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Photopeak efficiency and response function of various NaI(Tl) and CsI(Tl) crystals in the energy range up to 11 MeV
NUCLEAR
INSTRUMENTS
AND
METHODS
17 (1962)
310-320,
NORTH-HOLLAND
PUBLISHING
CO.
PHOTOPEAK EFFICIENCY AND RESPONSE FUNCTION OF VARIOUS NaI(TI) AND CsI(TI) CRYSTALS IN THE ENERGY RANGE UP TO 11 MeV L. J A R C Z Y K t, H. K N O E P F E L t t ,
J. L A N G , R. M t 3 L L E R a n d W . W ~ 3 L F L I
Laboratorium /itr Kernphysik, Eidg. Techn. Hochschule, Zi~rich R e c e i v e d 16 M a y 1962
T h e p h o t o p e a k efficiency for g a m m a - r a y s of e n e r g y r a n g i n g f r o m 661 k e V t o 10.83 MeV, for s c i n t i l l a t i o n c o u n t e r s w i t h NaI(Tl) c r y s t a l s of d i m e n s i o n s 2 # × 2 #, 3 # × 3 #, 5# × 4 u a n d a CsI(TI) c r y s t a l of 2 t " × 2 t * w a s d e t e r m i n e d . T h e m e a s u r e m e n t s were carried o u t w i t h a n a r r o w c o l l i m a t e d
a n d a b r o a d parallel g a m m a - r a y b e a m , u s i n g t h e (n,7)-reaction as a g a m m a source. T h e effect of t h e e n e r g y of t h e g a m m a q u a n t a on t h e s h a p e of t h e r e s p o n s e f u n c t i o n w a s also m e a s u r e d for t h e s a m e c r y s t a l s a n d energies.
1, I n t r o d u c 6 o n
scintillation counter. The quantity p(E) is the absorption coefficient for gamma radiation of energy E in the crystal. The latter, however, does not include Rayleigh scattering. Since the introduction of the scintillation counter for the detection of gamma radiation, a number of papers dealing with its properties have appeared. In particular, Maeder st al. 1) calculated analytically the photofraction for small crystals and energies not exceeding 1.28 MeV, and at the same time determined experimentally the values of p* for several values of the energy and several crystals. The following experimental papers are also noteworthy: Kreger2), Foote and Koch3), Kreger and Brown*), Schmidt5), and Vegars et al.6). The foregoing authors restricted their investigation to gamma quanta of energy not exceeding 3 MeV. Lazar et al. 7) carried out measurements
The various applications of the scintillation counter for detecting gamma radiation have greatly contributed to making its properties the object of investigation. In particular, interest has been concentrated on determining the shape of the response function and photopeak efficiency or photofraction in their dependence on the energy of the gamma quanta. The response function of a scintillation spectrometer with NaI(T1) or CsI(T1) crystals determines the pulse distribution for monochromatic gamma rays. The photopeak efficiency ~(E) is defined as the ratio of the number of pulses within the "full absorption peak" in the gamma radiation pulse spectrum of energy E to that of the gamma quanta of energy E incident on the scintillator; the photofraction p*(E) is defined as the ratio of the number of pulses within the "full absorption peak" to that of all pulses produced by the gamma quanta of energy E. In the case of a parallel beam of gamma rays of energy E incident along the direction of the crystal's axis, the following simple relation exists between photopeak efficiency and photofraction:
~(E) = p*(E). (1 -- e -"(EI'L) (1) where 1 - e -"t~)'L denotes the efficiency of the ? O n l e a v e f r o m t h e I n s t i t u t e of P h y s i c s , J a g e l l o n i a n U n i v e r s i t y , Cracow. tt Now at the Laboratorio Gas Ionizzati EURATOM-CNEN, Frascati (Roma).
1) D. Maeder, R. Miiller a n d V. W i n t e r s t e i g e r , Helv. P h y s . A c t a 27 (1954) 3. 3) W. E. K r e g e r , P h y s . R e v . 96 (1954) 1554. a) R. S. F o o t e a n d H. W. K o c h , R e v . Sci. I n s t r . 25 (1954) 746. 4) W. E. K r e g e r a n d R. M. B r o w n , Nucl. I n s t r . a n d M e t h . 11 (1961) 290. 5) C. T. S c h m i d t , I R E T r a n s a c t i o n s on N u c l e a r Science N S 7 (1960) 25. a) S. H. V e g a r s , L. L. M a r s d e n a n d R. L. H e a t h , P h i l i p s P e t r o l e u m Co. R e p o r t IDO, 16378 (1958). 7) N. H. L a z a r , I R E T r a n s a c t i o n s on N u c l e a r Science N S 5 (1958) 138; N. H. L a z a r , R . C. D a v i s a n d P. R. Bell, N u c l e o n i c s 14, (1956) 52.
310
PHOTOPEAK
EFFICIENCY
OF V A R I O U S
with gamma rays up to an energy of 7.5 MeV. Their experiments involved a NaI(T1) 3 " x 3" crystal. These authors placed the point source at a distance of 9.5 cm from the surface of the crystal. Further noteworthy results have been published b y Oostrum and MeyerS), Kockum and Starfeltg), and b y Nordhagen~°), who used the (p,?) reaction as a source of gamma rays up to 20 MeV. In some publications, the authors utilize the Monte-Carlo method for computing not only the photopeak efficiency or photofraction, but also the shape of the response function, together with their dependence on the energy of the gamma quanta. Berger and Doggett 11) made calculations for quanta up to 4.45 MeV and different NaI(T1) crystals. Miller et al. 12, ~3) determined the parameters under consideration for gamma quanta up to 15 MeV and different NaI(T1) and CsI(T1) crystals, for a parallel beam irradiating the entire surface of the crystal and for a collimated beam, as well as for a point source at different distances from the surface of the crystal. Further calculations were undertaken b y Zerby et al.'*). The aim of the present investigation consisted in determining the shape of the response function and the photopeak efficiency for scintillation counters with different NaI(T1) and CsI(T1) crystals and for gamma quanta of energies up to 10.83 MeV. The measurements were effected with a parallel beam of gamma rays varying its diameter from 6 mm to the diameter of the various crystals.
