Monte Carlo simulations of the Neutron Wall detector system

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Nuclear Instruments and Methods in Physics Research A 528 (2004) 741–762

Monte Carlo simulations of the Neutron Wall detector system Joa Ljungvalla,*, Marcin Palaczb, Johan Nyberga a

Department of Radiation Sciences, Uppsala University, Box 535, SE-75121 Uppsala, Sweden b Heavy Ion Laboratory, Warsaw University, Warszaw, Poland Received 29 March 2004

Abstract A Monte Carlo simulation of the Neutron Wall detector system has been performed using GEANT4. Mechanisms for the detection of neutrons in an aggregate of liquid scintillator detectors have been investigated in details, with the main aim to define optimum conditions for the detection and identification of multiple neutrons. Special emphasis was put on studying the scattering of neutrons between different detectors, which is the main source of the apparent increase of the number of detected neutrons, and hinders the selection of events with more than one emitted neutron. The results of the simulations were compared to experimental data obtained at the EUROBALL spectrometer using fusion–evaporation reactions. The quality of g-ray spectra gated by 2 neutrons was improved 40 times, in terms of the relative intensity of gray lines from nuclei produced with the emission of 2 and 1 neutrons. A similar increase of the relative g-ray intensity was achieved in case of lines associated with the emission of 3 neutrons, with respect to lines from both 2 and 1 neutron evaporation channels. The improvements were only possible with a significant reduction of the intensity of the true 3 neutron emission g-ray lines. The influence of small amounts of g-rays mis-interpreted as neutrons was studied. It was found that it dramatically reduces the quality of the reduction of the effects due to scattered neutrons. r 2004 Elsevier B.V. All rights reserved. PACS: 07.05.Tp; 29.30.Hs; 29.30.Kv; 29.40.Mc Keywords: Monte Carlo simulation; Liquid scintillator neutron detector; In-beam g-ray spectroscopy; GEANT4; EUROBALL; Neutron Wall

1. Introduction In-beam g-ray spectroscopy using heavy-ion fusion–evaporation reactions is one of the most powerful tools for studies of the high-spin structure of nuclides located far from the line of b stability. A unique identification of the residual *Corresponding author. E-mail address: [email protected] (J. Ljungvall).

nuclides, produced in the reaction after the decay of the compound nucleus, is of utmost importance, in particular while exploring unknown regions of the chart of nuclides. In the decay of the compound nucleus, several light particles, mainly protons, a particles, and/or neutrons, are emitted, followed by a cascade of g-rays. A common method used, for identification of the residual nuclides, is to detect all, or at least as many as possible, of the emitted light particles. The Z and

0168-9002/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2004.05.032

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A of the residual nuclides can then simply be determined by subtracting the summed Z and A of all detected particles from the Z and A of the compound nucleus. The most efficient detection systems for this type of studies are arrays of HPGe detectors with ancillary detectors for particle detection, such as the g-ray spectrometer EUROBALL [1,2], supplemented by the ancillary detectors: Neutron Wall [3], a 1p neutron detection array consisting of closely packed liquid scintillation detectors, and EUCLIDES [4], a 4p silicon ball for detection of protons and a particles. With stable (non-radioactive) heavy-ion beams, the most proton-rich nuclides, located close to the proton drip line, can only be produced in reactions where more than one neutron has been emitted. For example, in the region close to the doubly magic nuclide 100 Sn; the lightest Sn isotope studied in-beam is 102 Sn; which only can be reached by emission of at least two neutrons [5]. In a recent EUROBALL experiment, an attempt has been made to produce and study the nuclide 100 In; which only can be reached via a reaction channel in which at least three neutrons are emitted [6]. The cross-sections for production of these proton-rich nuclides, decrease typically by an order of magnitude or more for each emitted neutron. Therefore, an efficient and clean determination of the number of emitted neutrons becomes extremely important. With a closely packed array of neutron detectors, like the Neutron Wall, this is complicated by the ability of the neutrons to scatter between many detectors and give rise to a signal in several detectors. To better understand such multiple scattering processes and to identify methods for improving the discrimination between one neutron channels and channels where more than one neutron is emitted, a Monte Carlo simulation of the Neutron Wall detector array has been performed using GEANT4 [7]. This paper reports on the results of these simulations, which are compared with inbeam data taken at EUROBALL. Sections 2 and 3 briefly describe the Neutron Wall array and the EUROBALL experiments, respectively. The details of the simulations are described in Section 4 and the obtained results in Section 5.

2. The Neutron Wall The Neutron Wall consists of one pentagonal and 15 hexagonal detectors, which can be mounted in the forward hemisphere of EUROBALL, see Fig. 1. The hexagonal detectors, which are of two different types, are sub-divided into three detector segments. The pentagonal detector, located at y ¼ 0 relative to the incoming beam, is sub-divided into five segments. This makes a total of 50 separate detector segments, each with its own photo-multiplier tube (PMT). The symmetries of the detectors are such that the Neutron Wall has seven distinctly different types of detector segments, with central positions at the angles y ¼ 6:9 ; 18:5 ; 30:3 ; 34:9 ; 46:8 ; 47:2 ; and 57:2 relative to the incoming beam. In the analysis of events in which 2 or 3 neutrons have been detected in the Neutron Wall, the detector segments are grouped into geometrically different combinations, also called hit patterns (see Sections 5.8.3 and 5.9). There are 251 and 11,772 geometrically different two and three detector segment hit patterns, respectively, if the order is kept in which the segments are hit (Fig. 2). At EUROBALL, the Neutron Wall has a focal point located 50 mm down stream from the target position. The distance from the focus to the front edge of each detector segment is 510 mm: The walls of the detector cans are made of 2 mm thick aluminum, except for the back plate which is 20 mm thick. A large part of the back plate of each segment is covered by a 5–10 mm thick glass window, on which the PMT is mounted. An aluminum collar, with a height of 25 mm and a thickness of 9:7 mm; is located at the back of each detector. It is used for mounting the detectors by connecting them to each other in a self-supporting way. The part of the detector segments filled with scintillator liquid is 147 mm long, with a volume of 3.2 and 1:1 l; for the segments of the hexagonal and pentagonal detectors, respectively. The scintillator used in the Neutron Wall is BC501A [8], a carbon–hydrogen based liquid with the composition C6 H4 ðCH3 Þ2 (xylene). The mechanism for neutron detection in the scintillator liquid is mainly that of elastic scattering of neutrons and

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Fig. 1. The EUROBALL Neutron Wall detector array. The figure on the left shows the array as viewed from down stream, with the official numbering scheme of the detector segments. The 3D figure on the right shows the aluminum cans of the neutron detectors as modeled in GEANT4, with the beam direction indicated by the arrow, whose starting point is at the target position.

Number of Neutrons

10000

θ=6.9° θ=18.5° θ=30.3° θ=34.9° θ=47.0° θ=57.2°

8000 6000

by the PMT, which is viewing the scintillator liquid. For more information regarding the Neutron Wall see Refs. [3,9].

