Author Institution: University of DaytonThe intrinsic efficiency of a Ge(Li) detector was determined for gamma-ray energies between 150 keV and 1500 keV. Two experimental methods were used. One method made use of the known relative intensities of La140 and Eu154 gamma rays. The second method made use of the known intensities of several calibrated sources. The resulting experimental full-energy peak-efficiency curve is compared with a published semi-empirical relation given by 
k 
« =  [l-e-cr+Aoe-BE], 
c 
where e is the efficiency, and r and a are the photoelectric and Compton scattering absorption coefficients, respectively. The empirical constants k, A, B, and c are parameters, and E is the gamma-ray energy. It was found that the above relation agrees with the experimental results within an accuracy of 3%

Cothern, C. R.

Tokcan, G.

The Ohio Journal of Science

Author Institution: University of DaytonThe intrinsic efficiency of a Ge(Li) detector was determined for gamma-ray energies between 150 keV and 1500 keV. Two experimental methods were used. One method made use of the known relative intensities of La140 and Eu154 gamma rays. The second method made use of the known intensities of several calibrated sources. The resulting experimental full-energy peak-efficiency curve is compared with a published semi-empirical relation given by 
k 
« =  [l-e-cr+Aoe-BE], 
c 
where e is the efficiency, and r and a are the photoelectric and Compton scattering absorption coefficients, respectively. The empirical constants k, A, B, and c are parameters, and E is the gamma-ray energy. It was found that the above relation agrees with the experimental results within an accuracy of 3%

