summarized in Table I or to a characteristic cleavage m the remainder of the molecule Cleavage not directly induced by an obvious functional group must always be taken into account during the interpretation of mass spectra. Such cleavage may so dominate the spectrum that the presence of the functional group may not even be detected. Tendencies along this line may be seen in the spectra of ethyl S-cyclohexylcarbamate (Figure 5) , ethyl S-p-nitrophenylcarbamate (Figure 12), and ethyl N-piperaainocarboxylate (Figure 24). In these cases, the more intense ions do not
reflect the carbamate structure. Instead, as may be readily verified by examining the spectra of cyclohexylamine, p-nitroaniline, and piperazine (1). respectively, they are representative of characteristic fragmentations occurring ,within the S-substituted group. In view of this type of behavior, it would be futile to attempt to give a set of rules by which carbamates may be recognized by mass spectrometry. Let it simply be stated that ethyl carbamates often behave as indicated in Table I. The presence or absence of particular paths, as well as peaks not corresponding to one of the
given paths, may be interpreted in terms of structure. LITERATURE CITED
( 1 ) Am. Petrol. Inst., “Catalog of lfass Spectral Data,” API Research Project 44,New York, S . Y. (2) Beynon, J. H., “Mass Spectrometry and Its Applications to Organic Chemistry,” Elsevier, Kew York, 1960. ( 3 ) Biemann, K., “Mass Spectrometry, Organic Chemical Applications,” McGraw-Hill, New York, 1962. ( 4 ) Lewis, C. P., ANAL. CHEM.3 6 , 176 11964). ( 5 ) Lewis, C. P., Hoberecht, H. D., Zbid., 35, 1991 (1963). RECEIVED for review January 27, 1964. Accepted April 9, 1964.
Activation Analysis by Absolute Gamma-Ray Counting and Direct Calculation of Weights from Nuclear Constants FRANCESCO GIRARDI, GIAMPAOLO, GUZZI, and JULES PAULY Servizio Chimica Nucleare, Centro Comune
di Ricerche Euratom, lspra (Varese), ltaly
b A method based on neutron activation and gamma-ray spectrometry has been studied by irradiating samples of different elements, measuring the activities by means of a calibrated gamma-ray spectrometer, and calculating the weights of elements from the activation formula. The values obtained were compared with the weights of the irradiated samples. Then accuracy and precision were evaluated. The results show that random errors generally are not greater than those obtained by using the relative method, but that systematic errors may reach 20%, although in 1 1 cases out of 13 they were lower than 10%. Different causes of error have been evaluated. Calibration of the gamma ray spectrometer and neutron flux measurements do not cause any relevant error. Uncertainties in nuclear data taken from literature, especially those on decay schemes and activation cross sections, may be responsible for most systematic errors. If the nuclear constants are known and the precision required is not better than 2 0 ~ o , ~ t h e method can be applied to trace analysis by neutron activation and the experimental procedures considerably simplified.
Only a few examples of actual analysis (Z) are reported in the literature. The drawbacks of the direct method have been point’ed out by, among others, Taylor and Havens (22) in 1956. These included poor knowledge of t’he nuclear constants and difficulties in measuring exactly neutron fluxes and disintegration rates. On. the other hand t’he method presents some advantages over the more generally adopted relative procedure-i. e., diminution of the experimental work and elimination of errors due to inhomogeneity of the neutron flux within the irradiation capsule (19). In recent years many nuclear constants have become known with a better precision, and t’he techniques and instrumentation of nuclear detection have been greatly improved. These improvements were checked to determine whether the direct method was now competitive with the relative one. In this work the direct method has been applied to 13 elements which are among those most commonly determined by activat,ion analysis. Known quantities of elements were irradiated in Ispra I reactor; the weights were then calculated from the measured activities and compared with the actual weights. I n order to have the maximum accuracy, the different quantities appearing in the activation formula were considered, and an attempt was made to obtain the best values by studying the literature data on nuclear constants. The disintegration rates have been determined by absolute gamma spectrometry using a geometrical arrange-
T
H E DIRECT METHOD of activation analysis, based on the determination of weights by means of the activation relationship has always been considered as a semiquantitative method.