4000

3. Experimental details 2000 0

0

2

4

6

8 10 12 14 En [MeV]

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18 20

Fig. 2. Simulated energy distributions of neutrons in the laboratory system as obtained by evapOR and GEANT4 using the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ: The shown curves correspond to hits in the different groups of detector segments, with their central position angles indicated in the legend. The detector segments at y ¼ 46:8 and 47:2 are shown together as the y ¼ 47:0 curve. The total number of neutrons emitted in 4p was 106 in this simulation. The scale on the y-axis shows the number of neutrons emitted in each angular group.

protons. When the recoiling protons slow down and stop in the liquid, a part of their kinetic energy, gained in the elastic scattering process, is converted into internal excitations of the molecules of the liquid. When these molecules de-excite, they emit photons of wavelengths suitable for detection

Data from two different EUROBALL experiments have been used in this work. Both experiments were performed at the VIVITRON accelerator at IReS in Strasbourg. In experiment 1, a pulsed beam of 58 Ni ions, with a pulsing frequency of 3:076 MHz and an energy of 220 MeV; collided with a target of 56 Fe with a thickness of 10 mg=cm2 : In the beginning of this experiment the EUCLIDES silicon ball [4] was mounted in the center of EUROBALL. EUCLIDES was removed after the data used for the determination of the total neutron efficiency (see Section 5.5) were collected. In experiment 2, the CUP charged particle veto detector [10] was mounted in the center of EUROBALL, and a DC beam of 58 Ni ions with an energy of 205 MeV was used to bombard a 10 mg=cm2 thick 45 Sc target. The aim of the second experiment was to study excited states of the nuclide 100 In [6],

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produced via the emission of 3 neutrons from the compound nucleus 103 In: An exceptionally large statistics of events with 2 and 3 neutrons was acquired, which for the present work made it possible to evaluate the 3 neutron detection conditions. During experiment 1, the hexagonal detector with segments 23, 24, and 34 was not mounted on the array, segment number 10 contained no liquid, and segment number 46 was out of order. A major service of the neutron detectors, with complete renewal of the scintillation liquid of all detectors, was performed just before experiment 2, which was run with the complete set of 50 working detector segments. Each detector segment of the Neutron Wall produces three parameters for read out: time of flight (TOF), zero-cross-over (ZCO), and energy (QVC). The time of flight of neutrons and g-rays between the target and the detector segments is determined as the time difference between the constant fraction time (CFD) and a common time reference signal. External and internal time references were used for the TOF measurements in experiment 1 and 2, respectively. The RF signal from the VIVITRON beam pulsing system was used as the external time reference. The internal time reference was created as a logical OR of the constant fraction signals from all neutron detector segments. Thus, for each event, the first (fastest) detector segment produced the time reference. This signal is usually generated by a prompt g-ray from the fusion–evaporation reaction, but can also be the fastest neutron, in events where no g-rays were detected in the Neutron Wall, or a delayed or random g-ray, or a random neutron. The average time resolution between any two neutron detector segments was FWHM ¼ 1:5 ns; which defines the time resolution of the TOF measurement using the internal time reference. The external time reference gave a time resolution of FWHM ¼ 6 ns; which is determined mainly by the time resolution of the beam pulsing system. In Section 5, the difference in TOF between two detector segments that have registered a signal in the same event, the so-called DTOF parameter, is frequently used. The time resolution of this parameter is independent of the

time reference type and its value is FWHM ¼ 1:5 ns: The TOF parameter was calibrated using the standard method of delaying the time reference signal by a fixed and known time. The ZCO parameter was used to discriminate neutrons from g-rays, by using the difference in decay time of pulses generated by neutrons and grays in the scintillator liquid. It is also used for creating a signal, which can be used for fast triggering on the hardware pre-selection of the number of detected neutrons in the Neutron Wall. Together with the TOF parameter, the ZCO parameter is also used to set two-dimensional gates during the data analysis to discriminate grays from neutrons. A small fraction of counts inside these gates is due to g-rays, which have both a delayed TOF (e.g. random g-rays) and a delayed ZCO (e.g. due to pile-up). This gives rise to a neutron-g mis-interpretation probability, Png ; which is evaluated in Section 5.6. The QVC parameter, generated by a charge to voltage converter circuit in the Neutron Wall electronics, is proportional to the charge collected at the output of the PMT, and measures the energy deposited in each detector segment. An energy calibration of the QVC parameter was made using a radioactive source of 207 Bi: The low-energy thresholds of the QVC parameter, set by the CFDs of each detector segment, had values in the range 100–200 keV in experiment 1, with an average for all detector segments of about 130 keV: For experiment 2 the average CFD threshold was about 100 keV: A detector segment is said to have fired, when it has registered a signal from a neutron or a g-ray, which is large enough to cross the CFD threshold. Several different trigger conditions, which are used for defining valid events to be read out, were applied when the data sets used for this work were recorded. In experiment 1, the trigger used for determining the total neutron efficiency (see Section 5.5) was set to require the detection of at least two Compton-suppressed g-rays in the HPGe detectors, i.e. there was no trigger condition on the Neutron Wall. All other results from experiment 1 were obtained with a trigger condition defined as a logical OR of the following two conditions: (1) a coincidence between at least one hardware

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pre-selected neutron in the Neutron Wall and at least one Compton-suppressed g-ray in the HPGe detectors, and (2) a coincidence between any hit in the Neutron Wall (g-ray or neutron) and at least three Compton-suppressed g-rays in the HPGe detectors. In experiment 2 the trigger condition was set to require a detection of at least one Compton-suppressed g-ray in the HPGe detectors and either one or two (for different parts of the data set) hardware pre-selected neutrons in the Neutron Wall. Energy and efficiency calibrations of the HPGe g-ray spectra were made using standard radioactive sources. For further details on the electronics of the Neutron Wall see Ref. [9].

3.1. g-ray spectra Many of the results presented in Section 5, are based on the analysis of discrete peaks in gated gray spectra, recorded by the HPGe detectors of EUROBALL. The primary gate applied, was a two-dimensional (2D) gate set on the TOF and ZCO parameters, to determine the number of segments that detected neutrons in each event. In addition, other gates were set, as explained in Section 5. The gated g-ray spectra were sorted using the package tscan [11]. All relevant extracted results, are based on ratios of counts of peak areas in the gated spectra. The peak areas, corresponding to transitions in specific residual nuclides, were determined by using the GF3 program of the RadWare g-ray spectroscopy analysis package [12]. Results obtained from experiment 1 are based on transitions in the residual nuclides 110 Te; 111 Te; and 111 Sb; which are produced via the 2p2n, 2p1n, and 3p0n reaction channels, respectively. In experiment 2, transitions in 99 Cd; 99 Ag; and 99 Pd corresponding to the reaction channels 1p3n, 2p2n, and 3p1n, respectively, were used. A few of the g-ray spectra used in the analysis are shown in Figs. 3 and 4, with the applied neutron gate and other conditions written in the legend of each spectrum.

745

4. Monte Carlo simulation Two Monte Carlo based simulation programs were used in this work. The energy and angular distributions of the neutrons emitted in the heavyion fusion–evaporation reaction, were simulated by the evapOR package [13]. For the simulation of the interaction of the neutrons in the Neutron Wall, the GEANT4 detector simulation package from CERN [7] was used. In the following subsections the most important aspects of the Monte Carlo simulations will be discussed. 4.1. Geometry To make the implementation of the geometry in GEANT4 less complex, some simplifications were made. Only the aluminum cans and the scintillation liquid of the neutron detectors were included in the geometry. The g-ray absorbers in front of the detectors (1 mm Pb and 1 mm Cu), the glass windows between the detector and the PMT, the PMTs and their holders, voltage dividers, and other small details such as screws and screw holes, were all excluded. The influence of material surrounding the Neutron Wall was also investigated by simulations with materials of different Z. A plastic shell, with an inner radius of 10 cm and a thickness of 1 cm was simulated to model the support frame, cables, etc., of EUCLIDES. A concrete-like floor was simulated to model the structure of the experimental hall. Finally a 3p shell consisting of 210 kg of germanium was simulated to model the HPGe detectors of EUROBALL. None of these structures affected the results, and therefore, it was concluded that the structures outside the Neutron Wall could be excluded from the simulation. On the right-hand side of Fig. 1 a view of the Neutron Wall, as used in the GEANT4 simulation, is shown. 4.2. Event generation and physical processes In GEANT4, each event begins with a generation of the primary particles to be tracked, which in this work are neutrons. The energy and angular distribution of the neutrons in the laboratory

