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Investigation of the response of NaI(Tl) scintillation detectors using an x-ray monochromator
N U C L E A R I N S T R U M E N T S AND METHODS
164 (1979) 4 5 7 - 4 6 1 ,
~)
NORTH-HOLLAND
P U B L I S H I N G CO
INVESTIGATION OF THE RESPONSE OF NaI(TI) SCINTILLATION DETECTORS USING AN X-RAY M O N O C H R O M A T O R SAMI S SHERBIN1 and IRAJ SHAHABI
Nuclear Englneermg Program, Department of Mechanwal Engmeermg, Howard Umverstty, 2300 6th Street, N. W, Washmgton, D.C. 20059, U.S.A. Recewed 30 April 1979 The response of NaI(TI) scintillation detectors to low energy photons was studied The energy range extended from 25 keV to 90 keV. The variation of output pulse height as a function of photon energy was determined Also the variation of resolution as a function of photon energy A bent crystal spectrometer was used as the source of monoenergetic photons for the experiment.
1. Introduction Although semiconductor detectors have replaced NaI(TI) crystals in many applications involving Xray and gamma-ray spectroscopy, the scintillation detector is still used extensively because of its inherent advantages, which include large size, the possibility of manufacture in a variety of special shapes, and also convenience in use especially out of the laboratory, such as in environmental monitoring and well logging. Many investigators have studied the response of NaI(TI) to monoenergetic gamma-rays. Earlier investigators indicated that the response is linear over a wide energy range. Thus West and Meyerhoff found a linear response from 2 to 411 keV 1), and Eriksen and Jensen found the same behaviour from 50 to 500 keV 2). Pringle and Standil, however, observed some nonlinearity below 150 keV 3), and Freedman et al. reached similar conclusions for the range 24-146 keV 4). Engelkemeier found a nonlinear response over the entire range he investigated, namely from about 10 keV to over 1.3MeV 5). Iredale found a similar response in the range 46.5 keV to 1.33 MeV and noted that the differential nonlinearity did not exceed 3% for energies above 200 keV but was greater below that energy6). Jones investigated the response in the range of 2,4.7--46.5 keV using diffracted X-rays and found it to be nonlinearT). It now seems to be well established as a result of the works cited above and others that the response of NaI (TI) to photons is nonlinear over most of the energy range covering the emissions of radioactive isotopes. The nonlinearity is relatively slight at the upper end of the energy range but becomes quite marked at the lower energies, particularly in the range covering X-ray fluorescence emissions.
Almost all investigators used radioactive isotopes as sources of monoenergetic photons. The use of such sources often involves difficulties because in many cases the sources emit other, usually weaker, radiations besides the photons of interest, such as gamma photons of different energies, characteristic X-rays, or bremsstrahlung. Most workers did not indicate whether their results were corrected for such interferences, but some attempted to eliminate or correct for them by the use of filters or by subtraction of the interfering components from the main spectrum8). This problem is most severe in the energy range below 100 keV because of the relatively few gamma-ray emitters in this region and because of the interference of characteristic Xrays. The latter emissions are not directly usable as sources because they are not monoenergetic and the components are not resolved by NaI(Tl). This is particularly important when attempting to measure the resolution of the detector as a function of photon energy. Because of the interest of our group in using NaI(Tl) for low energy work, it was decided to study the response of this detector using an X-ray monochromator to produce pure monoenergetic photons of any desired energy below 100 keV. This paper describes the method and the results. 2. Method Two NaI(TI) photomultiplier tube assemblies were investigated. One was an integral assembly made by Bicron, model 2M2P, with a 2"× 2" crystal (detector #1). The second was assembled by optically coupling a Harshaw 2"× 1)'' crystal to an Amperex XP-1000 photomultiplier tube (detector #2). The photomultiplier tube output in each case was fed into a preamplifier, a spectroscopy amplifier and a
