Radioanalytical Applications of Gamma-Gamma Coincidence Techniques with Lithium-Drifted Germanium Detectors John A. Cooper Radiological Sciences Department, Battelle Memorial Institute, Pacific Northwest Laboratories, Richland, Wash. 99352 The radioanalytical applications of gamma-gamma coincidence techniques with Ge(Li) detectors have been examined with and without anticoincidence shielding. The Compton interference was reduced about 20 times more with the anticoincidence shield than without it when the interference was due to a radionuclide such as 6oCowhich emits coincident gamma rays but showed little difference when the interference was a single gamma-ray emitting radionuclide such as 54Mn. Background reductions of about 4 orders of magnitude and sensitivity improvements of about a factor of 5 were shown to be possible for radionuclides such as which emit low energy coincident gamma rays. The application of this technique to the general problem of radioanalytical chemistry is discussed.
LITHIUM-DRIFTED germanium, Ge(Li), gamma-ray detectors have been used for gamma-gamma coincidence studies of nuclear decay schemes for several years ( I , 2). However, the problems and requirements associated with their application to radioanalytical problems are distinctly different from those required for decay scheme studies. Competitive techniques for obtaining gamma-gamma coincidence relationships are not available to the nuclear spectroscopist and there is little reason for him to repeat such an experiment once the relationship has been determined. On the other hand, the analytical radiochemist has competitive alternatives, such as single Ge(Li) detectors and NaI(T1) multidimensional gamma-ray spectrometers (3,4), and must actually improve the analytical sensitivity per unit time. The parameters which are most significant in determining the analytical application of the gamma-gamma coincidence technique are the background reduction factors and the coincidence efficiency. The coincidence efficiency can be easily calculated from existing single detector efficiencies. In the past, it was obvious from the low single detector efficiencies that this technique was impractical from the analytical point of view for reasonable background reduction factors. However, recent advances in Ge(Li) detector fabrication have provided detectors with absolute peak efficiencies greater than 25% at 122 keV which should be more than sufficient for some gamma-gamma coincidence applications. Although background reduction factors of about two orders of magnitude have been obtained with small detectors ( I , 2), there is no indication of the magnitude of the background reduction factors to be expected for large detectors under various conditions and for different interfering radionuclides. This paper presents the results of an investigation into the analytical applications of gamma-gamma coincidence tech-
niques using two high efficiency Ge(Li) detectors with and without anticoincidence shielding. Background reduction factors are determined for various conditions and interfering radionuclides and discussed relative to possible analytical applications. INSTRUMENTATION The electronics block diagram of the spectrometer used to study the coincidence spectra is shown in Figure 1 (5). It consists of two 70 cm3 closed-ended coaxial Ge(Li) detectors which face each other and are located at the center of two 30-inch diameter by 15-inch thick NE 110 plastic phosphor anticoincidence shields. The efficiency of the Ge(Li) detectors for 1332 keV gamma rays is 12% relative to a 3-inch diameter by 3-inch thick NaI(T1) detector as measured at 25 cm. Their maximum absolute efficiencies for 122 keV gamma rays are 12% and 14%. The coincidence electronics are a modification of the standard “fast-slow” coincidence circuitry (6, 7). Four coincidence units are used; one (universal) to determine the “fast” coincidence events between the two Ge(Li) detectors, two (Time-to-Amplitude Converter) to determine the “fast” coincidence events between each of the Ge(Li) detectors and the plastic phosphor shield, and one (universal) “slow” coincidence unit to select those “fast” coincidence events which are also in coincidence with a selected energy pulse from one of the Ge(Li) detectors. The “fast” coincidence resolving times were set at 300 nanoseconds (full width at 0.005 maximum peak height) and were mainly limited by the high counting rate in the anticoincidence shield and the required large energy range. The slow coincidence resolving time was set at 3 microseconds and the overall true to chance ratio was greater than 1OOO:l. RESULTS AND DISCUSSION The factors which are most important in determining the applicability of this technique to radioanalytical problems are the background reduction factors, the coincidence efficiency for the radionuclide of interest, its half life, and competitive techniques. Contrary to the opinion of Pagden and Sutherland (8), the resolving capability of Ge(Li) coincidence spectrometers has little significance in determining the analytical application of Ge(Li) detectors to gammagamma coincidence problems. Although the improvement in resolution is important, it is not as significant as it is in the case of NaI(T1) detectors used for multidimensional gamma(5) J. A. Cooper and R. W. Perkins, Pacific Northwest Laboratory
( 1 ) G. T. Ewan, R. L. Graham, and J. K. MacKensie, ZEEE Trans. Nucl. Sci., 10th Scintillation Semiconductor Counter Symp. 13, 297 (1966). (2) J. A. Cooper, J. M. Hollander, and J. 0. Rasmussen, Nucl.
