Uncertainties in peak area determination of a 152Eu gamma source

N U C L E A R I N S T R U M E N T S AND METHODS

165 (1979) 5 7 7 - 5 8 2 ,

(~) N O R T H - H O L L A N D P U B L I S H I N G CO

UNCERTAINTIES IN PEAK AREA DETERMINATION OF A 'SZEu GAMMA SOURCE R F LAITANO, F ORS1TTO and E ROTONDI Comttato Na-tonale per I'Energta Nudeare C S N Casaccta - c p 2400 Roma, Italy Received 27 June 1978 and in revised form 25 June 1979 The use of the 152Eu gamma source to calibrate Ge detectors is here underlined owing to the presence of well separated photopeaks In the 122-1408 keV energy range Moreover it ~s shown that peak area determlnaUon, necessary m order to obtain a detector efficiency curve, can be carried out with satisfactory accuracy and w~thout resorting to very elaborate methods To prove this, two different peak integration procedures are analyzed with regard to the uncertainty in the final result Finally it ts shown that the more conventional method of using, in the effictency cahbratton, many mono-energet~c gamma sources does not necessarily ensure a greater accuracy whereas it is mol~ time consuming

1. Introduction The use of '52Eu as a standard cahbratmg photon source for Ge defectors has been suggested recently by a few authors '-3) Many advantages can be ascribed to this source such as

(1) a long half-hfe (about 13 3 y), (2) ten adequately intense gamma lines convemently distributed over a wide energy range (from 122-1408 keV), (fig 1) (3) a fairly fiat Compton continuum under the

Counts

122 Kev

344 Key

244 Key

779 Kev

964 Key

1408 Key

-J IL__ KQ¥

Fig 1 152Eu gamma spectrum Photopeaks other than that examined m this work are not reported, since they have a low intensity

578

R F LAITANOet al photopeaks, allowing an accurate background subtraction to be performed

Accordingly, the use ~52Eu overcomes, firstly, the problem of differences in counting rates of multiple-standard sources, which may determine electronic gain shift, so making the energy calibration more inaccurate Secondly, the uncertainties in the reproducibihty of the geometry and counting duration are avoided Calibrating sources are available with accurately known activity or photon emission rate, the associated uncertmnties are becoming less with time and are well determined anyway Thus, the accuracy in the efficiency calibration of a detector depends ultimately on the experimental apparatus and procedure, and in particular on the peak area evaluation Several methods of peak area determination have been used for many years They are based either on direct handling of digital data4-6) or on the fitting of the data to a function which, by integration, gives the peak area 7) This last approach is mostly suitable when dealing with precise energy peak determination in complex spectra with superimposed peaks, and it generally requires fairly large computing facilities In the case of the ten well-spaced gamma peaks of ~52Eu generated in a Ge detector, it is easier and less time consuming to treat the digital data directly, considenng that the accuracy in peak area determination is not necessarily lower than with the other procedures A comprehensive review of digital methods for photopeak integration has been made elsewhere s'9) From this analysis no conclusion on the choice of the best approach to peak area determination can be drawn, as the accuracy of each method is generally dependent on the particular gamma spectrum To make a decision about the most accurate peak integration procedure in the practicaF case of the ~52Eu spectrum, two very different methods have been examined The first is based on the elementary formula of Covell, with some modification, the second, the Quittner-method, is the most refined among the digital methods 2. P e a k area determination and uncertainties

The energy spectrum of 152Eu has been measured using a 43 c m 3 intnnsic Ge detector of closed-ended coaxial type whose resolution (FWHM) was 1 05 keV for 122 keV gamma rays Adequate, fixed

geometry was used dunng the irradiation obtaining a total counting rate slightly above 4000 cps Peak channels stability in the 4096 MCA was ensured during the measurements Adequate shielding resulted in a strong reduction of ambient background The photon emission rates (photons s -1) of the ~52Eu gamma lines were known with uncertainties of about 1% (at 68% confidence level) A detail of the spectrum showing the 244 keV peak is reported in fig 2 The peak area determination depends mostly on the particular shape of the baseline which is selected to reproduce the background under the peak In the Covell-approach, this baseline is given by a straight line drawn between the channels n and - n (full line in fig 2) so that the corresponding peak area is simply given by

An = ~ C,- (n+½)(Cn+C-n), l =

(1)

--n

where n is the number of channels to the left and the right from the centermost channel and C, is the number of counts in the channel t If the independent terms of (1) are assumed to follow a Polsson distribution, the standard deviation of An can be expressed as s (An) = rAn + (n - ½)2 (Cn + C_ n)] t/2

(2)

