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Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492

*Corresp

shington U

Louis, MO

935-6184.

E-mail a1 Present

National L2 Present

Ridge, TN3 Present

Chicago, IL

0168-9002/$

doi:10.1016

‘‘Neutron Shell’’: a high efficiency array of neutron detectorsfor g-ray spectroscopic studies with Gammasphere

D.G. Sarantitesa,*, W. Reviola, C.J. Chiaraa, R.J. Charitya, L.G. Sobotkaa,M. Devlina,1, M. Furlottia, O.L. Pechenayab, J. Elsona, P. Hausladenc,2,

S. Fischerc,3, D. Balamuthc, R.M. Clarkd

a Department of Chemistry, Washington University, 1 Brookings Dr., P.O. Box 1134, St. Louis, MO 63130, USAb Department of Physics, Washington University, 1 Brookings Dr., P.O. Box 1134, St. Louis, MO 63130, USA

c Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USAd Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

Received 26 January 2004; received in revised form 1 April 2004; accepted 19 April 2004

Available online 21 June 2004

Abstract

A shell of neutron detectors was designed, constructed, and employed in g-ray spectroscopy with Gammasphere. It

consists of up to 35 tapered regular hexagons that replace the same number of forward Ge-detector modules in

Gammasphere. The shell was designed for high detection efficiency and very good neutron–g discrimination. The

simultaneous use of time-of-flight, and two methods of pulse shape discrimination between neutrons and g rays is

described. Techniques for spectroscopy with efficient detection of two neutrons are discussed.

r 2004 Elsevier B.V. All rights reserved.

PACS: 29.30.Kv; 29.40.Mc; 25.70.Gh

onding author. Department of Chemistry, Wa-

niversity, 1 Brookings Dr., P.O. Box 1134, St.

63130, USA. Tel.: +1-314-935-6504; fax: +1-314-

ddress: dgs@wuchem.wustl.edu (D.G. Sarantites).

address: LANSCE-3, MS H855, Los Alamos

aboratory, Los Alamos, NM 87545, USA.

address: Oak Ridge National Laboratory, Oak

37831-6371, USA.

address: Physics Department, DePaul University,

60614, USA.

- see front matter r 2004 Elsevier B.V. All rights reserve

/j.nima.2004.04.243

1. Introduction

Recently the interest in the structure of nucleifar from stability, e.g. proton-rich species at andbeyond the N ¼ Z line, has created a great needfor highly efficient and highly selective detectionsystems for identifying exit channels. The con-struction of powerful arrays of g-ray detectorssuch as Gammasphere [1] has provided thenecessary first step in this direction. However,without additional detector systems for channelselection, the exploration of new phenomena in a

d.

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wide range of the nuclear chart would not bepossible.

Neutron detectors based on liquid scintillatorsthat provide n–g identification by pulse shapediscrimination and time-of-flight (ToF) have beenin use for decades. Of particular interest to ushere is neutron detection with high efficiency andclean separation from g-ray events to be used inconjunction with a g-ray multi-detector systemsuch as Gammasphere. Clearly, Gammaspheremodules have to be removed to allow neutronsto travel from the target to the detectors withoutintervening material.

Quite recently, an assortment of neutron detec-tors with hexagonal shape (five) from the Uni-versity of Pennsylvania and bullet-like ones (10)from the University of Manchester have beenused together with Gammasphere [2,3]. Morerecently, a wall of neutron detectors to beused in conjunction with the g-ray multi-detectorarray Euroball has been designed and con-structed [4].

In this paper we describe the design, construc-tion, and performance characteristics of a neutrondetector array, named ‘‘The Neutron Shell’’. Itconsists of up to 35 neutron detectors of regulartapered hexagonal prisms that pack closely. Thedetectors replace an equal number of Gamma-sphere modules (Ge detectors and their BGO anti-Compton shields) in the six most forward rings ofthe Gammasphere array. Several experimentsusing the Gammasphere plus Neutron Shellcombination have been performed and a repre-sentative case is discussed in detail and withemphasis on spectroscopy of 2n-channel selecteddata.

In Section 2, the detectors and their fabricationare described. In Section 3, the electronics setupfor the array is given. Section 4 outlines theresponse of the array to neutrons and g rays.Section 5 presents the performance of the arrayin an experiment using the Gammasphere, theNeutron Shell, and the Microball [5]. Alsoin Section 5, the various neutron-detectionefficiencies with emphasis on the two-neutrondetection are discussed, and recommendationsare given for methods of data acquisition anddata analysis.

2. Detection system

The design of the Neutron Shell and theelectronics setup was guided by the followingrequirements:

(1)

High total neutron-detection efficiency (grea-ter than 25%, cf. [4]).

(2)

Excellent n–g separation without loss inefficiency, to be obtained by combining ToFand pulse-shape discrimination.

(3)

The efficiency for detecting two coincidentneutrons should be optimized.

(4)

The timing resolution has to be optimal toallow good separation by time-of-flight forrelatively small target-to-detector distances.

(5)

Options to reduce acquisition dead-time, inparticular the implementation of a hardwareg-ray veto.

(6)

The geometric design has to be compatiblewith the Gammasphere detector geometry tofacilitate easy mounting and close packing.

2.1. The geometry

The compatibility of the shell geometry withGammasphere places rather strict constraints onthe design geometry of the Neutron Shell. In orderto find the optimal geometric configuration for theNeutron Shell detectors, Monte Carlo simulationswith the code GEANT were made. Factors such asefficiency, detector-to-detector scattering probabil-ity, and packing into the Gammasphere geometrywere taken into account in choosing the design.For simplicity, in the final design a set of regulartapered hexagons was adopted (rather than severalgeometries of irregular hexagons that were favoredby the simulations).

This arrangement provides a packing corre-sponding to 92% of the solid angle covered by theremoved Gammasphere modules. A schematicrepresentation of the geometry of the shell isshown in Fig. 1, a photograph of three neutrondetectors is shown in Fig. 2, and the detectorangles are listed in Table 1.

The red containers in Fig. 2 are welded to a3.05-cm thick supporting Al flange section, whichis the critical component of the detector assembly.

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Fig. 1. (a) Schematic view of the Neutron Shell as seen by the

beam, showing 30 detectors that can replace 30 Ge modules of

Gammasphere. The pentagon at the center permits the beam

exit pipe to go through. (b) Schematic side view of the Neutron

Shell with the beam entering from the left.

Fig. 2. A photograph showing three neutron detectors. The

detector at the center shows the mounting ring that connects the

detector to the Gammasphere Al frame. Three stainless-steel

rods connect the detector flange to the coupling ring. The

expansion bellows are seen with the plastic covers that normally

protect the bellows removed.

