Efficiency calibration of a 4″×4″ face-type NaI(Tl) double crystal gamma ray spectrometer

NUCLEAR

INSTRUMENTS

AND METHODS

155 ( 1 9 7 8 )

459-465

; Q

NORTH-HOLLAND

P U B L I S H I N G CO.

EFFICIENCY CALIBRATION OF A 4"×4" FACE-TYPE NaI(TI) DOUBLE CRYSTAL GAMMA RAY SPECTROMETER R. RIEPPO and R. V)~NSK,~

Department o] Physics, University of Oulu, Oulu, Finland Received 28 March 1978 The absolute photopeak efficiency calibration of a 4 " × 4" face-type NaI(TI) double crystal counting arrangement was obtained experimentally and by Monte Carlo calculation for some cylindrical source geometries in the gamma ray energy range 80-2000 keV using standard sources of 133Ba, 57Co, 22Na, 137Cs, 88y and 6°Co. A fairly good agreement was established between the measured and computed efficiencies which make possible their reliable use with estimated uncertainty in absolute counting applications and reproducible measurements. Efficiencies of 40-50% at a 150 keV (peak efficiency value), 10-14% at a 1.0 MeV and 6 - 7 % at a 2.0 MeV gamma ray energy were obtained for the four different geometries used.

1. Introduction To obtain an absolute response function of the detector system one has to find out the correct efficiency calibration associated with a specific counting arrangement. Especially in absolute counting techniques where systematic errors should be minimized reliable efficiency data are needed. With a lot of available gamma ray standard sources covering a large energy range the efficiency values can be generally measured experimentally with satisfactory results. An additional support to the experimental efficiencies may be acquired by Monte Carlo calculation method. A great number of computations on efficiency characteristics derived by this method for a wide variety of source shape-detector shape combinations is availablel-13). Some papers on experimental efficiency measurements for various NaI(Ti) detector sizes and source geometries in the low and intermediate gamma ray energy range have also been publishedl4-2~). Yet a sudden survey on literature shows a notable lack on combined experimental and computing study of efficiency in order to emphasize the accuracy of an individual efficiency measurement. The present work on an accurate efficiency calibration of the scintillation spectrometer was carried out in order to make the comparison and reliable use of the efficiency values obtained experimentally and by Monte Carlo calculation possible. The purpose was to display and avoid the contribution of systematic experimental errors and systematic errors related to the parameters employed in the computations, and also to demonstrate the validity of the correction factors obtained earlier

by Rieppo et al. :2) for the efficiency values given by Monte Carlo calculation.

2. Experimental and calculation procedures 2.1. SOURCES AND GEOMETRIES

In our counting equipment two 4"×4"NaI('I'l) face-type scintillation detectors (Harshaw) are used with ordinary amplifiers (Harshaw preamplifier, Ortec main amplifier) in conjunction with a 4096 channel pulse-height analyzer (Canberra Model 8100). The block scheme of the spectrometer is shown in fig. 1. The signal outputs of the preamplifiers are plugged into the common input of the main amplifier to produce a sum intensity of counts in the spectrum accumulated in the multichannel analyzer. The operating voltage of the preamplifiers is adjustable by an external control in order to adjust the pulse amplitudes from the detectors and thus to give the same channel address in the MCA for a gamma ray entering one or another crystal. For absolute efficiency calibration we used six standard sources in a HCI solution: 133Ba, 57Co, 22Na, 137Cs, 6°C0 (all from NEN) and 88y (from Amersham). Table 1 lists the energy, intensity and decay information adopted for the sources. As some of the standards (S7Co and 88y) are relatively short-lived and the efficiency measurements were run during a few months the true decay rates at the date of counting had to be obtained from the original activities by multiplication with the decay factor 2 -'/rl/2 where t is the decay time and T~/2 is the half-life of the nuclide. The standards for the efficiency calibration were

460

R. RIEPPO AND R. VANSK)~

8ph(E)

Nph =

Nph

N O -

At~ f(E)'

(2)

where Nph = NO =

n u m b e r o f c o u n t s u n d e r the p h o t o p e a k , number of photons of energy E emitted by the source in c o u n t i n g time to, A -- disintegration rate o f the source, tc = c o u n t i n g time, and f(E) = coefficient o f g a m m a ray intensity (phot o n s per decay). T h e n u m b e r o f c o u n t s u n d e r a p h o t o p e a k was calculated f r o m the data o f a p u l s e - h e i g h t s p e c t r u m u s i n g the f o r m u l a

