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Techniques and problems of low-level gamma-ray spectrometry
Appl. Radiat. 1sot. Vol. 43, No. 1/'2,pp, Int. J. Radiat. Appl. lnstrum. Part A
0883-2889/92 S5.00+ 0.00 Copyright © 1991 Pergamon Press plc
305-322, 1992
Printed in Great Britain. All rights reserved
Techniques and Problems of Low-Level Gamma-Ray Spectrometry WOLFRAM WESTMEIER GeseUscbaft fiir Kernspektrometrie mbH, 3557 MOlln, FRG and Institut for Kernchemie, Philipps Universitgtt, 3550 Marburg, FRG The origin of background events from internal and external sources is reviewed and methods of passive and active shielding are presented. It is shown that the shape of the background under a peak or multiplet can be evaluated directly from the experimental data without the u s e of a mathematical model shape. An algorithm for the computerized sub-division of a spectrum into regions is shown and problems associated with smoothing and a u t o m a t i c photopeak, or full energy-peak, detection methods are discussed. A time-dependent spectral analysis is thken as an example to demonstrate the use of averaging or trend analyses in quantitative spectrometry.
Introduction Parallel with the development of high-purity germanium detectors of increased efficiency and improved resolution there has been the development of new techniques and applications of gamma-ray spectrometry which involve the measurement of very weak s gurces. Major applications for high-precision low-level gamma-ray spectrometry are r:tdiological protection (Fry and O'Riordan, 1984), environmental and fallout studies (idoore, 1984), biological or biomedical investigations (Heusser, 1989), geological dating (Currie, 1972), environmental-risk studies, atmospheric transport surveys, planetary r~ apping (Yadav and Arnold, 1990), neutron-activation analysis, nuclear-reaction studies a;~d the whole field of x-ray applications. The primary task for the evaluator in these studies is the quantitatitive discrimination between counts originating from the effect u:~der investigation and interfering counts from other origins or secondary sources. Thus, tl~e success of these investigations is strongly dependent on a favourable signal-to-noise ratio, a thorough understanding of interferences, and good software techniques which help separate relevant information from the underlying internal and external background. Inlproved signal-to-noise ratios are usually gained through passive and, or, active shielding, sometimes combined with simple timing procedures (Currie, 1972). For the treatment of interferences, one must consider radioactive contamination, cosmic particles or secondary radiations which enter the detector, electronic artifacts and decay scheme sy~tematics, and, of course, the internal-background contribution which comes from the radioactive source under investigation. As far as software techniques are concerned, there are: a number of procedures available which help to quantify the continuum-background co~ltribution under the signal which the investigation seeks to quantify. In the case of 305
306
Software and evaluation of spectra
weak signals sitting on a high background, one may apply averaging, sloping, or smoothing methods to extract the average height of the background on either side of the peak. The shape of the background under the peak or multiplet is then determined by an appropriate procedure. If, however, a very weak signal is mixed into the background so that the human eye, which is a good peak detector, can hardly decide if a peak is there, one has to know systematic trends of the background and subtract them in order to separate a possible signal, with large uncertainty, from the continuum. In any case, it is a good ~:ecommendation to apply several evaluation techniques and combinations of methods to the same spectrum, in order to extract useful results and their uncertainties from spectral data of poor significance. This paper is not concerned in detail with the large number of attempts to define acceptable or reasonable criteria for the practice of peak-searching and peak-area quantification and the concurrent definition of uncertainties or limiting values (Currie, 1968; Currie, 1972; Mundschenk, 1980; Wojcik and Grotowski, 1980; Anicin and Yap, 1987; Polach, 1987) or observability (Yadav et al., 1989). We will rather concentrate on different means to optimize the signal-to-noise ratio, such as passive and active shielding, and on techniques for the spectral analysis of low-level data. Methods and techniques which are more specific to the counting of events rather than to spectrometry are extensively covered by the proceedings of the third international conference on Low-Level Counting (Povinec, 1986) and they will not be presented here. We will also omit methods which are concerned with geometrical (Mundschenk, 1980) or counting-time (Putman, 1962; Currie, 1968; Hut, 1986) optimisation techniques.
Background events Were it not for the background, the analysis of most peaks in a gamma-ray spectrum would be a very simple and straightforward summing of counts. Even very tiny peaks could then be easily analyzed. However, as Op de Beeck (1978) has already indicated in the framework of information theory, the germanium detector is a very poor transducer and most of the mono-energetic photons that interact with the detector are registered at channels in the spectrum other than those of the full-energy peak. This creation of a background component at energies lower than the peak energy is further complicated by many other smooth or peaking background components that shall be briefly reviewed. Whenever a photon interacts within a semiconductor detector, it will deposit therein part or all of its energy of which, again, some or all will be detected and finally registered. The measured distribution from mono-energetic photons is the desired photopeak, plus a Compton distribution ranging down into the electronic-noise region. Most of the Compton events lie in a smooth distribution for which Poisson statistics apply, except for the region around the Compton edge Ecompto n at an energy of Ecompto n = E 7 / (1 + m o
c2 / 2E~/)
(1)
where E,t is the energy of the incoming gamma-ray and moceis the electron rest energy (511 keV). Due to the limited detector resolution and charge losses in the crystal, the experimental maximum of the Compton edge is usually found at a somewhat lower
Software and evaluation of spectra
307
energy. For example, the Compton edge of the 1332.5 keV-peak of 6°Co is expected at Ecompton = 1118 keV, but a practical recommendation for the determination of the photopeak-to-Compton ratio (P/C) is to take the average number of counts per channel between 1050 keV and 1100 keV for the height of the Compton edge. It should be remembered that the peak-to-Compton definition as quoted in the detector data sheet refers to the measurement, with an unshielded detector standing far away from any solid material, of a source containing only 6°Co at about 1 kHz average count rate. Imposed onto the Compton continuum is the backscatter distribution, which is a very broad distribution around 250 keV or below. When photons of low energy are present, the backscatter bump is situated close to the full-energy peak, or it may even be amalgamated with the low-energy flank of the peak. Whenever photons with energies well above the threshold for pair-production of 1022 keV are present, the spectrum will contain the single- and double-escape peaks, where the latter are often more pronounced than the former. In addition, one will find the positron-annihilation peak at 511 keV from annihilations occurring outside the detector, or where one annihilation photon escapes from the detector° When low-energy gamma-rays are measured with a germanium detector, one will detect the analogous process to the escape peaks after pair production, namely, the complex series of germanium x-ray-escape peaks. A very detailed classification of background components detected in the assay of high-energy gamma-rays was published by Gardner (1986)o It should, however, be noted that the decomposition method of Gardner contains rather unnatural discontinuities of some components. Another contribution to the background are the fluorescence x rays from interactions of :he photons with any material around the detector. In most configurations, one will thus ~ee x rays of lead from the shielding, of gold from the contact on the detector crystal, of ton and its components in steel from the source holder, screws, or supports, down to the x "ays from argon in the air. When the active source contains nuclides which de-excite hrough two or more excited levels before the daughter ground state is reached, the ,tetector may register two or more cascading gamma rays as a coincidence-summing event Jn a channel representing the sum of the energies of the summed gamma rays. These true c:oincidences are unavoidable and cannot be suppressed by technical means. However, there are computerized methods to calculate the contribution of coincidence summing and t~ correct for it (Debertin and Sch6tzig, 1979; Smakhtin, 1986; Richardson and Sallee, 199(}; Semkow et al., 1990). The above background components are all more or less cirectly produced by the photons emitted from the source which we want to measure. These contributions are called internal background. In addition to these source dependent tackground contributions, one must consider external background contributions such as c:~smic rays (Damjantschitsch et al., 1983) and their secondaries, and natural radioactivity c:~ntained in the detector components (Hubert etal., 1986) and in surrounding c :instruction materials (Wogman, 1981), A major source of external background is 222Rn a ad its daughters from the natural-decay series of 238U. Due to its chemical inertness and it~ long half life of 3.8 days, this noble gas is easily emanated from clay, soil and concrete mid it migrates everywhere, even into seemingly tight lead castles. A frequent but mostly u aexpected background component comes from radioactive contamination of the detector, ~ e source holder, and the shielding (Wogman, 1981). One must also consider man-made a~tificial contamination of the environment from nuclear weapons tests or nuclear-facility accidents. Finally, one may have to deal with electronic or power-line noise which u~ually comes from power thyristors, defective switching units, RF-emitters like
