Commissioning of the BRIKEN detector for the measurement of very exotic $\beta$-delayed neutron emitters

The experiments were performed using primary beams of ²³⁸U at high intensity (20-50 pnA) accelerated to an energy of 345 MeV per nucleon by the accelerator complex of the Radioactive Isotope Beam Factory (RIBF) [7]. The beam hits a beryllium target 4 mm thick producing a large number of fast reaction products which are selected by the BigRIPS in-flight separator and guided to the F11 experimental area through the Zero-Degree Spectrometer (ZDS) [8]. Each ion in the cocktail of nuclei arriving at the measuring station is identified though measurement of 1) its atomic charge Z, and 2) its mass-to-charge ratio A/Q. These quantities are obtained from the magnetic rigidity B$\rho$, the time-of-flight (ToF) and the energy loss ($\Delta E$) of the ion. This information is provided by the spectrometer and its ancillary detectors: plastic scintillation detectors, position-sensitive parallel plate avalanche counters (PPAC) and multi-sampling ionization chambers (MUSIC). The last elements of the beam line were a pair of MUSIC detectors and a thin (1 mm thick) plastic scintillation detector (F11 plastic) with an area of $12~\mathrm{cm}\times 10~\mathrm{cm}$ (see Fig. 1). The ions of interest were implanted in the AIDA detector adjusting their velocity by means of an aluminum degrader of variable thickness situated after the F11 plastic. An identification plot of the ions implanted in AIDA during the commissioning run is shown in Fig. 2. The setting of the BigRIPS spectrometer was centered on ⁷⁶Ni. Neutron-rich isotopes from cobalt to gallium were implanted, most of which are $\beta$-delayed neutron emitters. This included 475 events for the doubly magic ⁷⁸Ni.

The implantation detector AIDA [9] consists of a stack of six silicon double-sided strip detectors (DSSD) with a spacing of 10 mm between them. The PCB frame of the DSSD is suspended at the corners on thin titanium rods inside the AIDA nose made of 1 mm thick aluminum with a cross-section of $10~\mathrm{cm}\times 10~\mathrm{cm}$. The nose is closed on the beam side by an aluminized Mylar foil to ensure light tightness. Each DSSD has a thickness of 1 mm and an area of $71.68~\mathrm{mm}\times 71.68~\mathrm{mm}$, with 128 strips 0.51 mm wide on each side. The strips on the two sides are perpendicular to each other and provide high resolution position information in the horizontal (X) and vertical (Y) directions. Specially made flat cables running inside the nose bring the strip signals to the front-end readout electronics located about 70 cm away. Dual electronic chains are used to process the signals from each strip. The low-gain branch (20 GeV range) is used to process the high energy implantation signals. The high-gain branch (20 MeV range) is used to identify the much lower energy signals from $\beta$ particles emitted in the decay of the radioactive ions. The dual electronic processing, implemented using ASICs, minimizes the overload recovery time for $\beta$ registration to a few $\mu$s. The stack of Si DSSDs is positioned at the geometrical centre of the neutron detector with the electronics located outside, downstream in the beam direction. A plastic scintillation detector of thickness 10 mm (AIDA plastic) is positioned on the beam axis 120 cm downstream of the stack to detect particles that pass through.

During the experiments in October-November 2017 the AIDA detector was replaced by the WA3ABi detector [10] which consists of a stack of four Si DSSDs with 3 mm wide strips. The advantage is that these DSSDs are narrower ($50~\mathrm{mm}\times 50~\mathrm{mm}$) allowing us to move the CLOVER detectors closer and increase the $\gamma$ detection efficiency. In addition we used a new implantation-decay detector made of YSO scintillation material developed at the University of Tennessee [11, 12]. This detector consists of an array of $48\times 48$ closely packed crystals with dimension $1~\mathrm{mm}\times 1~\mathrm{mm}\times 5~\mathrm{mm}$. The array is coupled through a light guide to a H8500B flat panel type photomultiplier tube (PMT) with an $8\times 8$ segmented anode that is readout with a resistor network. Both detectors were used at the same time with WA3ABi positioned off-centre $\sim 20$ mm upstream and the YSO detector positioned off-centre $\sim 20$ mm downstream. A full description of this implantation-decay setup and its performance will be given in a forthcoming publication.

During the May-June 2017 experiments we added a thin large area Si detector to the setup. The purpose of this $\Delta E$ detector is to help in the identification of light particles (p, d, $\alpha$, …) coming with the beam. It is a single sided strip detector of quasi-rectangular shape and dimension $134~\mathrm{mm}\times 123~\mathrm{mm}$ with a thickness of 330 $\mu$m. It has 26 horizontal strips combined into two readout channels (top and bottom). The detector was placed about 50 cm upstream before the neutron detector.

