Characterization of a neutron – beta counting system with beta-delayed neutron emitters

A new detection system for the measurement of beta-delayed neutron emission probabilities has been characterized using fission products with well known β-delayed neutron emission properties. The setup consists of BELEN-20, a 4π neutron counter with twenty 3He proportional tubes arranged inside a large polyethylene neutron moderator, a thin Si detector for β counting and a selftriggering digital data acquisition system. The use of delayed-neutron precursors with different neutron emission windows allowed the study of the effect of energy dependency on neutron, β and β-neutron rates. The observed effect is well reproduced by Monte Carlo simulations. The impact of this dependency on the accuracy of neutron emission probabilities is discussed. A new accurate value of the neutron emission probability for the important delayed-neutron precursor 137I was obtained, Pn = 7.76(14)%.


Introduction
Beta-delayed neutron emission is a form of decay that occurs for nuclei with a large enough neutron excess. For delayedneutron precursors the neutron separation energy in the daughter nucleus S n is smaller than the decay energy window Q β .

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As a result neutron unbound states can be populated in the decay. The process becomes dominant far enough from stability. The β-delayed neutron emission probability P n conveys information about the distribution and nature of nuclear levels populated in the decay, which is dictated by nuclear shell structure 10 and residual interactions [1]. P n values are also important inputs for the description of the astrophysical r process responsible for the synthesis of about half of the observed abundance of elements heavier than iron [2]. These two fields of interest, nuclear structure and nuclear astrophysics, explain why the 15 measurement of P n values for exotic nuclei is one of the goals of the DEcay SPECtroscopy (DESPEC) experiment [3] within the NUclear STructure and Astrophysics Research (NUSTAR) collaboration [4] at the Facility for Antiproton and Ion Research (FAIR) [5]. The BEta deLayEd Neutron (BELEN) counter has 20 been developed [6] for this purpose. It is based on the well * Tel.: +34 963543497, Fax: +34 963543488. Instituto de Física Corpuscular, Apdo. Correos 22085, E-46071 Valencia, Spain Email address: tain@ific.uv.es (J.L. Tain) proven technology [7,8,9,10,11,12] of combining an array of 3 He proportional tubes, selectively sensitive to low energy neutrons, with a hydrogenous neutron energy moderator. Detectors with large solid angle and detection efficiency can be built in 25 this way. The BELEN detector was conceived as a flexible and easily reconfigurable system. The current version has fortyeight 3 He tubes, but previous versions with twenty [13,14] and thirty [15] tubes have been used in different measurements. Some of these measurements were aimed at the accurate de-30 termination of P n values of fission products relevant in reactor technology. The fraction of neutrons in the reactor core coming from β decay is an important parameter for the safe control of reactor power [16]. This constitutes the third field of application of this detector. The BELEN detector is part also of the 35 largest neutron counter of this kind (more than 160 3 He tubes) that is being assembled by the BRIKEN collaboration [17] for the measurement of exotic nuclei at RIKEN.
In this work we describe the characterization of the detector setup installed at the Cyclotron Laboratory of the Univer- 40 sity of Jyväskylä during the 2010 measuring campaign [14]. For the characterization of the setup we used fission products which are delayed-neutron precursors with well known properties. The instrumentation includes BELEN-20 and a Si β detector, a fairly common arrangement. A novelty in our setup is the 45 introduction of a trigger-less data acquisition system. Its use al-lows continuous control of data quality, which leads to greater accuracy, with a minimum acquisition dead time. In this work we also discuss some of the systematic effects which appear in the use of β-neutron counting systems applied to the determi-50 nation of P n values.

Determination of P n values
The P n value is the fraction of all decays which undergo delayed-neutron emission. It is a common experimental approach, and the one we follow here, to obtain the number of 55 decays from the number of β particles registered in a β detector and the number of β-delayed neutron decays from the number of neutrons observed in a neutron detector. Taking into account the fact that detection efficiencies for both β particles and neutrons are energy dependent we can write In this equation i designates a level in the daughter nucleus Z+1 A at excitation energy E i populated with probability I i β , and f a level in the final nucleus Z+1 A − 1 at excitation energy E f , which is populated from level i with probability I i f n . N i f n is the number of detected neutrons with an efficiency ε i f n , which are 65 emitted in the transition i → f with energy E i f n = E i − E f − S n . N i β is the number of detected β particles with an efficiency ε i β , which are emitted in the decay of the parent nucleus Z A to level i. The right-hand side of Eq. 1 is the expression commonly employed to calculate the P n value but it emphasizes thatε β 70 andε n are average β and neutron efficiencies for all β particles and all neutrons. Note that the summation over levels in the daughter nucleus is restricted to neutron unbound states (E i > S n ) in the numerator of Eq. 1, but runs over all levels (including the ground state) in the denominator. From the form of Eq. 1 75 it is clear that the average efficiencies are nuclide dependent. Equation 1 assumes that only one neutron is emitted per decay. For multiple neutron emission appropriate formulae for P xn can be written.
Sometimes the quantity measured is the number of neutrons 80 in coincidence with the β particle. This is necessary to enhance the neutron detection sensitivity whenever the rate of βdelayed neutrons is comparable to or smaller than the rate of background neutrons. In this case the expression reads Here N i f βn is the number of detected neutrons from the tran-