308
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PC-monitors, HV units etc.. The latter units usually lead only to line broadening in the spectrum, and they do not generate a wide random background or even artificial peak structures. Knowing the numerous sources of background, one can take measures to reduce theft contribution in the spectrum and at the same time enhance the signal-to-background ratio to an evaluable level. A first-order background reduction comes from passive shielding of the detector crystal from external radiation by means of a lead castle or other high-Z shielding material (Blanchard and Lickly, 1984; Polach, 1987). As a rule-of-thumb, one may recall that the half thickness for the absorption of photons in lead rises approximately linearly with energy and the slope of the half-thickness function is I mm per 150 keV. For energies above about 1.5 MeV the half thickness of lead has a constant value of about 1 cm. Exact values can be calculated from known absorption coefficients. For most practical applications, a lead wall of I0 cm thickness is sufficient, where the lead must be of explicitly specified low-activity material, e.g., lead from Boliden in Sweden. The guaranteed radiological contamination of lead used for shielding purposes should not exceed 50 Bq/kg. Major contaminants found in low-activity lead are 21°pb/21°Bi and, less frequently, 4°K. For special purposes, one can use highly purified lead, which is available with _<3 Bq/kg radioactive contamination. The surface of lead bricks used for shielding purposes should be covered with purity-checked (Walford et al., 1972) paint or plastic, in order to allow for simple and effective decontamination. The oxidized surface of metallic lead is an efficient adsorbent that can only be decontaminated on a work-bench. The interior walls of a passive lead shield should be covered with additional layers of material with decreasing atomic number Z (Walford et alo, 1972). These layers are used to absorb or successively degrade secondary radiation such as x rays or Compton scattered radiation. Typical configurations of these absorbing layers are, e.g., 5 mm of tin + 2 mm of copper + 4 mm acrylic glass. In order to prevent radon gas from entering the shield, one may either exhaust the nitrogen from the LN 2 dewar vessel of the detector into the lead castle or, preferentially, maintain a flow of purified and aged nitrogen from the interior of the shield to the outside. An even better method to prevent radon from reaching the vicinity of the detector is to manufacture the whole interior of the shield as an evacuable chamber (Heusser, 1989). This construction, however, is very troublesome, expensive and rarely done. Commercially available low-activity lead is usually sold as bricks or sheets, sometimes with specially shaped edges for improved stacking. Although lead is easily shaped on a work-bench, it is very inconvenient to build up lead castles in other than rectangular shapes. When rounded shielding geometries are required or cavities must be ftlled, one may use double-walled containers of appropriate shapes which can be filled with mercury. A safer, cheaper, but less dense "fluid" that can be used for shielding purposes consists of leadshot, which is available in granule diameters ranging from about 0.1 mm to about 2 ram. Other frequently used shielding materials are iron (from old battleships), brass, and sometimes tungsten which is probably the cleanest shielding material (Pomanski, 1986). In applications where the detector must be shielded very effectively from high-energy cosmic radiation (Brodzinski et al., 1985), one may set up the whole experiment in an underground area, mine or tunnel where thick rocky layers serve as an additional shield (Looshi etal., 1986; Pomanski, 1986; Alessandrello et al., 1986; Hebert et al., 1986; Hebig and Niese, 1986). Using the passive shielding techniques mentioned above, one can very effectively reduce the external background contribution to
Software and evaluation of spectra
309
the spectrum. However, the background from Compton interactions of desired gamma rays will still prevail, and it may cover up small peaks. A considerable fraction of these disturbing Compton events can be discarded by active electronic shielding methods (Damjantschitsch etal., 1983; Hildingsson etal., 1986). The principle behind these anti-Compton guard shields is the installation of another detector around the high-resolution gamma-ray detector or detector array. This external device should cover as much solid angle as possible, and its interaction cross section with photons should be large. There is no need for good energy resolution of the anti-Compton detector. In a Compton interaction, only a fraction of the gamma-ray energy is deposited in the high-resolution detector, whereas the residual energy escapes. The escaping photon is detected by the external device, and the external signal is taken as a veto for the coincident signal from the high-resolution detector. Using Na/(TI), BGO, CsI(Na), or CaF2(Eu) as the external detector material and appropriate coincidence electronics, one can suppress the fraction of Compton events in the spectrum by a factor of 20 (Walford et al., 1972) or more with only marginal losses of the full-energy peak areas (Millard, 1984; Hildingsson et al., 1986). The anti-Compton shield is equally effective against background events from external sources such as cosmic rays or contamination. In these cases, energy is deposited in the guard detector and the remaining signal which may be registered by the high-resolution detector is vetoed from registration. Another rarely applied active method 9f background suppression is pulse shape discrimination (Funsten, 1962; Abe etal., 1968), which has become outdated because of the very uniform material of modern letectors. An active device which helps to clean up the background in a spectrum is the ;lectronic pulse-pile-up rejection. Especially at high counting rates, an input pulse may :'ollow so closely after the previous event that the electronic system has not yet returned to its quiescent state. The second event will then be added to an electronic bias of variable magnitude and polarity and the event will be counted in the spectrum in some incorrect ~:hannel. Pile-up events usually show up as pronounced tailing to the peak and as a ,trongly rising spectrum towards the low-energy region. The latter effect is caused by the ,ummation (pile-up) of very low-energy events and system noise. Using electronic t~ile-up rejection, these false events are rejected, but at the cost of artificially reduced c ount-rates. In any quantitative assay, one must therefore consider these rejected events t y some appropriate dead-time or count-rate correction. Knowing the above reasons for background production and applying appropriate measures to reduce the background contribution, one can accummulate spectra with an optimized signal-to-noise ratio, i.e. the smooth background under the peaks is as low as t~chnically feasible, but it has not disappeared. Background peaks (contamination, e;cape, summing, fluorescence) must be treated as real peaks during spectral analysis, and ttey may be identified and discarded later when the data reduction results are interpreted.
Separation of photopeaks from background The quantitative separation of a full-energy peak area from the underlying b~ckground is nowadays almost always made with the aid of sophisticated spectrometric ccmputer programs. Older analytical procedures, where a graph of the spectrum is measured with a ruler (Routti, 1968) or where the photopeak area is determined by
310
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gravimetic integration have practically ceased to exist. In certain applications, one may use methods of partial peak fit or partial integration (Sterlinski, 1968; Baedecker, 1971; Smakhtin, 1986; Loska, 1988), but the vast majority of modern computer programs for spectral analysis use nonlinear least-squares fit procedures to determine the area of a photopeak and sometimes also the underlying background. While the discrimination between a photopeak and the background seems to be simple when the peak is significant, there are a number of different approaches to the analytical description of the peak-shape and the shape of the background under the peak. In a recent publication (Westmeier, 1986) an arbitrary but very successful peak-shape function and a model for the shape of the background were presented. The background shape was calculated from the experimental numbers of counts per channel in the spectrum and it needed no a priori information about peaks or multiplets nor any mathematical model shape. In Fig. 1, the essential ingredients for the calculation of the intrinsic shape of the background under a peak or multiplet are reviewed. The background above the high-energy end of the peak is smooth and slowly decreasing. The jitter in the distribution of counts per channel shows no systematic trends, and it is governed by Poisson statistics. One can define the average background height above the high-energy side of the peak (HB,A), i.e. around the channel N where the high-energy flank of the peak merges with the background, by some appropriate averaging or smoothing method.