The BRIKEN neutron counter consists of an array of 140 ³He filled proportional tubes embedded in a large volume of polyethylene (PE) acting as a neutron energy moderator. Very low-energy neutrons have a large interaction probability with the gas in the tubes through the reaction $\mathrm{n}+\mathrm{{}^{3}He}\rightarrow\mathrm{{}^{3}H}+\mathrm{p}$. This reaction liberates an energy of 764 keV that is easily detected. The PE moderator has external dimensions of $90~\mathrm{cm}\times 90~\mathrm{cm}\times 75~\mathrm{cm}$, with a longitudinal hole (in the beam direction) of cross-section $11.6~\mathrm{cm}\times 11.6~\mathrm{cm}$ into which AIDA is inserted from the back. The PE moderator is constructed as a stack of 5 cm thick slabs in the longitudinal direction held together by stainless steel rods passing through the corners. The lateral sides and the top of the PE volume are covered with 1 mm thick Cd sheets and additional slabs of PE of 25 mm for neutron background attenuation. The two CLOVER detectors are inserted horizontally from opposite sides into transverse holes of cross-section $11~\mathrm{cm}\times 11.6~\mathrm{cm}$ facing the stack of DSSDs. Four different types of ³He tube were used in the array and their characteristics are summarized in Table 1. The UPC tubes come from the BELEN detector [13] and the ORNL tubes come from the 3Hen detector [14]. The RIKEN and ORNL tubes were manufactured by GE Reuter Stokes [15] and the UPC tubes by LND Inc [16]. The 60 cm long UPC, ORNL1 and ORNL2 tubes are arranged around the AIDA hole and are centred longitudinally on the DSSD stack. The shorter RIKEN tubes (30 cm) are disposed on both sides of each CLOVER detector hole. The transverse position distribution of the tubes is symmetrical and follows an approximate ring geometry as indicated in Fig. 3.

We have calculated the efficiency of the neutron detector with Monte Carlo (MC) simulations using the Geant4 Simulation Toolkit [17]. Figure 4 shows the total efficiency and the efficiency per ring as a function of neutron energy. Up to 0.5 MeV the total efficiency varies within $\pm 0.3\%$ and has an average value of 67.2%. The efficiency decreases to 65.5% at 1 MeV, then drops to 60.6% at 2.5 MeV and 51.9% at 5 MeV. We used experimental neutron spectra [18, 19] to simulate average efficiencies for a few known $\beta$-delayed neutron emitters with $Q_{\beta 1n}$ values between 2 MeV and 5.8 MeV. The resulting efficiencies vary from 67.2% to 66.1%. A similar simulation was made using the known spectrum of ²⁵²Cf [20] extending up to 20 MeV with an average energy of $\langle E_{n}\rangle=2.13$ MeV and a value of 61.8% was obtained . This value agrees well with the experimental result of 61.4(17)% obtained during the characterization of the BRIKEN neutron counter with a ²⁵²Cf source [21]. From these results we set the nominal neutron detection efficiency of the counter in the present configuration for isotopes with low or moderate $Q_{\beta 1n}$ windows to $\bar{\varepsilon}_{n}=66.8(20)\%$. This value is further investigated below (Section 5) using the results of measurements presented here.

We placed a PE shielding against fast neutrons coming from the beam line approximately 60 cm upstream of the neutron detector. The shielding has a thickness of 20 cm, a cross-section of $90~\mathrm{cm}\times 90~\mathrm{cm}$ and a central hole for the beam of $11.6~\mathrm{cm}\times 11.6~\mathrm{cm}$. Cadmium sheets were fastened to the back of the shielding. At the front of the shielding two large plastic scintillation detectors were attached, above and below the hole, with dimensions $45~\mathrm{cm}\times 20~\mathrm{cm}\times 1~\mathrm{cm}$. These detectors serve to discriminate against fast neutrons from the beam (VETO plastics).

The ³He tubes are connected to the preamplifiers via double-shielded coaxial cables to minimize noise pickup. These are Mesytec MPR-16-HV modules with 16 independent channels [22]. A total of 10 modules are used to accommodate all the tubes. Four of them have a differential output and the remainder have unipolar outputs. Before being sent to the sampling digitizer modules, the differential signals are converted into unipolar signals using 16 channel converter cards designed at the Accelerator Laboratory of the University of Jyväskylä (JYFL). A common high voltage (HV) is applied to all the tubes connected to a preamplifier module using a remotely controllable MPOD system from Wiener with ISEG HV cards [23]. The slow control system for this and other ancillary instrumentation was developed at ORNL (C. J. Gross and N. T. Brewer). The voltages applied are 1450 V for RIKEN and UPC tubes, 1350 V for ORNL1 tubes , and 1750 V for ORNL2 tubes. A common pulser signal is fed to all preamplifier modules. The pulse generator is driven by a precision clock running at 10 Hz. One of the pulser signals is sent directly to a free digitizer channel. The pulser is used to determine the data acquisition live time accurately.