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sition i → f in coincidence with betas populating level i. This requires detection of both the β particle (ε i β ) and the neutron (ε i f n ). On the right-hand side of Eq. 2 the symbolε β represents the β efficiency averaged over neutron unbound states, different from the β efficiency averaged over all levelsε β .

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Neglecting the energy dependency of the β and neutron detection efficiencies can be an important source of systematic error. For instance the neutron moderation process in a counter of the type used here can vary appreciably with initial neutron energy leading to large efficiency variations. Since the neu-95 tron energy distribution is often unknown such detectors are sometimes designed to produce an extremely flat efficiency response [18]. However such designs reduce the average detection efficiency and therefore designs where the detection efficiency is maximized are also favoured. In the latter case the av-100 erage neutron detection efficiency is more sensitive to the neutron energy spectrum given by i,E i >S n f I i β I i f n E i f n . The systematic correction toε n due to the neutron energy distribution for different β-delayed neutron emitters can be evaluated using Monte Carlo simulations as shown in Section 5.

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Due to the continuum nature of the β spectrum the low energy threshold in the electronic system introduces a strong energy dependence of the β counting efficiencies for small Q β − E i endpoint energies. This causes isotope dependent effects on the average β detection efficiency and, more importantly, it can intro-110 duce large differences betweenε β andε β . As a consequence the cancellation of the average β efficiencies on the right-hand side of Eq. 2, a usual assumption, can lead to large errors. In Section 5 we evaluate the magnitude of such errors for the present setup using Monte Carlo simulations. 115

Neutron and beta counters
The measurements were performed at the IGISOL mass separator [19] installed at the Cyclotron Laboratory of the University of Jyväskylä. A broad range of isotopes are produced in the 120 proton-induced (E p = 25 MeV) fission of a thin thorium target inside the ion source. Reaction products which exit the target are swept away by a Helium gas jet into the 30 kV electrostatic accelerating stage of the separator. The low energy ion beam is mass separated in a large dipole magnet with a modest mass 125 resolution M/∆M ∼ 250. In order to separate the nucleus of interest from accompanying isobars, the beam is directed to a double Penning trap system [20] working as a very high resolution mass separator. The purification cycle in the trap lasts for about 200 ms after which time the bunch of ions is released 130 towards the experimental station. The extracted beam is isotopically pure to a high degree. Isobars from the mass separator are effectively suppressed in the trap, provided their mass difference with respect to the selected isotope is large in comparison to the trap frequency width. This was the case in our measure-135 ment. An exception is the production of nuclei inside the trap by decay of the selected isotope towards the end of the purification cycle. Beta-decay daughters will be doubly charged and have huge motional amplitudes in the trap resulting in a very small chance, estimated to be on the level of few percent or 140 lower, to be extracted and implanted. This type of contamination could affect the measurement of isotopes with very short half-lives. The possible impact in our results is evaluated in Section 4.
The beam travels inside a 1 mm thick aluminium vacuum 145 tube with a diameter of 46 mm and is implanted on a movable tape supported on a two roller system situated at a distance of about 2 m from the exit of the trap (see Fig. 1). The space between the rollers is 12 mm. The tape used is a standard half-inch wide computer tape with the magnetic layer facing the beam. 150 We estimate that the implantation depth of the ions is about a few tens of nanometers. At a distance of 6 mm behind the tape is situated a 0.5 mm thick Si detector with an active diameter of 25 mm mounted on a PCB frame. The use of such a thin Si detector minimizes γ ray interactions. This detector has a geo-155 metrical efficiency of about 28% for counting β particles emitted by the implanted ion. During the initial measurements we found that the direction of the beam extracted from the trap was drifting with time. The effect is amplified by the long distance and as a result the implantation position was changing enough 160 to produce variations in the β detection efficiency as large as a factor of two when comparing different runs. This effect would have been disastrous for the determination of P n values, therefore two collimators with holes having diameters of 10 mm and 5 mm were placed at convenient positions along the tube. In 165 this way the change of β efficiency during the whole beam time was reduced to a negligible value as will be shown in Section 5. The beam tube was placed inside the central hole of the neutron counter in such a way that the implantation position is at the center of the detector. The BELEN-20 version of the neu-170 tron counter used in this measurement consists of twenty 3 He proportional tubes arranged in two rings, with eight and twelve tubes respectively, around the central hole (see Fig. 2) The central hole has a radius of 55 mm and the detector rings have radii of 95 mm and 145 mm. Each tube is placed inside a cylindri-175 cal hole made in the polyethylene moderator with a diameter of 27.5 mm. The proportional tubes were fabricated by LND Inc. [21] and have an external diameter of 25.4 mm. The gas volume has an active length of 600 mm. The total length of the tube including the HV connector is 676 mm. The tube wall is 180 made of stainless steel and has a thickness of 0.5 mm. The tube is held in position inside the hole by means of a polyethylene plug with a hole for the high-voltage connection (see Fig. 2). The gas is a mixture of 3 He with 3% of CO 2 at a pressure of 20 atmospheres. The neutron moderator block is made with slabs 185 of high density polyethylene (PE) with a measured density of ρ = 0.955 g/cm 3 . Seven slabs with a thickness of 100 mm and a cross section of 500 × 500 mm 2 make the core of the PE moderator. The eighth slab at the end acts as shielding against the external neutron background. The neutron shielding on the 190 sides of the moderator block has a thickness of 200 mm and is assembled from twelve different PE slabs. The overall dimensions of the PE block are 900 × 900 × 800 mm 2 . The distribution of tubes inside the neutron moderator was obtained [22] as a result of MC simulations with MCNPX [23] and Geant4 [24].