458
S S SHERBINI AND I SHAHABI
512-channel analyzer. The response of the electronics was checked using a precision pulse generator. The monoenergetic photons were obtained using a bent-crystal monochromator, shown schematically in fig. 1. The X-ray generator is a self-rectified unit with a maximum tube potential of 130 kV and a maximum continuous duty current of 3 mA. The generator is supported on the carriage of a modified lathe bed. This arrangement allows the generator to be moved relative to the diffracting crystal as the Bragg angle is changed, thus keeping the focal spot of the tube on the focal circle of the crystal, as illustrated in fig. 2. This spectrometer arrangement is known as the transmission-type or Cauchois geometry. The diffracting crystal is a single germanium crystal of dimensions 7 c m × 5 c m × 2 mm cut so that diffraction is by means of the (220) planes. It is clamped between shaped aluminum blocks which bend it to a radius of curvature equal to the diameter of the focal circle, in this case 2.00 m. A closeup of the crystal and clamping blocks is shown in fig. 3. The diffracted X-rays pass through a parallel slit collimator before reaching the detector. The detector itself is mounted in a lead housing supported on a trolley which moves on a pair of curved rails
placed on the floor of the laboratory. The detector and collimator move as a unit in an arc with a vertical axis centered over the diffracting crystal. The crystal and clamping blocks are mounted on a heavy, horizontal, triangular steel frame designed for rigidity. The frame is supported at one end on rollers and rotates about a vertical axis at the other end. The crystal clamping blocks are mounted directly over this axis of rotation. A vernier scale is attached to the frame for setting the desired Bragg angle. Fig. 4 shows the general configuration of the machine. The X-ray generator is not visible in this view. Figs. 5, 6 and 7 show typical spectra produced by the monochromator and detected by a NaI(TI) detector. Fig. 5 was obtained with a Bragg angle set for 70 keV photons. The X-ray generator was set at 110 kV. The small peak on the left is the iodine escape peak. Fig. 6 was obtained using a Bragg setting for 30 keV photons and a generator setting
Bent Crystal
x-ray Collimator
Generator
Detector / ~
F~g 3 Detail of the clampmg blocks and bent crystal
Lead}lousing F~g 1 Schernauc of the relative dtsposiuon of the rna,n components of the bent crystal spectrometer
Focal Circle Radlus B/2
/
~
" \
11
//~
, Source
Dl£fracted
//
II
k \
eam
/ /
.. ~
--
~
J
/
Crystal Bent
to
Badlus
R
Ftg 2. Onentauon of the radmuon source on the focal circle of the bent crystal The source m this case ,s the focal spot of the X-ray generator R = 1 00 m
F,g 4 Photograph of the spectrometer looking from the source stde of the crystal towards the detector.
459
RESPONSE OF Nal(T1) DETECTORS
Fig 5. Spectrum obtained w~th Bragg angle set for 70 keV and X-ray generator operated at 110 kV. Smaller peak is the ~odme escape peak
F~g 7. Spectrum obtained using the same Bragg angle as that for the spectrum in fig. 6 and X-ray generator operated at l l 0 k V
brate, however, to check for alignment and to find the exact location of the zero of the angle scale. This was done using the 60 keV photons from 241Am and checked using the 88 keV photons from t°9Cd. The overall accuracy after calibration was better than +__0.1%.