The CLOVER detectors come from the CLARION array of Oak Ridge National Laboratory [24]. The four crystals in each detector have a diameter of 50 mm and a length around 80 mm. They are assembled inside the Al nose at 10 mm from the front face. The nose has a section of $10.1~\mathrm{cm}\times 10.1~\mathrm{cm}$. We use the preamplified signals from the central contacts (eight in total) which are sent directly to a digitizer module. The HV is provided by the MPOD system.

A picture of the full setup can be seen in Fig. 5.

Both the AIDA detector and the BigRIPS spectrometer have their proprietary data acquisition systems (DACQ).

For the BRIKEN neutron counter we used the self-triggered Gasific DACQ developed at IFIC (Valencia) [25]. An upgrade was needed in order to handle the large number of electronic channels. The new system uses two VME crates to accommodate seven SIS3316 and seven SIS3302 sampling digitizers from Struck [26]. The SIS3316 features 16 digitizer channels, with 14 bits and a maximum sampling rate of 250 MS/s, while the SIS3302 has 8 digitizers channels with 16 bits and a maximum 100 MS/s sampling rate. For each channel amplitude and time information are registered for signals above a specified threshold. A common clock distributor SIS3820 is used to synchronize the sampling in all the modules. The clock frequency was set to 50 MHz. It is also possible to run some of the digitizers at a multiple of that frequency using a special feature of the firmware, which is an advantage when combining fast and slow detectors. The Gasific DACQ also handles the electronic pulses from the CLOVER detectors and other ancillary detectors such as the F11 plastic detector, the AIDA plastic detector, the VETO plastic detectors and the Si $\Delta E$ detector. It was also used to acquire the fast signals from the YSO detector at 250 MS/s, using the upscaling of the sampling rate feature in the DACQ. The signals from the fast plastic detectors were shaped before entering the digitizer. The digitized signals are processed on-board with a fast trapezoidal filter providing noise discrimination and timing information. Accepted signals are timestamped and processed with a trapezoidal filter with compensation for the preamplifier decay constant to obtain the amplitude (energy) information. The parameters of both digital filters are optimized for every detector type. Parameter setting, acquisition control and on-line data surveillance is performed by Gasific.

To perform a complete data analysis it is necessary to combine the information from the three independent DACQs: BigRIPS, AIDA and BRIKEN. This is done on the basis of the absolute time-stamps, thanks to the use of a common synchronization signal distributed to all three systems. Since maintaining the synchronization is crucial for the success of the measurement, we developed an on-line monitoring program that periodically spies on the timestamps on the three data streams and checks that the events are synchronized.

We developed an efficient scheme for data processing which gives us the possibility of performing a detailed off-line analysis with information from the three systems within a few hours (near-line analysis). This allows us to asses the progress of the measurement and to detect experimental issues that need corrective action. The scheme is shown in Fig. 6. A new run is started every hour and the data from the previous run is copied to a dedicated server. The raw data from every detector system are then processed with a specific sorting program which generates a ROOT TTree [27] file from each data stream. These TTrees contain for each event type the necessary information. The minimum information required, apart from the time-stamp, consists of: 1) BigRIPS: the Z and A/Q of each ion, 2) AIDA: the X, Y, Z position and the energy E of each ion or $\beta$ signal, and 3) BRIKEN: a detector identifier and the energy E of each signal.

To combine the information of the three TTrees in a single TTree a Merger software program has been developed. The program uses C++ containers to efficiently merge and order the data by time. It can also associate ROOT vectors with each output event, containing presorted time ordered data of different event types. This boosts the construction of time correlations in the off-line analysis. For example, each $\beta$ event can have a vector of implant events and a vector of neutron events occurring within specified time ranges around the $\beta$ event.

Figure 7 shows the energy spectrum registered in the ³He tubes during one run with beam. The shape of the tube response to neutrons, represented by the shadowed area, is the sum of all tube dependent responses. The characteristic full absorption peak at 764 keV serves to calibrate in energy all the tubes at the beginning of the run. In general the gain of the tubes is very stable during the measurement, with occasional minor jumps for some of them that do not even require a gain correction. The resolution and the tail produced by the wall effect determine the range of signals identified as neutrons: 175 keV - 850 keV. The data represented in the spectrum of Fig. 7 was taken with a very low acquisition threshold. The peak observed below 30 keV is dominated by electronic noise. Above 30 keV another component is seen, that we call $\gamma$-like. We associate this component with radiation induced by the beam on different material elements in its path close to the neutron detector. It extends well into the neutron signal range, thereby contributing to the accidental neutron background. See also the discussion related to Fig. 9 below. We found that the LND tubes are less sensitive than GE tubes to this background contribution which otherwise shows a radial intensity profile decreasing with distance from the beam axis.