Table 1

Positions and angles ðy;fÞ of the neutron detectors in

Gammasphere (GS)

Ring GS pos. y� f�

1 R1-1,B6 17.3 72.0

2 17.3 144.0

3 17.3 216.0

4 17.3 288.0

5 17.3 360.0

2 R2-1,C1 31.7 36.0

2 31.7 108.0

3 31.7 180.0

4 31.7 252.0

5 31.7 324.0

3 R3-1,D2 37.4 72.0

2 37.4 144.0

3 37.4 216.0

4 37.4 288.0

5 37.4 360.0

4 R4-1,B2 50.1 49.2

2 50.1 121.2

3 50.1 193.2

4 50.1 265.2

5 50.1 337.2

R4-6,B10 50.1 22.8

7 50.1 94.8

8 50.1 166.8

9 50.1 238.8

10 50.1 310.8

5 R5-1,C3 58.3 72.0

2 58.3 144.0

3 58.3 216.0

4 58.3 288.0

5 58.3 360.0

The angle definition is the same as in GS. Only 30 of the most

foward detector angles are listed.

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These flanges have appropriate grooves for sealingquartz windows that hold the scintillator liquid.They also provide the tight fit for the mu-metal

magnetic shields shown in black. In addition, theAl flanges have threads for three support rodsthat connect the detectors to the flanges thatcouple the detector to the Gammasphere frame.The alignment into the Gammasphere geometry isachieved by adjustment of the length of thethreaded portion of the three support rods at theflange position.

2.2. Detector fabrication

2.2.1. The scintillator containers

The liquid scintillator containers were fabricatedfrom 1 mm thick spun Al funnels. They were then

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pressed to a tapered hexagonal shape (the taperangle is 10�) and cut to the appropriate length toallow an active scintillator length of 15 cm: Theback end was welded to the supporting Al flange.Part of the mechanical design is a 6.4-mm thicktapered Pb absorber at the front end of eachdetector. It serves to attenuate the abundant low-energy g-radiation from the target. The front endis closed by welding a 4:83 mm Al plate thatpermits small threaded rods to support the Pbabsorber. The scintillator section corresponds tothe part painted red and the Pb absorbers to thepart painted green in Fig. 2.

2.2.2. The optical coupling

The 30.5-mm supporting Al flange holds thesealing quartz window (3:25 mm thick and127:8 mm diameter). The quartz window is sealedwith Torrseal (Araldite of Ciba turned thescintillator liquid yellow and for that reason itwas not used here). The optical coupling to a 5-in.diameter photomultiplier tube (PMT, see below)is done via a thin, 11.96-cm curvature-radiuslight guide machined from UVT (Bicron 800UV-transparent Lucite). It is flat on the quartzwindow side and spherically shaped on the PMTside. Both couplings are made with optical grease.

2.2.3. The expansion bellows

The detectors were filled with the scintillatorBC501A from the Bicron corporation. The solventfor this material is xylene. The relatively high-thermal expansion coefficient of xylene requiresprovision to be made for safe thermal expansion orcontraction due to ambient temperature varia-tions. We have accomplished this by connectingto the detector volume a thin Ni-wall bellows.The filling was done through the top of thebellows at a temperature of B23�C: The densityof xylene varies with temperature according to theexpression

dt ¼ ds þ 10�3aðt � tsÞ þ 10�6bðt � tsÞ2

þ 10�9gðt � tsÞ3

where ds ¼ 0:88151 g cm�3 is the densityat ts ¼ 0�C; a ¼ �0:8515 g cm�3 �C�1; b ¼�0:109 g cm�3 �C�2; and g ¼ �1:73 g cm�3 �C�3:

The density at 25�C is d25 ¼ 0:860126 g cm�3

and the rate of volume expansion with tempera-ture near 25�C is 0.10% �C�1: The volume of eachdetector is 2230 cm3: So upon warming from, e.g.,25� to 35�C the volume will increase by 22:3 cm3:Since the effective cross-section of the bellows is15:5 cm2; this increase in volume will result in atravel of the top of the bellows by Bþ 1:44 cm(DL=T ¼ 1:44 mm �C�1). The safe margin is twicethat length, so the safe maximum temperature forthese detectors is 45�C: We have confirmed theseexpansion estimates by measuring the travel ofthe top of the bellows as a function of theroom temperature for several detectors filledwith the BC501A scintillator. We find DL=T ¼1:4070:15 mm �C�1; which agrees well with thecalculated value of 1:44 mm �C�1: It should bepointed out that if a small Ar gas bubble isincluded in the bellows during filling and thensealed, the expansion parameter DL will bereduced since the compressible Ar gas absorbssome of the expansion, thus making the systemsafer.

2.2.4. The filling of the detectors

The detector volume was filled up to about 90%with the scintillator liquid via a threaded openingto which a stainless steel tube was attached toconnect to the expansion bellows. The scintillatorliquid was freed from O2 by bubbling Ar gasthrough the entire volume for 24 h: Then thebellows was attached and the rest of the liquidscintillator was filled through the top of the half-compressed bellows. A Teflon-coated screw capprovided the final seal. This permits easy openingand re-bubbling of the scintillator liquid if sodesired at a later time.

2.2.5. The photomultiplier system

The nominal 5-in. diameter PMT from RCAmodel no. 8854 were used for these detectors. ThePMT are firmly held in contact with their lightguides with the aid of the mu-metal shields (thepart in Fig. 2 painted black). Rubber gasketsprovide a firm coupling and black felt sheetsprevent ambient light from entering the PMTsensitive area. Since negative voltage is used for

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these PMTs, they are electrically isolated from thehousing of the detectors including the mu-metal.

2.2.6. The voltage divider (base)

It has been designed and fabricated at Wa-shington University, and a schematic diagram isshown in Fig. 3. Its housing had to accommodatethe restricted space available when these detectorsare used while Gammasphere is located in front ofthe Fragment Mass Analyzer (FMA) at theArgonne National Laboratory (ANL). All baseshave a length of only 4:1 cm: For six of these basesthe HV and signal connectors are located onthe side. For the remaining bases the connectorsare mounted radially. The maximum length of the

Fig. 3. Schematic diagram of the voltage divid

detectors from the Pb shield to the back of thevoltage divider is 51:3 cm:

2.3. The assembled system

Finally, a picture of the Neutron Shell inGammasphere is shown in Fig. 4. This picture isfrom an experiment also using the Microball, acharged-particle 4p array [5]. Sixteen Ge-BGOmodules of Gammasphere have been replaced withneutron detectors. The liquid scintillator vesselsare painted red and the 6.4-mm thick Pb absorbersare painted green. The remaining 14 detectors usedin this experiment are on the other hemisphere.

er used for the Neutron Shell detectors.

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Fig. 4. One half of the Neutron Shell is seen replacing 16 of the

Ge-BGO modules in the first 5 rings of Gammasphere. The

liquid scintillator vessels are painted red and the 6.4-mm thick

Pb absorbers are painted green. The scattering chamber is seen

open and shows the Microball. The beam is entering from the

right and the first quadrupole magnet of the FMA is seen on the

left in blue.

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3. Electronics setup and the hardware c-ray veto

The response of the detection system is char-acterized by five parameters: ToF, ‘‘zero-crossing’’time (see below), the digitized charge of thepulse (at two gains) from each detector, and thedigitized late part of the high-gain pulse from eachdetector. Complete use of all these parametersleads to considerable redundancy in the n–gdiscrimination.