1588
ANALYTICAL CHEMISTRY
ment which is generally employed for activation analysis by the relative method. The determination of the efficiency of the detector us. gamma ray energy was made by the absolute method proposed by Lazar, Davis, and Bell (16) after It was demonstrated that errors introduced by the presence of scattering material between source and detector in our geometrical conditions were negligible. EXPERIMENTAL
Principle of the Method. The disintegration rate, A , of a radioisotope formed by neutron activation is related to the weight, T I ’ , of the t’argetelement by means of the actitation formula
d
U B Q W ~-( I =
Jf
(1)
where u
0
= =
4 X
=
N
=
=
‘11 =
T t
= =
activation cross section natural isotopic abundance of the target nuclide neutron flux decay constant of the radioisotope formed Avogadro’s number at’omic weight of the target element irradiation time decay time
I n Equation 1, U , 8, 41;, X,and X can be obtained from the literature. T and t are experimental parameters which can be measured accurately without difficulty in most cases.
then calculated by using the literature data on gamma-ray abundances, a. A = -A O (3)
The neutron flux can be measured experimentally by irradiating the sample and a known quantity of a n element (neutron flux monitor) and using Equation 1 to calculate the neutron flux. The disintegration rates of both unknown sample and neutron flux monitor can be calculated from the experimental measurement of radioactivity if the measurement has been done by absolute methods ( 4 4 counting, P-7 coincidences, or y-ray spectrometry). Among these methods gamma-ray spectrometry is the most reasonable choice, as most radioactivity measurements in activation analysis by the relative method are made by this technique. The same equipment and basically the same measuring techniques can then be used for absolute measurements if the efficiency of the detector used us. gamma-ray energy has been accurately determined once for all.
a
The detector efficiency, E , may be determined us. gamma-ray energy by means of two different methods. (a) The photopeak counting rate of calibrated sources with a known gammaray emission rate is measured under the geometrical conditions used for analysis. The efficiency, E , is then calculated by means of Equation 2. This method has been used by several authors ( 7 , 8). It requires the availability of standardized sources, and its precision depends on the precision of calibration. (b) An absolute method has been used by several other authors such as Lazar, Davis, and Bell (26), Heath (IO),and Crouthamel (4). I t does not require any calibrated source and the experimental work to be done is rather simple. The efficiency is calculated through the relation E = etP (4) e l is the total absolute efficiency of the
T h e Gamma-Ray Spectrometer and Calibration. T h e gamma spec-
Its
trometer which is used in our laboratory for routine rclative analysis has been used for this study without a n y modifications. T h e detector is a Harshaw integral line assembly of a 3- x 3-inch diameter NaI(T1) crystal coupled to a 3-inch D u m o n t 6363 photomultiplier. It is placed in t h e center of a lead shield of 80 X 80 X 80 cm. internal dimensions and a thickness of 10 cm., with an inside lining of 1 mm. of cadmium and 0.25 mm. of copper to minimize the 0.072-m.e.v. x-ray peak produced by photoelectric absorption in the lead shield (IO). The radioactive sources (Figure 1) were generally counted as , solutions introduced in commercially available glass bottles of the type used for penicillin. These containers are filled for relative measurements to three different levels, A , B , and C, according to the volume of the solution to be measured. The determination of the detector efficiency has been made by using the lowest level, C, corresponding to 1 ml. of liquid put into the bottle. These sources may be considered as corresponding to a thin radioactive disk, whose center is on the central axis of the detector. This type of source is very practical for activation analysis as it is possible to count volumes as large as 25 ml. (level A ) . The bottles may be heated and centrifugated, and simple chemical operations can be made within them. Thus in eliminating the transfer of the liquid, the risks of loss of matter and activity involved are avoided. The disintegration rate of the radioisotope formed during irradiation can be deduced in gamma-ray spectrometry from the experimental measurement of the photopeak counting rate. The absolute emission rate of a gamma ray, Ao, is related to its photopeak counting rate, A,, through the relationship
where E is the efficiency of the detector for that particular gamma ray energy. From A. the disintegration rate, A , is
detector for that particular gamma-ray energy. It represents the fraction of the gamma rays emitted by the source that produces an interaction in the detector. This fraction can be calculated using both the absorption cross section of sodium iodide for gamma rays of a given energy and source detector geometry. Plottings of this quantity us. gamma-ray energy are known from literature for different source detector configurations (4, I O ) . P is the peak-to-total ratio or the fraction of the total number of interactions that produce a pulse within the photoelectric peak; this quantity can be experimentally determined (4, I O ) . This method is vary simple when the radioactive sources are measured under conditions of negligible scattering. Values of P reported in the literature can then be used and if the source detector geometry is known, the disintegration rate can be calculated. The comparison of the results obtained by this method and the method (a) showed agreement within k3Y0 (26). Cnfortunately, conditions of negli
Af-.j
1 '. .' ..