The neutron energy moderation process plus the time needed for a thermalized neutron to be absorbed in a ³He tube introduce a considerable delay between neutron production and its detection. Figure 8 shows the time distribution between neutron signals in the whole BRIKEN detector and signals identified as $\beta$ particles in AIDA. The tail of the distribution shows more than one exponential component but is essentially contained within the interval of 200 $\mu$s (99.6%). Compared with other neutron counters of the same kind (see for example Ref. [13]) this distribution is rather short. This is a consequence of the close packing of tubes in our arrangement. Based on the moderation plus capture time spectrum we decided to use a $\beta$-neutron coincidence time window of $\Delta t_{\beta n}=200$ $\mu$s to correlate neutrons with decays. Shorter windows could be used to reduce the ratio of accidentally correlated neutrons, represented by the flat background in Fig. 8, at the price of reducing the neutron detection efficiency.

The long coincidence window of 200 $\mu$s would introduce unnecessary common dead-time in a triggered event based DACQ. This is the main reason to use our DACQ where every individual channel runs in self-triggered mode. We determine the life-time for every channel as the ratio of counts in the pulser peak appearing in the ³He energy spectrum (located outside the range shown in Fig. 7) to the pulser counts registered in an independent channel where the pulser signals are directly connected. In general we observe a very small dead-time. For example during a measurement with a ²⁵²Cf source the total rate in BRIKEN was 15730 cps, including noise. The rate per tube varies strongly depending on the position of the tube. The highest channel rate amounted to 255 cps and the lowest to 11 cps. The measured channel dead-time fractions were 0.40% and 0.01% respectively. These numbers agree well with the estimation for a non-paralyzable system using the channel trigger gate length set via software. The global dead-time is 0.36%, obtained by weighting the channel dead-times with their relative contribution to the total number of counts. In comparison, an event-based DACQ with a 200 $\mu$s gate will have a dead-time of 76% at a rate of 15.7 kcps. During the experimental runs the rate in BRIKEN was never higher than a few hundred counts-per-second thus the acquisition dead-time corrections are negligible ($<0.1$%).

One of the issues encountered during the commissioning run was the large rate of beam induced neutrons, dominating the neutron background in BRIKEN. This came as no surprise since in a previous experiment [28] with the BELEN neutron detector at the GSI Fragment Separator (FRS) we observed in some cases more than 250 neutrons/s. The large background rate is a consequence of the high energy of the radioactive beam. We found the neutron rate at BigRIPS to be sensitive to the spectrometer setting and to the amount of material in the beam path, in particular close to the detector. Whenever possible we tried to move the material away from the experimental area. For example reducing the secondary beam energy in the early stages of the spectrometer allows us to reduce the thickness of the variable degrader controlling the implantation. In spite of these measures the observed rate is still large. During the commissioning run we measured up to 200 neutrons/s and in later experiments up to 160 neutrons/s. For comparison the rate induced by the natural background is 0.4 neutrons/s. This quite low rate is a consequence of the location of the experimental area, around 20 m underground.

We observed that a large fraction of background neutrons is time correlated with the signals of ions passing through the F11 plastic. Figure 9 shows the correlation time distribution, where the characteristic neutron moderation curve is seen. When comparing this figure with Fig. 8 two differences can be seen: the spike at $t=0$ and the longer tail of the distribution. The spike is due to $\gamma$-like signals within the neutron signal range. This is demonstrated by the grey filled histogram in Fig. 7 obtained gating on signals in the tubes above the noise but below 165 keV. The longer moderation time observed in Fig. 9, up to 500 $\mu$s, is likely to be the consequence of the high energy and direction of incidence of beam background neutrons.

We exploited this correlation to reduce the neutron background effect by imposing off-line a veto condition whenever a neutron is preceded a short time before by an ion signal in the F11 plastic. This veto condition introduces an analysis dead-time that is proportional to the rate in the F11 plastic. During the commissioning run the rate in the F11 plastic was 460 cps in average, thus we decided to use a veto time window of $\Delta t_{F11n}=200$ $\mu$s which captures 96.4% of background signals and gives a veto dead-time of 8.79%.