2. Experimental Procedure A scintillation spectrometer with various crystals? was used, namely NaI(T1) crystals of dimensions 2" x 2", 3" x 3", and 5" x 4", as also a 43,, X ~ ~4" CsI(T1) crystal. 2.1. GAMMA R A D I A T I O N S O U R C E S
The sources of gamma radiation listed in table 1 were used to measure the photopeak efficiency and shape of the response function. The source of gamma rays of energy 661 keV was a thin foil containing Cs '3v. Gamma radiation of energy 1.38 MeV and 2.76 MeV was obtained from t M a n u f a c t u r e d by t h e H a r s h a w Chemical C o m p a n y a n d b y Q u a r t z e t Silice.
NaI(T1) A N D CsI(T1) C R Y S T A L S
311
TABLE 1 G a m m a r a y sources. Element
T y p e of source.
Energy (MeV)
Cs T M
radioactive isotope
0.661
N a ~4 Na24 Si Si S Ca Pb N
Cross s e c t i o n for (n,~) reaction.
1.38 p~
(n,~) r e a c t i o n ,P P~
J,
2.76 3.54 4.93 5.43 6.43 7.38 10.83
130 m b 130 m b
490 m b 430 m b 170 m b
80 m b
radioactive Na 24, prepared b y activating a 0.5 g N a F target. Gamma rays of higher energies were obtained from the (n,?) capture reaction, using a reactor which, as shown in a paper b y Jarczyk et aI. 1 s), can be employed as an intense source of discrete gamma rays. The experiments were carried out with the reactor "Saphir" of the swimming pool type, at the Eidg. Institut fiir Reaktorforschung at Wiirenlingen. The target containing the element was placed in the centre of the tangential channel of the reactor. At a maximum power of 1 MW, the flux of thermal neutrons at the centre of the tangential channel amounted to 6 x 1012 n/cm 2 sec. The changes of the thermal neutron flux at the point where the target was situated were measured b y means of an ionisation chamber of high stability placed in the s) K. J. v a n O o s t r u m a n d A. C. Meyer, Nucl. Instr. and Meth. 10 (1961) 31. e) J. K o c k u m a n d W. Starfelt, Nucl. Instr. a n d Meth. 4 (1959) 171. 10) R. N o r d h a g e n , Nucl. Instr. a n d Meth. 12 (1961) 291. 11) M. J. Berger a n d J. Doggett, Rev. Sci. Instr. 27 (1956) 269; J. Res. Nat. Bur. Stand. 56 (1956) 355. 12) W. F. Miller, J. R e y n o l d s a n d W. J. Snow, Rev. Sci. Instr. 28 (1957) 717; A r g o n n e N a t . Lab. Rep. No. 5902 (1958). la) W. F. Miller, W. J. Snow, Rev. Sci. I n s t r . 31 (1960) 39; 31 (1960) 905; Argonne Nat. Lab. Rep. No. 6318 (1961); Nucleonics 19, No. 11 (1961) 174. 14) C. D. Zerby a n d H. S. Moran, Nucl. Instr. a n d Meth. 14 (1961) 115. is) L. Jarczyk, H. Knoepfel, J. Lang, R. MiiLler a n d W W61fli, Nucl. Instr. a n d Meth. 13 (1961) 287.
L. JARCZYK et al.
312
radial channel immediately above the centre of the tangential channel. Measurements by means of a magnetic pair spectrometer showed t h a t the changes in gamma flux in the tangential channel were proportional to those of the neutron flux as indicated by the ionisation chamber to within 1%. In order to obtain proper collimation of the beam, three different collimators were placed in the tangential channel as indicated in fig. 4, ref. is). The first yielded a parallel beam of dimension 42 by 42 ram, and was employed for the measurements using the magnetic pair spectrometer. The second collimation yielded a parallel beam having a diameter of 6 mm, while the third produced one of diameter 150 mm. Absorbers, one consisting of paraffin of thickness 350 mm, and one of iron 30 mm thick, reduced the gamma and neutron background from the reactor. The thermal neutron flux at the output of the channel amounted to approximately 10 n/cm 2 sec, and that of the fast neutrons to about 600 n/cm 2 sec. For the conditions described above, the flux of gamma radiation of energy 5.43 MeV was 2 x l0 s 7/cm 2 sec. When working with the beam of diameter 150 mm, lead blocks of a thickness of 150 m m with apertures of different diameters were used in addition. The diameters were chosen so as to obtain a ratio of r/R equal to 0.1, 0.3, 0.6 and 1, for the three NaI crystals utilized, where r is the radius of the beam and R that of the scintillator. The photopeak efficiency of the scintillation counters was determined by comparing it with that of a magnetic pair spectrometer. To this purpose, the ratio of the respective solid angles Os/Op must be known; measurements and computation led to the value Os = ( 2 5 . 4 +
~2p
1.0) x 10 - 3 .