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J. Ljungvall et al. / Nuclear Instruments and Methods in Physics Research A 528 (2004) 741–762 Condition ≥ 0n

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+

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Energy [keV] Fig. 3. g-ray spectra from the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ: The spectra shown in panel (a) and (b), use a subset of the data, which is suitable for determination of the efficiency of the Neutron Wall (see Section 5.5). The effects of using different conditions to reduce the influence of neutron scattering, are shown in the 2n gated spectra in panels (c–f), see Section 5.8.

system, were generated in two different ways. The first and simple way, was to use a flat energy distribution in the range 0–10 MeV and an isotropic angular distribution. Such distributions are used in Section 5.2, for the simulation of the

TOF and QVC response functions of the neutron detector segments. The second and more complex way, was to generate the neutrons by evapOR [13]. The evapOR simulations were run using default input parameters, for the same projectile–target

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Energy [keV] Fig. 4. g-ray spectra from the reaction 58 Nið205 MeVÞ þ 45 Scð10 mg=cm2 Þ: Spectrum (a) is made with the requirements that three neutrons have been detected in the Neutron Wall. Spectrum (b) has been produced using the scattering discrimination technique referred to as method 4 in Section 5.9.

combination, beam energy, and target thickness as in experiment 1. Neutron energy and angular distributions generated by evapOR for the reaction used in experiment 2 were compared to the distributions obtained for experiment 1. It was concluded that the small differences observed for the two reactions justify using one set of evapOR data for the simulation of neutrons in the two experiments. The GEANT4 simulations using neutrons generated by evapOR were either based on events taken directly from the evapOR output, or sampled from evapOR neutron energy and angular distributions, as illustrated in Fig. 2. In the simulation made in this work, it was assumed that the main contribution to the signals from the neutron detector segments, originates from elastic scattering of neutrons and protons. Inelastic scattering and neutron capture on carbon were also simulated, but their influence was assumed only to change the energy and direction of the incident neutrons, and not to produce enough scintillation light to be registered by the PMTs. This simplification is well justified, due to the low energy of the carbon recoils and the smaller light yield per unit energy for carbon compared to proton recoils.

The simulations were made both including and excluding the effects of g-rays hitting the Neutron Wall. g-rays were included using a simple model, randomly letting a g-ray hit a detector segment every 200th event. This corresponds approximately to the experimental neutron-g mis-interpretation probability Png ¼ 0:6% (see Section 5.6). The energy and time of flight distributions of the g-rays were flat and ranged from 0–5 MeV and 10–70 ns; respectively. The emitted neutrons were tracked by GEANT4 until they escaped from an 8 m3 volume of air, in which the Neutron Wall was placed, or until their kinetic energy was less than 50 keV: This energy limit was chosen to be low enough to give a negligible contribution to the total energy deposited in any detector segment. 4.3. Data obtained from the simulated events Simulated TOF and QVC parameters were produced in the GEANT4 tracking for each detector segment separately. The ZCO parameter was modeled simply by the inclusion of the neutron-g mis-interpretation probability mentioned in the previous subsection.

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The time of the first interaction, which deposited an energy larger than the CFD threshold, was used as the simulated TOF parameter. A random number, sampled from a Gaussian distribution with an expectation value of 0 and a width corresponding to the experimental time resolution, was added to the simulated TOF parameter. This represents the intrinsic time resolution of the neutron detectors. The simulated QVC parameter was created by converting the energy transferred to the recoiling protons in the elastic scattering process, Ep ; into electron equivalents, Eee ; according to the following relation: Ep p0:32 MeV;

Eee ðEp Þ ¼ A0  Ep ;

Ep > 0:32 MeV; Eee ðEp Þ ¼ a0  ½1  expða1  Epa2 Þ þ a3  Ep :

ð1Þ

5.2. TOF and QVC response functions The TOF and QVC response functions of the Neutron Wall, i.e. the TOF and QVC distributions recorded by each detector segment as a function of neutron energy, were calculated in the following way. A simulation was performed using an isotropic angular distribution with neutron energies in the interval 0–10 MeV; sampled from a flat energy distribution, with no correlations between energy and angle. A CFD threshold of 130 keV; corresponding to a recoil proton energy of 0:75 MeV; was chosen, which gives the best agreement with the experimental total neutron efficiency and neutron scattering probability (see Sections 5.5 and 5.7). This CFD threshold value was used in all simulations described below. The simulated TOF and QVC response functions for 2,

0.7 0.6 0.5

εi

These equations and the constants A0 ; a0 ; a1 ; a2 and a3 ; were taken from Ref. [14]. For neutrons, which have scattered several times in the same detector segment, the energy deposited in each scattering reaction, was converted into electron equivalents before summing. A random number sampled from a Gaussian distribution, with an expectation value of 0 and a standard 3=2 deviation of sQVC ¼ 0:04Eee ; was added to each QVC value [15]. The expression for sQVC represents the intrinsic energy resolution of the neutron detectors, and is the best estimate available for the detector segments of the Neutron Wall. Effects such as the attenuation of the light signal in the scintillator liquid and the different light collection characteristics, depending on where in the detector segment the energy was deposited, were not included in this work.

the recoil proton energies Ep ¼ 0:25; 0.50, 0.75, 1:0 MeV; and which give an average intrinsic efficiency of 55%, 50%, 45%, and 40%, respectively. The dips in the efficiency curves at about 6 and 8 MeV are due to an increase in the 12 Cðn; n0 gÞ12 C cross-section at these energies, resulting in scattered neutrons with too low energy to be detected. The sharp kink in the efficiency at about 3 MeV is due to a decrease in the crosssection for elastic scattering of neutrons on carbon (Fig. 5).

5. Results

0.4 0.25 MeV 0.50 MeV 0.75 MeV 1.0 MeV

0.3 0.2

5.1. Simulated intrinsic neutron efficiency The intrinsic efficiency of the Neutron Wall was calculated using GEANT4 as a function of neutron energy for different CFD thresholds as shown in Fig. 5. The thresholds used were 23, 68, 133, and 210 keV; which according to Eq. (2) correspond to

0.1 0 0

1

2

3

4

5

6

7

8

9

10

En [MeV] Fig. 5. Intrinsic neutron efficiency, ei ; as a function of neutron energy, En ; for different CFD thresholds as shown in the legend.

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DEn ¼ 2

Dt En t

ð2Þ

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Experimental TOF spectrum. Simulated TOF spectrum, neutron from evapOR. Simulated TOF spectrum, En=2 MeV. Simulated TOF spectrum, En=5 MeV. Simulated TOF spectrum, En=8 MeV.

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0

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TOF [ns] Fig. 6. Experimental and simulated neutron TOF distributions. The three curves with narrow peaks are simulated TOF response functions for neutrons with energies En ¼ 2; 5, and 8 MeV: The experimental distribution and the simulated one, with neutron energy distribution from evapOR, are for the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ: These two distributions were normalized to have the same number of counts in the region 0–90 ns: The arrow indicates the flight time of a 0:75 MeV neutron to the back of the detector segments.