KnowledgeBank at OSU

92 BRUCE MAY Vol. 69EFFICIENCY DETERMINATIONS FOR AGE(LI) DETECTOR1G. TOKCAN AND C. R. COTHERNUniversity of DaytonABSTRACTThe intrinsic efficiency of a Ge(Li) detector was determined for gamma-ray energiesbetween 150 keV and 1500 keV. Two experimental methods were used. One methodmade use of the known relative intensities of La140 and Eu154 gamma rays. The secondmethod made use of the known intensities of several calibrated sources. The resultingexperimental full-energy peak-efficiency curve is compared with a published semi-empiricalrelation given byk« = — [l-e-cr+Ao-e-BE],cwhere e is the efficiency, and r and a are the photoelectric and Compton scattering absorp-tion coefficients, respectively. The empirical constants k, A, B, and c are parameters,and E is the gamma-ray energy. It was found that the above relation agrees with theexperimental results within an accuracy of 3%.INTRODUCTIONSolid state detectors are increasingly being preferred to scintillation countersfor most gamma-ray spectroscopy experiments because of their better energy-resolution characteristics. One of the major drawbacks of using solid statedetectors is their low efficiency compared to Nal(TJ) detectors. Because theefficiency for solid-state detectors goes as Zn where 4<n<5 (Mayer, 1966),germanium is used more widely than silicon.Manuscript received May 6, 1968.No. 2 EFFICIENCY FOR GE(Ll) DETECTORS 93In gamma-ray experiments, the efficiency is a very important characteristic.The relative intensity of gamma transitions is a more important experimentalquantity than the energy. Several papers have appeared recently discussing theexperimental and theoretical aspects of determining the efficiency of solid-statedetectors (e. g., Arnell et al., 1967; Cline and Heath, 1967; Dooley, 1968; Donnellyet al, 1967; Ewan and Tavendale, 1964; Faria and Levesque, 1967; Hollander,1966; Kane and Mariscotte, 1967; Sandborg and Orth, 1968; Wanio and Knoll,1966). Because the theoretical calculations of efficiency are at present so complex,it is important to determine reliable experimental techniques for measuringefficiency. The efficiency considered in this paper is the intrinsic efficiency (seeFaria, 1967), which is the ratio of the number of radiations detected to the numberstriking the detector. As long as the source-to-detector distance is large enoughto prevent appreciable edge effects, the efficiency should be independent of solidangle.In this work two experimental methods were employed to determine theefficiency curve. In the first experiment, use was made of the known relativeintensities of La140 (Connor, 1966) and Eu154 (Ramaya, 1967). In the secondexperimental method, six calibrated sources (obtained from the InternationalAtomic Energy Agency, Division of Research and Laboratory, Vienna 4, January1967) of gamma rays of different energies were used and the efficiency curve wasobtained by comparing the apparent activities with the known activities of thesources. The results from these two experiments have been combined into asingle experimental efficiency curve, which is good within an error range of 8%.The least square fit to this data gave a statistical error of 3%. The dependenceof efficiency on live time has also been investigated. Finally, the experimentalefficiency in the energy range 150-1500 keV was fit by a semiempirical relationwith an overall accuracy of 3%, compared to the line of best least squares fit fromthe experimental work.EXPERIMENTAL METHODSThe detection system consisted of an Ortec (Oak Ridge Technical EnterprisesCorporation, Oak Ridge, Tennessee) 118A preamplifier, an Ortec 410 amplifier,and a TMC (Technical Measurement Corporation, North Haven, Connecticut)4096-channel pulse-height analyzer. The detector was a planar Ge(Li) type andhad an active volume of 2 cm3. The detector had an approximately squarefront-face area of 4 cm2 and was 5 mm deep. The sources were always placed atleast 25 mm from the detector so as to approximate a point source and pointdetector situation. The sources were always placed so as to achieve the sameanalyzer live time. The cryostat and detector chamber were the standard Ortecdevice, having a 0.020-inch aluminum face in front of the detector. No otherabsorbers were present