The spectrum of the electric pulses obtained at the output of the photomultiplier was measured by means of a multichannel analyzer 16). The magnetic pair spectrometer permitted gamma energy measurements from 2.6 MeV to 20 MeV. The resolving power ranged from 3.6 %
for an energy of 3 MeV down to 1% for 10 MeV, and the efficiency from 5 x 10 -9 for an energy of 2 . 7 5 M e V t o 9 x 10 -7 for one of 11 MeV. 2.2. DETERMINATION OF THE RESPONSE FUNCTION The shape of the response function for the crystals utilized was determined by measuring the pulse spectrum by means of a 128-channel amplitude analyzer. The measured spectrum had to be corrected for a background resulting from the reactor and the pulse spectrum of lines accompanying the principle line. In the case of the lead target, the reactor background was obtained from pulse spectrum measurements, utilizing a bismuth target of equal size, or a graphite target in the case of the remaining elements. Bismuth and graphite are best suited for this purpose. They have a low cross section for the (n,?) reaction (for Bi, a = 32 mb; for C, a = 3.2 rob), very simple gamma ray spectra, and scattering properties with respect to gamma rays resembling those of the elements measured. In the range under consideration, the spectrum of bismuth consists of the following three lineslT) : 4.052 MeV (28), 4.099 MeV (19), 4.166 MeV (34) (the numbers in the brackets give the relative intensities). Similarly, that of carbon presents three lines onlyl8) : 4.95 MeV (69), 3.68 MeV (31), 1.28 MeV (31). The required background curve is obtained by subtracting the respective lines from the spectrum measured. The reactor spectrum (at least for higher energies) displays no structure and can be accounted for by a smooth function. The energies and intensities of the associated lines are to be found in papers by Bartholomew and Higgs19), by Groshev et a/. 2°) and by Troubetzkoy21). The intensity of the concomitant lines in the neighbourhood of the principal line is generally is) R. Miiller, Z. angew. Math. Phys. 13 (1962) 13. 1~) H. T. Motz (private communication). 18) L. Jarczyk, J. Lang, R. Miiller and W. W61fli,HPA 34 (1961) 483. xg) G. A. Bartholomewand L. A. Higgs, Atomic Energy of Canada Ltd., Rep. 669 (1958). 2o) L. V. Groshev et al., Atlas of Gamma Ray Spectra from Radioactive Capture of Thermal Neutrons (Pergamon Press, London (1959). 3t) E. Troubetzkoy, Oak Ridge Nat. Lab. Rep. 2904 (1961).
PItOTOPEAK
EFFICIENCY
OF VARIOUS
lesser b y a factor of at least 10. In subtracting the associated lines, in addition to the change in their intensity, that of the counter efficiency and of the response function was taken into account.
NaI(T1) A N D CsI(T1) C R Y S T A L S
313
these lines have the same intensity, the resulting surface was divided according to the ratio of the total efficiencies of the crystal for the energies 1.38 MeV and 2.76 MeV.
5.43 MeV
ZOO0
,ooo
"..,-/
--_ --
=
'/
-
= ~ _ -
.
.
.
.
"4
~
8'0
I
.
.
I00
t
.
.
.
...
L~_=E___-..~
t 120 Pulse height
Fig. 1. M e a s u r e d s p e c t r u m of p u l s e h e i g h t , for s u p l h u r t a r g e t , o b t a i n e d w i t h a 3" × 3~ NaI(T1) c r y s t a l , t o g e t h e r w i t h a n a l y s i s C u r v e 1 : r e a c t o r b a c k g r o u n d ; c u r v e s 2 - 8 : a s s o c i a t e d lines.
This is exemplified in fig. 1, where the experimental spectrum as obtained for sulphur with the 3" x 3" NaI(TI) crystal is shown. Graph 1 is that of the reactor background, and graphs 2-8 are those of the shape of the various associated lines. On summation of all the corrections and subtraction from the measurements, new points were obtained determining the response function for a given crystal and gamma energy. The response function could not be determined for small pulses owing to increasingly large inaccuracy as a result of the increasing reactor background and summation of error in correcting for associated lines. Consequently the measured tail for all energies and crystals was extended horizontally to pulse height zero. For the Na 2. source, separation of the 1.38 and 2.76 MeV lines was effected as follows: As both
For each crystal and each w a y of irradiation the curves for the various energies were assembled in one diagram. The system was normalized so that the maxima of the photolines coincided. This causes, b y various accounts, the zero points of the spectra for different lines to be displaced. Such representation admits of a better comparison of the results and reveals regularities in the changes of the response function for different gamma energies. In particular, the changes in height of both escape peaks can be determined as a function of the energy, thus permitting an easy interpolation for all intermediary gamma energies. Two examples of such diagrams are shown in figs. 2 and 3t. Furthermore, for illustration, the response functions for one energy each, in function of the crystal dimensions and of the diameter of the gamma ray beam, are also outlined (figs. 4 and 5). 2.3. E V A L U A T I O N O F T H E P H O T O P E A K
t A n a l o g o u s figures for t h e o t h e r c r y s t a l s a n d for f u r t h e r b e a m g e o m e t r i e s (r/R = 0.6 a n d r/R = 1) as well a s m o r e a c c u r a t e c u r v e s of t h e p h o t o p e a k efficiency ~ (E) a r e a v a i l a b l e on r e q u e s t .
EFFICIENCY
In the case of a collimated beam, the photopeak efficiency was determined b y three methods. The first consisted in applying the results derived in the
L. J A R C Z Y K gt al.
314
Gamma I 2
3 4 ,5
Energies 10.03 MeV 7.38 ,, s.4a ,
,5.43 4.s3
i xA /l\ /" \
. .
/
\
/
E'g- 2.0 MeV
\
E¥-1.0 MeV
Elf
Fig. 2. Pulse height distribution for narrow parallel beam of gamma rays of energy ranging between 1.38 MeV and 10.83 MeV, obtained with the 3" × 3" NaI(T1) crystal.