Phys., A109, 603 (1967). (3) R. W. Perkins, Nucl. Imtrurn. Methods, 33, 71 (1965). (4) N. A. Wogman, D. E. Robertson, and R. W. Perkins, ibid., 50, l(1967).
838
ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
Report BNWL-SA-4021 (December, 1970). (6) A. H. Wapstra in “Alpha-, Beta-, and Gamma-Ray Spectroscopy,” Kai Siegbahn, Ed., North-Holland Publishing Co., Amsterdam, 1965, p 539. (7) S. De Benedetti and R. W. Findley in “Handbuch der Physik,” 45, Springer-Verlag, Berlin, 1958, p 222. (8) I. M. H. Pagden and J. C. Sutherland, ANAL.CHEM., 42, 383 (1970).
-
CANBERRA 145 DELAY
CANBERRA 14169 - A M P L I F I ER
T
ORTEC 4 5 4 ,TIMING FILTER A M P L I F 1 ER
*
ORTEC 417 FAST DISCRIMINATOR
4
-
CANBERRA 1408C
START ORTEC 4 3 7 T I M E T O A M P L I T U D E --* CONVERTER ;TOP
~
,
UCLEAR ENTERPRISES 10 PLASTIC PHOSPHOR
A
s -b ~
CANBERRA 1465A ~s u M5 - I N V E R T AMP L IFlER
1 UNIVERSAL
1
ANTI *COIN. nRTEC 418
DELAY
ORTEC 427 DELAY CANBERRA 1455 LOGIC SHAPER
G e i L i i DETECTORS COlNC IDENCE NUCLEAR iTnP
PREAMPLIFIER ORTEC 4 5 4 T I M I N G FILTER A M P L IF1 ER CANBERRA 14168
ORTEC 417
-HzGz+
T I M I NI RG A S C1 4A3 5
D I S C R I M IN A T O R
-
START
P LINEAR SIGNAL
Figure 1. Electronic block diagram of the circuitry used in the gamma-gamma coincidence studies ray spectrometers (3, 4 ) because the normal resolution of the Ge(Li) detector is sufficient to resolve the majority of peaks in analytical problems. By the time such restrictions as half life and method of production are placed on the sample, there are few unresolved peaks and by far the major interference is Compton events associated with higher energy gamma rays. In addition, radionuclides which might show improved sensitivities with gamma-gamma coincidence techniques must have at least two major peaks and it is unlikely that both of these would be unresolved. The main obji:ctive in applying the coincidence technique to Ge(Li) detectors is to improve the analytical sensitivity by reducing the Compton interference from higher energy gamma rays. It is essential to maximize the efficiency in gamma-gamma coincidence measurements since the coincidence efficiency depends on the product of the single detector efficiencies (6, 7). The most effective method of obtaining a high absolute efficiency in a coincidence experiment is to arrange the two Ge(Li) detectors facing each other with the source between them as illustrated in Figures 1 and 2A. However, with this arrangement, there is a relatively high probability of obtaining an unwanted but true coincidence from a gamma ray which scatters from one detector back through about 180' to the other detector where it is noted as a coincidence event. This type of spectral interference is illustrated in Figure 3 which shows the 136 keV coincidence gated spectrum of a mixture of 133Baand 75Se. The backscatter peaks at about 140, 170, and 215 keV could interfer with possible low energy coincident gamma rays. This backscatter interference is actually the result of a
GeiLi) LEAD COLLIMATOR
J
4SOURCE
A
B
INCIDENCE IELD
C
U
Figure 2. Schematic representation of the origin of interferences in gamma-gamma coincidence studies and their reduction considerable range of large angle scattering and can include events which have scattered through angles from about 120' to 180' because of the close detector arrangement. It can be greatly reduced though by using a thin Pb collimator (0.125 to 0.25 inch thick) as shown in Figure 2B. In this case, the source is located at the center of the collimator and the low energy backscattered gamma rays are absorbed ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
839
€1
COUNTING INTERVAL: 133Ba 81
1
NORMAL SPECTRUM
"Se
2Bo r 133n32B a ?