between the source and detector.In the first experiment, the spectra of Eu154 and La140 were taken for both90% and 60% live times and analyzed by measuring the area under each photopeakfor relative intensities. The spectra were also analyzed using a computer codedeveloped by Harvey and Stevens (1966) and Dooley et al. (1968) which fit askew-symmetric gaussian shape to the photopeak and polynomial to the comptontails and background. The computer code allowed the computer to choose thedegree of polynomial used, depending on the goodness of fit. In all cases in thiswork, a linear base line provided the best fit. Typical La140 curves are shown inFig. 1 (487.1 and 751.7 keV peaks). The two methods agreed within 2%.The experimental relative intensities found in the above ways were comparedwith the relative intensities given in the literature and efficiency values werefound for different energies. These results are shown in Tables 1 and 2.In the second experiment, six calibrated gamma-ray sources were used. Thegamma emission data, in terms of half life and activity, as well as in the percent94 G. TOKCAN AND C. R. COTHERN Vol. 69or number of gamma rays per disintegration, are given in Table 3. The spectraof these sources were taken with the same experimental geometry. The spectra25000.22500. +11L0. 1120. 1130. 11U0. 1150. 1160. 1170. 1L80. 1190. 1200. 1210. 1220CHRNNEL NUMBERFIGURE 1 (a). 487.1 keV peak in La140 spectrum.2500.2250.2000.1750.o1250.Q_co 1000.1760. 1770. 1780. 1790. 1800. 1810. 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890CHflNNEL NUMBERFIGURE 1 (b). 751.7 keV peak in La140 spectrum.No. 2 EFFICIENCY FOR GE(Ll) DETECTORS 95TABLE 1Efficiency of Ge(Li) 2cc Ortec Detector by using La140 y-ray relative intensitiesRelative IntensitiesEnergy from Literature(Connor, 1966)ExperimentalRelative Intensities Relative Efficiency131.1328.7432.9487.1751.7816.0867.8925.2+9201596.40.45419.062.9346.54.2525.86.1410.65100.00±0.022±0.95±0.15±2.3±0.21±1.3±0.31±0.53± 545.6± 6.1330 ±1034.6± 0.4354 ±1921.7± 0.374.6± 3.616.1± 2.223.9± 3.9100 ± 2.2102 ±1417.3 ±1.011.8 ±1.67.64±0.555.1 ±0.62.88±0.202.62±0.372.24±0.381.00 = 0.05TABLE 2Efficiency of Ge(Li) 2cc Ortec Detector by Using Eulib y-ray Relative IntensitiesEnergy (KeV)Relative Intensitiesfrom Literature(Ramaya, 1967)ExperimentalRelative Intensities Relative Efficiency122248591723.4873.41274.49521156035100± 9.0±0.0±0± 2± 1.3.2102824645815463100±44±39±12±11.3± 7.6± 610822.13.92.571.801.00±11±2.4±1.0±0.26±0.25±0.06TABLE 3y-emission dataRadio-nuclideActivity/xC) (Jan. 1,1967)Half LifePresent Activity(Sept. 16, 1967) Energy— (keV)7-Ray/dis .dis/sec(Sept. 16,1967)expected7-ray/secCo67Na22Hg203Am241Cs13710.5310.7220.5611.4211.3310.64271.6 day 5.47 2.02xl052.603year46.57 day485.1 year106.6 day8.90 3.29xlO60.44211.402.081.64xlO44.22xlO57.69xl0429.82 year 10.35 3.92xl06122136.4511.01274.6279.159.57897.51836.2661.5985.38.4179.799.9481.5535.99210084.61.72 xlO51.7 xlO45.9 xlO53.188xlO51.34 xlO41.52 xlO57.1 xlO47.69 xlO43.35 xlO5were plotted on linear graph paper and the area under each photopeak wasmeasured with a planimeter. The base lines under the peaks were assumed to belinear. The relative experimental area, the expected number of gamma rays persecond from each source, and the efficiency values for the given energies are shownin Table 4.The efficiency curves obtained by using the results of the two experimentswere superposed, by applying the method of least squares, to find the finalefficiency curve, as shown in Fig. 2. The error in absolute intrinsic efficiency isestimated to be 20%, due to uncertainty in solid angle. The final error in relativeefficiency is much smaller, as will be demonstrated later in this paper. The solidlines in figure 2 represent the error range for 90% live time. The dotted line isfor 60% live time and is normalized at 1.5 MeV to the 90% live-time curve.96 G. TOKCAN AND C. R. COTHERN Vol. 69TABLE 4Efficiency of Ge(Li) 2cc Or tec Detector by using several y-sourcesEnergy (Area)rel expected Eff =(Area)relRadionuclide (keV) 7-ray/sec 7-ray/sec 7-ray/secexperimental (theoretical)Note: Although the efficiency listed in the last column is absolute, it con-tains a solid angle factor.NTRINSIC FULL ENERGY PEAK EFFICIENCY(SOLID ANGLE EFFECT