Ii

I

Nph = ~--

~

j=l

N j----

2m

j=l

(ch 2 - c h 1 + 1),

(3)

ult ie~annel analyzer

where oh2

Nj = ~ Ni

=

Chl

Fig. 1. The step by step configuration of the scintillation spectrometer showing the principle of the detector arrangement. transferred f r o m the original glass a m p o u l e s by inj e c t i o n to p o l y e t h y l e n e vials to p r o d u c e t h e cylindrical source geometries. T h e descriptions o f the four different g e o m e t r i e s used are g i v e n in fig. 2. T h e s u c c e s s i v e t r a n s f e r o p e r a t i o n s o f activities implied s o m e losses o f activity. T h e s e losses were corrected for by absolute c o u n t i n g o f t h e s t a n d a r d s before and after t h e transfer in t h e s a m e g e o m e t r y conditions. A 0.1 N HC1 was u s e d as t h e dilute. T h e correction factor was simply the ratio o f t h e m e a s u r e d p h o t o p e a k area Nph(new) o f t h e n e w s t a n d a r d to the m e a s u r e d p h o t o p e a k area Nph(old) o f the preceding standard. T h e activity errors d u e to the t r a n s f e r operations were t h e r e b y m a i n l y attributed to c o u n t i n g statistics. T h u s t h e activity Anew o f t h e new s t a n d a r d was related to the activity A o~d o f the preceding s t a n d a r d by the relation Anew = Anld-Alost =

n

Anld -- Al°st

Aola

Aota

Nph(new)A =-Nph(Old) old.

(1) 2.2. MULTICHANNEL ANALYSIS E x p e r i m e n t a l l y t h e p h o t o p e a k efficiencies o b t a i n e d for a g a m m a ray e n e r g y E by

are

n u m b e r o f c o u n t s in the photopeak region in the j t h m e a surement,

TABLE 1

Energy, intensity and decay information a adopted for the standard gamma ray sources. Energy (keV) 80.9 122.0 b 136.5b 276.3 c 302.7 c 355.9 c 383.7 c 511 661.6 898.0 1173.2 1274.6 1332.5 1836.1

Nuclide

~

133Ba 57Co 57Co 133Ba 133Ba 133Ba 133Ba 22Na

7.2a 270 d 270d 7.2 a 7.2a 7.2 a 7.2 a 2.6a 30 a 107 d 5.26 a 2.6 a 5.26 a 107 d

137Cs

88y 6°Co 22Na 6°Co 88y

Intensity (photons/decay) 0.317 0 0.87 0.11 0.075 e 0.14 f 0.69 f 0.08 f 1.80 0.85 f 0.92 1.0 1.0 1.0 1.0

0.196 e 0.67 e 0.094 e

0.86 e

a Chiefly based on refs. 25 and 26. b For 57Co the weighted average energy of about 125 keV was considered with the corresponding intensity of 0.98. c For 133Ba the weighted average energy of about 350 keV was used with the corresponding intensity of 0.98. d From ref. 27. e From ref. 26. f From ref. 25.

FACE-TYPE

4"X4"

N a l (TI) D O U B L E

CRYSTAL

GAMMA

RAY

SPECTROMETER

461

a r ~~.

crystal

GEOMETRY

~SCLU~JI aX S

axis

axis

Nel

I

Detector

Detector

Nal

Nal

Nal

crystal

crystal

crystal

GEOMETRY

A

_

B

Detector

Detector

/

axis

axis

kn

Nal

Nal

Nal

Nal

crystal I

crystal

crystal

crystal

1_ GEOMETRY

C

GEOMETRY

a

Fig. 2. The source geometries used for the efficiency calibration. Geometries A and C represent h o m o g e n e o u s circular cylinders and geometries B and D cylinder shells of thickness d = 2 . 7 5 ram. T h e source dimensions H = 2 9 m m , D = 2 0 mm and the sourceto-detector distance h = 7 . 3 mm are the same in all geometries. ch: + k

BE=

E chi

N/

number of counts in the lefthand-side background region due to photopeak in the jth measurement,

N,

number of counts in the righthand-side background region due to photopeak in the jth measurement,

-k

ch2+k

BR=

E ch2-k

m=2k+l

/7 ch I ch 2

number of channels chosen for the left- and right-hand side background regions, number of individual measurements, start channel of the photopeak region, stop channel of the photopeak region.