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This particular arrangement is optimized to enhance neutron detection efficiency.  found that the use of the shaper allowed us to have a better separation from the noise. A home-made fixed frequency clock (10 Hz) is used to trigger a tail pulse generator model BH-1 from Berkeley Nucleonics Corporation. The pulser signal is sent to the test input of the preamplifiers and the height ad-210 justed to have a peak at a convenient location in the amplitude spectra. The pulser allows the precise measurement of the real data acquisition time (live time).

Self-triggered digital data acquisition system
The time for neutrons to moderate their energy in the 215 polyethylene and be captured in 3 He is quite long, up to several hundreds of microseconds (see Fig. 6 and Section 4). This affects the performance of conventional triggered data acquisition systems (DACQ). The registration of decay events including both the neutron and the prompt detected radiation, β particles or γ rays, requires an event gate of similar magnitude and is thus affected by a large dead time. The long event gate also enhances the chance of registering uncorrelated signals and the registration of multiple signals in the same channel. The separation of random and true coincidences is best done by studying 225 all time correlations in the event time window. But in addition to the time it is important to measure the amplitude of every registered signal. This allows one, for instance, to discriminate efficiently against fluctuating detector noise. However measuring the amplitude becomes difficult with multiple signals within 230 the gate. All of these issues can be resolved with a self-triggered DACQ based on sampling digitizers where each DACQ detector channel runs independently [25]. Such a system has a very much reduced intrinsic dead time. A potential problem with such systems is the large amount of data which needs to be 235 transferred (introducing additional dead time) and stored. The solution adopted for the BELEN DACQ is to use pulse self triggering and on-board processing of the digitized signal to obtain for every pulse a time reference (time stamp) and the amplitude [26]. This reduces tremendously the amount of data to be 240 transferred.
The DACQ used during the 2010 campaign is based on SIS3302 VME digitizers from Struck Innovative Systeme [27]. These are 8 channel modules with 100 MHz sampling frequency and 16 bit resolution. Every two channels share a Field 245 Programmable Gate Array (FPGA) that stores the firmware to process the digitized pulse. We use the standard Gamma firmware from the manufacturer which matches our requirements for on-board data processing. A trapezoidal Finite Impulse Response (FIR) filter produces a short waveform for dis-250 crimination purposes (fast filter). Signals out of the fast filter that are larger than a given threshold generate an internal trigger for processing the input pulse with a second FIR filter for precise amplitude determination (slow filter). At the same time the crossing of the threshold by the fast filter signal retrieves 255 the content of a sample counter with 48 bit capacity which provides an absolute time stamp with 10 ns resolution. The slow filter is of trapezoidal type with compensation. The latter term refers to a correction for preamplifier signal fall time, which the firmware presumes is the shape of the input signal. The param-260 eters of both filters can be adjusted independently according to the characteristics of the input signal. The timing resolution of the fast filter applied to the shaped signals was very poor (over 100 ns) but it is of no relevance in the present application. The application of the slow filter to Gaussian shaped signals (see 265 Section 3.1) produces some distortion of the amplitude spectrum (see lower panel in Fig. 3) which is also of no concern in the present application. The parameters of the slow filter that we use lead to a signal processing time of 10 µs. As every channel is independent the rate dependent dead time has to be 270 determined for every one. This is done with a fixed frequency pulser distributed to all channels via the preamplifiers as mentioned above.
Each acquisition channel has a 64 MByte on-board memory, where the result of the digital processing of the signal is stored.

