Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–91

Contents lists available at SciVerse ScienceDirect

Nuclear Instruments and Methods inPhysics Research A

0168-90http://d

n Corrnn CorE-m

hardy@

journal homepage: www.elsevier.com/locate/nima

Digital beta counting and pulse-shape analysis for high-precisionnuclear beta decay half-life measurements: Tested on 26Al

m

L. Chen n, J.C. Hardy nn, M. Bencomo, V. Horvat, N. Nica, H.I. ParkCyclotron Institute, Texas A&M University, College Station, Texas 77843-3366, USA

a r t i c l e i n f o

Article history:Received 18 March 2013Received in revised form30 May 2013Accepted 5 June 2013Available online 28 June 2013

Keywords:High-speed digitizer4π gas proportional counterHigh-precision half-life measurementDigital signal processingDigital β counting

02/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.nima.2013.06.039

esponding author. Tel.: +1 979 845 1411; fax:responding author.ail addresses: lchen@comp.tamu.edu (L. Chen)comp.tamu.edu (J.C. Hardy).

a b s t r a c t

A digital β�counting method has been developed for high-precision nuclear β�decay half-life experi-ments that use a gas proportional counter. An 8-bit, 1-GS/s sampling-rate digitizer was used to record thewaveforms from the detector and a software filter was designed, tested and applied successfully todiscriminate genuine β�decay events from spurious signals by pulse-shape analysis. The method of usinga high-speed digitizer for precision β counting is described in detail. We have extensively tested thedigitizer and the off-line filter by analyzing saved waveforms from the decay of 26Al

macquired at rates up

to 10,000 per second. The half-life we obtain for 26Alm

is 6345.3070.90 ms, which agrees well withprevious published measurements and is as precise as the best of them. This work demonstrates thefeasibility of applying a high-speed digitizer and off-line digital signal processing techniques for high-precision nuclear β�decay half-life measurements.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Precision measurements of nuclear β�decay, from which fruitfulphysics can be studied, has a long history in experimental nuclearresearch. Such measurements have played, and will no doubtcontinue to play, a crucial role in the development of electroweakinteraction theory. They also provide a very important tool forinvestigating nuclear structure and extracting data for nuclear-astrophysics applications. Though various types of detectors havebeen introduced for β�particle detection in these experiments, thebasic idea of event counting has not changed for a long time. In atraditional β counting system the detector signals generally followthe stages of amplification/shaping, discrimination and on-linecounting/histogramming. At each stage, qualified commercial analogmodules are generally applied for their specific functions.

We have long used a specialized version of this analogapproach in our laboratory to make high-precision superallowednuclear β�decay half-life measurements. We use a 4π gas propor-tional counter to detect the β particles. The counter is divided intotwo separate halves, which are located in very close geometry oneither side of a thin strip of aluminized Mylar tape containing anaccelerator-produced source. The two halves each have the samestandard single-wire configuration. The construction and opera-tion details of our gas counter can be found in Ref. [1]. In the past,the signal from our gas counter has always been processed by an

ll rights reserved.

+1 979 845 1899.

,

analog electronic chain [2] composed of well-tested and qualifiedmodules: a pre-amplifier, amplifier, discriminator, gate-and-delaygenerator and multichannel scaler (see Fig. 1). This conventionalβ�counting method has generally worked well and we havesuccessfully performed high-precision half-life measurements ofthe following superallowed βþ emitters: 10C [3], 22Mg [4], 26Si [5],34Ar and 34Cl [2], 38Ca [6] and 46V [7].

Nevertheless, there are some drawbacks to this kind of analogβ�counting system, which make it difficult, if not impossible, toreach a level of relative precision better than about 0.02%. Thedead time is relatively long (43 μs), thus limiting the maximumcounting rate that can be tolerated if dead-time corrections are tobe kept small; and experimental parameters such as detector bias,discriminator threshold and dead time must be systematicallychanged in repeated runs to ensure that their specific values donot have any significant effect on the half-life result. This makesfor inefficient use of beam time and limits the statistical precisionthat can be reached in any experiment of reasonable duration.Finally, spurious signals from the gas counter cannot be absolutelyguaranteed absent from the recorded data to the extent needed toallow a quoted half-life uncertainty below 70.02%.

It has been our goal to achieve higher precision by developing anew β�counting system that has a more robust β�discriminationmethod and greater efficiency in testing the parameter-dependenceof each half-life result. Our expectation was that digital countingcould help us achieve this goal.

Benefiting from recent developments in the field, high-precision measurement with modern fast digital devices is nowvery feasible. Signals can be digitized right after the detector orafter the (pre-)amplifier in cases where amplification is necessary.

Fig. 1. Comparison of analog and digital chains used for high-precision β countingin our experiments. Upper branch: the conventional analog chain consists of analogmodular instruments. The gate-and-delay generator is used to establish a singledominant non-extendable dead time. Lower branch: digital chain incorporating ahigh-speed digitizer.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–9182

The fast digitized data can then be saved for off-line analysis via ahigh-speed data bus (peak transfer rate of 133 megabytes/s if ahigh-speed PCI bus is used). Finally, digital signal processing (DSP)can be used to perform very subtle analysis of the recorded signals.Digital measurements are naturally free of the constraints ofon-line analog processing procedures. On-line signal processingcan be reduced or even eliminated so that maximum physicalinformation can be saved for later detailed off-line analysis. If on-linesignal processing is required, digital on-line processing can be set upeasily since digital devices are designed to perform such tasks withbuilt-in flexibility. In the off-line analysis stage one can use DSPalgorithms to build software analysis chains for data processing.Various chains can be built to investigate different physical quan-tities or to analyse the data from different perspectives. In brief,digital measurements are able to save maximum on-line informa-tion and provide the highest flexibility for off-line data analysis.A review of some of the pioneering work in the field of digitalcounting can be found in Ref. [8]. Also see Refs. [9–14] for someexamples of digitizers applied in physical experiments.

In this paper we present the first application of a high-speeddigitizer to a gas detector used for high-precision superallowednuclear β�decay half-life measurements. We will describe thedigital system used for our measurements, give the details of ouroff-line β�discrimination methods, and offer results from on-linemeasurements.

