, even up to 300 MeV α particles, the voltage applied to SiPM should be set as low as possible. However, the overall performance of the telescope array for high-energy particles, including the energy resolution, crosstalk, and charged-particle identification capability, must be assessed by performing online beam tests.

Fig. 7Full-screen View

(Color online) Performance of the CsI+SiPM detector under different operating conditions. Channel numbers (red line) and energy resolution (black line) depend on the voltage applied to the SiPM. Channel number is the readout from MDPP-32

summary

A novel detector array consisting of two DSSDs and a 5×5 cesium iodide scintillator array coupled with a SiPM array for particle identification and tracking of particle trajectories was designed and tested aiming at the detection of multiple α particle events with high position resolution. The high sensitivity and excellent timing performance of SiPM make it a good light signal readout module. CsI+SiPM detectors can be used in experiments to detect protons or deuterons with low energy. However, this is the first attempt to use the CsI+SiPM array to detect high-energy particles in heavy-ion collisions. The compact and robust telescope array is suitable for various experimental scenarios owing to the small size of SiPM and the sandwiching technology applied for CsI array.

Using the Geant4 tookit, the detector responses to α particles with different energies and angles have been simulated. The simulation results indicate that the detector array has high angular and energy resolutions, enabling accurate distinguishing of multiple α particle events. Additionally, the reconstruction result of ²⁸Si excitation energy using 7α is satisfactory. This telescope array coupled with SiPM is a novel design for nuclear physics experiments, which can be used not only in experiments investigating exotic toroidal structures but also in future experiments to study the excitation states involving nuclear clusters, contributing to the exploration of the decay and dynamics of exotic nuclear shapes.