'
5
Figure 1. Source-detector geometry of the gamma-ray spectrometer. 1 : Source container, may b e filled to three levels (A,B,C). 2: Radioactive source. 3: Lucite beta absorber. 4: Detector mounting, 5: Nal(TI) detector. Thicknesses: d = 2 mm., e = 4 mm., f = 6 mm. VOL 36, NO. 8, JULY 1964
1589
cs 137
I 0.1
1 0.2
I ou3
I
0.4
1 0.5
1
096
spectrum produced by the introduction of maFigure 2. Deformation of the terials between source and detector 0 0
No aluminum absorbers(wrface density: 1.02 grarnr/sq. cm.) With aluminum disks (surface density: 2 . 3 7 grams/sq. cm.)
.Grornrlcmf
Figure 3. Total counting rates of different radioactive sources vs. surface density of materials interposed between Nal(TI) crystal and source. The values obtained without external absorbers, corresponding to the surface density of the detector mounting (1.02 gram/sq. cm.), have been arbitrarily taken as unity. The dotted line refers to the geometry of Figure 1 (surface density: 2.1 14 grams/sq. cm.)
1590
ANALYTICAL CHEMISTRY
photons which partially lose their energy in the material surrounding the crystal, and can still be detected. The peak-to-total ratio is then diminished and the efficiency of the detector, E , varies correspondingly, thus compensating, partially or totally, for the diminution of the photopeak counting rate (Equation 2). T o check the magnitude of this effect, the gamma spectra of different isotopes were measured with our detector without any external material surrounding a weightless source, and with increasing amounts of scattering materials (aluminium disks) between source and detector. The total counting rate and the peak-to-total ratios were then measured. Figures 3 and 4 show the results. -1lthough the dependence of the values of peak-to-total ratios on the surface density of the material interposed between source and detector is rather pronounced, the total counting rate is fairly constant up to surface densities of the order of 2-3 grams per sq. em. The total number of detected photons for low surface densities is constant because the photons which are scattered within the absorber do not lose sufficient energy to be finally absorbed by photoelectric effect before reaching the detector. For higher surface densities the loss of energy can be sufficient to terminate the process with a photoelectric absorption outside the detector. The importance of the loss of photons by simple scattering interactions is reduced by the compensation which occurs between photons which were originally emitted within the solid angle source-detector and are scattered out of that angle by the interposed material, and photons which were originally emitted out of that solid angle source-detector but are scattered in that angle by the interposed material. Equation 4 can be used to calculate the photopeak efficiency of the detector without introducing any correction coefficient provided the peak-to-total ratios are determined experimentally for the geometry used. Figure 5 shows the peak-to-total ratios obtained in our geometrical arrangement us, gamma-ray energy. ~
gible scattering can rarely be obtained. NaI(T1) crystal is surrounded, in the commercially available units, by amounts of material (reflector, antishock layers, and mounting) which can attain a surface density of 1 gram per sq. cm., and additional material is introduced both by the source mounting and by a beta-ray absorber. I n our geometry the surface density of the material interposed between source and crystal is 2.1 grams per sq. cm. The presence of this material introduces a deformation of the gamma spectrum which is shown in Figure 2, for the CsI3' radioisotope. The photopeak counting rate is diminished and a correction factor must be applied to the experimental photopeak counting rate, if the literature peak-to-total ratios are used in the calculation (10). Such a correction factor cannot be obtained easily in most cases. Figure 2 shows clearly that a diminution of the photopeak counting rate is accompanied by an increase of the Compton continuum, caused by
P[
I 6.7
-
06
-
05
-
I
I
1
I
I
I
0.4 r
I I I
0
I
2
Grams/
3
4
cd
Figure 4. Peak-to-total ratios vs. surface density of materials interposed between source and crystal L% Counting geometry of Figure 1 (surface den. rity: 2.1 14 grams/sq. Em.)
with the calibrated sources in (a). The difference between the gamma ray emission rates obtained by the two methods is of the same order of magnitude of that found by Lazar, Davis, and Bell (16) under conditions of negligible scattering. The validity of this method is limited to surface densities lower t b n 2-3 grams per sq. cm. of scattering material between source and detector. Higher surface densities are used in practice only in exceptional cases.