2. Hardware and digital measurement

To achieve high precision, any β�decay half-life measurementmust ensure that genuine β�decay events are counted with veryhigh efficiency and accuracy. In order to achieve this goal withdigital counting, pulse waveforms must first be recorded withrelatively high definition so that detailed off-line analysis ispossible. The signals from our gas proportional counter aregenerally fast and their rise times are often a few nanoseconds.So in order to record the pulse shape properly the digitizer mustbe able to sample signals at the rate of 1 gigahertz. Besides thesampling rate, the other digitizer properties of greatest concern tous are the acquisition dead time and its ability to handle a highcounting rate. In our experiments, we aim for the shortest possibledead time so we only considered digitizers with a very short deadtime (o1 μs).

Our counting-rate requirements set other conditions on thespecifications we were seeking. The whole pulse waveform mustbe saved for detailed pulse-shape analysis and it is also helpful tosave some extra data points before and after the main pulse inorder to simplify peak location and to aid in data smoothing. Thetime durations of our gas-proportional-counter pulses are distrib-uted widely from ∼15 ns to a bit more than 100 ns, with a most

probable value of around 50 ns. Consequently the length of wave-forms we must capture is about 200 ns, or 200 samples in the caseof a 1 GHz sampling rate. The maximum counting rate we limitedourselves to with our analog counting system was about 5000per second, but our working goal for the new digital systemwas todouble that rate. Thus a data flow of at least 16 megabits/s wasanticipated for an 8-bit digitizer, and this clearly required a largeon-board memory. Even though the data can be transferred to thehost PC via a high speed bus, situations can occur where the hostPC is busy for a short period of time due to an unexpected task.Therefore, it is necessary that the digitizer be able to temporarilyhold the captured pulses for at least a few seconds. This impliesthat the on-board memory size should not be less than about 100megabits.

With these specifications in mind, and after a careful compar-ison of digitizers on the market when this study was started in late2009, we made the decision to acquire the PC-based high-speeddigitizer, NI PCI-5154 [15], which was available from NationalInstruments Corporation. The key characteristics of this digitizersatisfied our requirements well. The digitizer can sample 2 inputchannels at 1 GHz rate simultaneously (up to 2 GHz if operated insingle channel mode) and has a 256 megabytes on-board memoryfor each channel. The PCI-5154 is an 8-bit digitizer and the voltagedynamic range can be configured from 0.1 V to 5 V. The dead timeof the digitizer is less than 1 μs and is dominated by the so-calledreference trigger re-arm time, to be explained later. Our digitalchain incorporating this high-speed digitizer is shown schemati-cally in Fig. 1 where it is compared with the analog chain that wehave been using for high-precision half-life measurements.Obviously the digital method simplifies the experimental setupconsiderably, while yielding much more saved information avail-able for later analysis.

Since very high β�detection efficiency is essential for ourmeasurements, the signal from the detector must be amplifiedwith an extremely high gain. After extensive tests, we settled ontwo cascaded amplification stages, the first a fast timing pream-plifier, ORTEC VT-120A, and the second an SR445A amplifier fromStanford Research Systems. They amplify our gas-proportional-counter signal with a combined gain of 1000 (200�5). Bothamplifiers have a very short rise time (o1 ns). However, theirability to reproduce the fast gas-counter signal was somewhatlimited by the bandwidth of the amplifiers, which is 350 MHz inboth cases. With those specifications we believe that the originalpulse shape from our detector can be reasonably well reproducedfor digitizing. With �1000 gain the amplifiers provided a suffi-ciently strong signal for digitized sampling and, based on our off-line tests, we believe that our total β detection efficiency is499:5%.

The basic idea of our digital half-life measurement is to capturethe gas-proportional-counter pulses by the high-speed digitizerand then use off-line analysis to discriminate and count genuineβ�decay events. The concept of single-pulse capture is demon-strated in Fig. 2. When the digitizer is properly initialized, it startsdigitizing the signal in the feeding channel continuously. Eachpulse-capture process is triggered by a reference trigger, which isgenerated by the digitizer trigger system whenever the configuredtrigger condition is satisfied. Many options are provided to con-figure the digitizer reference trigger. For example, the triggersource can be the input analog signal or an external clock signaland the trigger type can be “analog edge” or even a softwaretrigger. Once a reference trigger is recognized, the digitizerswitches from pre-trigger sampling to post-trigger sampling. Apulse-capture process is complete when the specified number ofpost-trigger samples have been acquired. The captured pulse isthen held temporally in the on-board memory, ready to betransferred to the host PC memory via the high-speed PCI bus.

Fig. 3. Top: the measured re-arm time for the digitizer reference trigger is plottedas a function of waveform record length. Bottom: the re-arm time distribution of100,000 waveform-capture processes. All waveforms were captured with 200samples under 1 GHz sampling rate. The stability of the trigger re-arm time isobvious.

-300

-250

-200

-150

-100

-50

0

50

0 20 40 60 80 100

Trigger level

Captured samplesIgnored samples

Post-trigger samples

Reference trigger (timestamp)

Sampling rate: 1GS/s

Pre-trigger samples

Time (ns)

Am

plitu

de (m

v)

Fig. 2. Concept of waveform capture with the high-speed digitizer is illustrated byusing a generic pulse shape. The reference trigger is used to signal the starting ofpost-trigger data capture and to define the timing of the captured pulse.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–91 83

The maximum number of pulses that can be temporarily held on-board in our case is 100,000, which is actually not limited by thememory size but by other digitizer hardware settings. A longcontinuous measurement can be maintained since data are trans-ferred to the PC memory in parallel to the pulse capture process.Note that the pre-trigger samples can be saved as well and thelength of pre-trigger data can be set from zero up to the fullwaveform record length.

In our measurement the reference trigger was configured touse the analog edge trigger method: that is, a reference triggeroccurs if a (negative) pulse's falling edge crosses the triggerthreshold. After it has finished the pulse-capture process, thedigitizer then takes some time to re-arm its trigger system andthis re-arm time dominates the acquisition dead time. The nextpulse is ignored if it arrives before the trigger system is re-armed.In order to determine the exact trigger re-arm time we configuredthe reference trigger in a test measurement as immediate, whichmeans the digitizer starts to capture the next waveform as soon asit is re-armed. In this way the time gap between captured wave-forms, which was calculated from their recorded time stamps, is adirect measure of the trigger re-arm time itself. It turns out thatthe re-arm time of the digitizer is quite stable (jitter o1 ns) forany specified running configuration but varies as a function ofwaveform record length. The measured trigger re-arm time isplotted as a function of the waveform record length in the toppanel of Fig. 3. The re-arm time changes systematically as afunction of the waveform record length and ranges between495 ns and 650 ns. This results from the digitizer self-optimizingby changing the methods used for packing and aligning the data inthe on-board field-programmable gate array (FPGA). As the num-ber of samples in the waveform is varied, the time taken toperform the processing varies accordingly. In any case, as can beseen from the bottom panel of Fig. 3, the dead time is very stable ifthe configuration is not changed during data acquisition. The deadtime is also short enough for our purposes.