Gamma Energies I 2 3 4 ,5 6
~ T . ~
10.83 IVleV 7.38 ,, 8.42 ,, `5.43 , 4.93 " ~.,54 ,,
---:--~
I
----- - - - - - - " ~ I
E~-2MeV
/1\ /
\
/ /
....
,,~
\
/
\ .c.
.~l!~ "'/,'J !~
......
i
i
E ~ - IMeV
8
i
,
E~
Fig. 3. Pulse height d i s t r i b u t i o n for n a r r o w parallel beam of gamma rays of energy r a n g i n g between 1.38 M e V and 10.83 MeV, obt ai ned w i t h the 5= × 4 ~ NaI(T1) crystal.
PHOTOPEAK
I
EFFICIENCY
NaI(TI) A N D CsI(Tl) C R Y S T A L S
2"X 2" NOI
315
/~
J ...........
OF VARIOUS
/
~
t
,,A,
/.-7"-~.k.'/i 1,7,
_
\\
I 5.0 MeV
I 6.0 MeV
\ \'-,. £1 (MeV)
Fig. 4. R e s p o n s e f u n c t i o n for different scintillation crystals for n a r r o w parallel beam, E r = 6.42 MeV.
, ~/R = ,.oo ~/~ .o.~, ~,~ : o.~
/,\ /
6.0
Fig. 5. Variation of t h e pulse h e i g h t d i s t r i b u t i o n according to t h e value of of 7.38 M e ¥ ,
\
7.0
E~' (MeV)
r/R, for t h e 3" × 3" NaI(TI) c r y s t a l a n d an energy
316
L. J A R C Z Y K e t a/.
preceding section. From the known shape of the response function, the photofraction p* was determined as follows: A Gaussian curve was inscribed into the photopeak; the ratio of the area of the Gaussian curve to the total area yielded the photofraction p* for a given gamma energy. The photopeak efficiency was obtained on multiplying the photofraction p*(E) b y the total efficiency e(E). The latter quantity was calculated from the expression s(E) = 1 - e -~(E)'L with the values of the attenuation coefficient given b y Grodstein 22) and Bell et al.2a). The second method is based on a comparison of the photopeak efficiency of the scintillation counter with the efficiency of a magnetic pair spectrometer. This implied determining the absolute efficiency of the pair spectrometer, which was done in two steps. First, the relative shape of the efficiency curve of the magnetic spectrometer was determined. This was done b y using targets of two homogenously mixed substances. The ratio of the number of coincidences in the maximum of line nl relating to the first substance and that of line n2 of the second is given b y the f o r m u l a nA = Nt n2
" ffl
"
qtT(E1) " %(El)
(2)
N 2 " 0"2 " q2 T ( E 2 ) " ep(E2) '
where a is the cross section for thermal neutron capture, q - intensityin gamma-quanta per neutron capture, T ( E ) - the total attenuation of gamma rays of energy E in the target and along the path leading from the spectrometer to the target, ep(E) the efficiency of the magnetic spectrometer for the energy E, and N - the number of atoms of the isotope in the sample. Na, Pb and C were chosen for calibration. The q-values for these substances are known. For the 7.38 MeV line of Pb, q = 1 2o), for the 2.76 MeV activation line of Na 24, q = 1, and for the 4.95MeV and 3.68 MeV lines of carbon 0.69 and 0.31 respectively I s). In the measurements, targets were used, con32) G. W. Grodstein, X - R a y Attenuation Coefficients from 10 keV to 100 Me¥, National Bureau of Standard Circ. No. 583 (1957). 29) p. R. Bell, R. C. Davis, D. S. Hughes, W. H. Jordan and C. A. Randall, Oak Ridge National Laboratory Report No. 1415 (1953).
taining 700 g N a F and 300 g of graphite, mixed respectively with 600 g PbO and 170 g PbO. The following values were obtained: %(7.38) _- 7 0 . 2 ,
%(2.76) %(7.38) = 19.3, %(3.68) %(7.38) -- 5.2. %(4.95) Absolute calibration of the pair spectrometer was then carried out in measuring the gamma ray flux emerging from the reactor with the three NaI(T1) crystals. For this, the values of the photopeak efficiency as obtained b y the first method for the same crystals and an energy of 2.76 MeV were used. B y comparing the gamma ray flux of energy 2.76 MeV with the number of coincidences recorded b y the pair spectrometer, the absolute efficiency for energy 2.76 was obtained. The results from the three NaI crystals were in good agreement, maximum deviations from the average are less then 3 %. The mean value from several measurements yielded %(2.76) = 4.87 x 10 -9. Comparison with the absolute efficiency, obtained from integration of the Bethe-Heitlerformula for 4 different energies, proved good agreement. Above 7.4 MeV theoretical curves were used, as no test elements with exactly determined q-value are known. With the calibrated pair spectrometer, for gamma energies above 2.76 MeV, the photopeak efficiency of the various crystals could then be determined, using the following formula:
it(e) =
Ns(E ) • %(E). ap .¢p Np(E). as" d?s
(3)
Ns(E) is the number of pulses per photopeak per second, as given by the area of the inscribed Gaussian curve, N p ( E ) - the number of coincidences of the pair spectrometer, Op- the solid angle of collimationof the magnetic spectrometer, and ~ that of the crystal spectrometer.~bp/$, is the ratio of the neutron fluxes corresponding to measurement with the pair and crystal spectrometers.