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En=2 MeV En=5 MeV

5000

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Counts

5, and 8 MeV are shown in Figs. 6 and 7, respectively. The TOF response show the expected broadening due to the rather large thickness of the detector compared to the distance between the target position and the detector (see Fig. 6). The TOF of 5 MeV neutrons to the front and back of the detector segments is 17 and 23 ns; respectively. About 6% of the 5 MeV neutrons have TOF values larger than 23 ns: Similar numbers are obtained also for the other neutron energies. This effect is due to neutrons that have scattered against the hydrogen or carbon in the scintillator liquid, without giving rise to a signal large enough to cross the CFD threshold, or against the aluminum in the back plate before being detected. Such scattered neutrons lead to significantly larger TOF values, which is observed as a tail on the right-hand side of the TOF responses. The flight time of a 0:75 MeV neutron, corresponding to the CFD threshold, to the back of the detector segments is 60 ns; which is indicated by an arrow in Fig. 6. The finite time resolution will translate into a finite energy resolution according to the equation

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1.5

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Eee [MeV] Fig. 7. QVC response of the Neutron Wall for neutrons with energies En ; as shown in the legend. The histograms shown are for the summed QVC response, obtained by summing, in each event, the QVC values from all detector segments that detected a signal larger than a CFD threshold value of 130 keV: Each histogram was simulated using 105 events.

where t is the time of flight of the neutron and Dt is the time resolution of the detector. Using this equation, calculated energy resolutions are shown in Table 1, for neutrons with energies En ¼ 2; 5, and 8 MeV; with the t and Dt values obtained as the centroid and FWHM, respectively, in Fig. 6. The simulated QVC response function is shown in Fig. 7 for neutrons with energies En ¼ 2; 5, and 8 MeV: The shown curves were calculated as the total energy deposited in the Neutron Wall, i.e. by summing for each event the QVC values from all detector segments, which gave a signal larger than the CFD threshold. It is clear from Fig. 7 that the QVC response of the Neutron Wall is rather bad, a fact that is true for all liquid scintillator based neutron detectors. Due to the kinematics of the neutron scattering process in the liquid, there is a rather large probability that a neutron will deposit only a small fraction of its energy in the detector.

5.3. TOF distribution The experimental and simulated total neutron TOF distributions, summed over all detector segments, are shown in Fig. 6. The experimental data are from experiment 1. For the simulation,

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Table 1 Simulated energy resolutions for neutrons with energies 2, 5, and 8 MeV: The values in columns 2 and 3 are obtained from the data shown in Fig. 6. The energy resolution DE shown in column 4 is calculated using Eq. (2), using the values in columns 1–3 E (MeV)

t (ns)

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2 5 8

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0.67 2.0 5.3

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750

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20

30

40

50

60

θ [Deg.]

neutrons from evapOR were used as input to GEANT4 on an event by event basis. As can be seen in Fig. 6, the simulated neutron TOF distribution is shifted towards longer flight times (lower neutron energies) relative to the experimental one. The maxima of the two spectra are shifted by about 3:7 ns; corresponding to an energy shift from 2.7 to 3:6 MeV: The shift is probably due to differences in the experimental and simulated (evapOR) neutron energy distribution. The experimental and simulated TOF distributions for each detector segment look very similar to the total one shown in Fig. 6. The origin of the tail visible for large TOF values ð> 40 nsÞ in the experimental spectrum shown in Fig. 6 is not fully understood. The events in the tail are in coincidence with g-rays from the fusion evaporation reaction detected by the HPGe detectors of EUROBALL, i.e. they are not due to random coincidences.

Fig. 8. Experimental and simulated neutron angular distributions for the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ: The error bars of the simulated data points are smaller than the symbols used. See the text for further details.

5.4. Neutron angular distribution

The experimental and simulated total neutron efficiencies were evaluated from data taken in experiment 1. The experimental total neutron efficiency was determined from a subset of the data in which no trigger requirements were set on the Neutron Wall. The trigger for valid events, was instead defined as a detection of at least two g-rays by the HPGe detectors of EUROBALL. The experimental total neutron efficiency is defined as a ratio of two peak areas according to the following equation:

The experimental and simulated neutron angular distributions are compared in Fig. 8. The number of neutrons detected in each angular group of equivalent detector segments, with the detector segments at y ¼ 46:8 and 47:2 added together, divided by the number of detector segments per group, is plotted as a function of the angle of the central position of the detector segments relative to the incoming beam. The data points of the simulation are normalized to the experimental values according to the total number of detected neutrons. As can be seen in Fig. 8, the

agreement between the experimental and simulated angular distribution is not perfect. The difference is, however, small enough not to have any large influence on the results presented in this work. The error bars shown are the sample standard deviation, illustrating for the experimental data points the large spread in the number of counts recorded by detector segments located at the same y angle. A similar large spread was also observed for g-rays detected in the Neutron Wall. The reason for the spread is mainly due to differences in the CFD thresholds mentioned in Section 3. 5.5. Total neutron efficiency

en  P1n X1n ¼

A1n X1n A1n X0n

ð3Þ

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A1n X1n is the number of counts in the area of a peak, corresponding to a reaction channel in which one neutron has been emitted, indicated by the superscript ð1nÞ; in a g-ray spectrum created with the condition that at least one neutron was detected, indicated by the subscript ðX1nÞ: Similarly A1n X0n is the number counts in the same peak in a g-ray spectrum created without any conditions on the Neutron Wall. The strong peaks at 539, 683, and 716 keV; corresponding to g-ray transitions in 111 Te; produced via the 1n reaction channel 56 Feð58 Ni; 2p1nÞ111 Te; were analyzed, see the gray spectra in Figs. 3(a) and (b). The experimental total neutron efficiency obtained was about en ¼ 0:26; which is an average value calculated for the three chosen transitions. The quoted value is for the complete Neutron Wall, i.e. it has been corrected for the five missing detector segments in experiment 1. The simulated total neutron efficiency was en ¼ 0:32: The reason for the difference between the experimental and simulated result is not fully understood. The most important parameter that affects the efficiency is the CFD threshold. The CFD threshold value used in the simulation was 130 keV; i.e. identical to the average experimental threshold in experiment 1. This threshold value gives a good agreement between the experimental and simulated neutron scattering probabilities (see Section 5.7). Increasing the CFD threshold to 340 keV gives a simulated total neutron efficiency of E25%; but in this case the scattering probability is underestimated by a factor of two. The larger simulated total neutron efficiency is, however, not due to the difference between the experimental and simulated energy distributions in the region 5–10 MeV; mentioned in Section 5.3, since the intrinsic neutron efficiency is rather energy independent in this energy region (see Fig. 5). A difference between the experimental and simulated total neutron efficiencies could finally also be due to the scattering of some of the neutrons against other material than the Neutron Wall in the experiment. Such scattering effects may change the initial direction of the emitted neutrons in such a way that they do not enter the neutron

751

detector segments. The simulation of a plastic shell, as described in Section 4.1, was an effort made to study these effects. No noticeable effect on the total neutron efficiency could, however, be observed using a plastic sphere with an inner radius of 10 cm and a thickness of 1 cm: 5.6. Mis-interpretation of g-rays as neutrons The neutron-g mis-interpretation probability is defined as Png  P0n X1n ¼

A0n X1n A0n X0n

ð4Þ

where A0n X1n is the number of counts in a peak associated with a nuclide produced via a reaction in which zero neutrons were emitted, demanding that at least one neutron has been detected, and A0n X0n is the peak area of the same transition with no requirements on neutron detection. The misinterpretation probability was extracted from the 3p0n channel 111 Sb; using the 271 and 851 keV transitions. The result obtained was Png ¼ 0:63ð8Þ%: Note that this number depends rather strongly on the g-ray multiplicity associated with the specific reaction channel. 5.7. Scattering characteristics One of the major problems with a closely packed array of scintillator detectors used for neutron detection, is the scattering of neutrons between the different detectors. The scattering gives rise to signals from more than one detector, creating an ambiguity regarding the actual number of different neutrons detected. In Table 2, the experimental and simulated neutron scattering probability for experiment 1 is shown for different values of the parameter NS ; which gives the number of detector segments located between the two detector segments that have fired. For neighboring detector segments, with two sides facing each other, e.g. detector segment number 0 and 24 in Fig. 1, NS is defined to be 0, while NS ¼ 1 for neighboring detector segments, with only two edges lying close by (e.g. detector segment number 0 and 34). Using these