DIVIDED OUT)FIGURE 2. Intrinsic Full Energy Photopeak Efficiency of Ge(Li) 2cc Detector.No. 2 EFFICIENCY FOR GE(Ll) DETECTORS 97SEMI-EMPIRICAL METHODThe precise shape of the efficiency curve which fits the experimental valueswas determined by means of a semi-empirical formula, together with the publishedvalues for the photoelectric and Compton absorption coefficients for germanium(see Freeman and Jenkin, 1966). For the gamma energy range used in thiswork, the contributions to the full-energy peak come from two processes. Thefirst one is the photoelectric effect for which the absorption coefficients is repre-sented by a. The efficiency for the photoelectric effect is proportional to1—exp ( — TC),where c is a parameter which physically represents the thickness of the detector.The second contribution to the full energy comes from multiple Comptonevents, for which the absorption coefficient was denoted by a. The relationbetween the full-energy peak efficiency e and a can be written ase~A o- e~BE,where E is energy and e~BE represents the fraction of the Compton scatteredphotons which are totally absorbed by the photoelectric effect after scattering.This expression is an assumption and has no theoretical justification. Becausethe photoelectric absorption coefficient becomes smaller for higher energies, thisfraction is shown as a decreasing function of energy.Combining the above effects, the efficiency can be written ask rc Lwhere k, A, B are empirical constants to be determined by experiment. In thisexpression, e~rc can be expanded in terms of re and, for the higher energy gammarays for which r is smaller, an approximation can be made by taking only the firstterm of the expansion into consideration. For the 500 keV-1300 keV energyrange, the equation for efficiency becomese = k(r+A'(7e-BE), (1)where A' = A/c.To determine the empirical constants appearing in this equation, the followingprocedure was applied. Taking the logarithm of both sides of the equation (1),the relation can be put in the form:e r Blog = E+log A1,ak a 2.303which represents the equation of a straight line when appropriate coordinates areused. For a proper k value, the plot of log \-r_ ) against energy E should giveTOa straight line of slope — and intercept log A1. To do this, use was made ofthe efficiency curve shown in Fig. 2, obtained by the experimental methods givenin the previous sections, and of the r and a values given for Ge (see Table 5).Using this method, it was found that k = 9.5, B = 1.43, and A1 = 0.0848. The plotsfor several k values are shown in Figure 3. The values of the constant weredetermined using a goodness of fit statistical test.The efficiency values obtained by using the above constants (eq. 1) are com-pared in Table 6 with those from the experimental curve in Fig. 2. As seen fromthe table for the energies below 400 keV, the theoretical efficiency values deviateappreciably from the experimental values.98 G. TOKCAN AND C. R. COTHERN Vol. 69TABLE 5a and r values1 for Germanium for energy range between500 keV to 1350 keVGamma ray-Energy(keV)(barns/atom) (barns/atom)511785117313339.177.586.235.840.4450.1520.06970.0570j.05 .1 1.2FIGURE 3. Plots of Log \<rk a )versus energy for different k values.TABLE 6Efficiency for Ge(Li) Or tec 2cc DetectorEnergy(keV)1001502003004005117851333Efficiency(Experimental)53.524.714.26.63.812.361.060.394Efficiency(from eq. 1)1474620.47.023.872.381.050.382Efficiency(from eq. 2)22.620.014.16.373.692.381.050.382No. 2 EFFICIENCY FOR GE(Ll) DETECTORS 99To get a better agreement between the experimental and semi-empiricalmethod data, especially for the lower energies, the following exact form of thesemi-empirical relation was used:r i= — (l-e-CT)+Ao-e-BE IL JThe T and a values for lower energies for Ge (atomic number = 32) could be derivedby extrapolating the values given for Cu (Z = 29) by Davison (1966). Becausein general r~Z5 and cr~Z, the conversion ratio for T was found to be75 77^ 5 = 0.61, while the conversion ratio for a was determined to be ^ ^ = 0.907.The T and a values obtained for Ge for lower energies are listed in Table 7.TABLE 7Interpolated a and r values for GermaniumGamma-rayEnergy(keV)801001502003004005006008001000<T(barns/atom)16.5015.7314.1712.9811.310.19.248.557.516.74T(barns/atom)97.349.714.86.21.80.830.4570.290.1500.093To