Fig 6 Spectrum obtained with Bragg angle set for 30 keV and X-ray generator operated at 60 kV
of 60 kV. Fig. 7 was obtained using the same Bragg angle as that for fig. 6 but with a generator setting of 110 kV. The small peak on the left is due to the 30 keV diffracted beam. The large peak is due to second order diffraction and corresponds to 60 keV photons. Experimental readings for this project were made using first order diffraction. The monochromator is an absolute instrument and may be set to generate photon beams of any desired energy by setting the crystal to the appropriate angle obtained from Bragg's law n2 = 2d sin0, or E = nhc/(2d
sin0),
where n is 1 for first order diffraction, h and c are Plank's constant and the speed of light, respectively, and d is the spacing between the atomic diffraction planes of the crystal. It was necessary to cali-
3. Results The linearity of the electronics was checked prior to and following data collection. The maximum integral nonlinearity was found to be 0.12%. Readings were taken at 25 keV and from 30 to 90 keV at 10 keV intervals. Several workers have found that the shape of the photopeak produced by NaI(TI) is not exactly GaussianS,9). However, for the purpose of finding the center of the photopeak and also its full width at half-maximum, it was decided that the most accurate and consistant approach would be to fit a Gaussian plus quadratic function to the data. The quadratic part of the fit accounts for background and also for the tail end of the iodine escape peak, which starts to merge into the photopeak at the upper end of the energy range being considered. The equation has the form Y=alexp
[ -(xa'yl ]J +a4+aSx+a6x2" --2\
a3
The coefficients a ~ - a 6 were determined using a nonlinear least-squares fit. Fig. 8 shows a plot of the pulse height per unit photon energy versus photon energy for detectors #1 and #2. Also plotted is a set of results obtained by Engelkemeir for a 11,, ~ ×~I,, NaI(TI) crystalS). All
460
S
S
SHERBINI
AND
1
SHAHABI
13
4.3
12
ii
==
4.2
\
/
\\
\
i0
9 4.1 •
Detector # 2 a ....
7
%
Detector # 2
Engelkemelr 6
20
I 30
I 40
I 50
I
I
60
70
l 80
I 90
I i00
5 20
Photon ~rlerg~r, keV
F,g 8 Pulse height per unit energy vs energy for d~fferent detectors
data were normalized to the same value at 50 keV. Fig. 9 shows a plot of the resolution of each of the two detectors tested as a function of the incident photon energy. The resolution is expressed in terms of the full width at half-maximum of the photopeak as obtained from the least-squares fit of a Gaussian-plus-quadratic function to the data points. The full width at half-maximum at 60 keV was 10.6 keV for detector #1 and 18.8 keV for ~2. 4. Discussion The plots of pulse height per unit energy versus energy shown in fig. 8 confirm the results obtained by other workers on the nonlinear response of NaI(TI). This is particularly true for results in the low energy range obtained using characteristic Xrays. In such cases, the researchers had to perform fairly elaborate corrections to allow for the complex nature of these radiations. The general shapes of the response curves are similar and the abrupt drop in response occurs at about the same energy for all the detectors, namely at around 35 keV. This energy ~s close to the iodine K-absorption edge at 33.17 keV 10) and the effect has been theoretically analyzed by several authorsS,l'). The response curve has also been generated theoretically using Monte Carlo techniques and the results were found to be in good agreement with experimental data~2). Although the general shape of the response curve
I
I
i
i
i
i
I
30
40
50
60
70
80
90
i i00
Photon Energy, keV Fig 9
Full wldth at h a l f - m a x l m u m
of photopeak vs energy.
now appears to be well established, the detailed shape seems to depend on the particular detector used. Thus in this work, the two detectors used were tested under identical conditions with respect to source geometry and electronic equipment settings but the responses show different degrees of nonlinearity. Detector #2 was about half as thick as detector #1 and showed a greater degree of nonlinearity. Detector size, however, does not seem to be the main factor, as shown by the results of other mvestigatorsS). It should be noted that in this work, the detector includes the assocmted photomultiplier tube. However, much work has been done on the response of photomultiplier tubes using light pulsers and the results support the conclusion that the nonlinear response of the detectors is a property of the NaI (TI) crystal. Further work is needed to study the effects of different factors that might affect the detaded shape of the response curve. Untd such data becomes available, it is necessary to determine the exact shape of the response curve of each detector used if such a curve is needed. The variation as a function of energy of the photopeak width expressed in terms of the fwhm is shown in fig. 9. Straight lines were drawn through the data points. The strmght line fit to the data is quite good for detector #1 and is reasonably good for detector/~2. Published work on the resolution of NaI(T1) indicates that a plot of the relative square full width at half-maximum versus the inverse of
R E S P O N S E OF NaI(TI) D E T E C T O R S
photon energy should give a straight line fit. Data from this work were treated in this manner and gave a reasonably good fit, but a plot of fwhm versus energy gave a better linear fit. The data of Hill and Collinson ~3) were also plotted in this way fbr comparison and the linear fit was found to be very good. It should be noted that the maximum deviation from linearity in the case of detector//2 in fig. 9 is 4.7%. The slopes of the two lines were obtained from a least squares fit and were found to differ by slightly less than 3 standard deviations. A number of different functions were also fit to the data but the fit in each case was not as good as the linear. Since the manner in which the fwhm varies with photon energy in the low energy region appears to be complex, more work in this area is necessary, with readings taken at small energy increments.