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Table 2 Scattering characteristics of the Neutron Wall obtained for the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ; for different values of the parameter NS ; which gives the number of detector segments between the two detectors that have fired. The scattering probability P1n X2n is shown in columns 1–3 for the simulation without and with inclusion of mis-interpreted g-rays, and for experiment 1, respectively. Columns 5–7 show the same data as in columns 2–4, but normalized to 100% for the total scattering probability, which is given on the last row of the table. The average experimental QVC threshold of 130 keV; which corresponds to a proton recoil energy of 0:75 MeV; was also used in the simulation NS

P1n X2n Sim

Sim þ g

Exp

0 1 2 3 4 >4

0.056 0.0060 0.00058 0.00031 0.00034 0.00054

0.055 0.0062 0.0013 0.0011 0.00098 0.0015

0.0572(2) 0.0076(4) 0.0017(2) 0.0010(1) 0.00079(7) 0.00117(7)

X0

0.064

0.068

0.0695(3)

definitions, all larger values of NS can easily be obtained from Fig. 1. The experimental scattering probability P1n X2n ; is defined as the probability that one neutron is scattered in the Neutron Wall in such a way that it gives rise to a neutron signal in two or more detector segments. It is defined as a ratio of two peak areas according to the following equation: P1n X2n ¼

A1n X2n A1n X1n

ð5Þ

A1n X1n is the number of counts in the area of a peak, corresponding to a reaction channel in which one neutron has been emitted, indicated by the superscript ð1nÞ; in a g-ray spectrum created with the condition that at least one neutron was detected, indicated by the subscript ðX1nÞ: Similarly A1n X2n is the number counts in the same peak in a g-ray spectrum created with the condition that at least two neutrons were detected. Additional conditions, e.g. on NS ; may be set when the g-ray spectra are created, in order to study their effects on the scattering probability. The g-ray peaks selected for the determination of the experimental scattering probabilities were the same as used for evaluating the total neutron efficiency (see Section 5.5), namely the 539, 613, and 716 keV peaks due to transitions in 111 Te;

Sim (%) 88 9.4 0.91 0.48 0.53 0.84 100

Sim þ g (%) 82 9.7 2.1 1.6 1.6 2.8 100

Exp (%) 82(5) 10.9(7) 2.5(2) 1.4(2) 1.1(1) 1.9(1) 100

which was produced in the reaction Feð58 Ni; 2p1nÞ111 Te: As seen in Table 2, the scattering probability P1n X2n changes only marginally for values of NS X2: The reason for this is that scattered neutrons with large values of NS mostly travel across the Neutron Wall, outside the scintillator liquid, before interacting a second time. Experimentally, 6.95(3)% of the detected neutrons produce a signal in more than one detector segment (see last row of Table 2). For the simulation, with neutrons obtained from evapOR, the fraction of neutrons that causes a signal from more than one detector segment, is 6.4%. Adding the effect of misinterpreted g-rays, the simulated scattering probability increases to 6.8%, in good agreement with the experimental value. Depending on the exclusion or inclusion of mis-interpreted g-rays, 88% or 82%, respectively, of these false two neutron signals are from neighboring detector segments, which agrees well with the experimental value of 82(5)%. In experiment 2 the scattering probability was significantly higher, P1n X2n ¼ 12%: This can be partly explained by the lower QVC threshold used in this experiment. Other possible contributions to the higher scattering probability have been considered, such as more forward peaked neutron 56

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angular distribution due to the reaction kinematics, or larger average neutron energy. However, the higher P1n X2n value could not be fully explained. 5.8. Discriminating between 2n and scattered 1n events In this section, a 2n event is defined as two emitted and two detected neutrons, while a scattered 1n event is defined as one emitted and two detected neutrons. To quantify the success of the discrimination of scattered 1n events from 2n events, the following experimental enhancement factor is defined: R2n 1n ðxÞ ¼

2n A2n 2n ðxÞ=A2n : 1n A2n ðxÞ=A1n 2n

ð6Þ

This factor is a double ratio of four peak areas A; for which the superscript indicates the number of emitted neutrons and the subscript the number of detected neutrons, and x the additional conditions (see below). The ratio in the numerator of R2n 1n ðxÞ; 2n i.e. A2n 2n ðxÞ=A2n ; gives for a peak belonging to a reaction channel in which two neutrons were emitted, the fraction of counts left in the peak after condition x has been applied. Ideally, this ratio should be 1, in which case no 2n events were 1n lost. The ratio in the denominator, A1n 2n ðxÞ=A2n ; gives with identical condition x; the fraction of counts left in a peak belonging to a reaction channel in which only one neutron was emitted. If the scattering reduction method works perfectly, this ratio should be 0. Thus, the enhancement factor R2n 1n ðxÞ should be maximized, and it is a measure of how well the applied condition x enhances 2n events compared to scattered 1n events, without loosing too many of the 2n events. For the calculation of R2n 1n ðxÞ from simulated data, the number of events with two detected neutrons and one or two emitted neutrons were used instead of peak areas. The experimental R2n 1n ðxÞ factor were calculated using areas of the 513, 658, and 745 keV peaks due to g-ray transitions in 110 Te; which is produced in the 2p2n reaction channel, and areas of the 539, 683, and 716 keV peaks due to transitions in 111 Te; produced in the 2p1n reaction channel. These

753

peaks are labeled in the g-ray spectra shown in Fig. 3. In the next sections, four different conditions x; and combinations of them, are described. The results are shown in Table 3. 5.8.1. Neighbor rejection using NS A simple and straight forward technique to discriminate between 2n and scattered 1n events is the so called neighbor rejection. This technique assumes that neutrons detected in detector segments located close to each other are due to scattered neutrons. The parameter NS (see Section 5.7) is used as a measure of the distance between the detector segments. As seen in Table 3, the experimental and simulated (including mis-interpreted g-rays) R2n 1n ðNS Þ factor is about 7 for NS X2: In this case 44% and 52% of the 2n events are lost in the simulation and experiment, respectively. Increasing NS further gives only a marginal improvement of the R2n 1n ðNS Þ value. 5.8.2. DTOF and NS gating The neighbor rejection technique can be combined with gates on the time difference, DTOF; between the TOF signals from the two firing detector segments. It uses the fact that the correlation between the DTOF value and the distance from one interaction point to the other is different for 2n events and scattered 1n events [16]. Using NS as the distance parameter, the absolute value of the DTOF will increase with increasing NS for scattered 1n events, while for 2n events the DTOF will not change. This is illustrated in Fig. 9. The experimental distributions in Fig. 9 were obtained by gating on discrete g-rays detected by the HPGe detectors of EUROBALL. For the 1n events, background subtracted gates were set on the 539, 683, and 716 keV g-ray transitions in the 2p1n reaction channel, while for the 2n events gates were set on the 513, 658, and 745 keV transitions in the 2p2n channel. In the 2n spectra, with NS ¼ 0; about one-fifth of the events look like scattered 1n events. This is due to the rather high probability that two emitted neutrons will be detected as a two neutron event because one of the neutron has scattered while the

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Table 3 Enhancement of 2n events over scattered 1n events in the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ: Columns 1–3 give the different applied conditions, columns 4–6 the fraction of events left of a reaction channel with two emitted neutrons, and columns 7–9 the obtained enhancement factor R2n 1n ðxÞ: The parameter x indicates the different applied conditions. The results of the simulations are given both excluding and including mis-interpreted g-rays A2n ðxÞ 2n A2n 2n

Conditions x

R2n 1n ðxÞ

ð%Þ

NS

DTOF ðnsÞ

QVC and TOF

Sim

Sim þ g

Exp

X0 X1 X2 X3

— — — —

— — — —

100 70 56 43

100 71 56 43

100 63(1) 48.3(8) 37.4(7)