In the early experiments with this Neutron Shellall these were used but low-threshold leading-edgediscriminators were used for the ToF determina-tion. The hardware g-ray veto was then imple-mented at the output of the zero-crossingdiscriminators which showed no amplitude depen-dence in the timing. In later experiments, we haveopted to dispense with the zero-crossing discrimi-nators and replace the leading-edge discriminatorswith constant-fraction ones. This removed some ofthe redundancy but retained the capability of thehardware g-ray veto. The most recent electronicsdiagram for the operation of the Neutron Shellin conjunction with the Gammasphere is shownin Fig. 5.

The anode signals are amplified by a factor of 15via a LeCroy model 612M variable-gain fast

amplifier. One of the outputs is fed into a constantfraction discriminator which in turn feeds acomputer-controlled leading-edge discriminatorthat allows on line channel selection for signalmonitoring. The latter discriminator has 16 ECLoutputs that are fed into programmable ECLnanosecond delays for time matching. The time-matched signals are inserted into a 16-channeldiscriminator with a fast veto. The fast g-flashveto is derived from the RF of the accelerator.The g-veto pulse is adjusted to a width of B6 ns(covering the g-ray flash down to 5% of thepeak).

The time-matched ECL signals are delayed by500 ns and are used as individual channel stops ina time-to-FERA converter (TFC) operated in thecommon start mode. Its output signals provide theToF information for each detector.

The RF signal is enabled by a fast coincidencewith the Gammasphere pre-trigger, which typicallyarrives at about 150 ns from time zero. This isdelayed and used to provide the common start ofthe TFC. The enabled RF signal is fanned out andmakes the high-gain, low-gain, and late gates tothe FERA QDCs.

The second output of the 612M amplifier isdelayed by 385 ns via RG-174 cable delay and thenfed into a three-way fast linear attenuator (split-ter). The latter provides the anode signals for theFERA QDC’s at splitter ratios of �1;�1

5;�1

(outputs A, B, C in Fig. 5). The attenuation andimpedance matching is done resistively. Theinspection of the performance of the detectorsduring the experiment is done by a PC computer.The discriminator and a sample of the linear signalfrom the splitter/attenuator are selected viaappropriate multiplexing and routed to an oscillo-scope.

When the prompt g-ray veto is implemented,only neutron events outside the veto gate producea signal that is used to provide a neutron-presentbit. This signal is used to enable a copy of theGammasphere main-time signal. If the enabledmain-time signal is absent (no neutron bit), thenthe event is cleared at a dead time cost of about1 ms instead of B60 ms needed to process an event.This enriches the neutron-containing data on tapesignificantly.

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Fig. 5. A block diagram of the electronics.

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4. Response of the detection system and n2cdiscrimination

The data presented hereafter are from arepresentative in-beam experiment (rather thanfrom source measurements). In this experiment,the 130-MeV 32S þ 28Si reaction was used and only30 neutron detectors were included in the NeutronShell. The main focus of this section is on n–gray discrimination; the principal parametermaps (two-dimensional histograms) are shown inFig. 6.

4.1. ToF

The ToF of the neutrons usually provides goodseparation of the neutrons from the g rays. In thepresent case, the required high efficiency limitsthe distance of the center of the detectors to 35 cmfrom the target. The good timing resolutionof these detectors (B1 ns FWHM for 1:3 MeV grays) is sufficient to separate most of the neutronsfrom the g rays at this distance. The actual timingresolution in an experiment depends on the timingresolution of the pulsed beam of the accelerator.

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Fig. 6. Sample maps to illustrate the various possibilities of neutron–g separation. The maps are from the reaction 32S þ 28Si at

130 MeV and represent raw data. (a) Map of the late gate (on the high-gain signal) vs. the total gate shown in compressions of 4 and 8,

respectively; (b) pulse height (high gain compressed by a factor of 16) vs. leading-edge ToF (shown at 3:3 ns=channel); and (c) pulse

height (low gain) vs. zero-crossing time. In the latter case, the range for a g-ray hardware veto is indicated (see text).

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This adds in quadrature with the intrinsic resolu-tion of the detectors. The present array hasbeen used in conjunction with Gammasphereat the ATLAS facility at the ANL, where a timingresolution of 1:0 ns can be easily obtained,and at the 8800 Cyclotron at the LawrenceBerkeley National Laboratory (LBNL) where aresolution of B2:0 ns is achieved. These timingresolutions are adequate for n–g separation bythe ToF technique. An example of ToF separa-tion of neutrons and g rays is shown inFig. 6(b).

4.2. Discrimination by pulse shape

Other ways of separating g rays from neutronsrely on the fact that the decay times of the neutronpulses are longer than those of g rays. There aretwo methods for pulse-shape discrimination(PSD).

4.2.1. Charge integration technique

One integrates the total charge of the scintillatorpulse by gating on the entire pulse width.Similarly, one integrates the charge of the late

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part of the pulse beginning after the peak when thepulse falls to half its maximum height. The lategate starts typically after B100 ns from thebeginning of the pulse. A plot of the late integratedcharge vs. the total provides an excellent separa-tion of neutrons and g rays, see Fig. 6(a).

4.2.2. Zero-crossing technique

Here, one differentiates the anode pulse andmeasures the time between the beginning of thepulse and when the differentiated pulse crosseszero voltage. In this case, the neutron pulses crosszero later than the g rays, thus providing separa-tion between neutrons and g rays.

In the early experiments with the Neutron Shell,a variant of the zero-crossing technique wasemployed. The negative anode pulses were differ-entiated and inserted into a discriminator that firedat the crossing from negative to positive voltage.The discriminator output provided the stop of thetime signal, the start of which was derived fromthe accelerator RF enabled by the Gammasphere.The times measured in this way contain the sum ofthe separation by ToF and by the zero-crossingtechnique; an example is shown in Fig. 6(c). Asdocumented in Section 4.5, the zero-crossingtechnique gave a better separation than thatobtained by the ToF technique alone (but due tothe redundancy a combination of ToF and chargeintegration would be sufficient). Notice also that itis possible to obtain the ‘‘net’’ zero-crossingdiscrimination by subtracting the ToF from thelatter parameter. This is not illustrated in Fig. 6(nor in the corresponding figures in Section 4.5).

Since in the present experiment there are manylow-energy neutrons, it is important to expand thedynamic range of the acquired pulse heights. Forthis purpose, the pulse heights were digitized attwo gains differing by a factor of B5:0: This is thereason for the different parameters shown on theordinates of Figs. 6(b) and (c). Specifically, a mapof the low-gain pulse height vs. ToF plus zero-crossing is shown in Fig. 6(c).

4.3. Effects due to delayed g rays

The n–g separation by the charge-integrationtechnique is shown in Fig. 6(a). The abscissa is the

total gate and the ordinate the delayed gate. Sincehere the gates are derived from the RF, theneutron pulses are delayed by their ToF and thusreceive a larger late signal. This enhances the n–gseparation particularly at low energies. However,delayed g rays also receive somewhat larger chargein the late gate and this produces some eventsbetween the g-ray line and the neutron line. Theselie close to the g line and for nanosecond isomersdo not interfere with the pulse-shape discrimina-tion. The straight lines above the neutrons are dueto random pulses from the following beam burstswhich place higher amplitude g pulses in thelate gate. They can be removed by gating onthe prompt neutrons from the pulse-height vs.ToF maps.