The relations (1) and (2) are dependent on the value of n, though only slightly for n sufficiently large Moreover, a fixed value of n should give different shapes This may happen in a Ge detector in which the FWHM of the photopeaks varies according to the photon energy This indetermination of the Covell-method and of its further modifications8,9) disappears when the method is used, as it was originally, to normalize a photopeak of unknown intensity to a reference peak of the same radionuchde at the same energy (i e , relative quantitative analysis) In such cases the two peaks will have the same shapes and therefore any fixed value of n will provide a ratio of the areas which is equal to the photon emission ratio of the two radionuchdes at that energy But when a whOle detector efficiency curve e(Er)= A(Ey)/I(Er) has to be determined, in which I(E~) is the standard nominal photon emission rate of the E r line, the shapes of the peaks at different energies will generally be different Thus a fixed value of n for all energies would correspond to different fractions of the total

579

PEAK AREA DETERMINATION

n u m b e r of

D

oo~Lnts @

0 0

O

I' kL

IL----~a~ L

-

n

@

xp

n

= k~R

~

°

:R

p kR

n u m b e r of

channels

it,

1R F~g 2 |52Eu 244 keV photopeak with Covell and Qmttner parameters for peak area determinations (see text)

does not change appreciably with n, u(A) ts the the overall uncertainty of A expressed as the quadratic sum of the last two terms m c(E ) The values of s(A ) and o"(,4) represent respectiveThe above condltlon has the dmadvantage that those channels m the lower part of the peak, which ly the uncertainty due to (a) the statmtmcal fluctuaUons m the channel content, (b) the choice of the may have a pronounced varmbfltty, must be used In thin way the uncertainty in the background base- limits of the background basehne of the photohne ms increased and so m the uncertainty in A To peak Following thin "averaged" Covell-method the overcome thin failure the following procedure has areas of the other 152Eu photopeaks have been been adopted m the peak area determination For each 'S2Eu photopeak, many values of A determined As expected, the range of the values of have been calculated as many channels exmt n in which the various means values, A, were between those corresponding to the peak F W H M evaluated was found to be specific for each gamma and the channel, m the background regmon, the hne In the Quittner-method 6) the peak area m detercontent of which shows a non-statmtlcal change mined by using a non-linear basehne (dashed hne, The values of An increase w~th n untd they reach a fig 2) subtraction technique, where the background regmon of statmUcal varmblhty The real total peak area, A, has been assumed to under the peak is assumed to be described by the be the mean of the An values taken m thts last following cubic expression regmon, and accordingly, the uncertmnty arising from the choice of the basehne has been strongly B(X) = pL+qL(X--XL) + ( - - q R - - 2 q L + \ /L+/R reduced As an example, the numerical data concerning 3(pa-- pL)'~ / -2 / qL +qR + + the 244 keV photopeak are reported mn table 1, A is the mean of the An values m the range from A26 to A35 , 0"(.4) IS the standard devmUon of this mean, + 2(pL- PR)~ ( x - XL)3 (3) s(A) ms the average of the values ofs(An), calculated (IL+ 1R)3 } from expression (2), m the above region where s(An) areas of the various peaks Therefore the total area of each peak ms to be constdered to avomd ambmgmty

580

R F LAITANOetal

TABLE 1 Results of peak area determination of the 152Eu 244 keV gamma line

Channel number (1)

Net peak area (2)

Theoretical

n

An

deviation s(An) (96)

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

631 108 639 821 649 302 655 382 656 324 657 930 659 868 664 691 671 731 669 793 671 593 662 961 662 835 668 165 663 408 660 648

standard

0 52 0 52 0 53 0 54 0 60 0 60 0 61 A = 665 569 s(A)= 0 69% 0 62 or(A)= 0 66% 0 64 u(A) = s2(A)+ a2(A)= 0 93% 0 68 0 70 0 70 0 72 0 72 0 73 0 74

(3) (4) (5)

(1) Number of channels on the left and on the nght from the centermost peak channel (2) An is expressed m countlngs m the total measuring time (about 104 s) (3) A is the total peak area and is given by the mean of the An values m the range (A26-A35) Analogously s(A) ~s taken as the mean m the range [s(A26)-s(A35)] (4) a(A) Is the standard devlatmn of A (5) u(A) is assumed to be the overall uncertainty of A The above polynomial is fitted to the measured values, using 2KL +1 and 2KR +1 points around the channels XL =Xv--IL and XR =Xp+iR, the XL and xR lie respectively on the left and right c o n t i n u u m regions o f the peak, xv is the centermost peak channel which is IL and Ii~ channels far from XL and XR r e s p e c t w e l y , (qL, qR) and (PL, PR) are derived using the tables of Savltzky and Golay m°) and represent the values and the slopes o f the polynomml at XL and xR respectively The net area in the peak is NR