1.0 5.7 19 22

1.0 4.0 7.3 7.4

1.00 3.66(7) 7.2(2) 9.1(3)

X0 X1 X2 X3

jDTOFj > 10 1 > jDTOFj > 15 4oDTOFo6 9oDTOFo15

— — — —

51 47 45 39

51 47 44 39

44(2) 38.3(6) 35.4(6) 31.1(6)

6.5 51 103 103

5.2 16 23 22

3.51(8) 10.8(3) 27(1) 27(1)

—

Individual

—

53

53

42.6(7)

7  102

20

23.5(9)

X0 X2

— 4oDTOFo6

yes yes

49 26

48 25

63(1) 23.2(5)

1.9 6  103

2.0 120

0.92(2) 37(3)

NS = 0 Simulated 1n events 2n events

1000

20000

500 Simulated with γ 1n events 2n events

40000

⋅-7 10

Simulated with γ 1n events 2n events

⋅0

0

1000 500

20000 ⋅-7 10

0 Experimental 1n events 2n events

40000

Counts

Counts

0

0.6 ⋅ 0

Experimental 1n events 2n events

1000 500

20000 0

Exp

NS = 4

Simulated 1n events 2n events

40000

Sim þ g

Sim

-7 ⋅ 10

-50

0 ∆TOF [ns]

50

⋅0

-50

0 ∆TOF [ns]

50

Fig. 9. Experimental and simulated DTOF distributions obtained in the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ for 2n and scattered 1n events with NS ¼ 0 (left panel) and NS ¼ 4 (right panel). The simulated results are shown both with and without g-rays mis-interpreted as neutrons ðPng ¼ 0:5%Þ: For NS ¼ 0 the experimental and simulated distributions were normalized to have the same number of counts for scattered 1n events, while for NS ¼ 4 they are normalized to have the same number of counts for the 2n events. The 2n distributions with NS ¼ 0 and 1n distributions with NS ¼ 4 have been scaled up in the plots by a factor of 4.

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other one was not detected. The DTOF is defined as positive if the interaction with the highest deposited energy ðQVCÞ comes first. As can be seen in Fig. 9, this is most often the case. This definition is very useful, because it keeps the information regarding the difference in deposited energy between the two emitted neutrons, and shifts the DTOF distribution towards positive values. This is the reason why the chosen DTOF gates, listed in Table 3, are placed asymmetrically around DTOF ¼ 0 ns: The simulated distribution of 1n events with NS ¼ 4 (middle right panel of Fig. 9) have a larger proportion of mis-interpreted g-rays with negative DTOF than the experimental data. This is due to the flat QVC and TOF distributions of the simulated random g-rays. The upper QVC limit for neutrons ðEð1=t2 ÞÞ means that on average both the QVC and the TOF for simulated g-rays are larger than for neutrons. Combining neighbor rejection ðNS Þ and DTOF increases the experimental enhancement factor R2n 1n ðNS ; DTOFÞ to 27, which with NS X2 comes with a cost of loosing 65% of the 2n events, see Table 3. The simulated results for R2n 1n ðxÞ in column 7 of Table 3 do not agree very well with the experimental results, in particular for large NS values. The main reason for this is g-rays that have been mis-interpreted as neutrons. When the number of events with a required number of real detected neutrons is small compared to the number of grays, the mis-interpreted g-rays start having a large impact. In Fig. 9, the simulated DTOF distributions excluding and including mis-interpreted grays are shown together with the experimental distribution for 2n and scattered 1n events. The effects of including a fraction of 0.5% (see Sections 4.2 and 5.6) of mis-interpreted g-rays, is clearly seen as an enhancement of scattered 1n events in the region jDTOFjo20 ns in the NS ¼ 4 panel of Fig. 9. Thus, the mis-interpreted g-rays give rise to events that look like scattered 1n events, with small DTOF values, despite a large NS value. After inclusion of a fraction of 0.5% of mis-interpreted g-rays, the agreement between the experimental and simulated DTOF distributions is very good, as can be seen in the right panel of Fig. 9. The agreement between experimental and simulated

755

R2n 1n factors is also very good, see columns 8 and 9 in Table 3. The g-rays do not influence the 2n events very much, as is seen in columns 4 and 5 of the table. A conclusion regarding this is that if the fraction of mis-interpreted g-rays could be reduced, much larger R2n 1n factors (and cleaner g-ray spectra) could be achieved using a combination of the NS and DTOF conditions. An increased lead shielding of the Neutron Wall would reduce the neutron-g mis-interpretation probability, Png ; quite substantially. This is, however, difficult to implement from a technical point of view, due to the weight of the shielding material. With additional material close to the detectors, there is also a risk of creating additional neutrons by reactions with the lead, which could obscure weak reaction channels close to the proton drip line.

5.8.3. Individual DTOF gating In the previous section the DTOF gates were chosen based on the NS values, in which case all combinations of pairs of detector segments with the same NS value, use the same DTOF gate. Although the NS parameter is strongly correlated with the distance between the detector segments, the distance is not identical for all pairs. This is in particular true for all combinations involving segments of the pentagonal detector, which are much smaller than the segments of the hexagonal detectors. Instead, in this section we consider individual DTOF gates for each of the 251 geometrically different combinations (hit patterns) of pairs of detector segments (see Section 2). In theory, this should give better discrimination than just using different DTOF gates for each NS value. The individual DTOF gates were set by visual inspection of each of the 251 distributions of DTOF; using the simulated data set, without misinterpreted g-rays. In Fig. 10, two examples on how these gates were set, are shown. The gates were deliberately set wide, to keep a large fraction of the 2n events. The results of the individual DTOF gating is shown in Table 3. The experimental enhancement factor R2n 1n that was obtained is 24, with a loss of 57% of the 2n events.

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756 500 400

1n events Combination 0

2n events 300

Counts

200

-15 ns→19 ns

100 0 1000 800

1n events Combination 120

2n events

600 400

-6.3 ns→12 ns ns

200

0

-50

0 ∆TOF [ns]

50

Fig. 10. Examples of how the individual DTOF gates are set for discrimination of scattered 1n events. The vertical lines indicate the gates used. The DTOF distributions are obtained from a simulation excluding mis-interpreted g-rays. The detector segments belonging to combination 0 (e.g. segments 1 and 6) are further apart than those belonging to combination 120 (e.g. 3 and 34).

5.8.4. QVC and TOF gating In theory, it is possible to separate scattered 1n events from real 2n events by correlating the fastest time of flight with the total energy deposited by the neutrons in the Neutron Wall. With ideal neutron detectors, regarding TOF resolution, energy collection, energy resolution, and efficiency, there would be a clear separation of scattered 1n and 2n events. If the total deposited neutron energy is plotted against the fastest TOF for an ideal system, the scattered 1n events would be located on a discrete line (energy BTOF2 ), while the 2n events would be distributed over a large range. For each TOF value their total deposited energy would, however, always be larger than the total deposited energy for scattered 1n events. Thus, there would be no overlap of scattered 1n and 2n events in such a plot and the separation would be trivial. Correlating the energy deposited by the neutrons in the Neutron Wall with their flight times, to determine whether the event is of type 2n or scattered 1n, is complicated due to the imperfect energy and TOF responses (see Section 5.2). The energy response (QVC) is in particular very bad and leads to an incomplete collection of the energy of the neutrons that hit the Neutron Wall, as

shown in Fig. 7. In addition, the light output as a function of deposited neutron energy is non-linear (see Eq. (2)), which means it depends on how many times the neutron scatters in a detector segment, although this effect is rather small. Regarding the TOF response, the largest effect is due to the finite length of the detectors, which leads to a broadening of the TOF distribution (see Fig. 6). In Fig. 11, a 2D plot of the total collected energy, Eee ; which corresponds to the experimental QVC parameter summed over all detector segments, versus the fastest TOF is shown for a simulation of the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ: The calculation uses the TOF and QVC response functions described in Section 5.2. The background visible in the 1n plot is due to the way mis-interpreted g-rays are implemented in the simulation. They have no correlation between TOF and QVC and therefore give rise to a uniform background in this plot. Cuts in the 2D histogram shown in Fig. 11, at the TOF values 15, 20, 25, and 30 ns; are shown in Fig. 12. As can be seen in these figures and from the two identical polygons drawn in Fig. 11, there is a very large overlap of the QVC versus fastest TOF distribution for scattered 1n and 2n events.