We also observed that the beam-induced neutron background has a large multiplicity $M_{d}$ (number of tubes firing). This can be a limitation for the measurement of multiple neutron emission probabilities. Figure 10 shows the observed multiplicity distribution of neutrons coming within $\Delta t_{\beta n}$ after a $\beta$ signal during the commissioning run (black continuous line). It should be noted that in this run no multiple neutron emitters were produced. The figure also shows the multiplicity histogram obtained when the coincidence window is set before the $\beta$ signal, representing the accidentally correlated neutrons (red dashed line). In this distribution the high multiplicity of background neutrons is clearly seen: $M_{d}=2$ and 3 are 30% and 16% respectively of $M_{d}=1$. When the F11 plastic veto condition is applied a strong reduction of the higher multiplicities is obtained as observed in Fig. 10 (dotted blue line). The reduction factor is $\sim 2$ for $M_{d}=1$, $\sim 30$ for $M_{d}=2$, and $\sim 70$ for $M_{d}=3$, demonstrating the usefulness of the veto. A similar veto condition using the AIDA plastic detector can be added as well. This will reduce the neutron background contribution associated with light particles in the beam that go through AIDA. Light particles remain undetected in the F11 plastic because of the small thickness of this detector. For the $\mathrm{A}\sim 80$ run during May-June 2017 the addition of the AIDA plastic veto condition yields a 20% further reduction of the background. In later experiments with heavier beams the impact is larger. During the commissioning run the AIDA plastic veto condition had no significant impact. Likewise we found no significant reduction of the background vetoing with signals from the VETO plastic detectors attached to the PE shielding.

In spite of the reduction, the large rate of background neutrons prevents us from using direct neutron counting in the analysis. Decay neutron signals are buried in the background or result in a low accuracy. Therefore we have to rely on additional $\beta$-gating as a way to improve the signal-to-background ratio.

We construct the time correlation histograms $h_{i\beta}(t)$ and $h_{i\beta 1n}(t)$ for all implanted ions that are identified. We choose a time window from -10 s to +10 s that is appropriate for all the cases analyzed. The binning of the histograms for each nucleus is chosen balancing the need to have enough points to determine the activity evolution and minimize the statistical fluctuation in the bin counts.

A fitting subroutine was written using ROOT::Fit classes [27]. The inputs to the program are the measured time correlation histograms, the half-life and neutron emission probabilities of all nuclei involved and the corresponding $\beta$ and neutron efficiencies. All parameters have an associated uncertainty and can be fixed during the fit. The program automatically reconstructs the decay network based on the nuclei and $P_{xn}$ information provided.

For the fit we do not subtract the different background contributions from the measured histograms but rather include these contributions in the fit function. See A. This is the proper way to handle the corrections in view of the use of Maximum Likelihood estimators. Histogram subtraction destroys the Poisson character of bin counts leading eventually to negative counts for low statistics. In general we use the Binned Maximum Likelihood (BML) algorithm to fit the histograms, except when the very low statistics suggest the use of the Unbinned Maximum Likelihood (UML). In this case the event data are provided in list mode. The uncorrelated $\beta$-ion background is obtained from a fit to the negative time range for each of the $h_{i\beta}(t)$ and $h_{i\beta xn}(t)$ histograms taking into account the effect of the correlated neutron background correction histograms (see A). The fit to the positive time range skips the first few bins in order to exclude the initial 50 ms range where the ion induced $\beta$ background appears.

To evaluate the systematic uncertainty due to the parameters fixed during the fit (half-lives, neutron branchings, backgrounds, efficiencies) we use a Monte Carlo approach. For any chosen subset of parameters we define a multivariate normal distribution, using the adopted value of each parameter as the mean and the square of the quoted uncertainty as the variance. In general we assume that different parameters are uncorrelated (diagonal covariance matrix). The multivariate distribution is randomly sampled and the fit performed. The resulting fit parameters ($P_{1n}$, $T_{1/2}$, …) are histogrammed and at the end the standard deviation of the sample distribution (eventually asymmetric) is evaluated and quoted as the systematic uncertainty.

For the fit we need to define $\beta$ and neutron efficiencies. We assume that the nominal value of the neutron efficiency is $\bar{\varepsilon}_{n}=66.8(20)$% as discussed in Section 2.2. This efficiency has to be renormalized in order to take into account the neutron count loss because of the finite size of the $\beta$-neutron correlation window (0.43%), and the dead-time introduced in the analysis by the neutron veto from the F11 plastic detector (8.79%). This gives a value of 60.7(18)% for the effective neutron efficiency. This efficiency would have to be modified for decays with a particular hard neutron spectrum. The influence of $\beta$ efficiencies will be discussed in the next subsection.

The continuum nature of the $\beta$ spectrum together with the unavoidable minimum electronic thresholds introduce a $\beta$ end-point energy dependence in the $\beta$ detection efficiency [25]. In the case of an implantation-decay detector like AIDA the energy dependence is further complicated with a dependence on the implantation depth and with the method of reconstructing $\beta$ events. To illustrate the dependence with threshold and implantation depth we show in Fig. 15 the result of Geant4 simulations using the AIDA Si DSSD geometry. This efficiency does not include the effect of event reconstruction and the absolute values are not representative of the actual $\beta$ efficiencies.