A =

~

[C(xp+0-

B(xp+z)],

standard deviation of relation (4) is easily determined assuming a Polsson distribution. For each ~52Eu photopeak, many values of A have been determined from expression (4) varying the (XL, IL) and (xR, Is) pairs as m u c h as possible, consistently with the peak separation in the photon spectrum The selected values are those corresponding to the m i n i m u m relative standard deviation which is assumed to represent the overall uncertainty u(A). Since total peak areas are considered, the peak hmlt channels NL, NR have been suitably selected on the basis of the observed shapes of the photopeaks The relevant data refernng to both the procedures examined are reported in table 2 The statistical consistency o f the experimental results has been cheked as the long duration o f the single measurements (about 104 s) could result in a not negligible systematic component o f the uncertainty, mainly due to electronic mstablhtles T e n spectra have been successively measured, each one for a time duration o f 103s For every gamma energy, ten photopeak areas, A,, were determined so obtaining a mean value A and an experimental standard deviation S(A) Then the dispersion index Z2 =

10 ~ (A,--z~)2/S2(-~) 1=1

has been considered as a stathstlcal significance test The results are presented In table 3 where the theoretical standard deviation s (A) for each peak is also reported To compare the values of ,~/, A, S ( ~ ) and s(A) from the statistical point o f view the peak areas A~and A, m table 3, have been determined by the " a v e r a g e d " CoveU-method only Finally it has been considered useful to compare the uncertainties m the X52Eu peak area determination with the analogous uncertainties related to mono-energetlc standard gamma sources which are normally used for calibration purposes in the same energy range Both peak areas and associated uncertainties for eight of these sources have been determined by the " a v e r a g e d " Covell-method and the results are shown in table 4

(4)

I = --NL

where CO) is the n u m b e r o f counts measured in channel j and NL and NR are the n u m b e r o f channels on each side o f the peak, whose content is considered when determining the peak area The

3. Conclusions According to the data m table 2, the efficiency o f a Ge detector given by e(Er)=A(Ey)/I(E ~) can be determined by means of an 152Eu gamma source in the energy range from 1 2 2 - 1 4 0 8 k e V , with an

PEAK AREA DETERMINATION

581

TABLE 2 Peak area determination using both Qulttner method and "averaged" Coveli method Peajk energies

fwhm

Background

Percent deviation

/L

Qulttner parameters (3) k L /R k R N L N R

Partial uncertamtles

Overall uncertainties

u(A) (%)(5)

of tS2Eu

to p e a k

between

in "av "

(keV)

ratio (I)

peak areas computed by the two methods (2)

Coveil method (%) s(A)(4) a(A)(4)

"av " Covell method

Qulttner method

0 58 093 0 31 282 273 0 98 099 1 34 092 0 57

0 64 1 23 0 58 542 394 1 42 1 84 3 12 2 11 0 65

R - 1 (96) 122 244 344 411 444 779 964 1085 1112 1408 (1) (2) (3) (4) (5)

5 7 8 12 11 12 12 14 14 15

0 23 0 51 0 14 081 083 0 20 0 15 0 22 020 0 03

02 15 11 32 07 04 19 37 12 18

28 29 30 28 29 27 31 31 31 31

5 6 5 6 5 5 4 4 4 4

16 19 17 21 19 16 17 31 19 18

5 7 4 5 5 5 4 5 4 5

24 17 14 21 23 21 26 26 26 26

18 19 12 15 15 10 12 15 14 12

0 15 069 0 25 250 220 0 80 066 0 85 076 0 27

0 56 066 0 18 1 27 153 0 58 074 1 04 050 0 51

Ratio of the total background counts under the peak to the net peak area R is the ratm of the net peak areas determined by the "averaged" CoveU method to that determined by the Qmttner method These parameters (see text) are selected in correspondence with the minimum stan~lard dewatlon on A See text The relative overall uncertainties (at 6896 confidence level) are defined m the text for each method

TABLE 3 Results on the statistical consistency of the experimental data Peak energies of Eu152

3/A 0 )

S(A)(2) (96)

s(A)(3) (96)

x2/f (4)

ptz2)

(keV) 122 244 344 411 444 779 964 1085 1112 1408

0984 0 991 1000 1 001 1 013 0 996 1 000 0 993 0986 1 001

017 0 99 033 201 3 14 1 16 0 83 1 29 1 95 0 92

015 0 69 025 250 2 20 0 80 0 66 0 85 076 0 27

081 0 42 1 13 1 21 1 12 2 07 0 98 0 98 074 1 18

065 0 90 045 045 0 30 0 03 0 45 0 45 060 0 45

(1)

.~ IS the mean of 10 peak area values, At, corresponding to 10 successive measurements The peak area A refers to one single measurement whose duration IS ten times greater than that of A, Both .,/and A have been normahzed to the same measuring time, to be compared (2) Experimental standard deviation of

