The neutron array of the compact spectrometer for heavy ion experiments in Fermi energy region (2024)

2.1 Neutron detectors

Plastic scintillators have been extensively used in fast neutron measurement[28, 29] due to its high neutron detection efficiency and short light decay time. In our neutron array, each neutron unit consists of a $\rm 15~{}cm\times 15~{}cm\times 15~{}cm$ plastic scintillator coupled with a 2-inch photomultiplier tube (PMT) of Hamamatsu R7724, which is attached to the socket and base of Hamamatsu E5859-03. For the plastic scintillator, its C-H ratio is 1:1.1, the light decay time is 2.4ns, and the relative light yield is 50$\%$ $\sim$ 60$\%$ of the anthracene crystal. For the PMT, its transit time and transit time dispersion are 29 ns and 1.2 ns, respectively. The surface of the plastic scintillator is covered with polished aluminum foil of $\rm 15\mu m$ thickness to reflect photons, and the aluminum foil is packed with black PET plastic to avoid ambient light. The PMT and scintillator are coupled by optical silica gel to improve the light transmission efficiency. Finally, the scintillator and PMT are packaged in $\rm 5mm$ thick duralumin shell. Figure 1 (a) presents the schematic plot of one neutron detector unit.

To ensure proper space efficiency and energy resolution in the beam experiment, the 20 neutron units are placed in 5 columns and 4 rows on the spherical surface being 200 cm to the target. The units are mounted on a duralumin frame, and their relative positions are determined by the assembly holes on the frame, as shown in Figure 1 (b). The angular distance between each pair of neighbouring detectors is 6^∘ with respect to the target both horizontally and longitudinally.

2.2 Geant4 simulation

For time resolution, we have simulated the time difference of the muon passing through two vertically placed neutron units. The vertex of the muon is sampled uniformly in a 30 cm$\times$ 30 cm plane at the top of the upper unit, and its direction and energy is sampled according to the modified Gaisser formula[33]. Figure 3 (a) shows the energy deposition distribution of the muon in the two units. The distribution shows approximately two orthogonal straight bands. The events in the yellow circle indicate the muon crossing the two units vertically, resulting in nearly equal energy deposit. The vertically incident muon events are selected. The signals of the units in coincidence is then fitted by using the double Gaussian function ( shown in Figure 2), from which the time corresponding to the 30$\%$ peak height on the rising edge is defined as the arrival time of the muon. Figure 3 (b) presents the spectrum of the time difference of two units fired by vertically incident muons. The Gaussian fit yields a standard deviation of 249.6(5) ps for the total resolution of the time of flight.

To estimate the detection efficiency, mono-energetic neutrons are generated isotropically from the target position. The energy is set in the range from 1 MeV to 100 MeV. The influence of the threshold to the efficiency is also tested in the simulations. The neutron cross-sectiondata “G4NDL4.5” is adopted in the simulation. Due to quenching effect, the observed energy($E_{\rm obs}$) is usually lower than the actual neutron deposited energy($E_{\rm real}$), so we use the curve of quenching factor varying with neutron energy of plastic scintillator[34] to correct the simulated neutron deposited energy, which is smeared by a Gaussian random dispersion of an energy resolution of 40$\%$, which is typical for plastic scintillators[35, 36]. The detection efficiency at a certain energy is defined by the ratio of the events where the energy deposit (mainly induced by the $np$ scattering) exceeds the threshold to the total incident events of a mono energetic neutrons. Figure 4 shows the variation of the detection efficiency as a function of the neutron energy at different threshold. With the increase of neutron energy, the detection efficiency first increases rapidly before it declines as a function of the incident neutron energy. Interestingly, when the neutron energy is lower than 20 MeV, the detection efficiency exhibits some oscillations due to the capture and fission cross section of low-energy neutrons[37]. When the incident neutron energy exceeds 20 MeV, the characteristic peak of the energy deposit spectrum far exceeds the threshold values.