As can be observed in Fig. 15 there is a fast drop in the efficiency for end-point energies below $1-2$ MeV. When the $\beta$ particle is emitted from the middle of the DSSD the efficiency is quite large if the threshold is low (below about 150 keV). In this case increasing the threshold (250 keV in the example) has a substantial effect, with the efficiency dropping for increasing end-point energies. When the implantation occurs close to one of the DSSD surfaces, half of the $\beta$ particles have little chance of depositing enough energy and the efficiency drops. The effect of a threshold increase is smaller in this case. Because of the energy spread of implanted ions the implantation depth effect is partially smeared out. As explained in Section 3 this energy dependence can introduce differences in average efficiencies $\bar{\varepsilon}_{\beta}$ for different nuclei and decay branches, depending on the $\beta$ intensity distribution, which leads to systematic errors in the results of the fit. Note that the systematic effect is due to the relative differences and not to the absolute efficiency values.

It is not easy to determine experimentally the efficiency for every decay mode contributing significantly to the fit. One possibility is to use the intensity of decay $\gamma$-rays observed in the CLOVER detectors to obtain information on the average $\beta$ efficiency. This requires the comparison of $\beta$-gated with ungated $\gamma$ ray spectra [32], but it is in practice difficult to apply because of the large background and the limited statistics. Another approach is to calculate a realistic $\beta$ efficiency curve from Monte Carlo simulated data and use $\beta$ intensity distributions to compute the average efficiencies (Section 3). Since for most of the exotic decays this information is unknown or poorly known, one must rely on theoretical $\beta$-strength distributions to obtain an estimate. In spite of the uncertainties inherent in this approach it can give a representative value of the size of the systematic error. A third approach is to determine the $\beta$ efficiencies from the time correlation data as will be discussed below.

An important consideration is that the end-point energy dependence of $\varepsilon_{\beta}$ decreases as the threshold decreases (it disappears at threshold zero). Therefore minimizing the effective $\beta$-energy threshold in AIDA data is an important requirement to minimize this kind of systematic error. One can test the magnitude of the systematic error by analyzing data obtained with different $\beta$ thresholds. Such a test is shown in Fig. 16 for a set of Ni, Cu, Zn and Ga isotopes measured during the commissioning run. They span ranges of $Q_{\beta}=9.4-13$ MeV and $Q_{\beta 1n}=3.9-8.1$ MeV.

The fit to the time correlation histograms $h_{i\beta}(t)$ and $h_{i\beta 1n}(t)$ used to extract the $P_{1n}$ and $\beta$ efficiencies shown in Fig. 16, assumes that all $\bar{\varepsilon}_{\beta}$ are equal. In this case the $\beta$ efficiency factors out of the fit function (see Eq. 2 and Eq. 4) and can be determined from the result of the fit. The fit parameters are $P_{1n}$ and the normalization constant, equal to $\bar{\varepsilon}_{\beta}N_{1}$. The remaining parameters are kept fixed to the adopted values in standard databases [33]. Dividing the normalization constant by $N_{1}$ determined as the number of identified implanted ions we obtain $\bar{\varepsilon}_{\beta}$. The extracted efficiency is indicative of the effective $\beta$ threshold. In the sort with the low threshold the $\beta$ efficiencies vary between 30% and 42%. In the high threshold sort the efficiency range is 20-26%. The actual thresholds applied to AIDA $\beta$ data are strip dependent and vary between 100 keV and 250 keV in the high threshold sort and between 50 keV and 200 keV in the low threshold sort.

Figure 16 shows the ratio of $\beta$ efficiencies and the ratio of $P_{1n}$ values between the low threshold sort and the high threshold sort. The low threshold increases $\bar{\varepsilon}_{\beta}$ between 54% and 89% with respect to the high threshold. The impact on $P_{1n}$ is a reduction of all values by factors from 2.5% to 18%. We have not observed a clear correlation of the reduction factor with the size of the decay windows $Q_{\beta}$ and $Q_{\beta 1n}$.

Minimizing the thresholds in the AIDA sort is a challenging task because of the large number of channels and the nature of the noise, which is channel specific and time dependent. A compromise must be established between lowering the threshold and keeping a reasonable signal-to-noise ratio. For the commissioning run we adopt the low threshold sort discussed above that should reduce the effect of $\beta$ efficiency dependence in the data. The question is whether a residual effect still remains.

As a matter of fact we observe a small but systematic deviation between data and best fits for nuclei with high implantation statistics during the commissioning run. Figure 17 shows, relative values of fit residuals for implant-$\beta$ time correlation histograms $(h_{i\beta}(t)-f_{i\beta}(t))/f_{i\beta}(t)$. To show the effect more clearly the fit region is restricted to implant-$\beta$ correlation times in the range [1 s, 10 s]. As can be observed all show a similar pattern: there is a deficit of counts at short correlation times and a slight excess at long correlation times. We do not observe this effect in the fit of the neutron-gated implant-$\beta$ time correlation histogram $h_{i\beta 1n}(t)$. We interpret this result as a consequence of the difference in $\beta$ efficiency between the parent nucleus and descendants. In all cases except ⁸⁰Zn, this can be related to the much larger decay window $Q_{\beta}$ of the parent. The case of ⁸⁰Zn will be commented on later.