3. Digital pulse-shape analysis of gas counter signals

The data acquisition (DAQ) software, as well as all the off-lineanalysis applications, were developed on the LabVIEW platform.LabVIEW provided a native control of our digital devices (all madeavailable by National Instruments) and we found that using Lab-VIEW for digital data analysis was reasonably efficient since manyhandy functions for hardware control and data processing aremade ready to use in LabVIEW.

3.1. Identification of spurious pulses

The backbone of any high-precision β�decay half-life measure-ment must be the reliable identification of β events with anefficiency that is completely unaffected by counting rate. In aconventional analog counting system legitimate β events aredeemed to be those that pass on-line pulse-amplitude discrimina-tion. This approach has been taken in nuclear experiments formany decades. However, it faces two underlying difficulties. Thefirst is the spurious-pulse problem: When the counting rate from agas proportional counter is plotted against increasing bias voltagefor a given radioactive source, a “plateau” region is observed overwhich the recorded counting rate changes very little with increas-ing voltage. Such detectors are normally operated in this plateauregion. However, it is commonly observed that even in the centerof the plateau region the detected rate still has a small but definiteslope (≲1% per 100 V). The unanswered question is whether thisslope is due in part to spurious peak generation or simplyrepresents a true increase of efficiency as more very low-energy

-1

-0.8

-0.6

-0.4

-0.2

0

-1

-0.8

-0.6

-0.4

-0.2

0

-0.25

-0.2

-0.15

-0.1

-0.05

0

Time (ns)

Am

plitu

de (V

)A

mpl

itude

(V)

spurious pulses

pulses

weak pulses andstrong spurious pulses

Am

plitu

de (V

)

0 20 40 60 80 100

Fig. 4. Waveforms captured by the high speed digitizer from a 90Sr β source. Thetop panel shows three captured β signals and the central panel shows ninecaptured spurious pulses. The “flat top” of some β signals is due to the limits ofthe digitizer's dynamic range. In contrast to the waveforms in the top and centralpanels, whose identification is more or less straightforward, the five pulse wave-forms in the bottom panel require some additional pulse-shape analysis todetermine their character unambiguously.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–9184

β signals surmount the discriminator level. This problem wasreviewed in a relatively early paper [16]. Spurious pulses haveseveral potential causes but, in fact, their production mechanismsare not well understood [16,17]. Leading contenders as sources ofspurious pulses are X-rays emitted from excited gas atoms, andelectrons released from the detector's inner wall after a fastβ particle has impinged on it.

The second underlying difficulty with analog counting systemsis the decrease in gas-proportional-counter gain that can occurunder high counting rate situations (see, for example, [18]). Suchgain loss can be caused by two mechanisms. The first is the slightdown-shift of effective anode bias because a higher averagecurrent is drawn from the high voltage power supply, which isconnected to the detector anode via a large resistor. The second isspace charge effects, which could reduce the Townsend coefficientconsiderably [19]. Both the spurious-pulse and gain-loss problemscan introduce small systematic effects to the decay data and it isvery hard to clearly quantify their influence on the half-livesobtained. To solve both problems we need to devise a way todiscriminate genuine β�decay events that is insensitive to thedetector's effective gain.

The captured pulses have three origins: (a) genuine β�decayevents; (b) background events and (c) spurious pulses. The back-ground events, caused mainly by cosmic rays, have a constant rate,which is at least three orders of magnitude lower than the initialβ rate in our experiments. Although the background events areindistinguishable from genuine β�decay events, they cause littleconcern as they only contribute a small constant background tothe decay spectrum. It is the spurious pulses we need to take extracare to eliminate.

Some captured pulse waveforms are displayed in Fig. 4. Weobtained them using a 5 kBq source of 90Sr (t1=2 ¼ 29 years)deposited on thin Mylar tape, which was placed between thetwo halves of our gas detector. There are three genuine β�decaywaveforms in the upper panel and nine clearly distinguishablespurious pulses in the central panel. Generally, spurious pulseshave a quite different shape compared to genuine β�decay signals.Spurious pulses probably correspond to single-electron triggeredavalanches; the pulses are usually very fast and narrow althoughtheir amplitudes are distributed over a relatively large range.Unfortunately, not all pulses are so easily distinguished. The fivepulse waveforms shown in the bottom panel are more ambiguous:they correspond either to strong spurious pulses or to very lowenergy β particles and require more careful discrimination.

A typical amplitude distribution of captured pulses is displayedin the top panel of Fig. 5. The figure gives the raw results “beforefilter” and those obtained after a software filter for true betas hadbeen applied. The filter will be described later in this section. Notethat the effect of the upper limit to the digitizer's dynamic range,which is evident in the top panel of Fig. 4, manifests itself in thetop panel of Fig. 5 as the strong limit peak at 1100 mV. At an anodebias of 2750 V, about 95% of the captured β�decay events have apulse amplitude that reaches this limit. The spurious pulses have arather wide amplitude distribution and, although most have ratherlow amplitude, some have amplitudes large enough to exceed thedynamic range of the digitizer. It is obvious that simple amplitudediscrimination cannot be enough to separate spurious events fromreal ones.

The pulse-width distribution of captured pulses, shown in thecenter panel of Fig. 5, shows more promise. Here we have definedthe width of a pulse as being the number of its samples thatexceed a certain amplitude level. The pulse width in Fig. 5 wascalculated with that level specified to be −50 mV. Clearly the pulsewidth distribution manifests a more pronounced valley betweenspurious and real events than does the amplitude distribution inthe panel above. It is also superior to the pulse integral

distribution, which is plotted in the bottom panel. However,although the valley in the width distribution is quite deep, it isstill not deep enough to give a clean separation of β events fromspurious ones. Pulses contributing to the valley itself are a mix ofstrong spurious pulses and weak β waveforms generated by βparticles in the low energy tail. To illustrate the problem, five ofthese pulse waveforms are displayed in the bottom panel of Fig. 4.To remove all spurious pulses from the valley region with thehighest possible efficiency, we need to perform a more complexpulse-shape analysis.