PHOTOPEAK
EFFICIENCY
The third method was applied at the energies 7.38 MeV and 10.83 MeV only. It consisted in comparing the efficiency of the scintillation counter for a given value of the energy and that for 2.76 MeV. For this, a target containing 10 g N a F and 700 g PbO and one containing 10 g N a F and 600 g melamine were used. The substances were mixed homogeneously. Subsequently, the number of pulses in the photoline for gamma quanta of energy 7.38 MeV resp. 10.83 MeV was measured. The same measurements were carried out for the Na 2. activation line of energy 2.76 MeV with the reactor shut down. From the known time of activation and photopeak efficiency for 2.76 MeV, the photopeak efficiency for the energies of 7.38 MeV and 10.83 MeV, respectively, was determined, The resulting values of the photopeak efficiency obtained by these three methods are illustrated in The errors in the determination of the photopeak efficiency come from different sources, varying according to the method of measurement. With few exceptions they do, however, not exceed 8-12 %. On determination of the peak to total ratio [ Z(E)
0.7
~
0.6
I
I I 2 3 4
0.3
0.2
5"x4" Nal 2S//4"xZl/4" Ctl
3"x3" No! 2"x2" Nat
\
~
\
0.1
~
2
4
"-~t)....,~..~
6
- ~
8
317
OF V A R I O U S NaI(T1) AND CsI(T1) C R Y S T A L S
~ ,
I0 E~r (MW)
Fig. 6. Photopeak efficiency for narrow beam. • E v a l u a t e d from peak to t o t a l ratio (method 1). O Obtained b y comparison with t h e pair spectrometer-efficiency (method 2). [] F r o m measurements w i t h t a r g e t s of two mixed substances (method 3) t.
(method 1) errors up to 10 % are possible on deduction of associated lines with not sufficiently known q-values; furthermore an uncertitude occurs from the completion of the spectrum for small x (E) 0.7 5"x4" NaI z zW~zWc, t 3 3"x3"NaI 4 2"x2" Not
0.6
o.5 0.4 ~ \ oz \ ~ o.2 ~,.~
OA
2
4
6
8
I0 E~ (MIV)
Fig. 7. Photopeak efficiency for broad parallel beam. • Evaluated from peak to t o t a l ratio. [] Obtained b y comparison with narrow beam measurementst.
pulses. A better accuracy of approx. 3 % is obtained with Na 24 (2.76 MeV). This error is also transmitted to the results of the other methods. Furthermore, the measurements with the pair spectrometer (method 2) m a y cause inaccuracy in the curve of efficiency with errors of 5 % at 7.38 MeV and 10 % for other energies. The mixed target method (method 3) brings for gamma energy 7.38 MeV an accuracy of approx. 5 %, whereas at 10.83 MeV the accuracy is not more than 15 % in view of the divergence in the q-values. It should be noted that in all cases the experimental photopeaks extend to higher energies than the Gaussian curves inscribed therein. The difference in the area varies with gamma energy, ranging from 3 % for the lower energies to 8 % for higher energies. In calibrating the scintillation counters, the area of the Gaussian curve as inscribed into the experimental curve was always employed. t cf. foot note p. 52.
L. J A R C Z Y K et al.
318
Further measurements in order to determine the photopeak efficiency for a broad parallel beam were made using gamma rays having energies of 661 keV, 2.76 MeV, 5.43 MeV, 7.38 MeV and 10.83 MeV respectively. The measurement procedure was similar to the method 1 used for the narrow beam: From the given shape of the response function, the photofraction p*(E) and hence ~(E) were determined (fig. 7). Moreover the variation of the photofraction in function of the value of the r/R was determined. For this, lead blocks with apertures of radii r such as to yield an r/R ratio of 0.1, 0.3, 0.6 or 1.0 were placed in the path of the parallel beam irradiating the crystal. The Gaussian curve was inscribed into the photopeak of the response function. With the so-determined q u a n t i t y N, and the radius r of the beam incident upon the crystal, the ratio Nd=r 2 yields the variation of the photopeak efficiency ~(E) with r/R. In particular, the values were obtained for the beam irradiating the whole crystal. Fig. 8 depicts a curve of p*/p* versus r/R for the 3" x 3" NaI crystal and gamma quanta of 7.38 MeV. In a further run of measurements the scintil-
lators were irradiated with a narrow beam parallel to its axis. The point of incidence of the beam on the crystal was moved along the radius from the centre towards the edge, with gamma ray intensity constant. This procedure yielded the function p*(E,r') for a collimated beam ($ = 6 mm), with r' denoting the distance of the beam's axis from that of the crystal. The p*(E,r) values for different r]R were derived from the formula
f" p "(E, r')2nr' dr' p'(E,r) =
o
(4)
f
" 2~r' dr' 0
The points thus obtained for the 3" x 3" NaI crystal and 7.38 MeV are also given in fig. 8. The average values for the beam irradiating the entire scintillator, as obtained by the two last methods, are also included in fig. 7. The results obtained served also for determining the percentage variation of the photopeak efficiency for the broad as compared with that of the narrow beam; this is :
~/a.
R(E) = ~°(E) - ~cR(E) r0(E )
x 100%,
(5)
I.{2
0.8
with w0(E) denoting the photopeak efficiency for the collimated beam, and rR(E) -- t h a t for the wide beam irradiating the entire crystal. Table 2 summarises the results. The latter are correct to within
\
5%.
o,
0.2
0.4
0.6
0.8
3. Discussion of the Results
r/R
Fig. 8. Dependence of the photofraction on the ratio r/R, for the 3 " × 3" NaI(T1) crystal and an energy of 7.38 MeV.