Fig. 11. Simulation of the total energy, Eee ; converted to electron equivalents, versus fastest TOF for scattered 1n (upper) and 2n events (lower) produced in the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ: The region marked with a polygon is the same in both panels, and illustrates the small shift of the two distributions. The background visible for large QVC values in the 1n plot is due to mis-interpreted g-rays.

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20ns 1n 2n

3000

400

2000

200

1000

0 4000 3000

0 25ns 1n 2n

30ns 1n 2n

0 1500

Counts

Counts

600

757

1000

2000 500 1000 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 Eee [MeV]

Eee [MeV]

Fig. 12. Simulated total energy, Eee ; converted to electron equivalents, for 1 ns wide TOF cuts in the histograms shown in Fig. 11. The cuts were made at the TOF values shown in the legends.

Using only QVC and TOF gating, with no conditions on NS and DTOF; it was possible to achieve an R2n 1n ðxÞ factor of approximately 2 in the simulations, see Table 3. Experimentally the result was even worse (Fig. 12). The simulations, however, indicated that QVC and TOF gating together with conditions on DTOF and NS may give an improvement regarding the enhancement factor. The reason for this can clearly be seen in Fig. 13, showing simulated results of a 2D plot of QVC versus TOF with an applied DTOF and NS gate. In the simulation, the scattered 1n events, which were not rejected by the DTOF and NS gating, have a different QVC versus TOF distribution than the 2n events, since the scattered 1n events that are left consist mostly of mis-interpreted g-rays. The 2D gates, such as the one shown as a polygon in Fig. 13, were determined by a trial and error procedure guided by visual inspection of plots of QVC versus TOF. Separate plots were used for scattered 1n and 2n events, and the 2D gate was adjusted in order to maximize the enhancement ratio and to keep as many as possible of the 2n events. The QVC and TOF gating, together with conditions on DTOF and NS ; was also tried on the experimental data. In Fig. 14 experimental

Fig. 13. Same as Fig. 11 with the additional conditions that DTOFp10 ns and NS ¼ 4: The polygon marks the 2D gate, which was used to discriminate scattered 1n and 2n events.

plots of QVC versus TOF are shown. The upper and lower figures are gated on g-ray peaks belonging to a nuclide produced via emission of one and two neutrons, respectively. The 2D gate shown was determined in a similar way as for the simulated data, i.e. using a trial and error procedure to maximize the enhancement factor, without loosing too many of the 2n events. Using combined QVC and TOF and DTOF and NS gating, an experimental enhancement factor of

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Fig. 14. Experimental distribution of total QVC versus fastest TOF for the reaction 58 Nið220 MeVÞ þ 56 Feð10 mg=cm2 Þ are shown on the left hand side. The data used for these plot are the raw (un-calibrated) QVC and TOF parameters, with a TOF calibration of 13 ch=ns: The upper figure is gated on g-ray peaks (539 and 683 keV) belonging to the 2p1n reaction channel, while the lower one is gated on peaks (658 and 745 keV) belonging to the 2p2n channel. No other conditions were applied on these plots. A suitably normalized fraction of the total QVC versus TOF histogram was subtracted from each of the shown plots. The polygon marks the gate used for discriminating scattered 1n from 2n events. The spectra on the right show QVC distributions obtained by setting gates from channel 480 to 500 on the TOF parameter in the 2D histogram shown on the left side.

R2n 1n ðxÞ ¼ 37; with a loss of 77% of the 2n events, was obtained (see Table 3). This corresponds to a reduction of the areas of peaks associated with reaction channels in which one neutron was emitted, by a factor of 159 (inverse value of the denominator of Eq. (6)) at the expense of reducing the areas of peaks belonging to two neutron reaction channels by a factor of 4.3 (inverse value of the numerator of Eq. (6)). The simulations gave a much larger enhancement factor, which is due to differences in the shape of the distribution of the experimental and simulated mis-interpreted g-rays. 5.9. Discriminating between 3n, scattered 2n, and scattered 1n events The creation of clean g-ray spectra associated with rare reaction channels in which three neutrons are emitted, is a difficult challenge with a compact detector array like the Neutron Wall. Several new methods have been developed in this work to reduce the effects due to scattering of the neutrons. In this section, events with three detected neutrons are called 3n events if three neutrons

were emitted, scattered 2n events if two neutrons were emitted, and scattered 1n events if one neutron was emitted. Two enhancement factors, 3n R3n 2n and R1n ; are needed and they are defined in the same way as in Eq. (6). Five different approaches for 3n enhancements are described and the results are presented in Table 4. All experimental results shown in this section are based on data from experiment 2. The first method, referred to as method 1 in Table 4, is a three neutron analog to the neighbor rejection technique described in Section 5.8.1. Three separate GEANT4 simulations, with emission of one, two, and three neutrons were run, using the evapOR neutron distribution. Events with three detected neutrons, of type scattered 1n, scattered 2n, and 3n, were selected from each of the three simulations. The triple events were grouped into the 11,772 geometrically different triple detector segment combinations (hit patterns) of the Neutron Wall (see Section 2). For each of the three simulations a probability distribution of the different hit patterns was created. This was done by counting the number of events in every hit

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759

Table 4 Enhancement of 3n events over scattered 1n and scattered 2n events in the reaction 58 Nið205 MeVÞ þ 45 Scð10 mg=cm2 Þ for the five methods developed in this work. Columns 2–4 give the fraction of events left of a reaction channel with three emitted neutrons, 3n columns 5–7 and 8–10 the obtained enhancement factors R3n 1n ðxÞ and R2n ðxÞ; respectively. The parameter x indicates that some conditions were applied by the different methods. The results of the simulations are given both excluding and including mis-interpreted g-rays, with Png ¼ 0:05: A dash indicates that the method was not evaluated Method

1 2 3 4 5

A3n ðxÞ 3n A3n 3n

R3n 1n ðxÞ

ð%Þ

R3n 2n ðxÞ

Sim

Sim þ g

Exp

Sim

Sim þ g

Exp

Sim

Sim þ g

Exp

42 38 21 15 18

43 38 21 15 19

— — — 7.4(7) 5.8(5)

33 45 110 4  104 7  103

16 22 45 2  103 500

— — — 55(8) 34(5)

5.3 7.6 14 350 51

4.1 5.3 7.3 24 17

— — — 35(5) 14(2)

pattern, which then was assigned a probability by dividing the number of events for each hit pattern by the total number of events in all hit patterns. Thus, each hit pattern is associated with three probabilities for the detection of one, two, and three neutrons. An expanded view of the probability distributions is shown in the upper panel of Fig. 15. For each hit pattern, the distribution with the largest probability determines the assignment of the event to be either a scattered 1n, a scattered 2n, or a 3n event. For example if, for a specific hit pattern, the probability is larger for 3n than for scattered 1n or 2n, the event is assigned to be of type 3n. This is the case for combination number 2139 in Fig. 15, which corresponds to a hit in detector segments number 0, 3 and 11 (see Fig. 1). Scattered 1n events have a very distinctive hit pattern, with all three detector segments involved being located close to each other. An example of that is hit pattern number 2149 shown in Fig. 15, with hits in detector segments 0, 2, and 24. A rather clear case of a scattered 2n event is combination number 2150, with hits in detector segments 0, 22, and 23, where two detector segments are neighbors while the third one is further away. The probability distributions for 3n and scattered 2n events are, however, rather similar. The main reason for this is that almost 50% of the events with three emitted neutrons become scattered 2n events, because one of the three neutrons was not detected at all and one of the two other neutrons was scattered once.