43
Neutron
P.?
0.1 t 0.1
05
I
Figure 5. Peak-to-total gamma-ray energy
'
3
2
ratio
MeV
vs.
-Geometry used in the present work
---For point sources in conditions of negligible scattering
(IO),source
a t 3 cm. from the detector
The data reported by Heath (10) for a detector of identical dimensions, but for point sources under conditions of negligible scattering outside the crystal, are reported for comparison. e t is obtained from the literature. The sharp dependence of E L upon the distance source-detector in the high geometry condition makes it necessary to know accurately the distance between the upper face of the NaI(T1) crystal and the upper face of the detector housing. This distance has been measured in the present work by x-ray radiography. Most literature data on absolute efficiencv ( E , ) are referred to Doint sources." Vegors, Marsden, and Heath (IS)calculated the relationship for disk sources placed a t a certain distance from the detector. The d a t a calculated for disk sources of a diameter one third that of the crystal which corresponds to our experimental conditions show that for source detector distances equal to 1 and 3 cm., the ratio of the total absolute efficiencies for point and disk sources is about 1.05 between 0.3 and 3.0 m.e.v. This correction was applied to the total absolute efficiency e L (Figure 6 ) . The values of the correction factors were checked measuring experimentally the ratio between photopeak counting rates for disks and point sources. The agreement between calculated and experimental results was found to be within the experimental errors. The accuracy of the calibration obtained with this method has been checked a t a few points with the experimental method (aj. Sources of AuIg8, NaZ4, CoeO prepared from solutions of known disintegration rate were measured and the detection efficiency was calculated. In Figure 7 the curve corresponds to values obtained from the method (b) using for the literature data corrected for our counting geometry and the experimental peak-to-total ratio. The points refer to the measurements made
Flux
Determination.
Since reactor neutrons cover a rather large energy spectrum and activation cross sections depend on neutron energy, E , the product $ a of Equation 1, often referred to as the equilibrium reaction rate R , is more rigorously expressed by:
R
=
lm$(E)o(E)dE
(5)
This integral cannot be easily determined in most cases. However, if the irradiation position is well thermalized and, as in most (n,y ) reactions, the activation cross section decays rapidly with increasing neutron energy, the reaction rate may be simply obtained as the product of the effective
1
I
1
I
0.05 0,I
0.5
2
I
MeV
3
evaluated by comparing the C060 activity of the monitor with a C060 source of known disintegration rate. The epithermal flux in the irradiation facility used is about 1% of the total. Using a thermal neutron cross section of 36.4 barns and a resonance integral of 57.1 barns, the value determined by Eastwood (6) and employed previously for similar calculations, an effective cross section of 36.6 barns waq obtained. This value has been introduced in Equation 1 to calculate the neutron flux. Procedure. Known weights of 13 elements (Johnson-Matthey Specpure Reagents) as solid compounds or as dilute solutions were sealed in silica vials and irradiated together with a flux monitor. T h e irradiations were performed in the Ispra I reactor in well thermalized positions. T h e irradiation time varied from a few minutes to several days, depending either on the nature or on the concentration of the samples. The thermal neutron flux varied between 7 x 10'2 and 2 X l O I 3 neutrons per square centimeter per second. The photopeak counting rate of the radioisotopes formed was measured after dilution of the sample and the disintegration rate was calculated. The neutron flux was then calculated from the activity of the neutron flux monitor. Equation 1 was used to calculate the weight of the irradiated elements: this was finally compared with the actual weight. The procedure was repeated many times for each element with changes in some of the experimental parameters such as weight of sample, concentration of solutions, irradiation, and decay times.