171
TRUE TO R A N D O M R A T I O : BACKSCATTER COLLIMATOR:
r 1 3338B2a
:
:
7 5 ~ e r401
133Ba
7 437
( 8 1 ' t 356)
0
I 230
I
I
I
I
400
600
800
1000
~ ~ c.> ~ ,~ ..~. ..*. .~ ; '@%~'~-*.>*.*~ L.... -a' -.L..i.rb. -... **. C , . . *e:;
.e:
-0.
e . * . + . * 2.
0.
1
0
0..
..C.
0 . .
0.0 A V E R A G E B A C K G R O U N D C O U N T S
*
I
-
e.
. . I . .
I
I
200
o
*a..
C . * L
loo
--
400
I
I
600
800
I
1000
ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
843
Table I. Radionuclides Which Might Have Improved Sensitivities with Gamma-Gamma Coincidence Techniques Using Ge(Li) Detectors Neutron activated 48Sc 151Eu 60Co ls3Sm l60Tb 64Cua 169yb5 75Sea s2Brb 171Era llOmAgh
175yba
lZ4Sb
l8lHfa lS2Ta
l3IBa
Fission product 77Ge sZBrb
Environmental 46Sc 'To
92Y 9
lOSAgb
96Nbb
lz4Sb 134Cs 40Ba
3Y
lo6Ru,l66Rh
130Ib 136Csb
1lOAgb
1 4 0 h
*OBa lKzEu 40La 192Ira 40La 207Bi 162mE~ 23gNp ls3Sm a Likely to have significant improvements in sensitivity. Multiple gamma-ray coincidences. '34Cs
187WO
about two orders of magnitude less than the normal efficiency which would require at least a lo4 reduction in the background interference to obtain an improvement in sensitivity. Background reductions greater than 2 X l o 4 were obtained which illustrates the potential for obtaining improved sensitivities even at these energies. (The spectral response on the low energy side of the 1332 keV peak are mainly Compton events and should not be considered an interference.) This also suggests even greater improvements in sensitivities at intermediate energies where higher peak efficiencies will guarantee even greater improvements in sensitivities. Both Galloway (9) and Cooper (10) have shown the necessity of maintaining a high peak efficiency while reducing Compton interferences since the sensitivity depends on the first power of the peak efficiency but only the square root of the background interference. For example, if the peak efficiency is reduced by 100, the background interference must be reduced by more than l o 4 before any improvement in sensitivity can be obtained. Thus, it will be difficult to improve the sensitivity of any radionuclide whose normal efficiency is reduced by more than two orders of magnitude since the maximum background reduction factors were about lo4in the examples shown. The half life of the radionuclide must also be considered when searching for possible applications. For example, it will be difficult to improve the sensitivity of radionuclides with half lives of about one hour or less because data accumulation rates greater than about 105 counts per second (limit of the present technology) would be required to accumulate sufficient counts in the coincidence spectrum to observe a peak which would otherwise be obscured by the Compton interference in the normal spectrum. Table I lists those radionuclides of interest to the analytical radiochemist which might have improved sensitivities with gamma-gamma coincidence techniques using Ge(Li) detectors. Their selection was based on half life, detection efficiency of the coincident gamma rays, and an assumed background reduction factor of about lo4. It should be possible to obtain significant improvements in sensitivity for those radionuclides marked with an italic a while those marked with a b have coincidence cascades which involve more than two major gamma rays and may or may
(10) J. A. Cooper, Nucl. Instrum. Methods, 82,273 (1970). 844
ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
not have improved sensitivities depending on the particular type of interfering radionuclide. Activation analysis has the largest number of radionuclides for which this technique might be applicable while the environmental radionuclides show the least number and none of these appear very promising, particularly when one considers that these radionuclides are usually in low concentration in the environment. Although the measurement of 6OCo with this technique may show promise of improved sensitivity (Figure 9), it is not too likely to be of much value. Its long half life and high gamma-ray energy eliminate most of the interfering radionuclides