It is natural to expand the use of time differences, described in Sections 5.8.2 and 5.8.3, to the case of emission of three neutrons. The three pairs of DTOF values are located in a plane in the three dimensional DTOF space, as illustrated in the lower left panel of Fig. 15. The DTOF gates used to separate 3n, scattered 2n, and scattered 1n events will be 2D gates in this plane, of which a projection is shown in the lower right panel of Fig. 15. The exact shape of the 2D gates depends on the hit pattern, i.e. which combination of detector segments that have fired. The most advanced method is to define a 2D gate for each geometrically different hit pattern, giving a total of 11,772 gates. A simpler alternative is to use the three NS values calculated for each of the three detector segment pairs, which gives a total of 93 ¼ 729 gates, where 9 is the number of possible values of NS (NS ¼ 0–8, see Fig. 1). As can be seen in the lower right panel of Fig. 15, the two dimensional DTOF distribution of scattered 1n events is distinctly different from the distribution of 3n and scattered 2n events. However, the distributions of 3n events and scattered 2n are very similar, which means it is impossible to define the 2D gates in a way that as many as possible of the scattered 2n events are rejected, without loosing too many 3n events. The reason for the similarity of the 3n and scattered 2n two dimensional DTOF distributions is the same as already mentioned above, namely that almost half of the events with three emitted neutrons become

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Fig. 15. Illustration of simulated parameters for discrimination of scattered 1n, scattered 2n, and 3n events in the reaction 58 Nið205 MeVÞ þ 45 Scð10 mg=cm2 Þ: The upper panel shows the normalized probability distributions used in the neighbor rejection method (method number 1 in Table 4) for a small range of the 11,772 triple detector segment combinations in the Neutron Wall. The lower left panel shows a 3D view of the DTOF distribution of all events with three detected neutrons. The distribution is located in a plane, which is projected and shown in the lower right panel for (a) all events with three detected neutrons, (b) scattered 1n, (c) scattered 2n, and (d) 3n events.

scattered 2n events. The 2D gates were set to exclude the regions in the two-dimensional DTOF distributions, belonging to the different hit patterns, for scattered 1n and scattered 2n were the intensity was higher than a certain fraction of the maximum intensity. However, keeping a large fraction of the 3n events was prioritized since the complexity of the method only is justified if it can give large enhancement factors while still keeping large fractions of the 3n events. The method of using 11,772 gates was combined with the neighbor rejection technique (method 1), and is called method 2 in Table 4, while method 3 is a version using the 729 gates without any other conditions. The fourth method checks separately all possible pairs of detector segments using the method with individual DTOF gates described in Section 5.8.3, to discriminate between scattered 1n and 2n events. Each pair is checked in turn and if it is assigned to be a scattered 1n event, a counter giving the number of scattered neutrons is incremented. The number of emitted neutrons is then calculated as the number of detected neutrons

minus the number of scattered neutrons. If this difference is p0; but the number of detected neutrons was > 0; the number of emitted neutrons is set to be equal to 1. The fifth method uses the DTOF and NS condition for discriminating scattered 1n events from 2n events (see Section 5.8.2). Instead of analyzing all three pairs of detector segments, the largest DTOF value and the smallest NS value are selected. This is a simple and relatively effective method, which gave the best results by using the conditions NS X2 and jDTOFjp20 ns: The results obtained with the five different methods are summarized in Table 4. The first three methods did not give large enough enhancement factors to be of real interest and were therefore not tested on experimental data. Methods 4 and 5 were, however, judged to be useful and were tried also on experimental data. The experi3n mental enhancement factors R3n 1n ðxÞ and R2n ðxÞ were extracted from gg-coincidence data. The used coincident transitions were 607 and 226 keV; 730 and 916 keV; and 649 and 264 keV; which belong to the nuclides 99 Cd; 99 Ag; and 99 Pd and which

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were populated in the 1p3n, 2p2n, and 3p1n, reaction channels, respectively. In Fig. 4 spectra of the total projection of the gg-coincidence matrices are shown for events in which three neutrons were detected without any enhancement (top) and with an enhancement using method 4 (bottom). The coincident transitions used for determining the enhancement factors are labeled in the figure. As can be seen in Table 4, method 4 gives the best results, both experimentally and in the simulation. The simulated R3n 1n ratios are much larger than the experimental ones. They could be reduced by including multiple random g-rays in the simulations. Based on this, it was concluded that the reason for the difference between the experimental and simulated R3n 1n ratios is that a large fraction of A1n 3n comes from a neutron that was scattered ones together with detection of one or several random g-rays. The methods tested show that it is possible to effectively work with weak 3n reaction channels using the Neutron Wall as long as the number of collected events is large enough since it is inherently difficult to keep a large fraction of the 3n events if one requires a good discrimination of scattered 2n events. The reason for this was given above. With method 4, the loss of 3n events was about 93% experimentally.

6. Summary and conclusions In this work, Monte Carlo simulations of the EUROBALL Neutron Wall detector array have been performed using GEANT4. Several new methods for identifying scattered neutrons have been developed and tested. The simulations have been compared with experimental data taken at EUROBALL. The agreement between experimental and simulated results are in general very good. Using a combination of neighbor rejection, DTOF gating, and two dimensional gating on TOF and deposited energy (QVC), the peaks in 2n gated g-ray spectra associated with reaction channels emitting one neutron, could be reduced by a factor of about 160. This was done at an expense of a reduction of peak areas associated with the two neutron reaction channels by a factor

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of about 4. An enhancement factor, R2n 1n ; has been introduced in this work, which takes into account both the reduction of scattered 1n events and the loss of 2n events. The value of R2n 1n for the above case was 37. For the case of three detected neutrons, a version of the neighbor rejection and DTOF gating, applied on each of the three pairs of firing detectors, was shown to give the best results. With these conditions, the peak areas associated with both the one and two neutron reaction channels could be reduced by a factor of about 600; in the 3n gated g-ray spectra. The peak areas associated with three neutron reaction channels were in this case reduced by a factor of about 13; and the obtained enhancement factors were R3n 1n ¼ 55 and R3n 2n ¼ 35; for scattered 1n and scattered 2n events, respectively. The large loss of 3n events was shown to be due to the fact that a large portion of the reactions with three emitted neutrons are detected as scattered 2n events. Despite this large loss of 3n events, this work has showed that the Neutron Wall is useful for identifying 3n events. The influence of small amounts of g-rays misinterpreted as neutrons was also studied. The simulations showed that this effect dramatically reduces the quality of the reduction of scattered neutrons. A lowering of the neutron-g mis-interpretation probability, would lead to significantly larger enhancement ratios and, thus, cleaner neutron gated g-ray spectra.

Acknowledgements The excellent support and technical assistance provided by the VIVITRON and EUROBALL crews at IReS, Strasbourg, is greatly acknowledged. The authors wish to thank all persons who were involved in setting up the Neutron Wall and running the two experiments at IReS. This work was partly supported by the Swedish Research Council, the AIM graduate research program at Uppsala University, the Polish State Committee for Scientific Research (Grant no. 5P03B 046 20 and Grant no. 1 P03B 031 26), and by the EU under contract HPRI-CT-1999-00078.

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