The efficiency values were measured for each gamma ray energy of the standards in the following steps using 1) the single crystal counting arrangement, 2) the live timer counting, 3) an appropriate counting time, 4) the integration mode of the MCA to obtain the total number of counts in the background and the photopeak regions, 5) the equation (3) to calculate the number of counts under the photopeak, and 6) the substitution of calculated photopeak areas into the equation (2) to obtain the photopeak efficiency values. Single crystal counting was used in measurements for convenience. The efficiency values for the double crystal detector were obtained simply by multiplying the single crystal efficiencies by the

462

R. R I E P P O

AND R. VANSK,~

factor 2 on the assumption that the individual response functions of both crystals are identical. Live timer counting gave correction for counting losses due to the ADC dead time which ranged from 5 to 40% with the standards used. An appropriate counting time was the one to yield standard deviations of 1°/6 or less for the photopeak areas. 2.3. MONTE CARLO CALCULATION

Monte Carlo calculation can be used to evaluate photopeak efficiency values for various sourceshape and crystal-shape combinations. For present purposes the Monte Carlo computer program which requires the following parameters as input data, 1) source dimensions (height a n d diameter), 2) source-to-detector distance, 3) crystal dimensions (height and diameter), 4) photoabsorption coefficients of gamma rays for NaI crystal, 5) linear absorption coefficients of gamma rays for the source material for self-absorption correction, and 6) linear absorption coefficients of gamma rays

for aluminium for absorption correction in detector covering, was used to calculate the photopeak efficiencies, uncorrected for multiple scatterings of gamma rays in the NaI(TI) crystal, for the extended source geometries given in fig. 2. The use of the photoabsorption coefficients of gamma rays rejects other than full absorption events of gamma rays in the crystal in formation of a photopeak. Thus the obtained efficiencies are correct only in the gamma ray range below about 200 keV where the photoabsorption probability is dominant. At higher energies, however, Compton scattering cross sections become significant and a number of successive Compton scatterings plus a final photoabsorption of a single gamma ray do contribute to a full energy absorption. Thus the total photopeak intensity is increased as the gamma ray energy and the size of the crystal increase because of the increased probability for multiple scattering events. Correction for multiple scattering of gamma rays is done by using the semi-theoretical correction factors given by Rieppo et al.22).

TABLE 2 Measured (exp) and calculated (calc) photo-peak efficiencies with estimated uncertainties for the double crystal spectrometer with source geometries of fig. 2. Energy (keV)

80 81 100 125 150 200 300 350 400 500 511 600 662 800 898 1000 1173 1275 1332 1500 1836 2000

Nuclide

Photopeak efficiency geometry C exp calc

geometry A exp

geometry B exp

133Ba

0.426±0.043

0.456±0.046

0.360±0.036

57Co

0.460±0.045

0.508±0.049

0.400±0.039

geometry D exp

0.371 _+0.024

0.578 _+0.036 0.480 _+0.048

0.390 +_0.023

0.576 _+0.036 0.530 + 0.051

0.398 ± 0.024 0.374 ± 0.023 0.284 ± 0.022 133Ba

0.300±0.031

0.330_+0.034

0.260±0.027

0.554_+ 0.036 0.505 ± 0.036 0.372 ± 0.028 0.290 ± 0.030

0.234 ± 0.016 0.202 ± 0.012 22Na

0.230±0.023

0.240+0.024

0.198±0.020

0.300 ± 0.024 0.256 ± 0.020 0.222 ± 0.022

0.180±0.010

137Cs

0.172±0.017

0.181 ±0.018

0.164_+0.016

88y

0.125___0.010

0.136±0.011

0.120±0.010

6°Co 22 Na 60 Co

0.100±0.006 0.090 ± 0.009 0.084_+ 0.005

0.104±0.006 0.092 ± 0.009 0.090 ± 0.005

0.092±0.005 0.090 +_0.009 0.080_ 0.005

88y

0.067±0.005

0.072±0.005

0.064±0.005

calc

0.223±0.017 0.176_+0.017

0.143±0.009

0.173±0.013 0.128±0.010

0.121 ±0.009

0.145±0.010 0.100 ± 0.006 0.090 ± 0.009 0.085 ± 0.005

0.084 _+0.006

0.096 ± 0.008 0.068 ± 0.005

0.065 ± 0.006

0.073 ± 0.006

4"X4"