Figure 6. Total absolute efficiency of the detector vs. gamma-ray energy
(E,)
-Disk
sources
(23)
- - -Point sources ( 1 0). activation cross section thermal neutron flux (40):
R
=
(8)
and the
RESULTS AND DISCUSSION
The results obtained are reported in Table I as the mean of the ratios of the determined weights, Mid, to actual weights of the elements that were irradiated, JV,. The standard deviations for the mean values of the measure-
(6)
840
This method was introduced by Wescott, Walker, and Alexander (24)who assumed that the reactor neutron spectrum consists of a Maxwellian distribution of thermal energies and a d E / E epithermal distribution with a lower energy limit overlapping the Maxwellian part of the spectrum. The effective cross section ( 8 ) for the reactor neutrons may be calculated from the thermal neutron activation cross section, the resonance integral for the radioisotope formed, the cadmium ratio measured in the irradiation position. Once the effective cross section is known for a certain reaction, the neutron flux may be calculated by measuring the reaction rate and a m l v" ing Equaiion 6. Cobalt in the form of a 1% allov of cobalt in aluminum is used formeas&ing the neutron flux. The reaction rate is I
€ 7 t
Figure 7. Detector gamma-ray energy
efficiency
vs.
.
--
Calibratlon curve calculated with the method ( b ) Experimental points obtained with method (a)
VOL. 36, NO. 8, JULY 1964
1591
L
I
Mn56
A
bCi.78
A
1110m
I
0
'+Ma24
1
1
05
1.5
2
3 Me
2.5
Figure 8. Results obtained with the direct method vs. energy of the gamma rays used for the determination
ments and the literature data used in the calculations are also reported. Figure 8 shows the results as a function of the gamma-ray energy of the photopeak measured. This method of presenting the results is particularly useful in visualizing eventual systematic variations arising from errors in the calibration of the detect'or, measurement of the neutron flux, etc. The data reported show that' the deviation.< of the determined values are never greater than 20%, while for 11 elements out of the 13 analyzed they are lower then 10%. Khile the results
Table I.
Determination of Weights of 13 Elements by Calculation from Activities and Neutron Fluxes Measured after Irradiation. Nuclear Constants Taken from literature
U
Element Arsenic Barium Chlorine
are satisfactory, there are some cases of discrepancies that need interpretation. By considering the different quantities that could affect the results, some explanation mas obtained. Determination of t h e Neutron Flux. A systematic error in the determination of neutron flux would displace all the points along the y axis on Figure 8. No error in this kind seems evident, as the mean of all the values obtained is very close to one (about 1.015), the points being equally scattered on both sides of the horizontal line y = 1.
Isotope 'e As76 1. O O BaI3Q 0.7166 c 1 3 8 0.246
barn 4.2 0.5 0.39 15.9 36.6
Calculated disintegr. rate 2 02 x 107 9 46 x 105 9 77 x 105 4 76 X lo6 2 25 X lo8
Chromium Cobalt
Cr5l COB0
0.0431 1,oo
Copper Gallium
Cua4 Ga72
0.6909 0.398
Hafnium
Hf181
Iron
Fe59
0.3544 0,00335
10.0 1.01
7 17 X IOE 2 19 x 104
Manganese Scandium
Mn56
13.4 22.3
8 79 X lo7
Sc46
1 . 00 1.00
Silver
A4g110n 0.4865
2.8
4 56 X lo6
4.51 5.0
1 77 i 03
x 107 x 107
1 79 x 108
Gamma Gamma ray ray energy, abunm.e.v. dance 0.56 0.41 0.16 0.23 1 64 0.36 0 47 2.15 0 32 0 09 1 00 1 17 1 33 1 00 0 51 0 38 0 83! 0 89j O 84 0 48 0 84 1 10 0 57 1 29 0 43 0 85 0 978 0 89 1 00 1 12 1 00 0 65'
4
0 81
Sodium a
Sa24
1.00
0.525
8 25 x 106
:I::
1 37
275
C.p.m. per pg. at saturation for a 10'3 n/cm.2 8ec. neutron flux.