37Cs '
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Software and evaluation of spectra
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The background below the peak (HB,B) shows the same statistical characteristics as the background above, however, at higher count rate. Thus there is a "step" in the background when one goes from the high-energy end of the peak to lower energy. The height of the step is apparently proportional to the height of the peak. One can also see from Fig. 1 that the low energy background in the immediate vicinity of the peak is approximately constant (see dotted line at HB,B). A first-order approximation for describing a peak in a gamma-ray spectrum therefore assumes a one-channel wide distribution of some height H~ which sits on an extending background step of the height c~.H~. The magnitude of the normalization constant o~ is unknown. A real gamma-ray full-energy peak, however, has a finite width in channels, and one has to consider the content of each channel in the above manner. Starting from the high-energy end of the peak and going down in channels, each peak-fraction sits on top of the c~.H~ steps which originate from the higher channels. The background contribution in the channel j under a peak is given by: N HB,j = HB,A + ct Z H6,i
(2)
i=j+l
where HB, A is the average background height above the peak and N is the channel number where the peak ends at high-energy. The normalization constant c~ is easily calculated when one evaluates the sum of Eq. (2) for the whole peak from HB,B to HB, a and normalizes it to the experimental height of the step (see Fig. 1) N ot = ~2 HS, i / (HB, B - H B , A ) i=M
(3)
~.here M is the channel where the low-energy flank of the peak starts to rise out of the imckground. This very simple recipe is used to calculate the instrinsic background under i~eaks or multiplets from experimental data without any input other than the spectrum itself. One must define suitable channel numbers M and N for the lower and upper end of peak or multiplet and apply Eqs. (2) and (3) to calculate the background. Count (istributions remaining above the background are considered to be peaks and are treated cccordingly. When the above procedure of background calculation is applied to s~fficiently small peakless regions, the calculated "background" is nothing but a smoothed s~ectrum. Fig° 2 shows as an example the background calculated according to the above procedure for a multiplet in an 227Ac spectrum and the least-squares fit of the photopeaks. IT should be noted that this analysis using the intrinsic background calculation gave the first exact analysis of the peak area of the tiny peak at 267.7 keV o f I7,267. 7 = 0.037 + 0 005% (van Aarle, 1986).
Computerized analysis C)nsidering the fact that the background under a peak or multiplet is easily calculated fr,:~m the distribution of experimental counts in the peaks, the computerized peak analysis
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10' (I) (0 C.
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265
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Energy (keY) Fig. 2: Fraction of a ,/-my spectrum of 227Ac (histogram) with the intrinsic background and deconvoluted peaks.
of a spectrum can be reversed; the task in spectral analysis is to analyse the background what remains are potential peaks. In contrast to former peak-searching algorithms, the analysis program now has to find portions of the spectrum (regions) in which a common background can be assumed. These regions must not span over systematic discontinuities like Compton edges or backscatter bumps, and their width must be related to the width of possible peaks. A flexible and fast method to define the limits of regions, i.e. the first and last channel of a region, is to search for local minima in the count distribution (see arrows in Fig. 3). These local minima have the desired property that they (probably) do not interfere with possible peaks and that they underestimate the average height of the surrounding background. The distances over which to search for local minima are scaled by the full-width-at-half-maximum (FWHM) of expected peaks. The average height of the background around the local minima is then defined by appropriate smoothing or averaging procedures. In this step, one has to consider the fact that random deviations in low-level spectrometry are far away from the central-limit theorem, and that one has to apply the methods of robust statistics (Press et al., 1986) to find the desired average (outliers are much more frequent than they should be according to Gaussian or even Poisson statistics). Typical problem situations that must explicitly be considered by a computer program are real outliers, which are for example caused by data transfer errors, systematic background trends coming from closely-spaced peaks, or Compton edges in the vicinity of the local minimum. Once the average background height around the start- and end-channel of a region is defined, the course of the whole background in the region is
Software and evaluation of spectra
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calculated as described in the preceding paragraph. The distribution of counts above the spectrum is then scanned for peaks which are fitted by appropriate methods. When a region is analysed, the program continues to search for the next adjacent region where the end-channel of the current region is the start-channel of the next one.
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Fig. 3: Fraction of a 7-ray spectrum of poor statistical significance. The arrows mark cbannels which may be real local minima and thus constitute region limits.
There is a major advantage of the above-presented method of spectral zoning over the ttsually applied peak-search methods. The count distribution which is finally scanned for [,eaks or multiplets is free of the smooth underlying background, and small peak structures are much more prominent than they are on top of the background. Large peaks are of course as easily detected with or without the background, and the regioning method offers no advantages for their analysis. There are cases where the remaining distribution of counts above the background is t(~o scattered for a reliable, automatic peak detection and fit. In these (and only these) ctses, it may be advantageous to smooth the spectrum, in order to carry out an automatic aJ:mlysis or a least-squares peak-fit operation. In Fig. 4 is shown a traction of a gamma-ray spectrum which was taken from a very low activity sample of pine-tree needles (Jenderek, 1990). The fine-line histogram distribution shows the measured sFectrum and the thick line is the same spectrum after one smoothing pass, using a 5-channel sliding window (Mtiller, 1974).
314
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Spectrum Smoothing I
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Fig. 4: Fraction of -/-ray spectrum of poor statistical significance (thin histogram) and after one 5-point smoothing pass (tttick histogram). The method used in this example was a polynomial smoothing with equal weights to the data points. Despite small numerical differences, the conclusions below are unaffected when a triangular or other weighting of the points is chosen. One can see immediately from Fig. 4 that the scatter of the original count-rate distribution is strongly reduced in the smoothed spectrum and that peak structures are much more clearly visible. It should be noted, however, that the statistical significance of all these peak-like structures is very low because of the very low count rates, and that additional criteria are needed to discriminate a real peak from statistical fluctuations. The most reliable and straightforward criterion of whether or not a peak-like structure might be a real peak or not is to compare the width of the experimental distribution with the expected width at this energy as it was determined in calibration measurements. The term "width" should apply to the full-width-at-half-maximum (FWHM) of a photopeak as fitted by some appropriate procedure. If the fitted width is far away from the expected width, the experimental structure is very probably not a peak. Too small a FWHM usually means that the experimental distribution comes from just accidental statistical scatter whereas a much-too-wide fit either comes from statistics or from the fact that the distribution is a multiplet. The latter case must then be investigated further by appropriate algorithms. Other criteria that can be used to discriminate a peak or peak structure from just random noise are the symmetry of a structure, the relative skewness of the flanks, or the resemblence with a reference peak shape. In any case, the discrimination between peaks at low count rates and random statistics is usually made over the width of the distribution. This criterion, however, is so strongly influenced by every smoothing method that it is no
Software and evaluation of spectra
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longer usable, i.e. a reliable automatic peak search in a low count rate spectrum is no longer possible after spectral smoothing. The numbers relevant to the example peak from Fig. 4 are summarized in table I. A manual-analysis gave a peak area of 24 counts above background.
Table 1: Least-Squares peak-fit to the structure between channels 882 and 899 in Fig. 4 Original data Peak position, channel
Smoothed data
888.2 + 0.1
889.3 + 0.7
Peak area~ counts
24.8 _+ 6.4
22.5 + 8.9
FWHM, channels
2°9 __. 0.7
6.6 _+ J.8
reduced g 2
0.20
0.10
If one looks only at the reduced X2 as a quality-of-fit indicator, one might consider :his case to be a superior fit to the smoothed data. The uncertainties of the peak 9arameters clearly show, however, that the original, scattered data are fitted much better. i'his improved fit is supported by a comparison with the expected FWHM which fortuitously) is 2.88 channels for this peak. Having these numbers in mind, one would ~tccept the poor tit to the original data but reject the fit to the smoothed spectrum, or ~:rroneously consider this to be a multiplet. To summarize: the smoothing of spectra ~hould be avoided, and results calculated from smoothed spectra must be cross-checked ~/ith great care. One may of course define a region around a k n o w n peak position in a smoothed spectrum and fit a peak irrespective of the structure and scatter of the experimental data. The fitted peak position and peak area will then be good approximations to the real values, and the uncertainties should clearly reflect the quality of the fit (they are much larger than those calculated through a Gaussian matrix inversion ('fadav et al., 1989)). Another important step in the computerized analysis of spectra is automatic peak d,'.tection, which will be just shortly described here. There is a large body of literature at,out peak search and position approximations which include derivative methods (l~lariscotti, 1967), peak correlators (Black, 1969), and more recent ideas of maltiplet-components search (Lauterjung et al., 1985). All these methods are more or less de veloped and proven in spectra with prominent peaks and good statistical accuracy, if, hcwever, these methods are used for automatic peak-search in spectra with poor statistics, th,; results may seem arbitrary or 'at least incomplete. The principle behind this in~:ompleteness can be demonstrated by means of the simple derivative method. The first derivative of a peakless spectrum is a jitter around zero without systematic structure, wt ereas the first derivative of a peak yields a cluster o f positive values (about FWHM ch.mnels wide) significantly above zero, followed by a similarly significant cluster of negative values. The transient point is located at about the peak position. The upper box of 7ig. 5 shows, as a thin-line histogram, a fraction of a spectrum which was measured at a very high count rate and which has very prominent peaks. The thick-line histogram below the spectrum is the normalized first derivative of the spectrum. The horizontal line in the
316
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derivative plot marks the value zero. One can clearly visualize the steep zero-crossing corresponding to the derivatives at the peak positions, which is equally clear for the less prominent peaks but on a smaller numerical scale. In the lower box of Fig. 5, the same display is plotted for a fraction of the same spectrum after only a low total count had been accummulated. An analyst could easily detect by eye a "peak" located in the left half of the figure, but the first derivatives give no clear indication of such a peak° Following the proposals of Mariscotti (1967), one may use the second derivatives of the spectrum for peak location, as indicated in Fig. 6 for the same data as in Fig. 5. Peaks in the good statistics regions are undoubtedly indicated by a negative spike in the second-derivative plot. But in the poor statistics one finds many of these negative spikes which certainly do not indicate a peak. Also, the only "peak" suggested in the poor-statistics data is not indictated by a negative spike. Different methods thus work equally well for prominent peaks, but they yield very different and contradictory results when applied to data of poor statistical significance. The only way out of this dilemma is to apply several different peak locator methods to the same data, possibly combined with smoothing or gradient enhancing methods. Then one can generate a logical decision-tree from the individual results, which may finally indicate the possible presence of a peak. The procedure may be complicated, but the computing power of modem PCs is completely adequate for these tasks.