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Typically we reduce the stored pulse information to the minimum, which includes the time stamp and the amplitude of the slow filter output. This requires 24 bytes of space per pulse. It also includes a flag signaling pulse pile-up when a second pulse within the processing time produces an internal trigger. Other 280 event data storage options are available including the storage of the pulse waveform or the output of the slow filter. Each channel memory is divided into two banks. This allows one to accumulate data in one bank and at the same time retrieve the stored data from the second bank to the computer. This arrange-285 ment contributes to reducing the DACQ overall dead-time. The communication with the computer occurs via an optical link, which connects the SIS1100 PCI card with the SIS3100 VME interface card (both from Struck).
The gasificTL [28] data acquisition software is organized into 290 four parallel processes which are responsible for: 1) hardware configuration and control, 2) block data read-out, 3) data storage on permanent media, and 4) on-line analysis. A fifth process, the Graphical User Interface (GUI), facilitates the control of these tasks. The GUI is built using Qt software [29]. For the 295 communication and synchronization of the different processes we use Inter Process Communication (IPC) libraries available in POSIX [30]. Data is shared between processes though memory mapped files. The use of semaphores regulates the traffic of data and resolves conflicts between processes. Data storage 300 on disk has priority over the other processes. Read-out from a data bank, and accumulation on the alternative bank, is started by a Look At Me (LAM) signal generated when any channel memory is almost full or after a predetermined time. On-line analysis can be very demanding, in particular the reconstruction 305 of events and time correlations, and the software uses parallel processing to speed it up. Nevertheless typically only a fraction of the stored data is analyzed on-line. For construction, visualization and manipulation of histograms the DACQ relies on the ROOT data analysis framework [31]. The DACQ software 310 uses a custom library which provides services as input/output abstraction, allowing to process data from hardware, filesystem or network indistinctly, management of DACQ configuration and setup, time stamp sorting, event windowing for classification and packaging, and data transformation for second level 315 analysis. The library is written in C++ using the standard template library which provides genericity, predictable behavior in memory management and a well know algorithm cost. The latest version of the DACQ also uses the SIS3316, a 16 channel digitizer with 250 MSamples/s and 14 bit resolu-320 tion from Struck. The firmware incorporates new features, including a Constant Fraction Discrimination (CFD) algorithm which provides improved time resolution. The new DACQ was used successfully in a recent measurement with BELEN-48 at Jyväskylä. The new system has been upgraded to han-325 dle multiple VME crates, and a total of 192 acquisition channels. This extension is required to match the neutron detector of the BRIKEN project [17]. The DACQ has been also applied to other types of detectors like liquid scintillation detectors for neutron detection [32] and a NaI(Tl) total absorption γ-ray spectrometer [33].

Measurements and data analysis
To characterize the neutron-beta counting system we measured four well known β-delayed neutron emitters: 88 Br, 94 Rb, 95 Rb and 137 I. Table 1 gives their half-life T 1/2 taken from 335 ENSDF [34, 35,36,37], total decay energy Q β , and daughter neutron separation energy S n taken from [38] and the neutron emission probability P n taken from [39]. Table 1: Half-life T 1/2 , decay energy window Q β , daughter neutron separation energy S n , and neutron emission probability P n for each measured isotope.
Isotope  (38) Each β-delayed neutron precursor was implanted for a period of time equivalent to three half-lives. The measuring time 340 started 1 s before the accumulation period and lasted for a period of ten half-lives. At this point the activity on the tape was moved out, the time stamp scaler reset to zero and a new measurement cycle started. During the tape transport and accumulation "off" periods the primary beam is kept on target but the 345 secondary beam is deflected to a beam dump located far away from the experimental setup.
The amplitudes of the signals from the Si detector and each 3 He tube are calibrated in energy and histogramed as shown in Fig. 3. We use the position of the peak in the tube response and 350 assign it a value of 764 keV, the energy released in the reaction 3 He(n, p) 3 H, to calibrate the neutron spectrum. The calibration of the β spectrum is made by comparison with Monte Carlo simulations of the energy deposited in the Si detector (see Section 5). The good separation of neutron signals from the noise 355 can be seen in the lower panel of Fig. 3. We tag as neutron signals those which have an amplitude in the range of 130 keV to 920 keV. The noise level in the Si detector allows us to set a low energy threshold of 100 keV to tag β signals (see upper panel of Fig. 3). For each neutron or β event that fulfills the energy 360 condition we histogramed its time stamp. In this way growth and decay curves of the activity are reconstructed (see Fig. 4 and Fig. 5). We also construct β-neutron time correlation histograms from these events. For every β event the time stamp difference with all neutron events in a time interval ranging from 365 -1 ms to +1 ms is histogramed. Figure 6 shows an example. The asymmetric shape of the peak is due to the moderationplus-capture time distribution of neutrons in the detector. The mean value of this time distribution is approximately 80 µs but the distribution extends up to about 500 µs.