For the 130-MeV 32S þ 28Si reaction at lowamplitudes, a B3 ns isomer fills in the mapbetween the g rays and the neutrons at pulseheights t65 (arbitrary units) in Fig. 6(b) and atpulse heights t14 in Fig. 6(c). In Fig. 7 we showthe projections for two different software gates onthe Y -axis of the data in Fig. 6(b) demonstratingclearly the presence of a B3-ns isomer. Asdiscussed earlier, when the zero-crossing discrimi-nators are employed, subtraction of the ToF fromthe zero-crossing time (started by the RF) gives the‘‘net’’ zero-crossing time. In this way all the g raysfrom nanosecond isomers collapse on the g flash(this is not illustrated graphically here).

If only the ToF (with constant fraction dis-criminators) and the charge-integration methodsare used, then delayed g rays with t1=2\40 ns maynot be separated from neutrons. For half-livesgreater than B5 ns; the identification by ToF (e.g.as shown in Fig. 6(b and c)) is not sufficient sincesome of these g rays overlap with neutrons.However, the pulse-shape identification shown inFig. 6(a) identifies the delayed g rays between theg-ray and the neutron lines roughly up tot1=2t40 ns (see also Section 4.5 for an expandeddisplay of the PSD).

In the present PSD method, the late gate isstarted at a fixed time after the RF. A largerfraction of each neutron pulse, which is delayed bythe neutron ToF, falls within the late gate thanprompt g rays do. This opens up the n–gseparation lines specifically for the late vs. total

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Fig. 7. The presence of delayed g rays in the 130-MeV 32S þ28Si reaction. The top panel shows a pulse-height cut at

channels 80–85 in Fig. 6(b). The good separation by ToF is

clearly seen. The bottom panel shows a pulse-height cut at

channels 40–42. An exponential tail after the prompt g-ray flash

is seen corresponding to an approximate half-life of about 3 ns:

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maps, particularly at low energies. This is bene-ficial in the absence of isomers, but in theirpresence some or all of the n–g separation maybe taken by the delayed g rays. For t1=2t40 ns; theseparation should still be good enough to rejectmost of the delayed g rays. A comparison of theneutron and g-ray lines for channels with andwithout delayed g rays can easily be used toidentify their presence in the late vs. total maps.

In order to separate fully the delayed g raysfrom the neutrons, another approach is available.One could derive the start of the late gate from theconstant fraction discriminator of each detector(rather than from the RF) and give the gate aconstant width. Then all the delayed g rays will beon the same g lines as the prompt ones. Thisrequires use of individual-channel-gated QDCs.However, now the n–g separation at low energieswould be reduced somewhat. Such an approach is

not implemented in the present electronics setup,but could be easily accommodated in futureexperiments.

4.4. Counting rate effects

The n–g separation for weak channels could beaffected by very high-total counting rates in thescintillators. However, in experiments with Gam-masphere the counting rates are limited by pileupin the Ge detectors to B7000 c=s (signal-proces-sing time in a Ge detector is 10 ms leading to apileup of B7% in each Ge). Under such conditionsthe neutron detectors modules operate at totalrates of B9000 c=s (with some variation withangle). In view of the fast decay time of thesescintillators (total gate of B500 ns used in thepresent experiment, cf. Fig. 5), the anticipatedpileup is of the order of B0:45%: This indicatesthat any reaction channel including the very weakones suffer the same fractional loss of B0:45% dueto pileup. These losses could be reduced somewhatby shortening the gating times to 300 and 150 nsfor the total and late gates as opposed to 500 and350 ns used in the experiments described here. Thiswould reduce the losses to B0:27%: However,shortening the gating times may result in some-what worse n–g separation.

Thus, a typical loss of 0.5% of the neutronevents due to pileup is of no consequence inexperiments with Gammasphere and the presentneutron array. Much higher rates would berequired to have a significant impact in the n–gray discrimination.

4.5. Some useful analysis techniques

Data of the type shown in Fig. 6 can be analyzedoffline in a number of ways that display in full theexisting n–g separation especially at low energies.Since the pulse height from single-neutron or g-rayenergy resembles a Compton distribution it con-tains little information except in facilitating then–g separation.

We found that it is useful to combine the low-and high-gain pulse heights into one matchedvariable. First, we determine the exact attenuationratio for each detector by plotting the high- vs.

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low-gain pulse heights and taking the slope(typically about 5). This scaling factor can thenbe applied to the low-gain values that exceed thehigh-gain range, resulting in one combined para-meter hmatch: In order to conveniently display thisparameter in a single spectrum, one can calculatethe quantity H3 c1 � h

1=3match (here hmatch varies

from channel 0 to B10; 000; and c1 ¼ 20 forreasonable graphical presentation). The resultingspectrum has a larger dispersion at small pulse-heights than at large pulseheights, making the n–gseparation quite apparent for low pulseheights.Other expressions such as Hln ¼ lnðhmatchÞ workalso, but this expands the low-energy region morethan the H3 function. In this work, we adopted theH3 function. Its use is illustrated in Fig. 8(a)–(c).Clearly, the low energy is magnified and it is seenthat there are lower amplitude g-ray pulses thanneutron ones.

The low noise of the selected PMTs in this arrayallows triggering down to 20-keV g rays. Thiscorresponds to 0.23-MeV neutrons. A moreimpressive effect appears by converting the mapof Fig. 6(a) to one where the function Tail c2 � ðLateÞ0:4 is plotted vs. H3 (here Late variesbetween channels 0 and B2000 and c2 ¼ 10 forreasonable graphical presentation). This is shownin Fig. 9(a) using data without the g-ray veto. Nowthe neutron and g lines that converged to a pointin Fig. 6(a) are clearly separated. Furthermore,maps of H3 vs. 400 � Tail=H3 make the n–gseparation at the very low energies clearer as seenin Fig. 9(b).

Now one can see that at the very low-pulseheights the n–g separation is essentially complete.The n–g separation can be improved further if aconservative ToF gating is combined with thePSD technique as illustrated above. Furthermore,the B3-ns delayed g rays are clearly marked inFigs. 9(a) and (b).

5. Performance in Gammasphere

The capabilities of the Neutron Shell in con-junction with Gammasphere have been demon-strated in several experiments. The two majorissues, viz. the neutron-detection efficiency and the

performance of the Neutron Shell in spectroscopicwork for two-neutron reaction channels, arediscussed in Section 5.2. Again, an experimentusing the 130-MeV 32S þ 28Si reaction is chosenas a representative case with 30 detectors in theNeutron Shell.