4.1 Detector Setup

In the experiment, eight light charged particle telescopes and four BaF₂ detectors were installed in the Large Scattering Chamber (LSC) with 1.5 m inner diameter located at the last focal plane of RIBLL. Figure 7 presents a picture of the detector setup in the experiment. Telescope 1$\sim$6 are mounted to measure the charged particles of $Z\leq 6$ in the polar angular range $25^{\circ}<\theta_{\rm lab}<65^{\circ}$ and azimuthal angular range $40^{\circ}<\phi_{\rm lab}<120^{\circ}$ . Each telescope consists of a single-sided silicon strip detector (SSSD), a double-sided silicon strip detector (DSSD) and a $3\times 3$ CsI(Tl) scintillator array. For the performance of the telescopes, one can refer to [20] . Telescope 7$\sim$8 consist of ionization Chamber, DSSD and a $3\times 3$ CsI array [38], mounted at $\theta_{\rm lab}=90^{\circ}$ and $-70^{\circ}$, respectively, to measure the evaporated charged particles. A 15-unit CsI hodoscope, namely CSHINE-GAMMA [21], surrounded by thick plastic scintillators, was mounted out of the LSC at $\theta_{\rm Lab}$ = -110^∘ and 115 cm to the target, to measure the Bremsstrahlung $\gamma$-rays produced in the heavy ion reactions.

In addition to the existed detectors, The $4\times 5$ neutron array and one liquid scintillator barrel have been newly mounted on CSHINE to measure the neutrons. The liquid scintillator was placed at $\theta_{\rm lab}=80^{\circ}$ and 513 cm away from the target. The geometrical parameters ($R$, $\theta_{\rm lab}$, $\phi_{\rm lab}$) of the $\rm BaF_{2}$ detectors and the neutron array are listed in Table 1 and 2 respectively. Here $R\rm(cm)$ is the distance from the center of scintillator to the target, $\theta_{\rm lab}$(^∘) and $\phi_{\rm lab}$(^∘) represent the polar angle and the azimuthal angle in laboratory, respectively.

The readout electronic system of the neutron array, the $\rm BaF_{2}$ $T_{0}$ detectors and the liquid scintillator detector in the experiment is presented in Figure 8. The signal from each PMT is transferred to a constant fraction discriminator (CFD) and the thresholds of the CFDs for neutron array were set to a common level of $-60$ mV, corresponding to the $\gamma$ energy around 1 MeV in the beam experiment. The NIM logic fast timing output was transferred to the gate and delay generator (GDG) from the front panel of CFD to set a suitable delay before be digitized by the time-digit converter (TDC) CAEN V775N. And the ECL logic fast timing output was transferred to the trigger unit of CAEN V2495 from the back panel of the CFD to generate a global experiment trigger based onFPGA technology. The negative-polarized amplitude signals from the back panel of CFD which is a copy of the input PMT signal, were further transferred to CAEN N568E spectrometer amplifier, the OUT signals of N568E were digitized by the amplitude-digit converter (ADC) CAEN V785. Both the time and amplitude information were saved by the data acquisition (DAQ) system. For the electronics of the telescopes and CsI hodoscope, one can refer to[18, 21].

To accomplish the physical goals mentioned in Section 1, a global trigger has been generated by the trigger module V2495 as shown in Figure 9. All the sub-detectors produced logic signals by front-end electronics including:(1) NA.M1: the one-body neutron signal provided by neutron array. (2) T0: the logic signal with at least one $\rm BaF_{2}$ detector fired. (3)SSD.M1 and SSD.M2: The one-body and two-body light charged particle signal provided by the DSSD of the telescopes. (4) CsI.M1: the one-body $\gamma$ signal provided by CsI-calorimeter and (5) LS.M2: the coincidence signal of the PMTs at both ends of liquid scintillator detector.The above five kinds of discrimination signalswere used to produce six coincidence logical signals as shown in Figure 9, and the global trigger signal is obtained by the OR operation of the six logical signals. The trigger system has been implemented based on the Field Programmable Gate Array (FPGA) technology. For the details of the FPGA based trigger system, one can refer to[19]. The number of events acquired with different trigger is shown in Table 3.