FACE-TYPE

Nal (TI) D O U B L E

CRYSTAL

3. Results and discussion Absolute photopeak efficiencies of the 4 " × 4 " face-type NaI(T1) scintillation detector arrangement were measured experimentally at ten gamma ray energies in the range 81-1836 keV and cornputed by Monte Carlo method at twelve gammaray energies in the range 80-2000 keV for the source geometries of fig. 2. The results are listed in table 2 and plotted in figs. 3-5. For the geometries A and B no calculations were carried out because of geometrical difficulties. With the geometries C and D there exists an axial cylindrical symmetry which enables a favourable calculation. Thus the reliability of the experimental photopeak efficiencies due to the geometries A and B (fig. 3) will be evaluated on the basis of the results obtained for the geometries C and D (fig. 4 and 5). The Monte Carlo calculations involved correc-

mlO

GAMMA

o,

D z • _~ •

QEOM

O

CALC

•

EXP

C

•lU , , z i-

I

I

I

"t . O ~1

A

M

M

A

I

1 .m Ill

A

Y

•

g.O N

•

Ill

|

Y

[keY)

Fig. 4. Calculated and measured photopeak efficiencies vs the g a m m a ray energy o f the double crystal spectrometer for the geometry C of fig. 2. The curve is drawn through the calculated points.

sf lo_1

0

GEOMETRY

O

GEOMETRY

A

(EXp) B

(EXP)

< W

E

0 Z

1

I

|TRY

"

O.u

0

463

RAY S P E C T R O M E T E R

I

I

G

I

1.o

o.m

A

M

M

A

Im

I

,t.es A

Y

E

NI[

2.o R

Q

Y

tkeV)

Fig. 3. Experimental photopeak efficiencies vs the g a m m a ray energy o f the double crystal spectrometer for the geometries A and B of fig. 2.

tion for self-absorption in the source for the geometry C but not for the geometry D. As a result the effect of neglecting self-absorption is seen in fig. 5 as a difference between the measured and calculated efficiency curves, whereas the calculated efficiencies corrected for self-absorption in fig. 4 agree quite well with the experimental efficiency curve. Fig. 4 shows that the experimental efficiency values are somewhat lower than the calculated ones at energies above 0.9 MeV. This phenomenon may be attributed to gamma ray scattering from material surrounding the crystal23). The peak efficiency occurs at about 150 keV. The errors quoted to the calculated photopeak efficiency values are due to the ___2 m m change in the source-to-detector distance h plus the ___0.25 mm uncertainty in the source dimensions. The adopted absorption coefficients 24) were assumed erroneous as well as the semi-theoretical correction factors of Rieppo et al.22). Some sources emit coincident gamma rays which therefore produced random sum peaks in the spectrum and the photopeaks representing the individual gamma rays were reduced. Resulting losses in photopeak areas were corrected for the 22Na, 6°Co and 88y gamma rays.

464

R. RIEPPO, AND R. V,~NSKA, TABLE 3

x 10 -I

Estimates (___%) for the total uncertainties of the measured photopeak efficiencies. Source

(1)

(2) a

(3) b

(4) c

(5) a

Total

4.6 4.6

2.0 2.0

2.3 2.3

-

1.0 1.0

9.9 9.9

4.3 4.3

2.0 2.0

1.0 1.0

1.7 2.0

1.0 1.0

10.0 10.3

3.2

2.0

1.5

1.5

1.0

9.2

2.3 2.3

2.0 2.0

0.2 0.2

-

1.0 1.0

5.5 5.5

3.1 3.1

2.0 2.0

1.0 1.0

1.1 -

1.0 1.0

8.2 7.1

4.0

2.0

1.0

1.7

1.0

9.7

22Na 511 keV 1275 keV

GEOMETRY

0

CALC

•

EXP

]33Ba 81 keV 350 keV 137Cs 662 keV 60Co 1173 keV 1332 keV 88y 898 keV 1836 keV 57Co 125 keV

Non-calculated estimate for maximum error. b Based on ref. 28 or scatter in literature. c Based on scatter in literature. a

0.5 G

1.0 A

M

M

A

R

1.5 A

Y

E

N

2.0 |

R

G

Y

(keV)

Fig. 5. Calculated and measured photopeak efficiencies vs the gamma ray energy of the double crystal spectrometer for the geometry D of fig. 2. The curves are freely drawn through the points.