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The number of detected β particles N β and neutrons N n which are to be ascribed to the decay of the parent nucleus is obtained from a time analysis decomposition of the growth and decay curves. This allows one to separate out the contribution from descendants. The time evolution of the number of counts due to 375 all isotopes in the decay chain is described using the solution to the appropriate Bateman equations [40]. The experimental time distribution is fitted using either the chi-square minimization method or the maximum likelihood method for binned data. For that we use MINUIT optimization routines [41] which are N i (t) represents the number of i nuclei at time t, i representing the ordering number in the decay chain, N i (t 0 ) the number 385 of nuclei at the initial time t 0 , R i its constant rate of production, and λ i = ln2/T i 1/2 its decay constant. The term b k,k+1 represents the branching ratio between two successive isotopes in the decay chain. This formula is adjusted to the conditions of our measurement where only the parent nucleus was implanted. 390 We use two forms, one assuming constant continuous implantation (see Fig. 5), and the other a series of instantaneous implantations (see Fig. 4). The latter is applied for the very shortlived isotopes where the pulsed nature of the beam from the trap shows up in the time distribution as seen in Fig. 4. In the contin-395 uous implantation case we set all N i (t 0 ) and all R i equal to zero except R 1 . The function is defined in this way up to the end of the implantation period, determining the number of nuclei of each species formed up to this time which become N i (t impl ). Afterwards the time evolution is calculated setting R i = 0. In 400 the discrete implantation case we set to zero all R i and all N i (t k ) at each implantation time t k except N 1 (t k ).
All decaying isotopes contributing to the time distribution are included in the fit. In the cases studied here, only the parent happens to be a β-delayed neutron emitter. Therefore the fit 405 function for the β time distribution includes two decay chains with b 12 weights, 1 − P n and P n respectively. The actual function has the form iε i β λ i N i (t). In accordance with the discussion in Section 2 we use in this expression a different average β efficiency for each isotope. However, as will be shown later, 410 this dependency is very small in the present case and we can use the same efficiencyε β for all of them. In the case of the neutron time distribution only the parent is included and the actual function isε n P n λ 1 N 1 (t). A constant background is added to the fit function. The 1 s time period at the beginning of 415 the measuring cycle, before implantation starts, serves to fix the background level. In the case of neutrons the background rate was 0.9 cps during the measurements (accelerator on). For comparison, the rate descended to 0.7 cps when the accelerator was turned off. The presence of a β background, visible in 420 all time spectra, is explained because the beam collimation system described above could not avoid that a fraction of the beam was implanted outside the tape, on the tape supporting structure or on the detector. We calculated the time dependence of the accumulated activity, not removed by the tape system, and 425 concluded that after several measuring cycles it can be well represented by a constant value. For the nuclei analyzed here the values of T 1/2 for parent and descendants are well known. The same is true for the P n values. Therefore the only free parameter in the fit is the product of the number of implanted parent ions 430 (t impl × R 1 or k N 1 (t k )) times the detection efficiency. Integration of the parent activity curves provides N β and N n . Figures 4  and 5 show examples of the fits obtained.
We have verified the assumption that only the parent nucleus is implanted. From the discussion in Section 3 and the half-live 435 values in Table 1, one can conclude that contamination with daughter nuclei from decay in the trap is more likely to occur in the case of 95 Rb. Therefore we analyzed the time distribution of β signals in the upper panel of Fig. 4 using a fit function which includes the implantation of daughter nuclei in addition to par-440 ent nuclei. A new fit parameter is introduced that corresponds to the fraction of daughter to parent nuclei. If this parameter is left free the best fit corresponds to values consistent with zero. If the parameter is fixed to 5% one observes a clear deterioration of the chi-square while the number of β particles associated 445 with the parent decay N β only changes by 0.4%. Note that this fraction of daughter nuclei corresponds to the assumption that 10% of decay products produced in the trap are extracted an implanted, which is unrealistic. We conclude that for all practical purposes the beam is pure.

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The case of 137 I (Fig. 5) and 88 Br (not shown) were special. In both cases the β activity towards the end of the cycle was smaller than the calculated values. The solution to the puzzle came with the realization that both descendants 137 Xe and 88 Kr are noble gases with a tendency to diffuse easily from organic 455 plastic materials. The magnetic substrate of the implantation tape is actually composed of magnetic granules embedded in an acrylic layer. Therefore a fraction of daughter nuclei can escape from the tape and do not contribute to the measured β rate. A similar effect has been observed before [43]. To solve 460 the problem we added a loss term for Xe and Kr isotopes to the Bateman equations. The loss rate was assumed constant and the solution function was modified accordingly. The loss rate is an additional fit parameter in these cases. This adds a systematic uncertainty to the parent β rate determined from the fit but we 465 estimate that this uncertainty is small (see below).
[ms] To determine the number of β-neutron correlated events N βn we use the time correlation histograms (see Fig. 6). The negative time part of the histogram (backwards in time) represents faithfully the background of random correlated events under 470 the true correlations in the forward time direction. As can be seen the rate of random events is constant in this time window. Therefore a fit to the negative part of the histogram is used to subtract the background from the positive time events. The length of the time window, 1 ms, is long enough to ensure 475 that all the neutrons are collected.
We give in Table 2 the values of N β , N n and N βn obtained in the way described above for the four isotopes. These numbers have been corrected for data acquisition dead time, although the correction is very small, less than 0.3% in all cases. The dead 480 time correction for each acquisition channel was determined by comparison of the number of counts in the peak due to the fixedfrequency pulse generator and the total measuring time. This was calculated from the number of measuring cycles and the cycle time length, determined from the cycle time histograms 485 (such as those shown in Fig. 5).