It may be remarked here that in the conventional analogcounting chain the amplification stage commonly has a muchlonger shaping time (a few μs), which has the effect of reducingmost of the spurious signals to low enough amplitude that they donot trigger the discriminator and are thus not counted. However itis unlikely that this completely removes all spurious signals, which– as we have noted already – effectively limits the precision that isultimately possible with an analog system.

We have designed and tested a software filter, which combinesthe analyses of a number of different pulse properties. The filterwas designed to discriminate pulses in two steps. In the first step apulse is identified as a β event, a spurious event, or an ambiguousone, based on its most distinctive property: If the pulse width isgreater than 40 ns it must be a β pulse; if it is less than 10 ns it

Fig. 5. Pulse amplitude distribution (top panel), pulse width distribution (center)and pulse integral distribution (bottom). Pulses were recorded with an anode biasof 2750 V. The distributions before and after the β filter are both displayed. A 90Sr βsource was used. The strong limit peak at 1100 mV in the top panel is caused by thedigitizer's dynamic range and the lower limit of the amplitudes is due to the pre-setdigitizer trigger level.

Fig. 6. The top panel shows the detected β events in the 4π gas detector as afunction of detector bias. The data were taken with a 3 kBq 90Sr β source using thedigital counting method. The measuring time of each data point was 100 s. Thebottom panel shows the slope derived from the same data.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–91 85

must be a spurious event; otherwise it is considered ambiguous.(See the center panel of Fig. 5.) That positively identifies about 90%of the pulses but leaves the remainder, those pulses whose widthsare distributed around the valley of the distribution curve, requir-ing further more-detailed pulse-shape analysis in a second step.

The second step combines three factors: the pulse widthalready described, the pulse amplitude variability, and the ratioof the pulse amplitudes taken before and after a smoothing filter.To obtain a measure of each pulse's amplitude variability, we usethe 10 samples from the pulse that have the largest amplitude, sortthem in order of descending amplitude and fit the slope. Obviously,the sharper the pulse shape, the larger the fitted slope is and themore likely it is to be a spurious event. In addition, a Savitzky–Golay [20] filter with a moving window length of 7 data pointswas used to smooth the pulse waveform. We denote the ratioof the pulse amplitude before to that after the smoothing filterto be Aratio, and then use this ratio, together with the pulsewidth, Pwidth, and the fitted amplitude slope to define a pulseshape factor. After intensive tests, we defined the shape factor as

ðPwidthÞ2=ðslope� AratioÞ. This calculated shape factor for eachpulse was then used as a separation criterion in the second stepof the β filter. It is independent of the absolute amplitude of thepulse waveform and thus is quite insensitive to the actual detectorgain. We have tested that a common shape threshold can be set fora wide range of detector biases. For the measurements reportedhere, the threshold was set to 2800 when Pwidth is measured in nsand amplitudes are in mV. Clearly this particular choice of thresh-old is specific to our gas proportional counter and its operatingconditions.

3.2. Experimental test of spurious pulse separation

Proof of the effectiveness of our analysis appears in Fig. 6. Thefigure presents the results of successive measurements of our3 kBq 90Sr β source with the 4π gas detector operated at succes-sively higher bias voltages. The top panel shows the “plateau” inthe count rate between bias settings of 2375 V and 2925 V. Thebottom panel gives the slope of the curve in the top panel,showing that the slope of the plateau is below ∼0:5% per 100 Vbetween 2575 V and 2825 V. This plateau, as measured with ournew digital method, is wider and flatter than ones previouslyobtained with a conventional electronic chain. With the lattermethod, low-amplitude spurious pulses can be raised above thediscriminator threshold as the detector bias is increased, thusgiving a slope to the plateau. The near absence of a slope in ourdigitally acquired data indicates that spurious events have beeneffectively suppressed, leaving the apparent detector efficiencynearly independent of bias voltage in the plateau region. In anyprecise half-life measurement the source decay-rate typicallychanges by up to four order of magnitude during each detectioncycle, so the effective detector bias is slightly lower at thebeginning of the cycle than it is at the end. If the detector plateauis not flat, this change in bias would cause a change in the effectivedetector efficiency and introduce a systematic error into the

Fig. 8. The ratio of spurious pulses to β events as a function of anode bias. Datataken from the 4π gas detector with a 3 kBq 90Sr β source.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–9186

measured half-life. With the results in Fig. 6, we can be confidentthat near the center of the plateau any such systematic error isbelow 0.01%.

As a result of our pulse-shape analysis, we can clearly distin-guish a true β signal from a spurious one. Since we also record thetime of arrival of each pulse, we have been able to examine timecorrelations between the two types of events. The measured timeseparation between successive events is plotted in Fig. 7, wherethe two panels illustrate the same data but are displayed withdifferent time scales. The histograms identified as “β−β” give thedistribution of time-gaps between two identified β's. The histo-grams identified as “β�spurious” give the distribution of time gapsthat begin with an identified β event and end with a spurious peak.In the bottom panel, the β�spurious histogram exhibits threedifferent slopes, which are denoted as (a), (b) and (c). The first twocorrespond to fast spurious signals which appear within ∼1 μs and∼10 μs, respectively, after a β signal. The third has a slope verysimilar to that of the β−β histogram.

Before the results can be interpreted it is important to recog-nize that spurious events only occur when a β source is present.They are thus unquestionably caused in general by the occurrenceof β events. However, we must ask whether a given spurious eventis tightly time-correlated with a particular β event. The results inFig. 7 demonstrate that some are the events in the first 10 μs thatcontribute to the part of the histogram with slopes (a) and (b).However, the spurious events that constitute the remainder of theβ�spurious plot, with slope (c), are probably not – at least notwithin the time scale to which we are sensitive. Slope (c) isidentical to the slope of the β−β histogram and reflects the factthat, after a β event has “started the clock”, the appearance of asecond β stops the clock, thus eliminating the possibility of aβ�spurious correlation being recorded.

The relative number of spurious pulses depends strongly on thedetector bias as is demonstrated in Fig. 8, where the correlated and

Fig. 7. The top panel plots the time-gap distribution of pulses over a period of500 μs, measured with a 3 kBq β source at a detector bias of 2700 V. The bottompanel shows a zoomed-in plot of the same data to show the short-time details ofthe distribution. Note the three different slopes (a), (b) and (c) evident in theβ�spurious data.

uncorrelated spurious events have been plotted separately.Evidently the proportion of β events that are followed by acorrelated spurious event is almost constant at about 2% as thebias is changed from 2600 V to 2850 V, while the number ofuncorrelated spurious events increases rapidly with bias, reaching20% at 2850 V, which is well beyond the plateau region. We canconclude that it is the rise of the uncorrelated spurious pulses athigh bias that causes the plateau to end in a conventional countingsystem.