4.2 Neutron Spectrum

We concentrate on the analysis of the neutron array data here. To understand the performance of the neutron array in the experiment, around 4 million neutron events were analysed by selecting “$\rm T_{0}\&NA.M1$” trigger condition. Due to the manual adjustment uncertainty of the GDG, there is small difference in delay time between different $\rm BaF_{2}$ and neutron units. Formula (2) was used to fit the $\gamma$ peak on the TOF spectrum of all the combination of BaF₂ and neutron units, Figure 10 (a) shows the TOF spectrum of the $\rm 5^{th}$ neutron unit as an example by shifting all the $\gamma$ TOF peaks to zero. The abscissa is ${\rm TOF}-L/c$, where $L$ is the distance between the unit and the target position and $c$ is the speed of light. It is shown that the two components of $\gamma$ rays and neutrons are separated clearly. The overall experimental time resolution $\sigma_{\rm exp}=744\pm 40$ ps was obtained by fitting the $\gamma$ peak in Figure 10 (a) with formula (2), which is worse than the cosmic ray test result for a single unit, because in the cosmic ray test, the muon passes vertically through two units and the time variation caused by the variation of the incident position is relatively constant for the two fired units. However the fire position by the $\gamma$ rays originating from the reaction is varied due to the size of the unit, which is 15 cm in each dimension corresponding to about 700 ps uncertainty. In addition, In Figure 10 (a), an abnormal peak appears in the time range between 4 and 14 ns forms an insignificant, which originates seemingly from the background produced by a tiny portion of the beam particles hitting the vacuum pipe due to the long free space from the last quadrupole doublet to the target.

The neutron energy spectrum is obtained from the TOF distribution by subtracting the contributions of the $\gamma$ rays, the backgrounds and the small abnormal peak.For the high energy part with the TOF ranging in $-2.5\sim 16$ ns, we assume that the TOF distribution follows an exponential distribution[39, 40, 41] and use an asymmetric Gaussian distribution to fit the abnormal peak. The $\gamma$ ray peak was fit by a double Gaussian distribution. For the low energy part with TOF in 60 ns $\sim$ 150 ns, the exponential distribution with the superposition of a uniform background is adopted to describe the low energy neutrons. The ansatz (3) is used to describe the boundaries of the TOF distribution and to remove the abnormal peak and the background in the coincidence window.

Totally there are 14 fitting parameters in ansatz (3). The parameters $p_{\rm n_{0}}\sim p_{\rm n_{3}}$ are introduced for the description of the neutron spectrum, $p_{\gamma_{0}}\sim p_{\gamma_{4}}$ are for the $\gamma$ peak, $p_{\rm ab_{0}}\sim p_{\rm ab_{3}}$ are for the tiny abnormal peak and $p_{\rm bkg}$ is used to describe the uniform background on the TOF spectrum, respectively.

The fitting results are shown in Figure 10 (a) for one single unit. It is shown that the high and low energy boundaries of the TOF spectrum are well reproduced.

Figure 10 (b) presents the energy spectra of different components. By subtracting the abnormal peak (blue solid) and the background (black dashed) components, one can get the clean neutron energy spectrum (pink squares). It is shown that neither the background nor the tiny abnormal peak brings significant contribution to the neutron spectrum. The three arrows pointing to 100, 200, 300 MeV, corresponding to the TOF of 17.2, 12.9, 11.3 ns, respectively. Considering the time uncertainty of about 1 ns, the energy uncertainties at the three energy points are derived as 15, 50 and 106 MeV, respectively. With these uncertainties, the very high energy tail of the spectrum is problematic, yet the spectrum below 100 MeV is reliable and the influence of the abnormal peak is insignificant.

Figure 11 presents the neutron spectra of the five columns without correcting the detection efficiency. The abnormal peak and the background contributions are subtracted. The $\theta_{\rm lab}$ of each spectrum is averaged over all the units in the column. It is shown that the spectra exhibit approximately the exponential descending tail. An exponential function $\exp(-E_{\rm n}/T)$ was used to fit the energy spectra from 8 to 35 MeV. With the increase of $\theta_{\rm lab}$, the slope parameter $T$ decreases with $\theta_{\rm lab}$, listed here (20.40${}_{-0.07}^{+0.07}$ MeV,15.77${}_{-0.03}^{+0.05}$ MeV, 13.48${}_{-0.03}^{+0.03}$ MeV, 12.33${}_{-0.04}^{+0.03}$ MeV, 12.44${}_{-0.05}^{+0.05}$ MeV) for the 5 angles, respectively. Meanwhile, the yield of the neutrons also decreases slightly with $\theta_{\rm lab}$. Both trends are consistent with the kinetic feature of heavy ion collision in the energy domain. In addition, as shown in Fig. 11, a large number of neutrons are beyond the beam energy. It indicates that the high momentum tail of nucleons may exist as a signature of short range correlation in nuclei. Furthermore, a high statistics of two-body events of charged particles and neutrons can be utilized to analyze the neutron-neutron and neutron-proton correlation functions. Given the well detected neutrons shown here, along with the detection ability of the charged particles demonstrated in [18, 20], the feasibility of the aforementioned physics goals are promising and further prospective investigations are required.