5.1. Experimental conditions

The need to use the Neutron Shell is associatedwith fusion reactions that populate very neutron-deficient nuclei typically through the xpn; xan;xp2n; xa2n; xpyan; xpya2n; or the xa3n channels(xX1 and/or yX1). Here the reaction-channelcross-sections are very small—i.e. they may extenddown to a few mb: In order to obtain usefulstatistics in these weak channels one cannotincrease indefinitely the running time or beamintensity since in the latter case the data-acquisi-tion dead time becomes prohibitive. For the samereason, the event trigger must be carefully chosen.For example, if the event trigger were selected tobe a minimum g-fold, kg; of the Gammaspheredetectors (after Compton-suppression) denoted bykgX3 for all reaction channels, then a large deadtime would discard a significant fraction of the fewuseful events from the weak channels.

To reduce such dead-time losses, one can takeadvantage of the mixed trigger mode of Gamma-sphere. In the experiment under discussion threetypes of trigger conditions have been tested:

(a)

Triggering only on kgX4 events in Gamma-sphere,

(b)

Mixed trigger with (knX1ÞðkgX2Þ events withno hardware g-veto or Gammasphere withkgX4; and

(c)

The same as (b) but with the g-ray veto in theneutron scintillators employed.

Sample data were taken in all trigger modes,but in the actual experiment the mixed triggermode (c) was used. In the mixed trigger condi-tions, one adjusts the kg to a high enoughvalue (e.g. kgX4) so that the added dead time issmall.

Although the mixed trigger increases statisticsand enriches the acquired useful data for theneutron-deficient channels, it does not prevent the

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Fig. 8. Matched and linearized maps of the raw data from Fig. 6. Panel (a) shows samples of the data from Fig. 6(b) as H3 vs.

linearized ToF. Panel (b) shows samples of data of the type of Fig. 6(c) as H3 vs. zero-crossing+ToF. Panel (c) is the same as (b) but

with the prompt g-ray veto implemented.

D.G. Sarantites et al. / Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492484

Neutron Shell detectors from firing more often ong rays than on neutrons. This is related to the lowcross section for neutron evaporation channels inthe experiment discussed. In fact, in the 32S þ 28Sireaction, often the Neutron Shell detectors fired ong rays only. This situation again creates excessivedead time. It is then quite clear that in order toreduce further the acquisition dead time we mustreject events in which the Neutron Shell fired onlyon g rays. This can be achieved by applying a veto

for g events at the fast hardware level (the methodis indicated in the block diagram of Fig. 5).However, if a neutron triggers the Neutron Shell,all the scintillator information is read out sincein such an event the Neutron Shell g rays addto the g-ray multiplicity. This method reducessubstantially the acquisition dead time and itenriches considerably the number of neutronevents acquired relative to the g rays recorded(see Section 5.2).

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Fig. 9. Neutron-g discrimination by charge integration. Panel

(a) shows a map of the Tail vs. H3: Panel (b) shows a map of H3

vs. the ratio 400 � Tail=H3: (See text for definition of the

variables.)

D.G. Sarantites et al. / Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492 485

The need to optimize the overall neutron-detection efficiency led us to pack the detectorsof the Neutron Shell very close to each other. Thisintroduces a problem when clean two-neutrondetection is needed: a neutron that interacts with

the scintillator in a detector can scatter out andinteract with another one. This ‘‘cross-talk’’ affectsthe selection of two-neutron events and a proce-dure is devised to suppress the ‘‘cross-talk’’ eventsin software. Moreover, the probability for neutronscattering is highest at small forward angles andthus due to the close-packing of the detectors, thebulk of the ‘‘cross-talk’’ is expected to occurbetween the nearest neighbor detectors. Therefore,if two or more hits in the Neutron Shell arerecorded and if these hits occur in neighboringdetectors then the count with the smaller energydeposited in one the scintillators is rejected fromthe data (rejection of neighboring hit).

For the subsequent discussion, it is crucialto consider four different cases in the dataprocessing:

(1)

Trigger by Gammasphere only with kgX4; norejection of neighboring detector hits.

(2)

Mixed trigger, no hardware g-ray veto,no rejection of neighboring hits.

(3)

Mixed trigger, hardware g-ray veto, no rejec-tion of neighboring hits.

(4)

Mixed trigger, hardware g-ray veto, rejectionof neighboring hits.

Case no. 1 is only considered for determiningthe neutron-detection efficiency of the NeutronShell. Cases 3 and 4 are analyzed to discuss theissue of two-neutron detection, specifically the lossin two-neutron efficiency by the rejection ofneighboring detector hits and the cleanliness ofthe final spectrum. Case 2 serves as a comparisonwith the other cases.

As mentioned earlier, the Microball was alsoused in the 32S þ 28Si experiment. The Microballserved two purposes: (i) selection of the reactionchannel and (ii) aid in the precise Doppler shiftcorrection of the g-ray energies. Since the Micro-ball was not part of the trigger, but it was recordedif it fired, its presence does not affect theconclusions to be made.

5.2. Neutron-detection efficiencies

The geometric coverage of the Neutron Shellwith 30 detectors is 24% of 4p: For a typical

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Fig. 10. Set of g-ray spectra gated by reaction channels from

the 130-MeV 32S þ 28Si reaction. The channel gate is indicated

in the spectrum panel and the prominent g rays are identified.

The spectra are sorted for a set of data with no mixed trigger

and no g veto (case no. 1). Above channel 2400 the scales have

been changed by factors of 3 or 4.

D.G. Sarantites et al. / Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492486

neutron evaporation spectrum from a compoundreaction near the Coulomb barrier (40–70 MeVexcitation energy in the compound nucleus)the intrinsic efficiency of the Neutron Shell maybe 80% (20% of the neutrons pass through thedetectors without causing a trigger). Since theNeutron Shell covers azimuthal angles between 7�

and 55�; the kinematic focussing of the neutronsby the center-of-mass motion increases signifi-cantly the fraction of the neutrons that aredetected.4 Consequently, the neutron-detectionefficiency of the Neutron Shell should be (i) largerthan the value for its geometric coverage and(ii) reaction dependent.

The true neutron-detection efficiency of thearray is best determined when only one neutronis emitted and the counts Ci for a specific reactionchannel (as determined through unambiguouscharacteristic g-ray gating) are obtained, with thesubscript indicating the number of neutron hits inthe Shell. The total neutron efficiency is

OðmÞtot ¼

Pni¼1C

ðmÞiPn

i¼0CðmÞi

;

and the n-fold efficiency is On ¼ Cn=Otot: Thesuperscript (m) indicates the reaction channel. Theefficiencies for the 2p1n; 3p1n; and 4p1n channelswere obtained from spectra like the ones shown inFig. 10 (case 1) gated by the Microball and theNeutron Shell by 2p0n; 2p1n; 2p2n; or 2p3n gates(two protons in the Microball and 0, 1, 2, or 3neutrons in the Shell, respectively). These spectracontain the reaction channels 3p; 2pn; 3pn; 4pn;2p2n; and 3p2n: The 3p; 3pn; 3p2n; and 4pnchannels appear in the 2p Microball gate becauseone or two protons escaped detection by theMicroball.