In view of this result we will include in the fit, when necessary, as an additional adjustable parameter the relative $\beta$ efficiency of selected decay modes in the chain.

During the commissioning run we accumulated $3.5\times 10^{5}$ ions of ⁸²Ga, a good case to verify the neutron efficiency since the $P_{1n}$ for this decay is fairly well known. There are three previous measurements which give consistent values: 21.4(22)% [36], 19.8(10)% [37], and 22.2(20)% [32]. Their weighted average gives 20.4(12)%. In addition there are two values with larger uncertainty that deviate significantly from the other results, 31.1(44)% from [38] and 30(8)% from [39]. The new evaluation of $P_{x}$ and $T_{1/2}$ for $\beta$-delayed neutron emitters fostered by the IAEA [40] recommends a value of $P_{1n}=22.7(20)$%, obtained by a weighted average of all measurements except the first one.

⁸²Ga is the sole neutron emitter in its entire decay network. The one-neutron emission window is $Q_{\beta 1n}=5.290(3)$ MeV. This value and the values of other decay energy windows in this paper are taken from the 2016 Atomic Mass Evaluation [41]. The neutron energy spectrum has not been measured for this decay but it was for the lighter isotopes ^79-81Ga [18]. From the evolution of the shape one can deduce that most of the neutron spectrum for ⁸²Ga should be contained within 1 MeV. This is confirmed by theoretical calculations of the delayed neutron spectrum, which can be retrieved from the ENDF/B-VII.1 data base [19]. This spectrum is calculated from $\beta$-strength distributions obtained within the QRPA formalism [42] and neutron emission rates obtained within the Hauser-Feshbach formalism [43]. Thus we conclude that the use of the nominal neutron efficiency $\bar{\varepsilon}_{n}=66.8(20)\%$ (Section 2.2) should be appropriate in this decay.

Our data and the fits are shown in Fig. 18. There is a large difference between the fit and measurement at the first positive time bin in the $h_{i\beta}(t)$ histogram (with $6\times 10^{4}$ counts it is outside the range shown). This is caused by the ion-induced $\beta$ background. The corresponding histogram bin is not included in the fit region. The number of accidental one-neutron counts per detected $\beta$ is $r_{1}=0.006793(29)$, much smaller than the values obtained in the May-June 2017 run (see Section 4). This reflects the different background conditions in the two experiments. In the fit all the decay branches down to stable nuclei are followed. The half-life of all descendants is relatively well known [33]. The half-life of ⁸²Ga is also well known, $T_{1/2}=601(2)$ ms [40], and was fixed in the fit. Ambiguities appear in the case of ⁸¹Ge with two known $\beta$-decaying isomers. However, both have equal half-life within uncertainties according to [44], which minimizes the impact of the respective unknown population. Also in the case of ⁸²As two isomers are known but the decay of the $0^{+}$ ground state of ⁸²Ge will populate weakly the $(5^{-})$ isomer and it was neglected. The case of ⁸¹Se, again with two isomers, poses no problem since it contributes marginally to the decay activity.

The decay energy window for ⁸²Ga is large, $Q_{\beta}=12.484(3)$ MeV, much larger than the $Q_{\beta}$ for other contributing decays. In particular it is nearly 8 MeV larger than the $Q_{\beta}$ of the daughter ⁸²Ge, the second largest contributor in the decay chain. Therefore the fit was performed including as a free parameter the $\beta$ efficiency for the parent decay, resulting in a value of $P_{1n}=19.10(46)$%. If we keep all $\beta$ efficiencies fixed the fit is poorer ($\chi^{2}/\nu=1.3$ instead of 0.98, see also Fig. 17) and the result becomes 13% larger $P_{1n}=21.60(30)$%. The fitted $\beta$ efficiency is $84.6(20)$%, relative to the efficiency for the remaining decay branches, that are kept fixed. This can be interpreted in the light of the simulations presented in Fig. 15 showing that if on average the decay proceeds by large decay energies the efficiency can be lower than if it decays with smaller $\beta$ energies.

The uncertainty on $P_{1n}$ values quoted above is obtained from the fit and represents the statistical uncertainty. The systematic uncertainty due to the uncertainties in the half-life of the parent and all descendants was evaluated as 0.16% using the parameter sampling procedure described before. The uncertainty due to the assumed uncertainty in the neutron efficiency amounts to 0.61%. The uncertainty due to the background corrections (correlated and uncorrelated) is evaluated as 0.18%. The total systematic uncertainty is 0.65%. Combining quadratically the statistical and systematic uncertainties our result is $P_{1n}=19.10(80)$%. It agrees within uncertainties with the weighted average of previous measurements with the lower $P_{1n}$ values [36, 37, 32] , $P_{1n}=20.4(12)$%. The result confirms also the value of the nominal efficiency used.