Time-dependent spectral analysis It was stated before that the reliable automatic analysis of a spectrum may require .'everal approaches and combinations of different methods in order to find the most probable result. Taking the example of time-dependent spectral analysis (TDSA) (Esterlund, 1985), the merit of such combinations can be clearly shown. TDSA can be ~pplied to the analysis of spectra recorded in the multi-spectrum-scaling (MSS) mode f:om the same sample. The MSS mode is the analogue to the multi-channel-scaling mode (VICS), except that the complete energy-dispersive spectrum is stored for each time-bin rather than just the integral number of counts in a selected window as in MCS. The areas of a peak at the same energy in the sequence of spectra are assembled as a decay curve for tt:is peak. The curve is deconvoluted, and quantitative results for the one or several c,)nstituents are calculated° The MSS measuring method is frequently applied to the a~;say of radioactive nuclides in irradiated samples. The data of the example below (Schulte, 1989) stem from MSS sequences that were measured from reaction products from the nuclear reaction between 212 MeV 4OAr and 197Au. The products were deposited on catcher foils disposed at different angles, and the ar:gular distributions of the reaction products were recorded. Fig. 7 shows the same fraction around 1811 keV of the first twelve spectra of the MSS sequence. The 12 spectra cover the ftrst 17 hours of an MSS sequence going in total over 40 spectra and a decay time of about 6 months. In the first few spectra, one can detect visually a peak around chmnel 3621, which has apparently disappeared after spectrum # 9. An arrow indicates the position of the peak. The quantitative analysis of this peak was made with TDSA
ARI ~3:1/2-V
Software and evaluation of spectra
318
according to the following procedure. From the first spectra where the peak is well discernible and considering the FWHM of a peak at 1811 keV (at this energy one expects to find a peak from 56Mn with a half life of T1/2 = 2.58 h), one can define the start- and end-channel of a region around this peak. The course of the background in this region is calculated for all MSS spectra as explained above and the total number of background counts in the regions is displayed as a function of time (see Fig. 8). Analogously to the activities in the spectra the background also "decays" and the data are well described by a • '
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Fig, 7: The same fraction of twelve 2-ray spectra deposited on catcher foils at different angles (# 1 through # 12) measured consecutively in MSS mode from a radioactive sample produced by accelerated ion bombardment, multi-component decay curve. In the example, an acceptable fit to the data is achieved with two exponentially decaying components which are also indicated in Fig. 8. The sum of the two functions goes smoothly through the data points. This sum function is now taken as the background and the number of calculated background counts for a given spectrum is subtracted from the gross counts in the region, The remaining counts, i.e. experimental gross counts minus calculated background from the sum function, are taken as the peak area and plotted as a decay curve (stars) in Fig. 9. Only the first 15 data points are shown in Fig. 9. The decay curve analysis yields (Cumming, 1962) the expected half life of 56Mn and, with large uncertainty, a second component with TI/2 = 43.7 hours which is attributed to i881r with a half life of 41.5 hours. The cross section calculated for 188Ir from this 0.34% gamma ray is in good agreement with the cross section calculated for that nuclide from other much stronger lines. The data points plotted as squares in Fig. 9 are taken from an automatic computerized analysis of the same spectra with a commercial gamma-ray spectral analysis program which did not accept the structures past spectrum # 7 as a peak. Although the results of T D S A agree perfectly well within uncertainty with an automatic spectral analysis for 56Mn, the TDSA method is definitely superior. T D S A gives more
Software and evaluation of spectra
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Software and evaluation of spectra
320
good data points for the decay curve and it enables one to quantify the tiny second component which is otherwise undetected, even by an evaluator's eye. This principle of systematization or trend analyses of the background, or of structures, is always applicable when a larger number of consistent spectra are available.
Acknowledgement I want to thank my colleague Bob Esterlund for the careful reading of the manuscript and his valuable suggestions and comments.
References Aaltonen H. and Ugletveit F. (1989) Progress in Radiation Protection FS-89-48-T, 515 ISSN 1013-4506 Abe K., Kawamura N. and Mutsuro N. (1968) Nucl. Instr. Meth. 63, 105 Alessandrello A., Bellotti E., Cattadori C., Carom D., Cremonesi O., FioriniE., Liguori C., PuUiaA., Rossi L., Ragazzi S., Sverzellati P,P. and Zanotti L. (1986) Nucl. Instr. Meth. B17, 411 Anicm I.V. and Yap C.T. (1987) Nucl. Instr. Me~. A2,59, 525 Baedecker P.A. (1971) Anal. Chem. 43, 405 Black W.W. (1969) Nucl. Instr. Meth. 71, 317 Blanchard F.A. and Lickly T.D. (1984) Nucl. Instr. Meth. 219, 413 Brodzinski R.L., Brown D.P., Evans Jr. J.C., Hensley W.K., Reeves J.H., Wogman N.A., Avignone llI F.T. and Miley H.S. (1985) Nucl. Instr. Meth A239, 207 Cumming J.B. (1962) National Series Report NAS NS-3107, unpublished Currie L.A. (1968) Anal. Chem. 40, 587 Currie L.A. (1972) IEEE Trans. Nucl. Sci. NS-19, 119 Damjantschitsch H., WeiserM., Heusser G., Kalbitzer S. and Mannsperger H. (1983) Nucl. Instr. Meth. 218, 129 Debertin K. and SchOtzig U. (1979) Nucl. Instr. Meth, 158, 471 Esterlund R.A. (1985) private communication, Univ. Marburg Fry F.A. and O'R.iordan M.C. (1984) Nucl. Instr. Meth. 223, 540 Funsten H.O. (1962) IRE Trans. Nucl. Sci. NS.3, 199 Gardner R.P., Yacout A.M., Zhang J. and Verghese K. (1986) Nucl. Instr. Meth. A242, 399 HebertD., FrOhlichK., FrankeT., GellermannR., UnterrickerS., KimJ.H. (1986) Nucl. Instr. Meth. BIT, 427 Helbig W. and Niese S. (1986) Nucl. Instr. Meth. B17, 431
Software and evaluation of spectra
321
Heusser G. (1989) Progress in Radiation Protection FS-89-48-T, 468 ISSN 1013-4506 Hildingsson L., Beausang C.W., Fossan D.B., Piel Jr. W.F~, Byrne A.P. and Dracoulis G.D. (1986) Nucl. Instr. Metla. A252, 91 Hubert Ph., Dassie D., Lameu P., Leccia F., Menrtrath P., Chevallier J., Chevallier A., Henck R., GutknechtD., MoralezA., Nunez-LagozR., Morales J. and ViUarJ.A. (1986) Nucl. Instr. Meth. A252, 87 Hut G., (1986) Nucl. lnstr. Meth. B17, 490 Jenderek H. (1990) private communication, Univ. Hohenheim Lauterjung J., Will G. and Hinze E. (1985) Nucl. Instr. Meth. A2,39, 281 Loosli H.H°, M011 M., Oeschger H. and Schotterer U. (1986) Nucl. Instr. Meth. B17, 402 Loska L. (1988) Appl..Radiat. Isot. 39, 475 Vlariscotti M.A. (1967) Nucl. Instr. Meth. 50, 309 Vlillard Jr. H.T. (1984) Nucl. Instr. Meth. 223, 416 i¢loore W.S. (1984) Nucl. Instr. Meth. 223, 459 MUller LW. (1974) Report BIPM-74/1, Bureau Int. de Poids et Mesures, Sevres, France 14undschenk H. (1980) Nucl. Instr. Meth. 177, 563 ()p de Beeck J. (1978) Proceedings of the ANS Topical Conference, Mayaguez, Puerto Rico, CONF-780421 Folach H.A. (1987) Nucl. Instr. Meth. B29, 415 Fomanski A.A. (1986) Nucl. Instr. Meth. BIT, 406 P 3vinec P. (Editor) (1986) Nucl. Instr. Meth. B17, 377 - 574 Press W.H., Flannery B.P., Teukolsky S.A. and Vetterling W.T. (1986) "Numerical Recipes", Chapter 14, Cambridge University Press, Cambridge, UK. Pltman J.L. (1962) Int. J. Appl. Radiat. Isot. 13, 99 R chard.son A.E. and Sailee W.W. (1990) Nucl. Instr. Meth. A299, 344 R, tutti J.T. (1968) Anal. Chem. 40, 593 S
322
Software and evaluation of spectra
Walford G.V., Aliaga-Kelly D.T.W. and Gilboy W.B. (1972) [EEE Trans, Nucl, Sci, NS-19, 127 Westmeier W. (1986) Nucl. Instr. Me~. A242, 437 Wogman N.A. (1981) IEEE Trans. on Nucl. Sci. NS-28, 275 Wojcik M. and Grotowski K. (1980) Nucl. Instr. Metla. 178, 189 Yadav J.S., Brtickner J. and Arnold J,R. (1989) Nucl. Instr. Meth. A277, 591 Yadav J.S. and Arnold J.R. (1990) Nucl. Instr. Meth. A295, 241
0883-2889/92 S5.00+ 0.00 Copyright © 1991 Pergamon Press plc
305-322, 1992
Printed in Great Britain. All rights reserved
Techniques and Problems of Low-Level Gamma-Ray Spectrometry WOLFRAM WESTMEIER GeseUscbaft fiir Kernspektrometrie mbH, 3557 MOlln, FRG and Institut for Kernchemie, Philipps Universitgtt, 3550 Marburg, FRG The origin of background events from internal and external sources is reviewed and methods of passive and active shielding are presented. It is shown that the shape of the background under a peak or multiplet can be evaluated directly from the experimental data without the u s e of a mathematical model shape. An algorithm for the computerized sub-division of a spectrum into regions is shown and problems associated with smoothing and a u t o m a t i c photopeak, or full energy-peak, detection methods are discussed. A time-dependent spectral analysis is thken as an example to demonstrate the use of averaging or trend analyses in quantitative spectrometry.