Results and discussion
From the numbers given in Table 2 and the known P n value (Table 1) we can calculate the quantityε β /ε n using Eq. 1. This purely experimental quantity should be independent of the nu-490 cleus concerned except for the systematic effects discussed in Section 1. It characterizes the β-neutron counting setup and, once determined, allows one to obtain P n values for other isotopes. Figure 7 represents the ratio of average β and neutron efficiencies for the four isotopes. The dashed line connects the 495 uncorrected values and the solid line connects the values corrected by systematic effects onε β andε n as will be detailed below. As can be appreciated the corrections are very small. There is a very good agreement between the different isotopes which indicates that systematic errors are well under control, in 500 particular the variations of β efficiency with time. The weighted average of the ratio isε β /ε n = 0.506 (7), which has an uncertainty of only 1.4%. This value has been used to determine the P n values for other isotopes [14].
To compute the corrections to the neutron efficiency coming 505 from the neutron energy distribution we have used Geant4 MC simulations. We implemented a particle generator which reproduces the neutron energy distribution taken from the ENDF/B-VII.1 [44] nuclear data base. The data in this file come from the  evaluation work of Ref. [45] and are supplemented with the-510 oretical calculations [46] outside the measured energy range. Figure 8 shows the neutron energy distributions for 88 Br and 137 I. 94 Rb and 95 Rb are excluded for clarity. The figure shows also the neutron detection efficiency as a function of neutron energy obtained from the Geant4 simulations. The simulations 515 were performed with version 10.0 (patch 3) of the simulation toolkit. In the code we include a detailed geometrical description of the BELEN neutron counter. As can be observed the efficiency is rather constant below 0.5 MeV, with a value of about 47%, but decreases steadily with neutron energy above that en-520 ergy, being only 29% at 5 MeV. Although the energy window for neutron emission Q βn = Q β − S n varies from 1.9 MeV for 88 Br to 4.9 MeV for 95 Rb (see Table 3), the Fermi decay rate function shifts the neutron spectrum to rather low energies as observed in Fig. 8. In fact the largest average neutron energy 525 E n is 625 keV and corresponds to the decay of 137 I. Because of this one expects a modest isotope dependency for the average neutron efficiency. This is confirmed by the simulation as shown in Table 3.
In Table 3 and in Fig. 8 we also show data for the 252 Cf 530 spontaneous-fission neutron source. This source is often used to calibrate neutron detectors. The Californium neutron energy spectrum shown in Fig. 8 is taken from Ref. [47]. The spectrum reaches 25 MeV and has an average energy of 2.2 MeV. Thus it senses a portion of the efficiency curve different from 535 the fission products. The result of the simulation gives an average neutron efficiency of 39.5%. We used a calibrated 252 Cf source to measure the neutron detection efficiency and obtained a value of 40.9(8)% in good agreement with the simulation. It should be noted that this level of agreement could only be 540 reached after correction of some bugs [48] in Geant4 which have been incorporated in version 10.0 and later versions of the code. The ratio between the counts of the inner and the outer ring of 3 He tubes is quite sensitive to the neutron energy distribution [10]. The measured ratio is 1.499(3) in quite good 545 agreement with the result of the simulation 1.52. In addition it is worth mentioning that the simulation reproduces well the neutron moderation-plus-capture time distribution, like the one shown in Fig. 6. These results show the suitability of Geant4 for simulating the response of this type of neutron detector.