The proton-detection efficiency in this experi-ment is 75%, so that 42.2% of the 3p events stay inthe 3p gate and 42.2% end up in the 2p-gatedsubset. These ‘‘leaking-through’’ events could beremoved by appropriate subtraction. However, forthe present analysis we have opted to use theMicroball only for gating, and in this way showthe power of the Neutron Shell alone. In this way

4 For a typical neutron angular distribution in the lab see also

Fig. 12 in the following section.

we introduce also a strong 3p1n channel in thedata, which we subsequently remove only with theaid of the Neutron Shell. Indeed, the spectrum‘‘gate: 2p1n’’ in Fig. 10 (two protons detected inthe Microball and one neutron in the NeutronShell) is dominated by the 3p1n and to a lesserextent by the 3p2n; and 2p1n events, while g-raylines from 2p2n events are barely visible. Next, inthe spectrum ‘‘gate: 2p2n’’ the corresponding grays stand out (asterisks, diamonds), but strongbackground contributions mainly from the 3p1nchannel still remain. Finally, the bottom spectrumindicates that there is also a considerable numberof 2p2n and 3p2n events in ‘‘gate: 2p3n’’ (due tothe multiple hit probability discussed below).

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D.G. Sarantites et al. / Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492 487

As expected, the zero-fold neutron spectrum(‘‘gate: 2p0n’’) contains far too many channels andit is difficult to find clean g-ray lines from the 2p1n;3p1n; and 4p1n channels. Therefore, we createdg–g matrices with the same neutron gates and theng gated these with the appropriate channels toavoid contaminants. The representative g-ray lineschosen are from the 2577-, 1706-, and 479-keVtransitions in 57Ni þ 2p1n; 56Co þ 3p1n; and55Fe þ 4p1n; respectively [6]. In Table 2, wesummarize the neutron-detection efficiencies forthe 2p1n; 3p1n; and 4p1n channels.

From these data, the total neutron efficiency forthe 3p1n channel is Otot ¼ 0:302ð3Þ; and thedetector-to-detector neutron scattering can beestimated as S ¼ O2=ðO1 þ O2Þ; which is 0.148(3).The three-fold hits are down by about a factor of16 from the two-fold events. As expected, thefraction of the g rays in the spectra from the 3p2nand 2p2n channels increases as the neutron-detection fold increases. This is clearly seen inthe 2p2n and 2p3n gates in Fig. 10. Note that fromTable 2 we see a monotonic increase in efficiencyOtot from the 2p1n to 3p1n to 4p1n channels, dueto decreasing neutron energy as the number ofemitted protons increases. The scattering factor S

also decreases from 0.198(23) to 0.148(3) to0.144(11) for the 2p1n to 3p1n to 4p1n channels,respectively, indicating that the scattering de-creases with neutron energy. Note that lowerenergy neutrons from the reaction are moreforward peaked and less likely to pass throughthe scintillator without interacting.

Table 2

Neutron-detection efficiencies for the 2p1n; 3p1n; and 4p1n channels

2577 keV in 2p1n 1706 keV in

n-fold Counts Oi Counts

0 1702 (56) 0.730 (32) 50,539(300)

1 499 (30) 0.214 (14) 18,421(170)

2 124 (17) 0.053 (7) 3197 (75)

3 7 (5) 0.003 (2) 201 (17)PCi 2332 (66) 72,358 (353)

Otot 0.270 (16)

S 0.198 (23)

Notice that the counts are obtained from g-gated g–g coincidence ma

5.2.1. The mixed trigger with g-ray veto

We have argued that one can increase thestatistics of useful neutron data by introducing amixed trigger in which we require (knX1ÞðkgX2Þevents with hardware g-veto or Gammaspherewith kgX4: By introducing the neutron detectorsin the trigger, we bias against the kn ¼ 0 events ina complicated way, since such zero-fold eventscome from the kgX4 Gammasphere fraction of thetrigger and from those events in which the neutrondetectors fired only on g rays. Even if we veto thelatter this cannot be quantified. Nevertheless, thebenefit is substantial.

In Fig. 11 we show spectra from the mixedtrigger condition (case 3). Here the neighboringdetector hits were not rejected. The analysis gatesare 2p1n; 2p2n; and 2p3n (the 2p0n-gated spec-trum is not shown). Notice that all the dataavailable for case 1 have been sorted, while for thecases 3 and 4 small fractions of the data have beensorted that correspond to the same number ofevents on tape as in the case 1. Although thenumber of events for the spectra in Figs. 10 and 11are the same, the number of counts from neutronchannels in the latter figure is higher by a factor ofB4:3: Table 3 summarizes the yields obtained witha mixed trigger (case 3). The second column inTable 3 gives the counts in the 1706-keV line fromthe 3p1n channel, which is off scale in Fig. 11. Inaddition, the 2701- and 2973-keV g rays have beenincluded in the analysis representing the 56Ni þ2p2n [6] and 55Co þ 3p2n [6] evaporation pro-ducts, respectively. Note that the zero-fold counts

3p1n 479 keV in 4p1n

Oi Counts Oi

0.698 (5) 5304 (213) 0.640 (31)

0.255 (3) 2554 (87) 0.308 (14)

0.0442 (11) 430 (34) 0.052 (4)

0.0028 (2)

8288 (233)

0.302 (3) 0.360 (15)

0.148 (3) 0.144 (11)

trices.

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D.G. Sarantites et al. / Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492488

represent now a considerably smaller fraction ofthe total. The fraction of the g rays from 3p1n thatappear in a neutron-gated spectrum is now 64.0%compared to the true efficiency Otot ¼ 30:2%;and the real benefit is a factor of 4.3 increase inneutron data.

In contrast to the efficiencies for the one-neutron channels, the measurement of theefficiency for detecting two neutrons is morecomplicated. First of all, the low cross-sections

Fig. 11. Set of g-ray spectra using the same channel gates as in

Fig. 10 (except the 2p0n) but with the mixed trigger and the g-

ray veto applied (case 3).

Table 3

Spectra taken with a mixed trigger (case 3) with the indicated gates a

1706 keV in 3p1n 2701 keV

Fold Counts Fi Counts

0 197,873(997) 0.360 (2)

1 298,232(963) 0.543 (2) 36,743(35

2 50,408(383) 0.092 (1) 8316(166)

3 3005(98) 0.0055 (2) 1079(53)PCi 549,518(1428) 46,148(39

Ftot 0.640 (2)

Neighbor hits were not rejected. Fi and Ftot denote the fraction of eve

that contain the g ray of interest.

for the 2n channels make it difficult to measure thezero-fold yields in the data shown in Fig. 10. Inthis case, in the mixed trigger data the zero-foldspectra are not useful. Even so, now, in addition tothe detector-to-detector scattering, there is aprobability that the two neutrons hit the samedetector. Thus, the expression for calculating thehigher-fold probabilities is complicated.

A formalism that includes such effects waspresented in describing the behavior of the SpinSpectrometer (a 72-NaI 4p system, [7]). Specifi-cally, Eq. (10) in Ref. [7] might be used, in whichthe one-neutron efficiency and single-scatteringprobabilities are incorporated.