Introduction Parallel with the development of high-purity germanium detectors of increased efficiency and improved resolution there has been the development of new techniques and applications of gamma-ray spectrometry which involve the measurement of very weak s gurces. Major applications for high-precision low-level gamma-ray spectrometry are r:tdiological protection (Fry and O'Riordan, 1984), environmental and fallout studies (idoore, 1984), biological or biomedical investigations (Heusser, 1989), geological dating (Currie, 1972), environmental-risk studies, atmospheric transport surveys, planetary r~ apping (Yadav and Arnold, 1990), neutron-activation analysis, nuclear-reaction studies a;~d the whole field of x-ray applications. The primary task for the evaluator in these studies is the quantitatitive discrimination between counts originating from the effect u:~der investigation and interfering counts from other origins or secondary sources. Thus, tl~e success of these investigations is strongly dependent on a favourable signal-to-noise ratio, a thorough understanding of interferences, and good software techniques which help separate relevant information from the underlying internal and external background. Inlproved signal-to-noise ratios are usually gained through passive and, or, active shielding, sometimes combined with simple timing procedures (Currie, 1972). For the treatment of interferences, one must consider radioactive contamination, cosmic particles or secondary radiations which enter the detector, electronic artifacts and decay scheme sy~tematics, and, of course, the internal-background contribution which comes from the radioactive source under investigation. As far as software techniques are concerned, there are: a number of procedures available which help to quantify the continuum-background co~ltribution under the signal which the investigation seeks to quantify. In the case of 305
306
Software and evaluation of spectra
weak signals sitting on a high background, one may apply averaging, sloping, or smoothing methods to extract the average height of the background on either side of the peak. The shape of the background under the peak or multiplet is then determined by an appropriate procedure. If, however, a very weak signal is mixed into the background so that the human eye, which is a good peak detector, can hardly decide if a peak is there, one has to know systematic trends of the background and subtract them in order to separate a possible signal, with large uncertainty, from the continuum. In any case, it is a good ~:ecommendation to apply several evaluation techniques and combinations of methods to the same spectrum, in order to extract useful results and their uncertainties from spectral data of poor significance. This paper is not concerned in detail with the large number of attempts to define acceptable or reasonable criteria for the practice of peak-searching and peak-area quantification and the concurrent definition of uncertainties or limiting values (Currie, 1968; Currie, 1972; Mundschenk, 1980; Wojcik and Grotowski, 1980; Anicin and Yap, 1987; Polach, 1987) or observability (Yadav et al., 1989). We will rather concentrate on different means to optimize the signal-to-noise ratio, such as passive and active shielding, and on techniques for the spectral analysis of low-level data. Methods and techniques which are more specific to the counting of events rather than to spectrometry are extensively covered by the proceedings of the third international conference on Low-Level Counting (Povinec, 1986) and they will not be presented here. We will also omit methods which are concerned with geometrical (Mundschenk, 1980) or counting-time (Putman, 1962; Currie, 1968; Hut, 1986) optimisation techniques.
Background events Were it not for the background, the analysis of most peaks in a gamma-ray spectrum would be a very simple and straightforward summing of counts. Even very tiny peaks could then be easily analyzed. However, as Op de Beeck (1978) has already indicated in the framework of information theory, the germanium detector is a very poor transducer and most of the mono-energetic photons that interact with the detector are registered at channels in the spectrum other than those of the full-energy peak. This creation of a background component at energies lower than the peak energy is further complicated by many other smooth or peaking background components that shall be briefly reviewed. Whenever a photon interacts within a semiconductor detector, it will deposit therein part or all of its energy of which, again, some or all will be detected and finally registered. The measured distribution from mono-energetic photons is the desired photopeak, plus a Compton distribution ranging down into the electronic-noise region. Most of the Compton events lie in a smooth distribution for which Poisson statistics apply, except for the region around the Compton edge Ecompto n at an energy of Ecompto n = E 7 / (1 + m o
c2 / 2E~/)
(1)
where E,t is the energy of the incoming gamma-ray and moceis the electron rest energy (511 keV). Due to the limited detector resolution and charge losses in the crystal, the experimental maximum of the Compton edge is usually found at a somewhat lower
Software and evaluation of spectra
307
energy. For example, the Compton edge of the 1332.5 keV-peak of 6°Co is expected at Ecompton = 1118 keV, but a practical recommendation for the determination of the photopeak-to-Compton ratio (P/C) is to take the average number of counts per channel between 1050 keV and 1100 keV for the height of the Compton edge. It should be remembered that the peak-to-Compton definition as quoted in the detector data sheet refers to the measurement, with an unshielded detector standing far away from any solid material, of a source containing only 6°Co at about 1 kHz average count rate. Imposed onto the Compton continuum is the backscatter distribution, which is a very broad distribution around 250 keV or below. When photons of low energy are present, the backscatter bump is situated close to the full-energy peak, or it may even be amalgamated with the low-energy flank of the peak. Whenever photons with energies well above the threshold for pair-production of 1022 keV are present, the spectrum will contain the single- and double-escape peaks, where the latter are often more pronounced than the former. In addition, one will find the positron-annihilation peak at 511 keV from annihilations occurring outside the detector, or where one annihilation photon escapes from the detector° When low-energy gamma-rays are measured with a germanium detector, one will detect the analogous process to the escape peaks after pair production, namely, the complex series of germanium x-ray-escape peaks. A very detailed classification of background components detected in the assay of high-energy gamma-rays was published by Gardner (1986)o It should, however, be noted that the decomposition method of Gardner contains rather unnatural discontinuities of some components. Another contribution to the background are the fluorescence x rays from interactions of :he photons with any material around the detector. In most configurations, one will thus ~ee x rays of lead from the shielding, of gold from the contact on the detector crystal, of ton and its components in steel from the source holder, screws, or supports, down to the x "ays from argon in the air. When the active source contains nuclides which de-excite hrough two or more excited levels before the daughter ground state is reached, the ,tetector may register two or more cascading gamma rays as a coincidence-summing event Jn a channel representing the sum of the energies of the summed gamma rays. These true c:oincidences are unavoidable and cannot be suppressed by technical means. However, there are computerized methods to calculate the contribution of coincidence summing and t~ correct for it (Debertin and Sch6tzig, 1979; Smakhtin, 1986; Richardson and Sallee, 199(}; Semkow et al., 1990). The above background components are all more or less cirectly produced by the photons emitted from the source which we want to measure. These contributions are called internal background. In addition to these source dependent tackground contributions, one must consider external background contributions such as c:~smic rays (Damjantschitsch et al., 1983) and their secondaries, and natural radioactivity c:~ntained in the detector components (Hubert etal., 1986) and in surrounding c :instruction materials (Wogman, 1981), A major source of external background is 222Rn a ad its daughters from the natural-decay series of 238U. Due to its chemical inertness and it~ long half life of 3.8 days, this noble gas is easily emanated from clay, soil and concrete mid it migrates everywhere, even into seemingly tight lead castles. A frequent but mostly u aexpected background component comes from radioactive contamination of the detector, ~ e source holder, and the shielding (Wogman, 1981). One must also consider man-made a~tificial contamination of the environment from nuclear weapons tests or nuclear-facility accidents. Finally, one may have to deal with electronic or power-line noise which u~ually comes from power thyristors, defective switching units, RF-emitters like
308