The total uncertainties in the experimental photopeak efficiencies result from several facts: 1) activity errors given by the manufacturer, 2) transfer of activities, 3) uncertainties in half-lives, 4) uncertainties in gamma ray intensities, and 5) errors due to counting statistics in the determination of photopeak areas. Corresponding contributions are given in table 3. As a result of the successful experimental and computation study on the absolute photopeak efficiency values for extended cylindrical gamma ray sources in the double crystal detector arrangement described we conclude that reliable efficiency calibration with reasonable uncertainty is achieved for all counting geometries considered. References 1) M. L. Yates, in Alpha-, beta- and gamma-ray spectroscopy (ed. K. Siegbahn; North-Holland, Amsterdam, 1965).

2) M. L. Verheijke, Intern. J. Appl. Radiation Isotopes 15 (1964) 559. 3) M. L. Verheijke, Intern. J. Appl. Radiation Isotopes 13 (1962) 583. 4) K. Verghese, R. P. Gardner and R. M. Felder, Nucl. Instr. and Meth. 101 (1972) 391. 5) B. J. Snyder and G. L. Gyorey, Nucleonics 23 (1965) 80. 6) B. J. Snyder, Nucl. Instr. and Meth. 53 (1967) 313. 7) p. Holmberg, R. Rieppo and K. Blomster, Comment. Phys.-Math. 43 (1973) 21. 8) B. F. Peterman, Nucl. Instr. and Meth. 101 (1972) 61i. 9) R. Rieppo, Nucl. Instr. and Meth. 107 (1973) 209. ]0) R. Rieppo, P. Holmberg and K. Blomster, Intern. J. Appl. Radiation Isotopes 26 (1975) 558. ll) R. Rieppo and K. Blomster, Intern. J. Appl. Radiation Isotopes 27 (1976) 365. 12) R. Rieppo, Intern. J. Appl. Radiation Isotopes 27 (1976) 491. 13) T. Nakamura, Nucl. Instr. and Meth. 105 (1972) 77. ]4) D. Ber6nyi, S. M6szfiros, S. A. H. Self El Nasr and J. Bacs6, Nucl. Instr. and Meth. 124 (1975) 505. 15) E. Waibel and B. Grosswendt, Nucl. Instr. and Meth. 131 (1975) 133. 16) M. Sriramachandra Murty, A. Lakshmana Rao and J. Rama Rao, Nucl. Instr. and Meth. 99 (1972) 147. ]7) p. Rama Prasad, J. Rama Rao and E. Kondaiah, Nucl. Instr. and Meth. 78 (1970) 255.

4"x4"

FACE-TYPE

Nal (TI) DOUBLE C R Y S T A L

18) B. Chinaglia and R. Malvano, Nucl. Instr. and Meth. 45 (1966) 125. 19) p. N. Tiwari and E. Kondaiah, Nucl. Instr. and Meth. 42 (1966) 118. 20) R. M. Green and R. J. Finn, Nucl. Instr. and Meth. 34 (1965) 72. 21) D. Redon, G. S. Mani, J. Delaunay-Olkowsky and C. Williamson, Nucl. Instr. and Meth. 26 (1964) 18. 22) R. Rieppo and P. Holmberg, Intern. J. Appl. Radiation Isotopes 25 (1974) 188. 23) C. E. Crouthamel, in Applied gamma ray spectrometry (ed.

24 25 26 27 28

G A M M A RAY S P E C T R O M E T E R

465

C. E. Crouthamel; Pergamon Press, New York, 1960) p. 101. G. W. Grodstein, X-Ray attenuation coeJJicients Jrom 10 keF to lOOMeF, NBS Circular 583 (1954). C. M. Lederer, J. M. Hollander and 1. Perlman, Table o / isotopes, 6th edition (John Wiley, New York 1967). M. A. Wakat, Nucl. Data Tables A8 5 - 6 (1971). W. D. Schmidt-Ott and R. W. Fink, Z. Phys. 249 (1972) 286. M J. Martin and P. H. Blichert-Toft, Nucl. Data Tables A8 (1970) 1.