However, this procedure does not describeexactly the correct neutron fold ratios. We alreadyhave seen a significant dependence of the one-neutron efficiency with exit channel and thusneutron energy. So instead of using the averageone-neutron efficiency we searched for the best fitto the yield ratios for the values of O2n and thescattering factor S that give the best values for theratios of the 3p2n channel, namely F1=F2 ¼ 4:0ð1Þ;F2=F3 ¼ 6:9ð5Þ: We employed the following ex-pression (Eq. (10) of Ref. [7]):

PNk ¼ ð�1ÞkN

k

� �Xk

n¼0

ð�1Þnk

n

� �1 � O2n

�

� 1 �n

N1 � S 1 �

n � 1

N � 1

� �� �� ��Mn

: ð1Þ

Here, PNk is the probability that k detectors out ofN fire when Mn neutrons are emitted from thetarget. The best agreement with experiment was

pplied

in 2p2n 2973 keV in 3p2n

Fi Counts Fi

4) 0.796(10) 23,700(353) 0.778(15)

0.180(4) 5895(161) 0.194(6)

0.0234(12) 858(51) 0.028(2)

5) 30,453(391)

1.00(1) 1.00(2)

nts for each neutron fold and the sum of folds 1–3, respectively,

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Fig. 12. Neutron angular distributions for the channels

indicated in terms of the laboratory angle of the rings of the

Shell (see text). Connecting lines are shown to guide the eye.

Inset: A typical Neutron Shell hit pattern (2p2n gate).

D.G. Sarantites et al. / Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492 489

found for O2n ¼ 0:25; and S ¼ 0:10: We obtainedP30;0 ¼ 0:5625; P30;1 ¼ 0:3392; P30;2 ¼ 0:08719;P30;3 ¼ 0:01058; and P30;4 ¼ 0:00054 for Mn ¼ 2:The ratios are P30;1=P30;2 ¼ 3:89; and P30;2=P30;3 ¼8:24: The calculated ratio P30;1=P30;2 (the experi-mental ratio was denoted as F1=F2Þ is in agreementwith the experimental value within 1:1s; while theratio P30;2=P30;3 (F2=F3) is larger than experimentby 2:7s: Therefore, the overall two-neutron-detec-tion probability can be taken approximately to beP30;2 þ P30;3 ¼ 0:0978:5

We note that Eq. (1) was derived for a 4p systemwith equivalent detectors (all having the samenumber of neighbors) and with near isotropicangular distributions of the g rays. In usingEq. (1), we have ignored the strong angularcorrelation effects present here. Those are shownin Fig. 12 with the channel-gated neutron angulardistributions normalized to a value of 1 for theinner ring of the Neutron Shell. Also, the detectorsin the perimeter of the Shell have neighbors onlyon one side so that the detectors in the Shell arenot equivalent in terms of number of neighbors.We also observe that the angular distributionsdepend on the number of emitted neutrons, withthe 2n channels having more forward-peakedangular distributions than the 1n channels.

To explore the sensitivity of these results toangular distributions and edge effects, we per-formed Monte Carlo (MC) simulations thatincluded these effects in addition to the inter-detector scattering. The probabilities of neutrondetection and scattering were initially taken fromthe above values of O2n and S: A total of 106

events were simulated in which two neutrons weredetected according to these probabilities. If twoneutrons entered the same detector, they weretreated as a single count. The P30;k values obtainedthrough Eq. (1) were reproduced for a flat angulardistribution to within 1% of the number of events.Using a strongly forward-peaked neutron angulardistribution, such as shown in Fig. 12, altered the

5 Note that Eq. (1) for Mn ¼ 1; O1n ¼ 0:302 and S ¼ 0:148

gives P30;1 þ P30;2 ¼ 0:2573 þ 0:04496 ¼ 0:302 ¼ O1n; but of

course predicts P30;3 ¼ 0; since it does not include consecutive

scattering. In this case the experiment gave F3 ¼ 0:0028ð2Þ (see

Table 2 for the 1706-keV g ray).

results only slightly (less than 0.3%), indicating aweak dependence on the angular distributions.The main difference between the MC simulationsand Eq. (1) thus comes from the treatment of edgeeffects. We repeated this procedure for differentvalues of O2n and S; and subsequently found via aleast-squares fit that MC simulations using thevalues O2n ¼ 0:24 and S ¼ 0:13 best reproduce theexperimental ratios F1=F2 and F2=F3; the predictedvalues are 3.9 and 8.2, respectively. The former iswithin uncertainties of the measured value, whilethe latter is too large by 2:6s: This discrepancymay be, in part, due to multiply scattered neutronsthat would contribute more to F3 and less to F2;reducing the F2=F3 ratio; this effect has not beenincluded in the MC simulations.

In principle, the overall probability for two-neutron detection should be close to the estimatedvalue of 0.0981 given above. This efficiency shouldcorrespond approximately for the yield of the2p2n þ 2p3n or the 3p2n þ 3p3n gates. FromTable 3 the corresponding fractions 0.2034 and0.2228 for the 2p2n and 3p2n channels are listed,

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Table 4

Loss of counts due to nearest-neighbor rejection

Neutron Counts Counts Fraction

fold no rejection after rejection rejection/no rej.

1706 keV in 3p1n

0 197,873(997) 198,028(936) 1.001(7)

1 298,232(963) 342,465(1020) 1.148(5)

2 50,408(383) 8374(152) 0.166(3)

2701 keV in 2p2n

1 36,743(354) 43,074(388) 1.172(15)

2 8316(166) 3343(96) 0.402(14)

Combination — 3099(111) 0.373(15)a

2973 keV in 3p2n

1 23,700(353) 27,545(385) 1.162(24)

2 5895(161) 2904(92) 0.493(21)

Combination — 2909(106) 0.496(26)a

The values reported in the columns labeled ‘‘Fraction’’ are

obtained from the ratio of counts in the third column of this

table and Table 3 reproduced in column two. In the rows

labeled ‘‘Combination’’ are reported the results from the linear

combinations discussed in the text.a Fraction with respect to the counts obtained for neutron

fold 2 and no rejection.

D.G. Sarantites et al. / Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492490

but these fractions were obtained without the zero-fold events. The higher yield for the 3p2n over the2p2n may be due to the lower energy neutrons thathave a higher detection probability, thus furtherconfirming the expected channel dependence of thetwo-neutron-detection efficiency.

5.2.2. The mixed trigger with g-ray veto and

neighbor rejection

We proceed now to create clean two-neutron g-ray spectra. Let us examine the spectra in Figs. 10and 11. The spectra from the ‘‘gate: 2p2n’’ arestrongly contaminated with background that comesfrom the neutron ‘‘cross-talk’’—i.e. mainly from the3p1n channel and to a much lesser extent from the2p1n channel. Because of the presence of theMicroball in this experiment, it would be easy toremove the 3p1n and the 3p2n channels bysubtracting a multiple of the 3p gate in the Microballfrom these spectra. However, the contribution fromthe weaker 2p1n channel cannot be removed in thismanner by use of the Microball alone.