S(4) = [" '~ (A,-.,t)2]t/2/3

uncertainty from 1 - 4 % This figure also includes the uncertainty of the photon emtsston rate, I(E:,), which can be held within 1% (at 68% confidence level) if the source is standardized in a metrologtcal or advanced laboratory Therefore the accuracy in efficiency cahbrat~on ~s dependent mainly on the determmaUon o f the photopeak area A (Er) TABLE 4 Statistical uncertainties in peak area determination of monoenergetic gamma sources Source peak energy (keV)

57Co (122) 139Ce (166) 2°3Hg (279) 113Sn (392) SSSr (514)

137Cs (662) 54Mn (835) 65Zn (1115)

Partial uncert

Partial uncert

Overall uncert

S(.4) 0/6 (I)

0(.4) 96 (1)

/2(.4) 96 (2)

0 45 0 45 0 48 0 38 0 50 0 52 0 50 0 45

0 27 0 13 0 23 0 25 0 27 0 26 0 16 0 20

0 52 0 47 0 53 0 45 0 57 0 58 0 52 0 49

1=1

(3) Theoretical standard dewatlon of A [relation (2) m the text] (4) The degree of freedom, f, equals 9 m each case

(1) Both s(A) and o(.4) have been determined by the "averaged" Covell method (2) u(A) is determined as quadratic sum of s(A) and a(A)

582

R F LAITANOetal

It is worth pointing out that of the two methods which have been used for peak integration, the stmplier one, namely the so-called "averaged" Covell-method, has given the best results as far as the uncertmnty is concerned (columns 13, 14 in table 2) independently of the peak energies and of the peak height-to-background hetght ratio (columns 1,3 m table 2). The uncertainties, a(A) (table 2), m the baseline determination are of the same order as (m some cases greater than) the uncertainties, s(A), in the fluctuations of the channel content This suggests the importance of the "averaging" procedure which has been adopted for the Covell method The values of the total peak areas are very similar for both methods (column 4 m table 2) and their deviations are generally within the overall uncertainty u(A ) According to other worksS'H), the Quittner-method should provide better accuracy than other digital peak integration procedures This has not occurred m the present work probably because both Qulttner and Covell-method have been used either with very different parameters (l e those in columns 5, 10 table 2) or with some modification (as for the Covell-method) with respect to the conditions under which these methods have been compared m the above mentioned works These different conditions resulted from the necessity of determining the best possible value of the total peak area in order to obtain a non-ambiguous efficiency curve Adequate care has been taken to ensure the stability of the experimental conditions as is proved by the results in table 3 The values of the parameters in columns 2, 5, 6 of table 3 confirm the statistical consistency of the experimental data Nevertheless some discrepancies characterize the results in columns 3, 4, as the theoretical and experimental standard deviauons should agree more closely than appears from the values In the table The slight difference between S(A) and s(A ) is probably due to the fact that relation (2) is not rigorous

and may lead to incorrect values when counting rate and dead times become very large, as could have happened m these measurements From the data in column 4, table 4, and those in column 13, table 2, a comparison can be made with the uncertainties which result when, only the 152Eu source or, more conventionally, different monoenergetic gamma sources are used for efficiency cahbration In the latter case the accuracy is better since, for mono-energetlc sources, the shape of the photopeaks is more regular and the photon emission rate can be known with a lower uncertainty (about 0 5%) than in the case of 152Eu sources On the other hand, this advantage might disappear because of the greater systematic uncertainties present when more than one source is used All calculations have been carried out using a IBM 370 owing to the large number of computations which have proved to be necessary for this analysis On the other hand, when considering the "averaged" Covell-method which has been fairly accurate for 152Eu peak area determinations, a medium desk computer IS sufficient provided that a careful, not necessarily time consuming, analysis of the experimental spectrum is made References t) p Mukherjee and A K Sengupta, Nucl Instr and Meth 68 (1969) 165 2) G Aubm, J Barrette and S Monaro, Nucl Instr and Meth 76 (1969) 93 3) A Notea and E Ehas, Nucl Instr and Meth 86 (1970) 269 4) D F Covell, Anal Chem 41 (1959) 1504 5) S Sterhnskl, Anal Chem 40 (1968) 1995 6) p Qutttner, Anal Chem 41 (1969) 1505 7) j T Routtl and S G Prussm, Nucl Instr and Meth 72 (1969) 125 8) p A Baedecker, Anal Chem 43 (1971) 405 9) L Kokta, Nucl Instr and Meth 112 (1973) 245 10) A Savltzky and M J E Golay, Anal Chem 36 (1964) 1627 11) p Qulttner, Nucl Instr and Meth 76 (1969) 115