In spite of the amount of work put into research on the scintillation counter, the essential point of
TABLE 2
Reduction R(E) of the photopeak efficiency, comparing broad beam with narrow beam measurements. Energy (MeV) Crystal
NaI 2" NaI 3" NaI 5" CsI 2~"
× X X ×
2" 3" 4" 2~~
0.661
1.38
2.76
5.43
21% 22% 22%
27% 26%
30%
42% 42% 42%
28% 27%
32% 32% 32%
39%
7.38
10.83
45%
53%
44% 43 % 44%
52%
50% 50%
P t I O T O P E A K E F F I C I E N C Y O F V A R I O U S NaI(T1) A N D
difficulty in the w a y of comparing the results resides in the diverging conditions of irradiation of the crystals with gamma rays. A comparison of the response function between ctf= 4.45 MeV
/l),/l \ A
CsI(T1) C R Y S T A L S
319
TABLI~ 3 Photofraction results compared 2" × 2" NaI(T1) crystal, broad beam Gamma energy (MeV)
Results of Miller
2.68 4.49 6.13 7.10 8.00
0.189 0.II0 0.069 0.056 0.045
Results of present work
et al. 13)
4
'
0.156 0.075 0.049 0.042 0.035
Table 4 Photofraction results compared 5 " × 4" NaI(T1) crystal, narrow beam Pulse h~ht
Gamma I energy
g~= 6.13 MeV
(MeV)
iI
Pulse height
Fig. 9. Response function obtained experimentally (dashed line) and the one calculated by Miller 12) (continuous line).
our results and those calculated b y Miller and Snow 13) is possible for the 2" x 2" NaI crystal and broad beam. Fig. 9 gives the response function obtained from Miller's results extended to finite resolution, together with those interpolated from the experimental curves of the present investigation. The agreement in the area of escape peaks is considerable; yet for the higher energies the calculations yield somewhat too great values. More important, however, is the discrepancy in the tail, where the calculated results are lower throughout. This explains also the difference in the values of the photofraction as illustrated in table 3 for the same crystal, or in table 4 for a 4" x 5" NaI crystal with narrow parallel beam. Errors in the experimentally determined response function might occur on account of beam scattering from source, collimator, etc. This can, however, in no case completely explain the dis-
0.661 1.33 2.62 4.45
Results due t o : present Miller x2) Berger n) Schmidt~) F°°teS) I work 0.819 0.651 0.510 0.447
0.821 0.667 0.531 0.491
0.71
0.46 0.29
0.8
0.74 0.55 0.41 0.31
crepancy, since then the photofractions obtained b y methods 2 and 3, for the determination of which the tail was not required, would not agree with those of method 1. The Monte-Carlo calculations contain simplifications, the influence of which cannot be estimated easily. To mention only the assumption that with pair production positron and electron should obtain the same energy, wherefore the escape of bremsstrahlung is underestimated. Zerby and Moran 14) mention that their calculations show considerably lower values in the photofraction than those of Miller and Snow. Unfortunately, these authors have not calculated a case that can be compared with the present experimental results. Moreover, measurements dealing with the variations of the photofraction as a function of beam width can also be compared: Berger and Doggett t i) calculated that, at 0.661 MeV, the variation of the photofraction lies between 18 % and 20%, according to the size of the crystal. Kreger*) obtained 2 4 % at 661 keV and 2 7 % at 1.11 MeV for a 4 " x 4" NaI crystal. The present investigation yielded, for all crystals utilized, 22 % at an energy of 0.661 MeV, and 26 % at 1.38 MeV.
320
L. J A R C Z Y K a a / .
Acknowledgements The authors wish to thank Prof. P. Scherrer and Prof. P. Marmier for their kind interest in the present investigation and Mr. R. Boesch for his experimental assistance. The authors are also in-
debted to the staff of the Saphir reactor, in particular to Dr. P. Schmid. One of us (L. J.) expresses his very sincere thanks to the Schweizerische Schulrat, for the grant of a scholarship which enabled him to participate in the present investigation.
INSTRUMENTS
AND
METHODS
17 (1962)
310-320,
NORTH-HOLLAND
PUBLISHING
CO.
PHOTOPEAK EFFICIENCY AND RESPONSE FUNCTION OF VARIOUS NaI(TI) AND CsI(TI) CRYSTALS IN THE ENERGY RANGE UP TO 11 MeV L. J A R C Z Y K t, H. K N O E P F E L t t ,
J. L A N G , R. M t 3 L L E R a n d W . W ~ 3 L F L I
Laboratorium /itr Kernphysik, Eidg. Techn. Hochschule, Zi~rich R e c e i v e d 16 M a y 1962
T h e p h o t o p e a k efficiency for g a m m a - r a y s of e n e r g y r a n g i n g f r o m 661 k e V t o 10.83 MeV, for s c i n t i l l a t i o n c o u n t e r s w i t h NaI(Tl) c r y s t a l s of d i m e n s i o n s 2 # × 2 #, 3 # × 3 #, 5# × 4 u a n d a CsI(TI) c r y s t a l of 2 t " × 2 t * w a s d e t e r m i n e d . T h e m e a s u r e m e n t s were carried o u t w i t h a n a r r o w c o l l i m a t e d
a n d a b r o a d parallel g a m m a - r a y b e a m , u s i n g t h e (n,7)-reaction as a g a m m a source. T h e effect of t h e e n e r g y of t h e g a m m a q u a n t a on t h e s h a p e of t h e r e s p o n s e f u n c t i o n w a s also m e a s u r e d for t h e s a m e c r y s t a l s a n d energies.