1592
Measurement of the Disintegration OF THE DETECRate. CALIBRATIOX TOR. The agreement between the ttvo independent methods of calibrating the detector indicates t h a t the error introduced in the determination of the absolute gamma-ray counting rate is negligible. As a further check, note that, the points on Figure 8 are uniformly scattered on the y axis, and show no evident systematic variat,ion of the distance from the y = l line with energy. EVALUATIOKO F THE PHOTOPE.4X AREA. .1 correct evaluation of a photopeak area is often not a simple task, particularly when the photopeak is superimposed to a high continuum component (the Compton component of a gamma ray of higher energy, for example) or when another peak is overlapping. In the cases in which the peak was sufficiently defined to justify a simplified procedure, the method shown in Figure 9, was used to inscribe the gamma peak in a triangle. The error then involved in determining the area of the photopeak Gaussian from that of the triangle \ T a j found to be negligible. In the case of overlapping peaks a subtraction procedure of the type used by Heath ( 9 ) was adopted. I t consists of determining the shape of the speclrum of a single gamma ray a t any wanted energy by interpolation between different spectra, which were obtained experimentally from isotopes emitting a single gamma ray. This procedure was used for example in the case of Co60 (overlapping
ANALYTICAL CHEMISTRY
E 0.094 0.22 0.0351 0,0275 0.152 0,0485 0.0435 0.105 0,064 0.112 0.0515 0.0445 0,064 0.063 0.0505 0,083
4.67 X lo5
0 935
6 1
3
0.0635
2.92 x 105
0 938
3 4
3
0.041 0.022
3 . 3 8 X lo5 1.81 x 105
0 968 0 94
1 3 1 3
4 4
w d -
wt
1 09
0 922
1 015 0 965 1 14 1 0% 0 975 0 922 0 952 0 965 1Oi
1 1 1 1
055
005 175 165
Std. dev.,
Number
Calculated counting rate" 7 8 X lo5 4 77 x 104 i 24 x 104 1 265 x 104 6 51 X l o 4 1 09 x 107 9 8 X lo6 7.06 x 105 5.54 x 105 6.75 X lo5 6 42 X l o 2 4.18 X lo2 5.51 x 106 1 . 1 3 x 107 9 . 0 5 x 106
7c
1 75
1 1 1 5 1
27 7 5 4 3 2 04 1 3 5 8 8 7 2 5 4 9 2 8 1 5 1 1
of
detns. 3 7 4 4 5 7 7 6
4 3 7
5 5 3 3
235
1 00 O1 100
of the peaks at 1.17 and 1.33m.e.v.) and C1J8 (overlapping of the 1.64-m.e.v. peak with the single escape peak of the 2.15m.e.v. gamma ray). The evaluation of the photopeak surfaces may be one of the reasons for the lack of precision and accuracy of many results. This kind of error can also affect the determinations made with the relative method, if the gamma spectra of the unknown and of the standard are not identical (for example, if the sample contains several gammaemitting isotopes, while only one isotope is present in the standard). The impurities present in the sample can also produce an error in the evaluation of the photopeak areas, if they have nearly the same gamma-ray energies as the isotope to be measured. This source of error has been found during the determination of iron by means of Fe5g. The results can be affected by the presence of cobalt, which upon irradiation gives Co60, an isotope with gamma peaks of nearly the same energies as those of Fe5g. Therefore the determination of iron has been made by using pure compounds from Johnson, Matthey & Co., Ltd., and the absence of cobalt was controlled by measuring the coincidence peak of Co60 at 2.50 m.e.v. EFFECTOF COINCIDENCES BETWEEN DIFFERENTGAMMARAYS. A certain number of the isotopes studied emit two gamma rays in cascade. These gamma rays can penetrate simultaneously into the detector and produce the formation of a coincidence peak. The photopeak areas evaluated for the single photopeaks are then too small, as a certain number of gamma rays that have been produced by the isotope are counted in the region between the coincidence peak and the measured A correction for this photopeak. effect has been applied by using a method described by Heath (10) and Crouthamel (4). If the radioisotope studied emits a cascade of two gamma rays (1 and 2), the area under the sum-peak, A,, is given by A,
=
AoE1Ezw
(7)
while that under one of the main peaks, for instance 1, is:
Eliminating the angular correlation factor, w , it is possible to derive from Equations 7 and 8 a corrected v a u e for the photopeak area, A1eDrl :
The correction is made after the experimental determination of the sum-peak area. I t has been applied for several