Software and evaluation of spectra
PC-monitors, HV units etc.. The latter units usually lead only to line broadening in the spectrum, and they do not generate a wide random background or even artificial peak structures. Knowing the numerous sources of background, one can take measures to reduce theft contribution in the spectrum and at the same time enhance the signal-to-background ratio to an evaluable level. A first-order background reduction comes from passive shielding of the detector crystal from external radiation by means of a lead castle or other high-Z shielding material (Blanchard and Lickly, 1984; Polach, 1987). As a rule-of-thumb, one may recall that the half thickness for the absorption of photons in lead rises approximately linearly with energy and the slope of the half-thickness function is I mm per 150 keV. For energies above about 1.5 MeV the half thickness of lead has a constant value of about 1 cm. Exact values can be calculated from known absorption coefficients. For most practical applications, a lead wall of I0 cm thickness is sufficient, where the lead must be of explicitly specified low-activity material, e.g., lead from Boliden in Sweden. The guaranteed radiological contamination of lead used for shielding purposes should not exceed 50 Bq/kg. Major contaminants found in low-activity lead are 21°pb/21°Bi and, less frequently, 4°K. For special purposes, one can use highly purified lead, which is available with _<3 Bq/kg radioactive contamination. The surface of lead bricks used for shielding purposes should be covered with purity-checked (Walford et al., 1972) paint or plastic, in order to allow for simple and effective decontamination. The oxidized surface of metallic lead is an efficient adsorbent that can only be decontaminated on a work-bench. The interior walls of a passive lead shield should be covered with additional layers of material with decreasing atomic number Z (Walford et alo, 1972). These layers are used to absorb or successively degrade secondary radiation such as x rays or Compton scattered radiation. Typical configurations of these absorbing layers are, e.g., 5 mm of tin + 2 mm of copper + 4 mm acrylic glass. In order to prevent radon gas from entering the shield, one may either exhaust the nitrogen from the LN 2 dewar vessel of the detector into the lead castle or, preferentially, maintain a flow of purified and aged nitrogen from the interior of the shield to the outside. An even better method to prevent radon from reaching the vicinity of the detector is to manufacture the whole interior of the shield as an evacuable chamber (Heusser, 1989). This construction, however, is very troublesome, expensive and rarely done. Commercially available low-activity lead is usually sold as bricks or sheets, sometimes with specially shaped edges for improved stacking. Although lead is easily shaped on a work-bench, it is very inconvenient to build up lead castles in other than rectangular shapes. When rounded shielding geometries are required or cavities must be ftlled, one may use double-walled containers of appropriate shapes which can be filled with mercury. A safer, cheaper, but less dense "fluid" that can be used for shielding purposes consists of leadshot, which is available in granule diameters ranging from about 0.1 mm to about 2 ram. Other frequently used shielding materials are iron (from old battleships), brass, and sometimes tungsten which is probably the cleanest shielding material (Pomanski, 1986). In applications where the detector must be shielded very effectively from high-energy cosmic radiation (Brodzinski et al., 1985), one may set up the whole experiment in an underground area, mine or tunnel where thick rocky layers serve as an additional shield (Looshi etal., 1986; Pomanski, 1986; Alessandrello et al., 1986; Hebert et al., 1986; Hebig and Niese, 1986). Using the passive shielding techniques mentioned above, one can very effectively reduce the external background contribution to
Software and evaluation of spectra
309
the spectrum. However, the background from Compton interactions of desired gamma rays will still prevail, and it may cover up small peaks. A considerable fraction of these disturbing Compton events can be discarded by active electronic shielding methods (Damjantschitsch etal., 1983; Hildingsson etal., 1986). The principle behind these anti-Compton guard shields is the installation of another detector around the high-resolution gamma-ray detector or detector array. This external device should cover as much solid angle as possible, and its interaction cross section with photons should be large. There is no need for good energy resolution of the anti-Compton detector. In a Compton interaction, only a fraction of the gamma-ray energy is deposited in the high-resolution detector, whereas the residual energy escapes. The escaping photon is detected by the external device, and the external signal is taken as a veto for the coincident signal from the high-resolution detector. Using Na/(TI), BGO, CsI(Na), or CaF2(Eu) as the external detector material and appropriate coincidence electronics, one can suppress the fraction of Compton events in the spectrum by a factor of 20 (Walford et al., 1972) or more with only marginal losses of the full-energy peak areas (Millard, 1984; Hildingsson et al., 1986). The anti-Compton shield is equally effective against background events from external sources such as cosmic rays or contamination. In these cases, energy is deposited in the guard detector and the remaining signal which may be registered by the high-resolution detector is vetoed from registration. Another rarely applied active method 9f background suppression is pulse shape discrimination (Funsten, 1962; Abe etal., 1968), which has become outdated because of the very uniform material of modern letectors. An active device which helps to clean up the background in a spectrum is the ;lectronic pulse-pile-up rejection. Especially at high counting rates, an input pulse may :'ollow so closely after the previous event that the electronic system has not yet returned to its quiescent state. The second event will then be added to an electronic bias of variable magnitude and polarity and the event will be counted in the spectrum in some incorrect ~:hannel. Pile-up events usually show up as pronounced tailing to the peak and as a ,trongly rising spectrum towards the low-energy region. The latter effect is caused by the ,ummation (pile-up) of very low-energy events and system noise. Using electronic t~ile-up rejection, these false events are rejected, but at the cost of artificially reduced c ount-rates. In any quantitative assay, one must therefore consider these rejected events t y some appropriate dead-time or count-rate correction. Knowing the above reasons for background production and applying appropriate measures to reduce the background contribution, one can accummulate spectra with an optimized signal-to-noise ratio, i.e. the smooth background under the peaks is as low as t~chnically feasible, but it has not disappeared. Background peaks (contamination, e;cape, summing, fluorescence) must be treated as real peaks during spectral analysis, and ttey may be identified and discarded later when the data reduction results are interpreted.
Separation of photopeaks from background The quantitative separation of a full-energy peak area from the underlying b~ckground is nowadays almost always made with the aid of sophisticated spectrometric ccmputer programs. Older analytical procedures, where a graph of the spectrum is measured with a ruler (Routti, 1968) or where the photopeak area is determined by
310
Software and evaluation of spectra
gravimetic integration have practically ceased to exist. In certain applications, one may use methods of partial peak fit or partial integration (Sterlinski, 1968; Baedecker, 1971; Smakhtin, 1986; Loska, 1988), but the vast majority of modern computer programs for spectral analysis use nonlinear least-squares fit procedures to determine the area of a photopeak and sometimes also the underlying background. While the discrimination between a photopeak and the background seems to be simple when the peak is significant, there are a number of different approaches to the analytical description of the peak-shape and the shape of the background under the peak. In a recent publication (Westmeier, 1986) an arbitrary but very successful peak-shape function and a model for the shape of the background were presented. The background shape was calculated from the experimental numbers of counts per channel in the spectrum and it needed no a priori information about peaks or multiplets nor any mathematical model shape. In Fig. 1, the essential ingredients for the calculation of the intrinsic shape of the background under a peak or multiplet are reviewed. The background above the high-energy end of the peak is smooth and slowly decreasing. The jitter in the distribution of counts per channel shows no systematic trends, and it is governed by Poisson statistics. One can define the average background height above the high-energy side of the peak (HB,A), i.e. around the channel N where the high-energy flank of the peak merges with the background, by some appropriate averaging or smoothing method.