which make it relatively easy to measure in most samples with normal Ge(Li) detectors. In addition, NaI(T1) multidimensional spectrometers ( 3 , 4) are usually more than competitive for the measurement of this radionuclide and applicable to much lower intensity samples. Scandium-46, on the other hand has higher efficiency for its lower energy gamma rays and is more likely to have an improved sensitivity. In addition, its peaks are sometimes interfered by other radionuclides such as 6oCo and 65Zn. However, NaI(T1) multidimensional spectrometers usually have superior sensitivity. Copper-64 is often the only short-lived positron-emitting radionuclide in neutron activated material and although gamma rays with energies greater than 1022 keV may interfere, there are occasions when this type of interference is not significant. In this case, there is a high probability of obtaining a significant increase in the sensitivity for measuring e4Cu with gamma-gamma coincidence techniques because the two 511 keV annihilation photons are emitted in opposite directions. If one detector observes a 511 keV photon, the probability of the other detector observing the coincident 511 keV photon is determined essentially by the intrinsic efficiency of that detector for detecting 511 keV gamma rays and not its absolute efficiency. Since the 511 keV intrinsic efficiency of large Ge(Li) detectors can be greater than lo%, the possible 104 reduction in background is two orders of magnitude greater than the 100-fold reduction required for improved sensitivity and should provide a significant increase sensitivity. in the 64Cu Radionuclides such as szBr which emit several coincident gamma rays in a cascade may not have improved sensitivities with this technique because of the high probability of the anticoincidence shield detecting one of the coincident gamma rays and cancelling the Ge(Li) coincidence event. However, this may not be significant if the Ge(Li) detectors and the collimator shield the anticoincidence shield from the primary source of gamma rays, or if the interference is mainly a noncoincident gamma-ray emitting radionuclide such as 4Mn since the shield could then be omitted without seriously affecting the background reduction. In addition, the COincidence efficiencycan be increased by gating on all the peaks in cascade, For example, the coincidence efficiency for measuring such radionuclides as 1301 which emits 4 gamma rays in its cascade should approach 10% of its normal efficiency by using multiple gating windows and in some cases should have a high probability of having improved sensitivities. The radionuclides such as 75Se, 169Yb, l71Er, etc., which are marked with an a have a high probability of having significantly improved sensitivities with this technique and are without strong competition from standard NaI(T1) multidimensional spectrometers because of their low energy gamma rays. Some of the rare earths are of particular interest to those studying the chemical composition of geological,
meterioritic, and lunar materials by neutron activation because of the large Compton interferences by other radionuclides and the complexity of the low energy portion of the gamma-ray spectrum. Because of the high counting rate requirement, this technique is generally most applicable to small relatively intense sources. However, this usually isn’t too restrictive in the neutron activation and fission product applications. As the size and efficiency of the Ge(Li) detectors increase, greater improvements in sensitivities will be obtained and the technique will be applicable to larger samples and higher energy gamma rays.
ACKNOWLEDGMENT
The author wishes to acknowledge the counting and electronic assistance of R. M. Campbell, R. T. Brodazynski, and J. R. Kosorok, sample preparation of J. H. Reeves and D. R. Edwards, and the many helpful comments of L. A. Rancitelli, W. A. Haller, C. E. Jenkins, R. W. Perkins, and C. W. Thomas. RECEIVED for review December 30,1970. Accepted February 15, 1971. This paper is based on work performed under United States Atomic Energy Commission Contract AT(45-1)1830.