compare efficiencies determined by experiment and by the exact form ofthe semi-empirical relation given by Eq. 2, the value of c was found as follows.Equation 2 was put in the form of:e-Acr e-BE 1= - (1-e—),k cwhere, for a given value of E,is constant. The c values which satisfy the above relation for several E valuesin the low-energy region were averaged to get the value c = 0.150 atom/barn.Therefore Eq. 2 becomes9.5E0.150The efficiencies for different energy values were evaluated by means of theabove relation and compared with the ones obtained by equation 1 and also withthe experimental values. It can be seen in Table 6 that agreement was obtainedwith 3% accuracy over the energy range between 150 and 1500 keV. Better100 G. TOKCAN AND C. R. COTHERN Vol. 69accuracies are obtained when a smaller energy range is considered. This is quiteconsistent with the results of Freeman and Jenkin (1966), who obtained a 1%accuracy in the energy range of 500-1500 keV.ACKNOWLEDGMENTThe author wishes to thank Dr. J. A. Harvey, Mrs. M. Stephens and Mr. JohnDooley for making available their Computer Codes.REFERENCESArnell, S. E., R. Hardell, A. Hosselgren, L. Jonsson, and O. Skeppstedt. 1967. ThermalNeutron Capture Gammas Measured With Ge(Li)-Spectrometers and Internal ReactorTargets Nuc. Instr. and Met. 54: 165-180.Connor, R. D. 1966. University of Manitoba, Winnipeg, Canada, Private Communication.Cline, J. E. and R. L. Heath. 1967. Annual Progress Report, Gamma-Ray Spectrometry ofNeutron-Deficient Isotopes. Phillips Petroleum Company Report IDO-17222.Davison, C. M. 1966. Gamma-Ray Attenuation Coefficients. "Alpha, Beta, and GammaRay Spectroscopy" Volume 1, page 835. K. Siegbahn, Editor. (North Holl and PublishingCompany, Amsterdam, Netherlands).Dooley, J. A., J. H. Gorrell, M. Young, and P. Polishuk. 1968. Computerized QuantitativeAnalysis of High-Resolution Spectra. Paper to be given at the 1968 International Conference(October 7-11, 1968), National Bureau of Standards, Gaithersburg, Maryland.Dooley, J. A. 1968. Measurement and Comparison of Detector Efficiencies. Paper to begiven at the 1968 International Conference (October 7-11, 1968) National Bureau of Stand-ards, Gaithersburg, Maryland.Donnelly, D. P., H. W. Baer, J. J. Reidy, and M. L. Wiedenbeck. 1967. The Calibration of aGe(Li) Gamma-Ray Spectrometer for Energy and Relative Intensity Measurements.Nuc. Instr. and Met. 57: 219-226.Ewan, G. T. and A. J. Tavendale. 1964. High Resolution Studies of Gamma-Ray SpectraUsing Lithium-Drifted Germanium Gamma-Ray Spectrometers. Can. J. Phys. 42:2286-2331.Faria, N. V. DeCastro and R. J. A. Levesque. 1967. Photopeak and Double-Escape PeakEfficiencies of Germanium Lithium Drift Detectors. Nuc. Instr and Met. 46: 325-332.Freeman, J. M. and J. G. Jenkin. 1966. The Accurate Measurement of Relative Efficiencyof Ge(Li) Gamma-Ray Detectors in the Energy Range 500 to 1500 KeV. Nuc. Instr. andMet. 43: 269-277.Goulding, F. S. 1966. Semiconductor Detectors for Nuclear Spectrometry, I. Nuc. Instr.and Met. 43: 1-54.Harvey, J. A. and M. M. Stevens. 1966. Analysis of High-Resolution Gamma-Ray Spectra,Oak Ridge National Laboratory Report 4082: 65-68.Hollander, J. M. 1966. The Impact of Semiconductor Detectors on Gamma-Ray and ElectronSpectroscopy. Nuc. Instr. and Met. 43: 65-109.Kane, W. R. and M. A. Mariscotte. 1967. An Empirical Method for Determining the RelativeEfficiency of a Ge(Li) Gamma-Ray Detector. Nuc. Instr. and Met. 56: 189-195.Mayer, J. W. 1966. Semiconductor Detectors for Nuclear Spectroscopy, II. Nuc. Instr.and Met. 43: 55-64.Ramaya, A. V. Vanderbilt University, Nashville, Tennessee, Private Communication.Sandborg, A. and J. Orth. 1968. Relative Pull Energy Efficiencies of Ge(Li) Detectors ofVarious Shapes and Volumes. Paper delivered at Chicago National Meeting of the Societyof Applied Spectroscopy.Wainio, K. M. and G. F. Knoll. 1966. Calculated Gamma Response Characteristics of Semi-conductor Detectors. Nuc. Instr. and Met. 44: 213-223.

Efficiency Determinations for a Ge(Li) Detector

https://kb.osu.edu/bitstream/1811/5457/1/V69N02_092.pdf

Efficiency Determinations for a Ge(Li) Detector

Abstract

Similar works

Full text

Available Versions

KnowledgeBank at OSU