4. 26Alm

half-life on-line experiments

To characterize the performance of our digital counting system,we performed an on-line test experiment to measure the 6.345-shalf-life of the superallowed βþ emitter 26Al

m. The half-life of

26Alm

has been measured before by a number of groups withconsistent results [21–23] so it could serve as a good standard fortest purposes.

In our experiments, we produced an 26Alm

beam by impinginga 23 MeV/u 27Al primary beam from the K500 superconductingcyclotron at Texas A&M University on a liquid-nitrogen-cooledhydrogen gas target. The reaction products were analyzed by theMARS spectrometer [24] and the purified 26Al ions were extractedout of vacuum at the MARS focal plane through a 51�μm�thickkapton window. The ion beam then passed though a 0.3-mm-thickplastic scintillator and a set of degraders for further purificationand energy adjustment before being stopped in the center of a76�μm�thick aluminized mylar tape, which was periodicallymoved automatically to a shielded counting location where thetape stopped with the source positioned exactly at the center ofthe 4π gas detector.

Before beginning the measurement and periodically during themeasurement, we inserted a 1-mm-thick 16-strip position-sensi-tive silicon detector (PSSD) at the focal plane of MARS. Fig. 9 showsthe energy deposited in the detector versus position in the focalplane. From this spectrum and the amount of 26Al

mactivity we

collected on the tape, we could determine that the purity of 26Alm

at the MARS focal plane was about 40%, with the main contami-nant being 26Al

g, which is effectively stable with a half-life of

7.4 �105 years. All the other contaminants identified in the figureare also stable isotopes so the stopped 26Al

mwas essentially pure

as far as our decay data were concerned.The sequence followed in data taking with the digitizer is

illustrated in Fig. 10. After being configured and initialized, the

Fig. 10. The data taking sequence used in on-line measurements with the digitizer.

Fig. 9. Deposited energy versus position as recorded in a PSSD at the MARS focalplane. The dashed lines show the position of the extraction slits, which we usedduring these measurements. All identified isotopes are labeled.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–91 87

digitizer waits for an acquisition start trigger before starting dataacquisition. When a start trigger is received from the tape systemindicating that a fresh source has entered the gas detector, thedigitizer starts digitizing the pre-trigger samples continuouslyand, at the same time, monitors for the occurrence of a reference(stop) trigger. When a reference trigger is recognized, the digitizercaptures the corresponding waveform starting at a preset timebefore the trigger's arrival and continuing to a preset time after.This pulse-capture process is repeated until the end of thedetection time is reached. The captured pulses are saved tempora-rily in the on-board 256 megabytes memory and then transferred,while pulse captures continue, to the host PC via a high-speed PCIbus. In this experiment the reference trigger was configured to usethe analog-edge-trigger method, with the digitizer trigger level setto −120 mV (see Fig. 5 for how the trigger level will affect thecapture of low amplitude pulses). The trigger level was chosenwell above the electronic noise (∼50 mV) but was still low enoughto maximize the detection efficiency for β particles. We deter-mined the onset of electronic noise by lowering the trigger levelwhen no source was present until the trigger rate started to riseabove the intrinsic detector background rate.

The tape-transport system and the digital devices were syn-chronized by TTL signals, which were generated by the tape-drivesystem. In a cycle-by-cycle mode [2,3], two TTL signals were sentin each cycle from the tape-drive system to control the data

acquisition. The first TTL signal was sent at the beginning of thecollection period, during which the 26Al

mions were accumulated

on the tape; this triggered the DAQ to count the signals from theplastic scintillator (just outside the kapton window) using a digitalcounter (PCIe-6320, from NI). The second TTL signal, which wasused as the acquisition start trigger for the digitizer, was sent justafter the collected sample had reached the center of the 4π gasproportional counter.

In each cycle we collected the 26Alm

ions for 0.5–2 s dependingon the beam intensity and desired counting rate. At the end of thecollection period, the tape-transport system moved the implantedsample in ∼185 ms to the gas detector. The β activity of the samplewas then measured for 125 s, which corresponds to just under20 half-lives of 26Al

m. To test the performance of our system we

took data at various initial counting rates, ranging from 3000per second to about 10,000 per second. In principle, high rates upto ∼40k per second can be handled by the digitizer, which islimited by the data transfer speed between the digitizer and thehost PC. However, other tests have shown that our gas propor-tional counter cannot handle counting rates above 10,000 per secondwithout a drop in gain sufficient to render precision half-lifemeasurements unfeasible.

We also tested the effect on our results of changing otherexperimental parameters. Four different detector biases, 2650 V,2700 V, 2750 V and 2800 V, were used to test any dependence onthat parameter. A few runs were also taken with a trigger level of−160 mV instead of −120 mV. We also did a few measurementswith an artificially extended digitizer dead time (2 μs). In total wecollected about 120 million waveforms from about 1700 individualcycles.

5. Data analysis

5.1. Dead time correction

Our data-processing procedure, developed and extensivelytested off-line with a 90Sr β source, has already been describedin Section 3. In analyzing the 26Al

mdecay data obtained on-line,

we used the same procedure to tag each recorded event as beingeither spurious or genuine. Next we corrected for dead-timelosses. The digitizer capture time we used for our on-line mea-surement was 200 ns, so the hardware dead time – the trigger re-arm time – was 620 ns (see Fig. 3). Since the total capture timeincorporated 180 ns after the trigger itself, the total dead time foreach event was 800 ns. To correct for lost events we followed theshadow window technique, which was introduced by Lynch in arecent measurement of the muon half-life [25]. Here we use amodified version of the technique, which is briefly described in thefollowing paragraphs.

The conventional dead-time correction method used in event-counting experiments employs the following analytic formula toobtain the number of true events, Ni, from the number of observedevents, N0i, in the i th time-bin of width t

Ni ¼N0i

1−N0iδt=tð1Þ

where δt is the non-extendable dead time of each event. Thisequation is exact for a constant count-rate, but is only anapproximation if the count-rate changes over the finite width ofa time-bin, which is of course what happens to some extent in anydecay measurement. At high counting rates, where the dead-timecorrection can be large, this is a serious concern if precision isthe goal.