As mentioned in Section 5.2.1, the ‘‘cross-talk’’can be largely suppressed by the rejection of theneighboring hits. The effect on the efficiency dueto rejection of counts in neighboring detectors issummarized in Table 4. Thus, for the 3p1n channelwe find that 16.6% of the ‘‘cross-talk’’ remainsafter rejection, so that 83.4% of the scatteringinvolves neighboring detectors. Therefore, theneighbor rejection in general suppresses the 1nbackground by a factor of B5:0:

By necessity, the neighbor rejection also rejectssome good two-neutron events that occur inneighboring detectors. This loss of two-neutronefficiency appears to be channel dependent as isseen in Table 4. This loss in statistics amounts toremaining fractions of 40.2% and 49.3% forthe 2p2n and the 3p2n channels, respectively.The higher loss in the 2p2n channel compared tothe 3p2n must be due to lower energy neutronsassociated with the 3p2n channel. Since the 3p1nbackground was reduced by a factor of B5:0 whilethe loss in 2n statistics is about a factor of 2, thebackground is suppressed by a factor of 2.5causing the 2n channels to stand out well abovebackground. This is seen in the middle panel inFig. 13.

Now we deal with the remaining 3p1n back-ground. We also note that the spectrum of the‘‘gate: 2p3n’’ without neighbor rejection (bottompanel in Fig. 11) is nearly of the same quality asthat from the ‘‘gate: 2p2n’’ after rejection and inaddition it contains about 30% of the 2p2n counts.If we add the spectrum in Fig. 13(b) to thespectrum in ‘‘gate: 2p3n’’ of Fig. 11 and subtract3.6% of the spectrum ‘‘gate 2p1n’’ from Fig. 11(no rejection) we obtain a clean spectrum contain-ing only the 2n channels as shown in the bottompanel of Fig. 13. We call this the ‘‘combination’’spectrum. In the 2701-keV transition, the combi-nation spectrum contains 3099(111) counts. Alter-nately, the same counts are obtained as follows:1079ð53Þ (Table 3, column 4) þ3343ð96Þ (Table 4,column 3) �0:036 � 36743ð354Þ (Table 4,column 2). This spectrum now contains 37.3%and 49.6% of the total statistics of the 2p2nand 3p2n channels, respectively. Using the overalltwo-neutron-detection probability reported inSection 2, the clean 2n spectrum was obtainedwith approximate efficiencies of ð9:81%Þ � 0:373 ¼3:7% for the 2p2n channel, and ð9:81%Þ � 0:496 ¼

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Fig. 13. The spectra in panels (a) and (b) are generated under

the same conditions as in Fig. 11 but with the rejection of the

neighboring hit of smaller pulse height. The spectrum in (c) is a

linear combination of three spectra: above spectrum (b) plus the

bottom spectrum in Fig. 11 minus 3.6% of the top spectrum in

Fig. 11.

D.G. Sarantites et al. / Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492 491

4:9% for the 3p2n channel. Clearly, the aboveprocedure produces pure 2n spectra with a reason-able yield and allows complete identification of allg rays associated with the 2n-exit channels.

As stated earlier, for this particular reaction, the3p2n background could be removed by subtractingthe Microball 3p-gated spectrum, and then the2p1n lines could be removed subsequently with thehelp of neutron gating by a similar subtraction ofthe 2p1n-gate via suitable normalization.

Here, we should also point out that the linearcombination employed above produces clean 2n g-ray spectra with an efficiency which is independentof the magnitude of the 2n-cross-sections. Thus, ifthe 2p2n-cross-section were, say, ten times smaller,and if the conditions that govern the neutron‘‘cross-talk’’ (neutron energies and angular dis-tributions) were the same, still an identical fractionof the 2p2n yield would be lost by the above-linear-combination (with subtraction of the samefraction of 3.6% of the 2p1n-gated spectrum). Thedifference now would be that the clean 2n

spectrum would have a larger statistical scatterdue to the subtraction.

5.3. Suggested procedures for data acquisition and

spectroscopic analysis

Finally, below we summarize some suggestedprocedures for the acquisition and spectroscopicanalysis of data on the neutron-deficient side of thenuclear chart with the Gammasphere, the NeutronShell, the Microball and/or the fma.

For data acquisition scenarios we distinguish:

(1)

If the Microball is the only other ‘‘auxiliary’’device present, then it is advantageousto include the Neutron Shell in the triggerwith the g-ray veto implemented. For themixed trigger option, a Gammasphere condi-tion kgX4 may not be necessary and aðknX1ÞðkgX2Þ trigger may be sufficient. Thiswill provide the highest statistics of useful oneor two neutron-channel data.

(2)

If the fma is the only other ‘‘auxiliary’’ devicepresent and its parameters are required in thetrigger, then because of low efficiency of thefma, it is not necessary to introduce theNeutron Shell in the trigger but insteadacquire all the information provided by itwhen it fires. The g-ray veto is not necessary inthis case either.

(3)

If both the Microball and fma are present,then a mixed trigger in which both theNeutron Shell and the fma are in the triggeris preferred. The g-ray veto should be im-plemented.

For data analysis we consider the followingpossibilities:

(a)

If the Microball is present (scenarios (1) or (2)above), then the analysis scheme described inSection 5.2.2 is appropriate for identifyingall new transitions associated with the 2nexit channels. Then, the g–g spectroscopywith Gammasphere should be done with the1n-gated spectra after rejection of neighboringhits. In such a case, the gain in statistics overthe linear combination spectrum is a factor of13.9 (see column 3 in Table 4) for the 2p2n

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D.G. Sarantites et al. / Nuclear Instruments and Methods in Physics Research A 530 (2004) 473–492492

channel or a factor of 9.5 for the 3p2nchannel. If, for example, analysis for the weak2p1n channel is required, then the strongbackground from the 3p1n channel can besubtracted with the aid of the Microball. Thespectra to analyze then should be 2p1n-gatedwith the neighbor hits removed.

(b)

If the fma is used [scenarios (2) or (3) above],then it provides a mass gate. In this case, in the2p2n gate, for example, significant backgroundcontribution from the isobaric 3p1n channelappears by virtue of the ‘‘cross-talk’’. Thisbackground can be reduced by rejectingneighbor hits, provided the loss of statisticsby a factor of about 2.5 permits it. If, on theother hand, the Microball was also present,then the 3p1n background could be subtracted.Analysis of a weak 1n channel such as 2p1ncan be cleaned up by neutron coincidence fromthe isobaric strong 3p channel.

Acknowledgements

The excellent craftsmanship of the staff ofthe Department of Chemistry Machine Shop at

Washington University during the construction ofthe Neutron Shell is greatly appreciated. Theinterest and support of this project by Dr.L. Schroeder of LBNL is greatly appreciated.Useful discussions with C.J. (Kim) Lister areappreciated. This work was supported in partby the US Department of Energy, Division ofNuclear Physics under Grant no. DE-FG02-88ER-40406 (Wash. U.) and Contract no. DE-AC03-76SF00098 (LBNL), and the US National ScienceFoundation under Grant no. PHY95-14597(U. Penn).

References

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