550
The correction factor to be applied toε n for each isotope is calculated as the ratio of the simulated efficiency in Table 3 to the average value for the four isotopes. The correction is small, varying between −1.1% for 95 Rb and +1.2% for 88 Br. However the correction can be important for decays where the Q βn 555 window is large and the β intensity distribution is sizable at excitation energies well above S n . Such a situation can be found in lighter nuclei. It is also possible that nuclear structure effects could produce a similar situation for other nuclei with very low level density, such as those close to doubly magic nuclei. It is 560 obvious that this way of calculating the corrections to the average neutron efficiency can only be applied if the β-delayed neutron energy spectrum is known. When this is not the case the magnitude of the systematic error due to the unknown neutron energy distribution can be obtained from assumptions or 565 calculations of the β intensity distribution. For detectors having more than two rings of tubes, an improved estimate of the average neutron efficiency can be obtained using the information from the ratio of counts between different rings [10].  We now consider the corrections to the β efficiency coming 570 from the β intensity distribution. In Fig. 9 we show the β efficiency as a function of end point energy obtained from Geant4 simulations. The simulation application includes a detailed description of the geometry of the implantation setup (see Fig. 1): tape, rollers, supporting structure, Si detector and mounting, vacuum tube and end-cap. For the efficiency calculation we assume a β spectrum shape of allowed type. The use of forbidden shapes has a minor impact on the efficiency. The simulated efficiency is scaled down with a factor of 0.806 to take into account that part of the beam is implanted outside the tape and 580 is not seen by the Si detector. How this factor was determined is explained below. As can be observed the efficiency varies strongly up to 2 MeV due to the effect of the 100 keV detection threshold in the Si detector. In the figure we also show the β intensity distributions for the four fission products. The distribu-585 tions are scaled for clarity. The lower panel shows the intensity I βγ that is followed by γ emission or feeds the ground state in the daughter nucleus. For 95 Rb and 137 I the distribution is taken from the ENSDF data base [36,37] and was obtained with highresolution γ-ray spectroscopy using germanium detectors. For 590 88 Br and 94 Rb we show the result of recent experiments [49] using total absorption γ-ray spectroscopy (TAGS). The upper panel shows the β intensity distribution that is followed by neutron emission I βn . This intensity distribution was obtained from the deconvolution of the neutron spectra shown in Fig. 8. The 595 total β intensity I β is obtained from summation of the two distributions I βγ and I βn with the proper normalization, 1 − P n and P n respectively. This intensity distribution can be used as input for a Geant4 simulation to determine the average β efficiencyε β which is shown in Table 4. As can be observed the dependency 600 on the nucleus concerned is very small, a maximum variation of half-a-percent with respect to the average. This was expected from the large values of the average end-point energy for the decay Q β − E x I β also shown in Table 4. A comment on the accuracy of β intensity distributions is per-605 tinent at this point. Intensity distributions coming from highresolution spectroscopy are often affected by systematic errors, as a consequence of the limited efficiency of germanium detectors. Gamma rays de-exciting high energy levels can be easily missed or cannot be placed in the level scheme. This leads to an 610 incomplete and distorted level scheme with too much intensity assigned to levels at low excitation energy. This can be clearly seen in the case of the decay of 94 Rb where the ENSDF data evaluation [35] locates only 66% of I βγ . Total absorption spectroscopy with large 4π scintillation detectors gives the correct 615 intensity distribution. Indeed the TAGS result for 94 Rb [49] places considerable intensity at high-excitation energy. In spite of that the calculated average β efficiency does not change significantly. Summarizing, the corrections due to the energy distribution 620 of neutrons and β particles on the ratioε β /ε n for the measured isotopes are very small and do not add much to the systematic uncertainty of the result. From the four isotopes, 137 I is the one with the largest relative uncertainty on the P n value. According to the evaluation 625 of Ref.
[39] the uncertainty amounts to 5.2% (see Table 1 and Fig. 7). We can use the P n values for the other three isotopes to obtain an improved estimate of the β-delayed neutron emission probability for this important β-delayed neutron precursor. 137 I is one of the single largest contributors to the delayed neutron 630 fraction in a reactor. The ratioε β /ε n determined with the ex-clusion of 137 I is 0.508(8), only marginally different from the number given above. With this ratio we determine a more accurate neutron emission probability P n = 7.76(14)% for 137 I. As was explained in Section 4 the measurement for this isotope is 635 affected by the escape of the daughter nuclei from the implantation tape. This introduces a systematic uncertainty on the number of β counts N β related to the modeling of this effect in the fit function. However this uncertainty is very small. 137 Xe decay is the only significant additional contribution to the growth and 640 decay curve (see Fig. 5). Since the half-life of the daughter is nine times longer than the parent half-life, the contribution is small during the first part of the measuring cycle. Restricting the fit of β counts in Fig. 5 up to the end of the implantation period (73 s), and removing the loss term from the fit function, 645 we obtain a number of counts in the full cycle N β which differs only by 0.4% from the value given in Table 2. We assume that this difference gives the magnitude of the xenon loss systematic error and include it in the quoted uncertainty given above. Our new determination of 137 I P n value has thus an uncertainty of We turn now to consider the effect of the β particle energy distribution on the determination of P n values using β-neutron coincidences Eq. 2. From observation of the upper panel of Fig. 9, which shows the β intensity distribution followed by 655 Table 4: Average β end-point energy Q βn − E x I β , average Geant4 simulated β efficiencyε β , average β end-point energy in the neutron emission window Q β − E x I βn , and Geant4 simulated average β efficiency for decays to neutron unbound statesε β , for each measured fission product. neutron emission, one expects a larger influence than in the case of independent β and neutron counting. These distributions sample with a large weight the portion of the β efficiency curve which varies strongly because of the low energy threshold. Figure 10 shows the average β efficiencyε β determined 660 experimentally as the ratio N βn /N n (compare Equations 1 and 2). In the figure the isotopes are plotted in the order of decreasing average β end-point energy Q β − E x I βn , to make the trend clearer. The experimental value of the efficiency for detecting a β particle in coincidence with the emitted neutron is 665 25% smaller for 137 I than for 94 Rb or 95 Rb. This would have been the magnitude of the systematic error in the coincidence method for 137 I if this effect was ignored. The experimental determination ofε β gives us the opportunity to verify the accuracy of β efficiencies obtained from 670 Geant4 simulations in the region of strong variation. This is important not only for estimating the corrections in the coincidence method of P n determination but in other types of decay measurements, that also require β tagging. In particular the TAGS technique [49], where the coincidence with the β par-675 ticle eliminates the huge background in the large scintillation detector thus facilitating the measurement of rare isotopes. Determining accurately the β intensity distribution close to the Qvalue depends critically on our knowledge of the β efficiency curve. In order to compare with the measurement we have gen-680 erated β events from the I βn distribution assuming an allowed β shape. Figure 11 compares the experimental and simulated energy spectrum registered in the Si detector. It is remarkable that the simulation is able to reproduce the shapes, distinct for each isotope, which are sensitive to the details of the β inten-685 sity distributions. The integral values are compared in Fig. 10. The MC simulation has been scaled down by a factor of 0.806 to match, on average, the experimental values. The simulation was performed assuming that the implantation position was at the centre of the tape. As was mentioned above, part of the 690 beam was deposited on the supporting structure, which stopped the β particles, thus the effective efficiency was 20% smaller than the nominal value. Apart from this geometrical factor the simulation reproduces the tendency of the measured values to better than 4.5%. The scaled values are shown in Table 4.