461
References 1) H I West, Jr., W.E. Meyerhof and R Hofstadter, Phys Rev 81 (1951) 141 2) V.O Enksen and G Jensen, Phys Rev 85 (1952) 150 3) R W Prlngle and S Standil, Phys Rev. 80 (1950) 762 4) M S Freedman, A. H Jaffey, F. Wagner, Jr, and J May, Phys Rev. 89 (1953) 302. 5) D Engelkemelr, Rev. Sci Instr 27 (1956) 589 6) p Iredale, Nucl. Instr. and Meth 11 (1961) 336 7) T H Jones, Nucl. Instr. and Meth 15 (1962) 55 8) R L Heath, R.G. Helmer, L A Schmlttroth and G A Cazler, Nucl Instr and Meth. 47 (1967) 281 9) T S Mudhole and N. Umakantha, Nucl Instr and Meth. 116 (1974) 401 10) C M. Lederer, J M Hollander and I Perlman, Table of isotopes (J Wdey, N Y., 1968) p. 567 11) A. J L. Collinson and R Hill, Porc. Phys. Soc. 81 (1963) 883. 12) C D Zerby, A Meyer and R. B- Murray, Nucl Instr and Meth 12 (1961) 115. 13) R Hill and A J L Colhnson, Proc. Phys. Soc. 85 (1965) 1067
164 (1979) 4 5 7 - 4 6 1 ,
~)
NORTH-HOLLAND
P U B L I S H I N G CO
INVESTIGATION OF THE RESPONSE OF NaI(TI) SCINTILLATION DETECTORS USING AN X-RAY M O N O C H R O M A T O R SAMI S SHERBIN1 and IRAJ SHAHABI
Nuclear Englneermg Program, Department of Mechanwal Engmeermg, Howard Umverstty, 2300 6th Street, N. W, Washmgton, D.C. 20059, U.S.A. Recewed 30 April 1979 The response of NaI(TI) scintillation detectors to low energy photons was studied The energy range extended from 25 keV to 90 keV. The variation of output pulse height as a function of photon energy was determined Also the variation of resolution as a function of photon energy A bent crystal spectrometer was used as the source of monoenergetic photons for the experiment.
1. Introduction Although semiconductor detectors have replaced NaI(TI) crystals in many applications involving Xray and gamma-ray spectroscopy, the scintillation detector is still used extensively because of its inherent advantages, which include large size, the possibility of manufacture in a variety of special shapes, and also convenience in use especially out of the laboratory, such as in environmental monitoring and well logging. Many investigators have studied the response of NaI(TI) to monoenergetic gamma-rays. Earlier investigators indicated that the response is linear over a wide energy range. Thus West and Meyerhoff found a linear response from 2 to 411 keV 1), and Eriksen and Jensen found the same behaviour from 50 to 500 keV 2). Pringle and Standil, however, observed some nonlinearity below 150 keV 3), and Freedman et al. reached similar conclusions for the range 24-146 keV 4). Engelkemeier found a nonlinear response over the entire range he investigated, namely from about 10 keV to over 1.3MeV 5). Iredale found a similar response in the range 46.5 keV to 1.33 MeV and noted that the differential nonlinearity did not exceed 3% for energies above 200 keV but was greater below that energy6). Jones investigated the response in the range of 2,4.7--46.5 keV using diffracted X-rays and found it to be nonlinearT). It now seems to be well established as a result of the works cited above and others that the response of NaI (TI) to photons is nonlinear over most of the energy range covering the emissions of radioactive isotopes. The nonlinearity is relatively slight at the upper end of the energy range but becomes quite marked at the lower energies, particularly in the range covering X-ray fluorescence emissions.