The shadow window technique, schematically illustrated inFig. 11, is a statistically correct method which is also independent

Fig. 11. A schematic illustration of the shadow window technique used to correctfor dead time. P0 is the original pulse and P1 and P2 are events that may appear(or may not) in the first and second-order shadow window, respectively. The firstorder shadow window has the same length as that of the system dead time. Thesecond-order window, if required, has a length equal to the part of the first-orderwindow that is made dead by the appearance of P1. The process continues to athird-order window if P2 occurs, and so on.

Fig. 12. The decay curve of 26Alm

measured by the digital counting system andsummed over all accepted cycles; an imposed dead time of 4 μs was used. Thebottom panel shows the normalized fitting residuals. The normalized χ2=N of thesum fit is 1.08 with N¼497.

Fig. 13. Half lives obtained from the measured decay of 26Alm

plotted as a functionof the imposed dead time used in analysis. Note that the total dead time is equal tothe imposed dead time or the inherent system dead time (800 ns), whichever isgreater. The data from all runs are included in the figure.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–9188

of the counting rate. After each recorded event, real or spurious,there is a dead-time during which real β events might be missed.We determine the possible loss for each event by placing a time-window with the same length as the dead-time at some pre-determined time later (or earlier) in the same cycle. If the timebetween the observed event and this shadow window is muchshorter than the decay half-life being measured, then the contentsof the shadow window accurately reflect the loss due to theoriginal dead-time. If the shadow window includes an event, thenit too is partially dead and a second (shorter) shadow window toaccount for its dead time must be applied after a second delay.This process continues until no event is observed in the shadowwindow. In principle, to be reliable this method requires only thatthe delay time between the event and the shadow window bemuch shorter than the decay half-life; in reality, we found that theshadow window cannot be placed too near the original pulse inthe down-stream side since there is a significant probability of acorrelated β�spurious pair of events within a few hundred μs ofone another (see Fig. 7). We chose to avoid this problem by placingthe shadow window 10 ms later than the original pulse to totallyavoid this problem. That is corresponding to a 0.16% shift in termsof the half-life of 26Al

m. And in our analysis, we got consistent

results when the shadow window was placed 50 μs in the up-stream side or 5 ms in the down-stream side.

After dead-time corrections had been applied in this manner,we built a decay spectrum for each tape cycle. We then used thesame fitting procedure as described in our previous papers (forexample, Ref. [5]). Briefly, we began by checking the data quality ofeach cycle. All the cycles with low beam current and consequentlytoo few β's (o5000) were excluded. Next, cycles in which the tapedid not move correctly to the center of the gas counter wereeliminated based on the ratio of the number of recorded β eventsrelative to the number of 26Al ions detected in the scintillator: Ifthe ratio was less than 80% of the maximum ratio, the cycle wasrejected. In total, about 10% of all cycles were excluded from thefinal data set used for half-life evaluation.

To reach this point we have considered only the inherentsystem dead time of 800 ns, the sum of the after-trigger pulse-capture time and the trigger re-arm time. There is a problem,though, with this approach. Events that occur near the end of thedead time can spill over into the subsequent live time, leaving onlypartial information: If this were a true β event, it might then looklike a spurious or ambiguous event, which could skew the half-liferesult. To circumvent this difficulty, we artificially introduced intoour software analysis a dead time after each event, which wassignificantly longer than the system's inherent 800 ns dead time.This way the software could also examine if any events appearednear the end of the imposed dead time and increase the shadowlength in that case to incorporate the component of the inherentdead time that extended beyond the end of the imposed one. Wereanalyzed our data a number of times with imposed dead timesthat ranged from 2 μs to 12 μs.

5.2. Half-life extraction

In Fig. 12 we present a typical fitted decay spectrum for thesum of all accepted cycles; the normalized residuals are shownbelow. The spectrum was fitted with the ROOT Minuit2 packageusing the Maximum Likelihood method. Our fitting code was alsotested with Monte Carlo generated decay data. In this simulateddata set, there were 109 events with a decay half-life set to6.34500 s. The half-life we obtained from fitting the simulateddata was 6.34502(25) s, which successfully confirmed our fittingroutines.

The result shown in Fig. 12 came from an analysis in which weused an imposed dead time of 4 μs. The decay curve and fitobtained with other imposed dead times were indistinguishableby eye from those shown in the figure although there were slightchanges in the fitted half-life itself. The fitted half-lives are plottedas a function of the imposed dead time in Fig. 13. As can be seen inFig. 13, the half-lives are consistent when imposed deadtimechanged from 2 μs to 12 μs. Our final results are reported fromanalysis when imposed deadtime was set to 4 μs.

Fig. 15. Fit of experimental decay spectrum of identified spurious events (top) andcomparison of fitting residuals between a Monte-Carlo-simulated spurious decayspectrum and the experimental one (bottom). The Monte-Carlo-simulated spuriousdecay spectrum, which was built from identified spurious pulses in the simulateddata, was fitted with the same procedure as we used to fit experimental data. Theinitial β�decay rates in both cases were 5000 per second and the rates dropped to330 per second after 25 s. The data in the first 25 s were excluded from the fit.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–91 89

We made a second test of the analysis technique to see if theextracted decay half-life was sensitive to our filter settings. In thiscase, we artificially adjusted the shape threshold in the filter (seeSection 3) away from the value we believe provides the bestseparation between spurious and genuine events. Test results fromone run of 26Al

mdata are plotted in Fig. 14 as a function of the

number of selected β events relative to the “best” setting. Negativevalues on the abscissa correspond to a filter that removes somegenuine β's from the selected events, while positive valuescorrespond to a filter that leaves some spurious events amongthe selected β events. Note that the half-life reaches a minimumvery close to the 0 value of the abscissa, an outcome that stronglysupports our choice of filter parameters.

We argue that there are good reasons to conclude that thepoint where the shortest half-life is reached corresponds to wherethe best separation of spurious from β events has been achieved.The first reason, illustrated in Fig. 15, is that the spurious events, ifconsidered as a whole, tend towards a longer half-life than thegenuine β events. The upper panel of the figure shows the decaycurve corresponding to identified spurious events obtained fromour on-line data. Unlike the decay of identified β events in Fig. 12,the decay of spurious events cannot be fitted well with a singleexponential (plus a constant background): this is made very clearby the bottom panel, in which are plotted the residuals from ahalf-life fit based on the data recorded after 25 s. The decayconstant for this fit is consistent with that of the 26Al

mβ decay.