Summary and conclusions
We have described a new β-neutron counting system for the measurement of β-delayed neutron emission probabilities. The setup is adapted for measurements at on-line mass separators. The neutron counter uses twenty 3 He tubes distributed inside 700 a large polyethylene neutron moderator. A thin Si detector is used as β counter. A novelty of the apparatus is the use of a self-triggered digital data acquisition system with small acquisition dead time. The time and energy for every detector signal are stored for subsequent analysis. This allows a flexible re-705 construction of events and full control of experimental issues in the data. The characterization of the counting system was performed using fission products with well known β-delayed neutron emission properties: 88 Br, 94 Rb, 95 Rb and 137 I. The ratio of β to neutron detection efficiencies for this setup, which 710 is the parameter used for the determination of P n values, was determined with an uncertainty of 1.6%. This allowed us to improve the P n for the important β-delayed neutron precursor 137 I. Our new value is (7.76 ± 0.14)%.
We studied the effect of β and neutron energy distributions 715 on the average detection efficiencies. They can introduce a systematic error in the determination of P n values. We used Geant4 MC simulations to quantify the effect. For the method of independent β and neutron counting we found that the corrections are very small for the four isotopes investigated. To a large ex-720 tent this is related to the strong energy dependence of the Fermi rate function which leads to large average β end-point energies and small average neutron energies. In the general case, the corrections can be important for decays where the β intensity distribution concentrates at very high excitation energies, due to nuclear structure, and/or onto few levels, as can happen for light nuclei or close to shell closures. The situation is quite different for the β-neutron coincidence counting method. The inevitable noise discrimination threshold in the β counter leads to a strong efficiency variation with end-point energy in the upper part of 730 the decay window. Thus the average efficiency for detecting a β particle in coincidence with a neutron can be very different from the average efficiency for detecting any β particle. The effect is exacerbated when the window for neutron emission decreases. We observed a 25% difference between 137 I and 94 Rb 735 or 95 Rb. This would have been the magnitude of the systematic error if this effect is ignored. On the other hand we found that Geant4 simulations are able to reproduce the isotope dependency of the neutron-gated β efficiency within 4.5%. Likewise Geant4, with the corrected thermal neutron treatment in version 740 10.0 and later versions, was able to reproduce the neutron detection efficiency of a calibrated 252 Cf source within 3.5%. This confirms the suitability of Geant4 to quantify systematic corrections to the P n value coming from the dependency of efficiency with energy. However to evaluate these corrections one needs 745 information on the β intensity distribution and the neutron energy spectrum. For the cases where this information is missing an estimate of the corrections can be obtained from theoretical calculations of the intensity distribution or from some reasonable assumption about this distribution.