Computerized Learning Machines Applied to Chemical Problems Optimization of a Linear Pattern Classifier by the Addition of a “Width” Parameter L. E. Wangen, N. M. Frew, and T. L. Isenhour Department of Chemistry, Unicersity of North Carolina, Chapel Hill, N . C. 27514 The binary linear pattern classifier has been improved by the addition of a “width” parameter which defines a null region in the pattern space. In the case of separable pattern sets, the width is maximized in an attempt to produce the maximum prediction for unknown patterns. For inseparable cases with slightly overlapping distributions, the null region contains the subset of patterns which prevent linear separation, thereby making the remaining patterns linearly separable. The method is illustrated with computer generated 2-dimensional Gaussian data and its utility for classifying spectrometric patterns is demonstrated with examples taken from mass spectrometry.
PREVIOUS WORK has shown the usefulness of Computerized Learning Machines for the interpretation of spectrometric data (1-6). In such an approach, the spectra are represented as points in a d 1-dimensional pattern space which are to be separated by d-dimensional planes into binary subsets according to various chemical and/or structural criteria. The linear pattern classifier is developed from a training set of patterns by an error-forcing iterative process, employing negative feedback, which is designed to maximize learning rate. The sole criterion for complete convergence is correct classification of all patterns in the training set. Upon cessation of training, the resulting linear pattern classifier (denoted by a weight vector W) can be tested according to its ability to correctly classify “unknown” spectra (predictive ability) not contained in the training set. Although the binary linear pattern classifier is easily implemented and has yielded useful results with chemical data, it suffers from certain limitations.
+
(1) P. C. Jurs, B. R. Kowalski, and T. L. Isenhour, ANAL.CHEM., 41, 21 (1969). (2) P. C. Jurs, B. R. Kowalski, T. L. Isenhour, and C. N. Reilley, ibid., p 690. (3) Zbid., p 1949. (4) Zbid., 42, 1387 (1970). (5) B. R. Kowalski, P. C. Jurs, T. L. Isenhour, and C. N. Reilley, ibid., p 1945. (6) L. E. Wangen and T. L. Isenhour, ibid., 42,737 (1970).
(1) Linearly inseparable sets may not be completely classified, In the case of nonconvergence after a maximum number of feedbacks for a pair of categories, it is assumed that the categories are for practical purposes not linearly separable. In these instances the category distributions may be overlapping and, because the convergence criterion requires correct classification of all training patterns, W will oscillate indefinitely until training is arbitrarily discontinued. AS a result of this oscillation, the utility and reproducibility of W for prediction and recognition (as measured by ability to classify training patterns) may be greatly diminished. Hence it would be desirable as a first approach to assume that the distributions are only slightly overlapping. Consequently omission of the samples in the overlapping region would allow complete linear separation of the remaining samples. (2) The successfully trained W is not guaranteed to be an optimum classifier. Due to the relatively simple yes/no convergence criterion, there is no guarantee that the decision surface will optimally separate the two pattern distributions. Consequently, there may be considerable variation in predictive ability for different classifiers developed with the same training set. (3) The linear pattern classifier gives no dependable method of assigning a confidence value to each classification. A confidence figure is especially desirable where binary decisions are to be used in a “branching tree” fashion. In such a system the propagation of a single incorrect decision may have deleterious effects unless the user has some indication that the result is in doubt. Watanabe et al. used “dead zone maximization” to maximize separation of an artificially generated character set (7). The purpose of this work is to demonstrate how the simple addition of such a “width” to the decision surface can minimize or eliminate the above limitations while still retaining (7) S. Watanabe, P. F. Lambert, C. A. Kulikowski, J. A. Buxton,
and R . Walker, “Computer and Information Sciences-11,” J. T. Tou, Ed., Academic Press, New York, N. Y . , 1967, P 107~. ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
845