an error on their relative abund:ince produces a difference in the weights determined by the direct method, if one or the other gamma ray is used. It may be seen from Figure 7 that the points referring to one element are a t about the same distance from the y = 1 axis, thus demonstrating that a t least the ratio of the gamma-ray abundances was correct. A better knowledge of the decay schemes of the isotopes used for activation analysis should_ improve the accuracy of the determinations to a great extent. Often literature data on abundances are so largely discrepant, that it is not always reasonable t o take the media of the different determinations, but it is necessary to decide which of the different values should be used. Figure 9. Evaluation of the photopeak Neutron Activation Cross Sections. area Literature d a t a on Table I are t'aken from t h e compilations made by Hughes and Harvey (12). Only for isotopes: Co60, S C ~ CIB, ~ , and ?;az4. C133, a value determined by Durham For other isotopes it has not been used, and Girardi (6) has been used. For as the decay schemes are too complex. Co60 the value of the effective cross The coincidence effect could be section previously evaluated for the flux greately diminished by placing the determinations was used. source a t a greater distance from the Inaccurate literature data on cross detector. However, this would cause a sections would introduce a systematic corresponding decrease in the sensitivity error. For isotopes emitting several of the analysis, which is often undegamma rays, the corresponding points sirable. LITERATUREDATA ON GAMMA-RAY on Figure 7 would be displaced the same distance from the horizontal line, y = 1. ABUNDANCES. There are many cases of This effect is observed for several large discrepancies (among different isotopes, for example Fe5g, .ig*lo", authors) concerning the ganma-ray Xaz4. For chlorine, Cia, the weights abundances, and it is often difficult to determined by means of the cross choose the best known value for this section of 0.56 barn, reported in the quantity. The abundances that we compilations, gave an error of 30%. have used were taken from reference F y introducing the value of 0.39 barn (20). of (6) for this quantity the error was In case of discrepancies one would reduced to 3.5%. obviously be tempted to use the value Cross sections are rarely known with that minimizes the error in Table I. a precision better than 10% ( I d , 13). This has been done in only two cases The error on this quantity influences (C1B and Ba13g) in which the choice the accuracy of the determinations by seemed reasonable. the absolute method (18). Ai certain A research of literature data on the error may also be produced by the decay scheme of CIB has shown that assumption that all the neutrons of the for the 1.64-m.e.v. gamma ray the reactor are thermal, which is the only abundance of 3101,, determined by justification for using thermal activaLanger (15) and generally reported in tion cross sections. In practice there is compilations, corresponds to a ratio of an epithermal component in the neutron intensities of the 1.64 and 2.15-m.e.v. flux that can contribute a t a certain gamma rays smaller than that given extent to the neutron activation. .in by four other references (5, 11, 14, 21). improvement could be made by deterWe have preferred to use the decay mining an effective cross section for all scheme from reference (11) which the reactions used in analysis, as for the seems more reliable and fits our experireaction used for monitoring the neutron mental results. flux. This procedure would certainly For 13a13gthe value of gamma-ray be more precise, but it would be of little abundance given in the compilation general interest, because it is valid for (20) is quite different from most deteronly one neutron spectrum. If the minations. 1t7e have adopted a value epithermal activation were imimrtant. of 23y0 which corresponds to the then for elements with rwonanrr intedeterminations of Macklin, Lazar, and grals greater than that of the ncutron Lyon (17) and those of Bunker and flux monitor (Co), t,he weighty dPterStarner ( 3 ) . mined would be greater than the For isotopes decaying with the emission of more than one gamma ray, irradiated weights. No systematic VOL. 36, NO. 8 , JULY 1964
a
1593
trend of this sort can be seen in Figure 7. In any case the effect should be rather small, as the epithermal flux in the irradiation positions used is not greater than 1% of the thermal flux. Natural Isotopic Abundances. T h e numerical values reported in Table I are taken from a compilation done by Bainbridge and Nier ( I ) . The natural isotopic abundances are thought to be a rather minor source of error, as this quantity is known with a good precision. Decay Constant. If the decay cons t a n t is not precisely known, a systematic error could be introduced for short-lived radioisotopes, as measurements are always made some time after the end of irradiation. An increase in random error should be observed, if the different measurements are made after different decay times. As random errors observed for shortlived radioisotopes are not especially great, this effect should not play a n important part. ACKNOWLEDGMENT
The suggestions and criticisms of G. B. Bertolini are gratefully acknowledged. Thanks are also extended to R. Fantechi
for the standardization of the radioactive sources used for calibrating the gamma-ray spectrometer. LITERATURE CITED
(1) Bainbridge, K. T., h’ier, A. O., “Rela-
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