1, I n t r o d u c 6 o n
scintillation counter. The quantity p(E) is the absorption coefficient for gamma radiation of energy E in the crystal. The latter, however, does not include Rayleigh scattering. Since the introduction of the scintillation counter for the detection of gamma radiation, a number of papers dealing with its properties have appeared. In particular, Maeder st al. 1) calculated analytically the photofraction for small crystals and energies not exceeding 1.28 MeV, and at the same time determined experimentally the values of p* for several values of the energy and several crystals. The following experimental papers are also noteworthy: Kreger2), Foote and Koch3), Kreger and Brown*), Schmidt5), and Vegars et al.6). The foregoing authors restricted their investigation to gamma quanta of energy not exceeding 3 MeV. Lazar et al. 7) carried out measurements
The various applications of the scintillation counter for detecting gamma radiation have greatly contributed to making its properties the object of investigation. In particular, interest has been concentrated on determining the shape of the response function and photopeak efficiency or photofraction in their dependence on the energy of the gamma quanta. The response function of a scintillation spectrometer with NaI(T1) or CsI(T1) crystals determines the pulse distribution for monochromatic gamma rays. The photopeak efficiency ~(E) is defined as the ratio of the number of pulses within the "full absorption peak" in the gamma radiation pulse spectrum of energy E to that of the gamma quanta of energy E incident on the scintillator; the photofraction p*(E) is defined as the ratio of the number of pulses within the "full absorption peak" to that of all pulses produced by the gamma quanta of energy E. In the case of a parallel beam of gamma rays of energy E incident along the direction of the crystal's axis, the following simple relation exists between photopeak efficiency and photofraction:
~(E) = p*(E). (1 -- e -"(EI'L) (1) where 1 - e -"t~)'L denotes the efficiency of the ? O n l e a v e f r o m t h e I n s t i t u t e of P h y s i c s , J a g e l l o n i a n U n i v e r s i t y , Cracow. tt Now at the Laboratorio Gas Ionizzati EURATOM-CNEN, Frascati (Roma).
1) D. Maeder, R. Miiller a n d V. W i n t e r s t e i g e r , Helv. P h y s . A c t a 27 (1954) 3. 3) W. E. K r e g e r , P h y s . R e v . 96 (1954) 1554. a) R. S. F o o t e a n d H. W. K o c h , R e v . Sci. I n s t r . 25 (1954) 746. 4) W. E. K r e g e r a n d R. M. B r o w n , Nucl. I n s t r . a n d M e t h . 11 (1961) 290. 5) C. T. S c h m i d t , I R E T r a n s a c t i o n s on N u c l e a r Science N S 7 (1960) 25. a) S. H. V e g a r s , L. L. M a r s d e n a n d R. L. H e a t h , P h i l i p s P e t r o l e u m Co. R e p o r t IDO, 16378 (1958). 7) N. H. L a z a r , I R E T r a n s a c t i o n s on N u c l e a r Science N S 5 (1958) 138; N. H. L a z a r , R . C. D a v i s a n d P. R. Bell, N u c l e o n i c s 14, (1956) 52.
310
PHOTOPEAK
EFFICIENCY
OF V A R I O U S
with gamma rays up to an energy of 7.5 MeV. Their experiments involved a NaI(T1) 3 " x 3" crystal. These authors placed the point source at a distance of 9.5 cm from the surface of the crystal. Further noteworthy results have been published b y Oostrum and MeyerS), Kockum and Starfeltg), and b y Nordhagen~°), who used the (p,?) reaction as a source of gamma rays up to 20 MeV. In some publications, the authors utilize the Monte-Carlo method for computing not only the photopeak efficiency or photofraction, but also the shape of the response function, together with their dependence on the energy of the gamma quanta. Berger and Doggett 11) made calculations for quanta up to 4.45 MeV and different NaI(T1) crystals. Miller et al. 12, ~3) determined the parameters under consideration for gamma quanta up to 15 MeV and different NaI(T1) and CsI(T1) crystals, for a parallel beam irradiating the entire surface of the crystal and for a collimated beam, as well as for a point source at different distances from the surface of the crystal. Further calculations were undertaken b y Zerby et al.'*). The aim of the present investigation consisted in determining the shape of the response function and the photopeak efficiency for scintillation counters with different NaI(T1) and CsI(T1) crystals and for gamma quanta of energies up to 10.83 MeV. The measurements were effected with a parallel beam of gamma rays varying its diameter from 6 mm to the diameter of the various crystals.
2. Experimental Procedure A scintillation spectrometer with various crystals? was used, namely NaI(T1) crystals of dimensions 2" x 2", 3" x 3", and 5" x 4", as also a 43,, X ~ ~4" CsI(T1) crystal. 2.1. GAMMA R A D I A T I O N S O U R C E S
The sources of gamma radiation listed in table 1 were used to measure the photopeak efficiency and shape of the response function. The source of gamma rays of energy 661 keV was a thin foil containing Cs '3v. Gamma radiation of energy 1.38 MeV and 2.76 MeV was obtained from t M a n u f a c t u r e d by t h e H a r s h a w Chemical C o m p a n y a n d b y Q u a r t z e t Silice.
NaI(T1) A N D CsI(T1) C R Y S T A L S
311
TABLE 1 G a m m a r a y sources. Element
T y p e of source.
Energy (MeV)
Cs T M
radioactive isotope
0.661
N a ~4 Na24 Si Si S Ca Pb N
Cross s e c t i o n for (n,~) reaction.