The importance of a proper correction of accidentally correlated neutron background in the case of weak two-neutron emitters was demonstrated in Section 4. ⁸⁰Zn with $Q_{\beta 1n}=2.828(3)$ MeV and a small $P_{1n}$ value is a good example of the importance of background correction for weak one-neutron emitters. It serves also as a test case to study the sensitivity limit of our experiment for $P_{1n}$ determination. There are two previous measurements of the delayed neutron emission probability in ⁸⁰Zn. A rather uncertain value of 1.0(5)% is reported in [45] and an upper limit, $P_{1n}<1.8$%, is reported in [39]. The new evaluation [40] adopts the value of [45].

One million ⁸⁰Zn ions were implanted during the commissioning run. In the decay chain [40], ⁸⁰Ga is a known $\beta$-delayed neutron emitter with a weak neutron branching $P_{1n}=0.846(73)$% and ⁷⁹Ga is an even weaker emitter with $P_{1n}=0.084(29)$%. Two isomers are known [46] in ⁸⁰Ga with $T_{1/2}=1.3(2)$ s $(J_{\pi}=3^{(-)})$ and $T_{1/2}=1.9(1)$ s $(J_{\pi}=6^{(-)})$, but the high-spin isomer is only weakly populated in the the decay of the ⁸⁰Zn $0^{+}$ ground state and it was ignored. The $Q_{\beta}$ of ⁸⁰Zn, $7.575(4)$ MeV, is actually smaller than that of the daughter ⁸⁰Ga, $10.312(4)$ MeV, at difference with the remaining cases shown in Fig. 17. Another characteristic of the decay of ⁸⁰Ga is the sizable population of a $2^{+}$ state at $E_{x}=659$ keV that emits conversion electrons and of a $0^{+}$ state at $E_{x}=639$ keV that can only decay by electron conversion to the $0^{+}$ g.s. (E0 transition) [47]. These low-energy conversion electrons are easily detected in AIDA increasing the apparent $\beta$ efficiency for ⁸⁰Ga decay. Therefore we leave this efficiency as a free parameter of the fit. The lower panel of Fig. 19 shows the good quality obtained in the fit to the $h_{i\beta}(t)$ histogram. The adjusted $\beta$ efficiency is 15% larger than the efficiency for other decay branches that are kept fixed. This result can be understood as the effect of conversion electrons.

The upper panel of Fig. 19 shows the fit to the implant-$\beta$-1n histogram without correction for the accidental correlated one-neutron background and the central panel the fit including the correction. As can be seen this correction represents the largest contribution to the measured histogram. Without correction the fit to $h_{i\beta 1n}(t)$ is poor because the correlated background has the shape of $h_{i\beta}(t)$ (see Section 4) and the resulting $P_{1n}=2.79(11)$% is too large. After correction we obtain $1.36(11)$% in agreement with previous results. A fit where all $\beta$ efficiencies are kept fixed results in a value of 1.28(11)%. The systematic uncertainty due to background correction is 0.06%. The one due to the fixed parameters in the fit (all $T_{1/2}$ and $P_{1/2}$ of descendants) is 0.02% and that of the neutron efficiency is 0.04%. Combining all uncertainties our final result is $P_{1n}=1.36(12)$%.

This case shows also that rather accurate $P_{1n}$ values on the order of one percent can be extracted from our data. This statement of course depends on the implantation statistics. We have tested that analyzing one tenth of the present statistics ($10^{5}$ ions) one can still obtain a reasonable result of $P_{1n}=1.62(47)$%.

The decay window for neutron emission in ⁸¹Ga is $Q_{\beta 1n}=3.836(3)$ MeV. It is the only neutron emitter in the decay chain network. There are three previous $P_{1n}$ measurements that agree relatively well: 12.0(9)% [36], 10.6(8)% [37], and 12.9(8)% [38]. The new evaluation [40] recommends the value of $P_{1n}=12.5(8)$%. The half-life is also well known $T_{1/2}=1.217(4)$ s. The number of implanted ions during the commissioning run was 4400. Thus this case serves to test the sensitivity limit of our setup with low statistics.

Figure 20 shows the result of the fit using the nominal neutron efficiency and fixing the half-life of descendants to the values in the ENSDF database [33]. The $\beta$ efficiencies were kept fixed during the fit. A total of 190 neutrons stand out from a background of 820 neutrons. The $P_{1n}$ from the fit is 11.3(23)%. The systematic uncertainty due to parameters that are kept fixed in the fit is 1.2%. Our result is then $P_{1n}=11.2(26)$ in agreement with previous results.

This demonstrates that with a few thousand ions we are able to measure $P_{1n}$ values of the order of 5-10% with accuracies in the order of 25%.