Almost all investigators used radioactive isotopes as sources of monoenergetic photons. The use of such sources often involves difficulties because in many cases the sources emit other, usually weaker, radiations besides the photons of interest, such as gamma photons of different energies, characteristic X-rays, or bremsstrahlung. Most workers did not indicate whether their results were corrected for such interferences, but some attempted to eliminate or correct for them by the use of filters or by subtraction of the interfering components from the main spectrum8). This problem is most severe in the energy range below 100 keV because of the relatively few gamma-ray emitters in this region and because of the interference of characteristic Xrays. The latter emissions are not directly usable as sources because they are not monoenergetic and the components are not resolved by NaI(Tl). This is particularly important when attempting to measure the resolution of the detector as a function of photon energy. Because of the interest of our group in using NaI(Tl) for low energy work, it was decided to study the response of this detector using an X-ray monochromator to produce pure monoenergetic photons of any desired energy below 100 keV. This paper describes the method and the results. 2. Method Two NaI(TI) photomultiplier tube assemblies were investigated. One was an integral assembly made by Bicron, model 2M2P, with a 2"× 2" crystal (detector #1). The second was assembled by optically coupling a Harshaw 2"× 1)'' crystal to an Amperex XP-1000 photomultiplier tube (detector #2). The photomultiplier tube output in each case was fed into a preamplifier, a spectroscopy amplifier and a
458
S S SHERBINI AND I SHAHABI
512-channel analyzer. The response of the electronics was checked using a precision pulse generator. The monoenergetic photons were obtained using a bent-crystal monochromator, shown schematically in fig. 1. The X-ray generator is a self-rectified unit with a maximum tube potential of 130 kV and a maximum continuous duty current of 3 mA. The generator is supported on the carriage of a modified lathe bed. This arrangement allows the generator to be moved relative to the diffracting crystal as the Bragg angle is changed, thus keeping the focal spot of the tube on the focal circle of the crystal, as illustrated in fig. 2. This spectrometer arrangement is known as the transmission-type or Cauchois geometry. The diffracting crystal is a single germanium crystal of dimensions 7 c m × 5 c m × 2 mm cut so that diffraction is by means of the (220) planes. It is clamped between shaped aluminum blocks which bend it to a radius of curvature equal to the diameter of the focal circle, in this case 2.00 m. A closeup of the crystal and clamping blocks is shown in fig. 3. The diffracted X-rays pass through a parallel slit collimator before reaching the detector. The detector itself is mounted in a lead housing supported on a trolley which moves on a pair of curved rails
placed on the floor of the laboratory. The detector and collimator move as a unit in an arc with a vertical axis centered over the diffracting crystal. The crystal and clamping blocks are mounted on a heavy, horizontal, triangular steel frame designed for rigidity. The frame is supported at one end on rollers and rotates about a vertical axis at the other end. The crystal clamping blocks are mounted directly over this axis of rotation. A vernier scale is attached to the frame for setting the desired Bragg angle. Fig. 4 shows the general configuration of the machine. The X-ray generator is not visible in this view. Figs. 5, 6 and 7 show typical spectra produced by the monochromator and detected by a NaI(TI) detector. Fig. 5 was obtained with a Bragg angle set for 70 keV photons. The X-ray generator was set at 110 kV. The small peak on the left is the iodine escape peak. Fig. 6 was obtained using a Bragg setting for 30 keV photons and a generator setting
Bent Crystal
x-ray Collimator
Generator
Detector / ~
F~g 3 Detail of the clampmg blocks and bent crystal
Lead}lousing F~g 1 Schernauc of the relative dtsposiuon of the rna,n components of the bent crystal spectrometer
Focal Circle Radlus B/2
/
~
" \
11
//~
, Source
Dl£fracted
//
II
k \
eam
/ /
.. ~
--
~
J
/
Crystal Bent
to
Badlus
R
Ftg 2. Onentauon of the radmuon source on the focal circle of the bent crystal The source m this case ,s the focal spot of the X-ray generator R = 1 00 m
F,g 4 Photograph of the spectrometer looking from the source stde of the crystal towards the detector.