If a single exponential were fitted to the entire decay spectrum,the agreement would be poor but it would produce a half-lifelonger than the 26Al

mβ�decay result. The underproduction of

spurious pulses at the beginning of the decay curve is quiteobvious. Evidently, although some genuine β events are followedby a correlated spurious event, if a second genuine β event comesfirst it “cancels out” any spurious pulse correlated with the originalβ event. Since this effect is more pronounced at high decay rates, itaccounts for the depletion of spurious events at the beginning ofthe decay curve in Fig. 15.

This explanation was confirmed by a Monte Carlo simulation.The fitting residuals obtained from the simulated data are com-pared with the residuals from the experimental data in the bottompanel of Fig. 15. The simulation was done using the spurious-to-βratio from Fig. 8, and spurious event-correlation times from Fig. 7.The decay half-life of β events in the simulation was set to 6.345 s.

Fig. 14. This plot illustrates how the fitted half-life obtained from a single rundepends on the value of the shape threshold used in our software filter. See text.The points are plotted against the relative number of events that were identified bythe filter as being legitimate β events. The zero point on the abscissa corresponds tothe setting that best separates genuine from spurious events. The solid line simplyconnects the data points to show the trend.

In the simulation, any potential after-pulsing spurious eventsinduced by β events were ignored if a second β event occurred.The agreement between the measured spurious spectrum and thesimulated one is striking, and confirms our postulate that theappearance of a second genuine β event does indeed “cancel out”any correlated spurious pulse from the preceding β. Of course, asthe β�decay rate decreases this cancellation effect becomes lesssignificant, thus allowing the spurious spectrum to be fitted withan exponential function (plus a constant background). In Fig. 15 agood fit was achieved only if the data from the first 25 s – about4 half lives – was ignored. Clearly, even if a very small number ofspurious events were to be included in the β spectrum, the effectwould be to increase the apparent half-life. This explains theincrease in half-life for positive values of the abscissa in Fig. 14.

The rise in half-life for negative values of the abscissa in Fig. 14originates in the fact that principally low-energy β's are beingeliminated in this region and that the fraction being removeddepends slightly on counting rate: at high rates there is a tinyreduction in the gain from the gas proportional counter. This is tobe expected since the high-voltage power supply is connected tothe detector anode via a large resistor, across which the voltagedrop must increase as the average current increases. Also spacecharge effects are more serious at high counting rate, whichfurther decreases the actual detector gain. Fig. 16 demonstratesthis clearly. The data, which include only identified β events, weretaken from the on-line measurements with an initial decay rate of7000 per second. The top panel shows that the fraction of β pulsesabove 1.1 V (the saturated pulses in the top panel of Fig. 5)increases as the counting rate decreases; the bottom panel showsthat the average pulse width increases at the same time. Both arecharacteristic of a gain change with counting rate. Thus, if our filteris cutting into the genuine β spectrum, the fraction it removes willdecrease as the counting rate decreases. This will increase theapparent half-life.

Fig. 17. The evaluated half-lives of 14 runs. The runs with bias 2650 V, 2700 V,2750 V are represented by diamond, square, and circle, respectively.

Fig. 18. The evaluated half-lives of as a function of initial decay rates. Cycles areregrouped in 6 groups according to their initial decay rate (in thousandper second): (2–4), (4–5), (5–5.5), (5.5–6), (6–7) and (7–10). The ranges for eachgroup were chosen to include approximately equal numbers of events. The half-liferesults are plotted at the mid-point of each range.

Fig. 16. Top panel: the percentage of identified β pulses with amplitudes of 1.1 V(or above) plotted as a function of decay time in units of the 26Al

mhalf-life. Values

are obtained from on-line decay spectra with an initial decay rate of ∼ 7000per second. Bottom panel: a similar plot of the average pulse width. The increase ofboth parameters with decay time indicates clearly that the detector gain decreasesslightly as count rate increases.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–9190

With this understanding of the effect that our filter has on theextracted half-life, we can explain the behavior shown in Fig. 14.We can also see from the figure, though, that the minimum aroundthe central point (0 on the abscissa) is very shallow. This gives usconfidence that the filter is working well and that the results donot depend sensitively on the specific setting of the shape thresh-old (see Section 3). It is worth noting as well that Fig. 16demonstrates that amplitude discrimination used by itself wouldonly be sufficient under low count-rate conditions: a moresophisticated filter, such as the one we have described, is essentialif high count rates are to be analyzed.

6. 26Alm

half-life

The evaluated half-lives of the 14 runs taken with 2650, 2700and 2750 V detector bias are plotted in Fig. 17. Four runs with2800 V bias, which is just above the plateau region, had signifi-cantly more spurious events (see Fig. 8) and their overall analysiswas not as satisfactory as it was for the other runs with lower biasvoltages well within the plateau region, so we decided to eliminatethem entirely. The average value of the results in Fig. 17 is6345.3070.90 ms, with a normalized χ2=N of 1.45.

In Fig. 18 we regroup the individual cycles according to theirinitial β�decay counting rate and obtain a half-life from eachgroup. In previous sections we have discussed the problems thatcould potentially be caused by higher counting rates, so it isgratifying to see that there is no systematic dependence of themeasured half-life on the experimental counting rate apparent inthe figure.

As demonstrated by Fig. 9 all potential impurities identified at theMARS focal plane are stable isotopes so there is no need to incorporateany systematic uncertainty to our 26Al

mhalf-life result to account for

sample impurities. We can therefore quote our final result for the26Al

mhalf-life to be 6345.3070.90 ms where the uncertainty is

determined by the counting statistics. This result is consistent withthe 2009 published world average [21], 6345.071.9 ms, but has twicethe precision. Our result also agrees with twomeasurements that havebeen published since 2009: 6346:5470:46stat70:60syst ms [22] and6347.872.5 ms [23].

7. Conclusions

We began this project with the expectation that by replacingour analog electronics with a fast digital acquisition system wewould be able to reduce our overall dead time and improve ourrejection of spurious pulses coming from our gas proportionaldetector. Our goal was to be able to double our counting rate andthus achieve improved precision. While our goal has essentiallybeen achieved, we encountered some unexpected difficultiesalong the way. The most obvious was that with fast electronicsthe number of spurious pulses detected increased considerably.Very short spurious pulses, which have now revealed themselves,would have been integrated by our slow analog system andconsequently most would have had an amplitude below ourdetection threshold. Now they have to be carefully handled witha software filter. The digital system has allowed us to create andcontrol a filter to reject spurious pulses, but at the same time it haspresented us with more spurious pulses to be filtered.