37Cs '
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Software and evaluation of spectra
3ll
The background below the peak (HB,B) shows the same statistical characteristics as the background above, however, at higher count rate. Thus there is a "step" in the background when one goes from the high-energy end of the peak to lower energy. The height of the step is apparently proportional to the height of the peak. One can also see from Fig. 1 that the low energy background in the immediate vicinity of the peak is approximately constant (see dotted line at HB,B). A first-order approximation for describing a peak in a gamma-ray spectrum therefore assumes a one-channel wide distribution of some height H~ which sits on an extending background step of the height c~.H~. The magnitude of the normalization constant o~ is unknown. A real gamma-ray full-energy peak, however, has a finite width in channels, and one has to consider the content of each channel in the above manner. Starting from the high-energy end of the peak and going down in channels, each peak-fraction sits on top of the c~.H~ steps which originate from the higher channels. The background contribution in the channel j under a peak is given by: N HB,j = HB,A + ct Z H6,i
(2)
i=j+l
where HB, A is the average background height above the peak and N is the channel number where the peak ends at high-energy. The normalization constant c~ is easily calculated when one evaluates the sum of Eq. (2) for the whole peak from HB,B to HB, a and normalizes it to the experimental height of the step (see Fig. 1) N ot = ~2 HS, i / (HB, B - H B , A ) i=M
(3)
~.here M is the channel where the low-energy flank of the peak starts to rise out of the imckground. This very simple recipe is used to calculate the instrinsic background under i~eaks or multiplets from experimental data without any input other than the spectrum itself. One must define suitable channel numbers M and N for the lower and upper end of peak or multiplet and apply Eqs. (2) and (3) to calculate the background. Count (istributions remaining above the background are considered to be peaks and are treated cccordingly. When the above procedure of background calculation is applied to s~fficiently small peakless regions, the calculated "background" is nothing but a smoothed s~ectrum. Fig° 2 shows as an example the background calculated according to the above procedure for a multiplet in an 227Ac spectrum and the least-squares fit of the photopeaks. IT should be noted that this analysis using the intrinsic background calculation gave the first exact analysis of the peak area of the tiny peak at 267.7 keV o f I7,267. 7 = 0.037 + 0 005% (van Aarle, 1986).
Computerized analysis C)nsidering the fact that the background under a peak or multiplet is easily calculated fr,:~m the distribution of experimental counts in the peaks, the computerized peak analysis
312
Software and evaluation of spectra
10' (I) (0 C.
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275
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Energy (keY) Fig. 2: Fraction of a ,/-my spectrum of 227Ac (histogram) with the intrinsic background and deconvoluted peaks.
of a spectrum can be reversed; the task in spectral analysis is to analyse the background what remains are potential peaks. In contrast to former peak-searching algorithms, the analysis program now has to find portions of the spectrum (regions) in which a common background can be assumed. These regions must not span over systematic discontinuities like Compton edges or backscatter bumps, and their width must be related to the width of possible peaks. A flexible and fast method to define the limits of regions, i.e. the first and last channel of a region, is to search for local minima in the count distribution (see arrows in Fig. 3). These local minima have the desired property that they (probably) do not interfere with possible peaks and that they underestimate the average height of the surrounding background. The distances over which to search for local minima are scaled by the full-width-at-half-maximum (FWHM) of expected peaks. The average height of the background around the local minima is then defined by appropriate smoothing or averaging procedures. In this step, one has to consider the fact that random deviations in low-level spectrometry are far away from the central-limit theorem, and that one has to apply the methods of robust statistics (Press et al., 1986) to find the desired average (outliers are much more frequent than they should be according to Gaussian or even Poisson statistics). Typical problem situations that must explicitly be considered by a computer program are real outliers, which are for example caused by data transfer errors, systematic background trends coming from closely-spaced peaks, or Compton edges in the vicinity of the local minimum. Once the average background height around the start- and end-channel of a region is defined, the course of the whole background in the region is
Software and evaluation of spectra
313
calculated as described in the preceding paragraph. The distribution of counts above the spectrum is then scanned for peaks which are fitted by appropriate methods. When a region is analysed, the program continues to search for the next adjacent region where the end-channel of the current region is the start-channel of the next one.
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There is a major advantage of the above-presented method of spectral zoning over the ttsually applied peak-search methods. The count distribution which is finally scanned for [,eaks or multiplets is free of the smooth underlying background, and small peak structures are much more prominent than they are on top of the background. Large peaks are of course as easily detected with or without the background, and the regioning method offers no advantages for their analysis. There are cases where the remaining distribution of counts above the background is t(~o scattered for a reliable, automatic peak detection and fit. In these (and only these) ctses, it may be advantageous to smooth the spectrum, in order to carry out an automatic aJ:mlysis or a least-squares peak-fit operation. In Fig. 4 is shown a traction of a gamma-ray spectrum which was taken from a very low activity sample of pine-tree needles (Jenderek, 1990). The fine-line histogram distribution shows the measured sFectrum and the thick line is the same spectrum after one smoothing pass, using a 5-channel sliding window (Mtiller, 1974).
314
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Software and evaluation of spectra
315
longer usable, i.e. a reliable automatic peak search in a low count rate spectrum is no longer possible after spectral smoothing. The numbers relevant to the example peak from Fig. 4 are summarized in table I. A manual-analysis gave a peak area of 24 counts above background.
Table 1: Least-Squares peak-fit to the structure between channels 882 and 899 in Fig. 4 Original data Peak position, channel
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If one looks only at the reduced X2 as a quality-of-fit indicator, one might consider :his case to be a superior fit to the smoothed data. The uncertainties of the peak 9arameters clearly show, however, that the original, scattered data are fitted much better. i'his improved fit is supported by a comparison with the expected FWHM which fortuitously) is 2.88 channels for this peak. Having these numbers in mind, one would ~tccept the poor tit to the original data but reject the fit to the smoothed spectrum, or ~:rroneously consider this to be a multiplet. To summarize: the smoothing of spectra ~hould be avoided, and results calculated from smoothed spectra must be cross-checked ~/ith great care. One may of course define a region around a k n o w n peak position in a smoothed spectrum and fit a peak irrespective of the structure and scatter of the experimental data. The fitted peak position and peak area will then be good approximations to the real values, and the uncertainties should clearly reflect the quality of the fit (they are much larger than those calculated through a Gaussian matrix inversion ('fadav et al., 1989)). Another important step in the computerized analysis of spectra is automatic peak d,'.tection, which will be just shortly described here. There is a large body of literature at,out peak search and position approximations which include derivative methods (l~lariscotti, 1967), peak correlators (Black, 1969), and more recent ideas of maltiplet-components search (Lauterjung et al., 1985). All these methods are more or less de veloped and proven in spectra with prominent peaks and good statistical accuracy, if, hcwever, these methods are used for automatic peak-search in spectra with poor statistics, th,; results may seem arbitrary or 'at least incomplete. The principle behind this in~:ompleteness can be demonstrated by means of the simple derivative method. The first derivative of a peakless spectrum is a jitter around zero without systematic structure, wt ereas the first derivative of a peak yields a cluster o f positive values (about FWHM ch.mnels wide) significantly above zero, followed by a similarly significant cluster of negative values. The transient point is located at about the peak position. The upper box of 7ig. 5 shows, as a thin-line histogram, a fraction of a spectrum which was measured at a very high count rate and which has very prominent peaks. The thick-line histogram below the spectrum is the normalized first derivative of the spectrum. The horizontal line in the
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derivative plot marks the value zero. One can clearly visualize the steep zero-crossing corresponding to the derivatives at the peak positions, which is equally clear for the less prominent peaks but on a smaller numerical scale. In the lower box of Fig. 5, the same display is plotted for a fraction of the same spectrum after only a low total count had been accummulated. An analyst could easily detect by eye a "peak" located in the left half of the figure, but the first derivatives give no clear indication of such a peak° Following the proposals of Mariscotti (1967), one may use the second derivatives of the spectrum for peak location, as indicated in Fig. 6 for the same data as in Fig. 5. Peaks in the good statistics regions are undoubtedly indicated by a negative spike in the second-derivative plot. But in the poor statistics one finds many of these negative spikes which certainly do not indicate a peak. Also, the only "peak" suggested in the poor-statistics data is not indictated by a negative spike. Different methods thus work equally well for prominent peaks, but they yield very different and contradictory results when applied to data of poor statistical significance. The only way out of this dilemma is to apply several different peak locator methods to the same data, possibly combined with smoothing or gradient enhancing methods. Then one can generate a logical decision-tree from the individual results, which may finally indicate the possible presence of a peak. The procedure may be complicated, but the computing power of modem PCs is completely adequate for these tasks.