459
RESPONSE OF Nal(T1) DETECTORS
Fig 5. Spectrum obtained w~th Bragg angle set for 70 keV and X-ray generator operated at 110 kV. Smaller peak is the ~odme escape peak
F~g 7. Spectrum obtained using the same Bragg angle as that for the spectrum in fig. 6 and X-ray generator operated at l l 0 k V
brate, however, to check for alignment and to find the exact location of the zero of the angle scale. This was done using the 60 keV photons from 241Am and checked using the 88 keV photons from t°9Cd. The overall accuracy after calibration was better than +__0.1%.
Fig 6 Spectrum obtained with Bragg angle set for 30 keV and X-ray generator operated at 60 kV
of 60 kV. Fig. 7 was obtained using the same Bragg angle as that for fig. 6 but with a generator setting of 110 kV. The small peak on the left is due to the 30 keV diffracted beam. The large peak is due to second order diffraction and corresponds to 60 keV photons. Experimental readings for this project were made using first order diffraction. The monochromator is an absolute instrument and may be set to generate photon beams of any desired energy by setting the crystal to the appropriate angle obtained from Bragg's law n2 = 2d sin0, or E = nhc/(2d
sin0),
where n is 1 for first order diffraction, h and c are Plank's constant and the speed of light, respectively, and d is the spacing between the atomic diffraction planes of the crystal. It was necessary to cali-
3. Results The linearity of the electronics was checked prior to and following data collection. The maximum integral nonlinearity was found to be 0.12%. Readings were taken at 25 keV and from 30 to 90 keV at 10 keV intervals. Several workers have found that the shape of the photopeak produced by NaI(TI) is not exactly GaussianS,9). However, for the purpose of finding the center of the photopeak and also its full width at half-maximum, it was decided that the most accurate and consistant approach would be to fit a Gaussian plus quadratic function to the data. The quadratic part of the fit accounts for background and also for the tail end of the iodine escape peak, which starts to merge into the photopeak at the upper end of the energy range being considered. The equation has the form Y=alexp
[ -(xa'yl ]J +a4+aSx+a6x2" --2\
a3
The coefficients a ~ - a 6 were determined using a nonlinear least-squares fit. Fig. 8 shows a plot of the pulse height per unit photon energy versus photon energy for detectors #1 and #2. Also plotted is a set of results obtained by Engelkemeir for a 11,, ~ ×~I,, NaI(TI) crystalS). All
460
S
S
SHERBINI
AND
1
SHAHABI
13
4.3
12
ii
==
4.2
\
/
\\
\
i0
9 4.1 •
Detector # 2 a ....
7
%
Detector # 2
Engelkemelr 6
20
I 30
I 40
I 50
I
I
60
70
l 80
I 90
I i00
5 20
Photon ~rlerg~r, keV
F,g 8 Pulse height per unit energy vs energy for d~fferent detectors
data were normalized to the same value at 50 keV. Fig. 9 shows a plot of the resolution of each of the two detectors tested as a function of the incident photon energy. The resolution is expressed in terms of the full width at half-maximum of the photopeak as obtained from the least-squares fit of a Gaussian-plus-quadratic function to the data points. The full width at half-maximum at 60 keV was 10.6 keV for detector #1 and 18.8 keV for ~2. 4. Discussion The plots of pulse height per unit energy versus energy shown in fig. 8 confirm the results obtained by other workers on the nonlinear response of NaI(TI). This is particularly true for results in the low energy range obtained using characteristic Xrays. In such cases, the researchers had to perform fairly elaborate corrections to allow for the complex nature of these radiations. The general shapes of the response curves are similar and the abrupt drop in response occurs at about the same energy for all the detectors, namely at around 35 keV. This energy ~s close to the iodine K-absorption edge at 33.17 keV 10) and the effect has been theoretically analyzed by several authorsS,l'). The response curve has also been generated theoretically using Monte Carlo techniques and the results were found to be in good agreement with experimental data~2). Although the general shape of the response curve
I
I
i
i
i
i
I
30
40
50
60
70
80
90
i i00
Photon Energy, keV Fig 9
Full wldth at h a l f - m a x l m u m
of photopeak vs energy.