The digital system has also given us the opportunity to dealwith dead time in a way that is statistically much more secure. Wehave used an artificially added dead time combined with theshadow method, which together make it possible to correctprecisely for dead-time losses and to account as well for the effectof signals arriving just before the end of the dead time. In the end,we have not significantly reduced the dead time compared to ouranalog system. We have simply improved the accuracy of thecorrection we can use for dead-time losses.

L. Chen et al. / Nuclear Instruments and Methods in Physics Research A 728 (2013) 81–91 91

In this work we have studied the properties of spurious pulsesgenerated in our gas proportional counter. We have found someinteresting features by recording the pulse waveforms and analyz-ing the timing correlation between β events and subsequentspurious ones. However, the specific generation mechanism forthe spurious pulses is unclear and remains a interesting topic forfuture work. Nevertheless, after extensive analysis we have beenable to filter out most of the spurious pulses (499%) from ourmeasured β�decay spectrum. This means that less than about 0.1%unfiltered spurious pulses remain relative to the total number ofpulses analyzed. Undoubtedly, there is still room for improvement,as evidenced by our having to reject data taken with a highdetector bias of 2800 V, but we are confident that our system isnow capable of making a reliable half-life measurement at rates upto 10,000 per second and with detector biases between 2600 and2750 V. Our on-line measurement of the 26Al

mhalf-life supports

that confidence. Particularly the higher rate performance of thehigh-speed digitizer with digital pulse analysis represents asignificant improvement over the conventional data-processingchain based on analog modular instruments.

Acknowledgments

We thank the Cyclotron Institute accelerator specialists forproviding the beam for our on-line test experiments. The workwas supported by the U.S. Department of Energy under contractno. DE-FG02-93ER-40773 and by the Robert A. Welch Foundationunder grant no. A-1397.

References

[1] V.T. Koslowsky, E. Hagberg, J.C. Hardy, R.E. Azuma, E.T.H. Clifford, H.C. Evans,H. Schmeing, U.J. Schrewe, K.S. Sharma, Nuclear Physics A 405 (1983) 29.

[2] V.E. Iacob, J.C. Hardy, J.F. Brinkley, C.A. Gagliardi, V.E. Mayes, N. Nica,M. Sanchez-Vega, G. Tabacaru, L. Trache, R.E. Tribble, Physical Review C 74(2006) 055502.

[3] V.E. Iacob, J.C. Hardy, V. Golovko, J. Goodwin, N. Nica, H.I. Park, L. Trache,R.E. Tribble, Physical Review C 77 (2008) 045501.

[4] J.C. Hardy, V.E. Iacob, M. Sanchez-Vega, R.G. Neilson, A. Azhari, C.A. Gagliardi,V.E. Mayes, X. Tang, L. Trache, R.E. Tribble, Physical Review Letters 91 (2003)082501.

[5] V.E. Iacob, J.C. Hardy, A. Banu, L. Chen, V.V. Golovko, J. Goodwin, V. Horvat,N. Nica, H.I. Park, L. Trache, R.E. Tribble, Physical Review C 82 (2010) 035502.

[6] H.I. Park, J.C. Hardy, V.E. Iacob, A. Banu, L. Chen, V.V. Golovko, J. Goodwin,V. Horvat, N. Nica, E. Simmons, L. Trache, R.E. Tribble, Physical Review C 84(2011) 065502.

[7] H.I. Park, J.C. Hardy, V.E. Iacob, L. Chen, J. Goodwin, N. Nica, E. Simmons,L. Trache, R.E. Tribble, Physical Review C 85 (2012) 035501.

[8] John Keightley, Tae Soon Park, Metrologia 44 (2007) S32.[9] K. Rytsölä, J. Nissilä, J. Kokkonen, A. Laakso, R. Aavikko, K. Saarinen, Applied

Surface Science 194 (2002) 260.[10] F. Bečvář, J. Čížek, I. Procházka, J. Janotová, Nuclear Instruments and Methods

in Physics Research Section A 539 (2005) 372.[11] M. Nakhostin, T. Oishi, M. Baba, Radiation Measurements 43 (2008) 1493.[12] Mark A. Nelson, Brian D. Rooney, Derek R. Dinwiddie, Glen S. Brunson, Nuclear

Instruments and Methods in Physics Research Section A 505 (2003) 324.[13] S. Akkoyun, A. Algora, B. Alikhani, et al., Nuclear Instruments and Methods in

Physics Research Section A 668 (2012) 26.[14] L. Bardelli, M. Bini, G. Casini, et al., Nuclear Instruments and Methods in

Physics Research Section A 654 (2011) 272.[15] ⟨http://www.ni.com/digitizers⟩.[16] P.J. Campion, M.W.J. Kingham, International Journal of Applied Radiation and

Isotopes 20 (1969) 479;P.J. Campion, Nuclear Instruments and Methods in Physics Research Section A112 (1973) 75.

[17] H. Genz, D.S. Harmer, R.W. Fink, Nuclear Instruments and Methods in PhysicsResearch Section A 60 (1968) 195.

[18] Carmen C. Bueno, M.M. Fraga, A.C. Josemary Gonçalves, R. Ferreira Marques,A.J.P.L. Policarpo, M. Damy de S. Santos, Nuclear Instruments and Methods inPhysics Research Section A 408 (1998) 496.

[19] G.F. Knoll, Radiation Detection and Measurement, third ed., John Wiley & Sons,Inc., 2000.

[20] A. Savitzky, M.J.E. Golay, Analytical Chemistry 36 (8) (1964) 1627.[21] J.C. Hardy, I.S. Towner, Physical Review C 79 (2009) 055502.[22] P. Finlay, S. Ettenauer, G.C. Ball, J.R. Leslie, C.E. Svensson, C. Andreoiu,

R.A.E. Austin, D. Bandyopadhyay, D.S. Cross, G. Demand, M. Djongolov, P.E. Garrett, K.L. Green, G.F. Grinyer, G. Hackman, K.G. Leach, C.J. Pearson, A.A. Phillips, C.S. Sumithrarachchi, S. Triambak, S.J. Williams, Physical ReviewLetters 106 (2011) 032501.

[23] R.J. Scott, G.J. O'Keefe, M.N. Thompson, R.P. Rassool, Physical Review C 84(2011) 024611.

[24] R.E. Tribble, R.H. Burch, C.A. Gagliardi, Nuclear Instruments and Methods inPhysics Research Section A 285 (1989) 441.

[25] Kevin R. Lynch, Nuclear Physics B – (Proceedings Supplements) 189 (2009) 15.