Time-dependent spectral analysis It was stated before that the reliable automatic analysis of a spectrum may require .'everal approaches and combinations of different methods in order to find the most probable result. Taking the example of time-dependent spectral analysis (TDSA) (Esterlund, 1985), the merit of such combinations can be clearly shown. TDSA can be ~pplied to the analysis of spectra recorded in the multi-spectrum-scaling (MSS) mode f:om the same sample. The MSS mode is the analogue to the multi-channel-scaling mode (VICS), except that the complete energy-dispersive spectrum is stored for each time-bin rather than just the integral number of counts in a selected window as in MCS. The areas of a peak at the same energy in the sequence of spectra are assembled as a decay curve for tt:is peak. The curve is deconvoluted, and quantitative results for the one or several c,)nstituents are calculated° The MSS measuring method is frequently applied to the a~;say of radioactive nuclides in irradiated samples. The data of the example below (Schulte, 1989) stem from MSS sequences that were measured from reaction products from the nuclear reaction between 212 MeV 4OAr and 197Au. The products were deposited on catcher foils disposed at different angles, and the ar:gular distributions of the reaction products were recorded. Fig. 7 shows the same fraction around 1811 keV of the first twelve spectra of the MSS sequence. The 12 spectra cover the ftrst 17 hours of an MSS sequence going in total over 40 spectra and a decay time of about 6 months. In the first few spectra, one can detect visually a peak around chmnel 3621, which has apparently disappeared after spectrum # 9. An arrow indicates the position of the peak. The quantitative analysis of this peak was made with TDSA
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Software and evaluation of spectra
318
according to the following procedure. From the first spectra where the peak is well discernible and considering the FWHM of a peak at 1811 keV (at this energy one expects to find a peak from 56Mn with a half life of T1/2 = 2.58 h), one can define the start- and end-channel of a region around this peak. The course of the background in this region is calculated for all MSS spectra as explained above and the total number of background counts in the regions is displayed as a function of time (see Fig. 8). Analogously to the activities in the spectra the background also "decays" and the data are well described by a • '
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Software and evaluation of spectra
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Software and evaluation of spectra
320
good data points for the decay curve and it enables one to quantify the tiny second component which is otherwise undetected, even by an evaluator's eye. This principle of systematization or trend analyses of the background, or of structures, is always applicable when a larger number of consistent spectra are available.
Acknowledgement I want to thank my colleague Bob Esterlund for the careful reading of the manuscript and his valuable suggestions and comments.
References Aaltonen H. and Ugletveit F. (1989) Progress in Radiation Protection FS-89-48-T, 515 ISSN 1013-4506 Abe K., Kawamura N. and Mutsuro N. (1968) Nucl. Instr. Meth. 63, 105 Alessandrello A., Bellotti E., Cattadori C., Carom D., Cremonesi O., FioriniE., Liguori C., PuUiaA., Rossi L., Ragazzi S., Sverzellati P,P. and Zanotti L. (1986) Nucl. Instr. Meth. B17, 411 Anicm I.V. and Yap C.T. (1987) Nucl. Instr. Me~. A2,59, 525 Baedecker P.A. (1971) Anal. Chem. 43, 405 Black W.W. (1969) Nucl. Instr. Meth. 71, 317 Blanchard F.A. and Lickly T.D. (1984) Nucl. Instr. Meth. 219, 413 Brodzinski R.L., Brown D.P., Evans Jr. J.C., Hensley W.K., Reeves J.H., Wogman N.A., Avignone llI F.T. and Miley H.S. (1985) Nucl. Instr. Meth A239, 207 Cumming J.B. (1962) National Series Report NAS NS-3107, unpublished Currie L.A. (1968) Anal. Chem. 40, 587 Currie L.A. (1972) IEEE Trans. Nucl. Sci. NS-19, 119 Damjantschitsch H., WeiserM., Heusser G., Kalbitzer S. and Mannsperger H. (1983) Nucl. Instr. Meth. 218, 129 Debertin K. and SchOtzig U. (1979) Nucl. Instr. Meth, 158, 471 Esterlund R.A. (1985) private communication, Univ. Marburg Fry F.A. and O'R.iordan M.C. (1984) Nucl. Instr. Meth. 223, 540 Funsten H.O. (1962) IRE Trans. Nucl. Sci. NS.3, 199 Gardner R.P., Yacout A.M., Zhang J. and Verghese K. (1986) Nucl. Instr. Meth. A242, 399 HebertD., FrOhlichK., FrankeT., GellermannR., UnterrickerS., KimJ.H. (1986) Nucl. Instr. Meth. BIT, 427 Helbig W. and Niese S. (1986) Nucl. Instr. Meth. B17, 431
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Heusser G. (1989) Progress in Radiation Protection FS-89-48-T, 468 ISSN 1013-4506 Hildingsson L., Beausang C.W., Fossan D.B., Piel Jr. W.F~, Byrne A.P. and Dracoulis G.D. (1986) Nucl. Instr. Metla. A252, 91 Hubert Ph., Dassie D., Lameu P., Leccia F., Menrtrath P., Chevallier J., Chevallier A., Henck R., GutknechtD., MoralezA., Nunez-LagozR., Morales J. and ViUarJ.A. (1986) Nucl. Instr. Meth. A252, 87 Hut G., (1986) Nucl. lnstr. Meth. B17, 490 Jenderek H. (1990) private communication, Univ. Hohenheim Lauterjung J., Will G. and Hinze E. (1985) Nucl. Instr. Meth. A2,39, 281 Loosli H.H°, M011 M., Oeschger H. and Schotterer U. (1986) Nucl. Instr. Meth. B17, 402 Loska L. (1988) Appl..Radiat. Isot. 39, 475 Vlariscotti M.A. (1967) Nucl. Instr. Meth. 50, 309 Vlillard Jr. H.T. (1984) Nucl. Instr. Meth. 223, 416 i¢loore W.S. (1984) Nucl. Instr. Meth. 223, 459 MUller LW. (1974) Report BIPM-74/1, Bureau Int. de Poids et Mesures, Sevres, France 14undschenk H. (1980) Nucl. Instr. Meth. 177, 563 ()p de Beeck J. (1978) Proceedings of the ANS Topical Conference, Mayaguez, Puerto Rico, CONF-780421 Folach H.A. (1987) Nucl. Instr. Meth. B29, 415 Fomanski A.A. (1986) Nucl. Instr. Meth. BIT, 406 P 3vinec P. (Editor) (1986) Nucl. Instr. Meth. B17, 377 - 574 Press W.H., Flannery B.P., Teukolsky S.A. and Vetterling W.T. (1986) "Numerical Recipes", Chapter 14, Cambridge University Press, Cambridge, UK. Pltman J.L. (1962) Int. J. Appl. Radiat. Isot. 13, 99 R chard.son A.E. and Sailee W.W. (1990) Nucl. Instr. Meth. A299, 344 R, tutti J.T. (1968) Anal. Chem. 40, 593 S
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Walford G.V., Aliaga-Kelly D.T.W. and Gilboy W.B. (1972) [EEE Trans, Nucl, Sci, NS-19, 127 Westmeier W. (1986) Nucl. Instr. Me~. A242, 437 Wogman N.A. (1981) IEEE Trans. on Nucl. Sci. NS-28, 275 Wojcik M. and Grotowski K. (1980) Nucl. Instr. Metla. 178, 189 Yadav J.S., Brtickner J. and Arnold J,R. (1989) Nucl. Instr. Meth. A277, 591 Yadav J.S. and Arnold J.R. (1990) Nucl. Instr. Meth. A295, 241