now appears to be well established, the detailed shape seems to depend on the particular detector used. Thus in this work, the two detectors used were tested under identical conditions with respect to source geometry and electronic equipment settings but the responses show different degrees of nonlinearity. Detector #2 was about half as thick as detector #1 and showed a greater degree of nonlinearity. Detector size, however, does not seem to be the main factor, as shown by the results of other mvestigatorsS). It should be noted that in this work, the detector includes the assocmted photomultiplier tube. However, much work has been done on the response of photomultiplier tubes using light pulsers and the results support the conclusion that the nonlinear response of the detectors is a property of the NaI (TI) crystal. Further work is needed to study the effects of different factors that might affect the detaded shape of the response curve. Untd such data becomes available, it is necessary to determine the exact shape of the response curve of each detector used if such a curve is needed. The variation as a function of energy of the photopeak width expressed in terms of the fwhm is shown in fig. 9. Straight lines were drawn through the data points. The strmght line fit to the data is quite good for detector #1 and is reasonably good for detector/~2. Published work on the resolution of NaI(T1) indicates that a plot of the relative square full width at half-maximum versus the inverse of
R E S P O N S E OF NaI(TI) D E T E C T O R S
photon energy should give a straight line fit. Data from this work were treated in this manner and gave a reasonably good fit, but a plot of fwhm versus energy gave a better linear fit. The data of Hill and Collinson ~3) were also plotted in this way fbr comparison and the linear fit was found to be very good. It should be noted that the maximum deviation from linearity in the case of detector//2 in fig. 9 is 4.7%. The slopes of the two lines were obtained from a least squares fit and were found to differ by slightly less than 3 standard deviations. A number of different functions were also fit to the data but the fit in each case was not as good as the linear. Since the manner in which the fwhm varies with photon energy in the low energy region appears to be complex, more work in this area is necessary, with readings taken at small energy increments.
461
References 1) H I West, Jr., W.E. Meyerhof and R Hofstadter, Phys Rev 81 (1951) 141 2) V.O Enksen and G Jensen, Phys Rev 85 (1952) 150 3) R W Prlngle and S Standil, Phys Rev. 80 (1950) 762 4) M S Freedman, A. H Jaffey, F. Wagner, Jr, and J May, Phys Rev. 89 (1953) 302. 5) D Engelkemelr, Rev. Sci Instr 27 (1956) 589 6) p Iredale, Nucl. Instr. and Meth 11 (1961) 336 7) T H Jones, Nucl. Instr. and Meth 15 (1962) 55 8) R L Heath, R.G. Helmer, L A Schmlttroth and G A Cazler, Nucl Instr and Meth. 47 (1967) 281 9) T S Mudhole and N. Umakantha, Nucl Instr and Meth. 116 (1974) 401 10) C M. Lederer, J M Hollander and I Perlman, Table of isotopes (J Wdey, N Y., 1968) p. 567 11) A. J L. Collinson and R Hill, Porc. Phys. Soc. 81 (1963) 883. 12) C D Zerby, A Meyer and R. B- Murray, Nucl Instr and Meth 12 (1961) 115. 13) R Hill and A J L Colhnson, Proc. Phys. Soc. 85 (1965) 1067