1.38 p~
(n,~) r e a c t i o n ,P P~
J,
2.76 3.54 4.93 5.43 6.43 7.38 10.83
130 m b 130 m b
490 m b 430 m b 170 m b
80 m b
radioactive Na 24, prepared b y activating a 0.5 g N a F target. Gamma rays of higher energies were obtained from the (n,?) capture reaction, using a reactor which, as shown in a paper b y Jarczyk et aI. 1 s), can be employed as an intense source of discrete gamma rays. The experiments were carried out with the reactor "Saphir" of the swimming pool type, at the Eidg. Institut fiir Reaktorforschung at Wiirenlingen. The target containing the element was placed in the centre of the tangential channel of the reactor. At a maximum power of 1 MW, the flux of thermal neutrons at the centre of the tangential channel amounted to 6 x 1012 n/cm 2 sec. The changes of the thermal neutron flux at the point where the target was situated were measured b y means of an ionisation chamber of high stability placed in the s) K. J. v a n O o s t r u m a n d A. C. Meyer, Nucl. Instr. and Meth. 10 (1961) 31. e) J. K o c k u m a n d W. Starfelt, Nucl. Instr. a n d Meth. 4 (1959) 171. 10) R. N o r d h a g e n , Nucl. Instr. a n d Meth. 12 (1961) 291. 11) M. J. Berger a n d J. Doggett, Rev. Sci. Instr. 27 (1956) 269; J. Res. Nat. Bur. Stand. 56 (1956) 355. 12) W. F. Miller, J. R e y n o l d s a n d W. J. Snow, Rev. Sci. Instr. 28 (1957) 717; A r g o n n e N a t . Lab. Rep. No. 5902 (1958). la) W. F. Miller, W. J. Snow, Rev. Sci. I n s t r . 31 (1960) 39; 31 (1960) 905; Argonne Nat. Lab. Rep. No. 6318 (1961); Nucleonics 19, No. 11 (1961) 174. 14) C. D. Zerby a n d H. S. Moran, Nucl. Instr. a n d Meth. 14 (1961) 115. is) L. Jarczyk, H. Knoepfel, J. Lang, R. MiiLler a n d W W61fli, Nucl. Instr. a n d Meth. 13 (1961) 287.
L. JARCZYK et al.
312
radial channel immediately above the centre of the tangential channel. Measurements by means of a magnetic pair spectrometer showed t h a t the changes in gamma flux in the tangential channel were proportional to those of the neutron flux as indicated by the ionisation chamber to within 1%. In order to obtain proper collimation of the beam, three different collimators were placed in the tangential channel as indicated in fig. 4, ref. is). The first yielded a parallel beam of dimension 42 by 42 ram, and was employed for the measurements using the magnetic pair spectrometer. The second collimation yielded a parallel beam having a diameter of 6 mm, while the third produced one of diameter 150 mm. Absorbers, one consisting of paraffin of thickness 350 mm, and one of iron 30 mm thick, reduced the gamma and neutron background from the reactor. The thermal neutron flux at the output of the channel amounted to approximately 10 n/cm 2 sec, and that of the fast neutrons to about 600 n/cm 2 sec. For the conditions described above, the flux of gamma radiation of energy 5.43 MeV was 2 x l0 s 7/cm 2 sec. When working with the beam of diameter 150 mm, lead blocks of a thickness of 150 m m with apertures of different diameters were used in addition. The diameters were chosen so as to obtain a ratio of r/R equal to 0.1, 0.3, 0.6 and 1, for the three NaI crystals utilized, where r is the radius of the beam and R that of the scintillator. The photopeak efficiency of the scintillation counters was determined by comparing it with that of a magnetic pair spectrometer. To this purpose, the ratio of the respective solid angles Os/Op must be known; measurements and computation led to the value Os = ( 2 5 . 4 +
~2p
1.0) x 10 - 3 .
The spectrum of the electric pulses obtained at the output of the photomultiplier was measured by means of a multichannel analyzer 16). The magnetic pair spectrometer permitted gamma energy measurements from 2.6 MeV to 20 MeV. The resolving power ranged from 3.6 %
for an energy of 3 MeV down to 1% for 10 MeV, and the efficiency from 5 x 10 -9 for an energy of 2 . 7 5 M e V t o 9 x 10 -7 for one of 11 MeV. 2.2. DETERMINATION OF THE RESPONSE FUNCTION The shape of the response function for the crystals utilized was determined by measuring the pulse spectrum by means of a 128-channel amplitude analyzer. The measured spectrum had to be corrected for a background resulting from the reactor and the pulse spectrum of lines accompanying the principle line. In the case of the lead target, the reactor background was obtained from pulse spectrum measurements, utilizing a bismuth target of equal size, or a graphite target in the case of the remaining elements. Bismuth and graphite are best suited for this purpose. They have a low cross section for the (n,?) reaction (for Bi, a = 32 mb; for C, a = 3.2 rob), very simple gamma ray spectra, and scattering properties with respect to gamma rays resembling those of the elements measured. In the range under consideration, the spectrum of bismuth consists of the following three lineslT) : 4.052 MeV (28), 4.099 MeV (19), 4.166 MeV (34) (the numbers in the brackets give the relative intensities). Similarly, that of carbon presents three lines onlyl8) : 4.95 MeV (69), 3.68 MeV (31), 1.28 MeV (31). The required background curve is obtained by subtracting the respective lines from the spectrum measured. The reactor spectrum (at least for higher energies) displays no structure and can be accounted for by a smooth function. The energies and intensities of the associated lines are to be found in papers by Bartholomew and Higgs19), by Groshev et a/. 2°) and by Troubetzkoy21). The intensity of the concomitant lines in the neighbourhood of the principal line is generally is) R. Miiller, Z. angew. Math. Phys. 13 (1962) 13. 1~) H. T. Motz (private communication). 18) L. Jarczyk, J. Lang, R. Miiller and W. W61fli,HPA 34 (1961) 483. xg) G. A. Bartholomewand L. A. Higgs, Atomic Energy of Canada Ltd., Rep. 669 (1958). 2o) L. V. Groshev et al., Atlas of Gamma Ray Spectra from Radioactive Capture of Thermal Neutrons (Pergamon Press, London (1959). 3t) E. Troubetzkoy, Oak Ridge Nat. Lab. Rep. 2904 (1961).
PItOTOPEAK
EFFICIENCY
OF VARIOUS
lesser b y a factor of at least 10. In subtracting the associated lines, in addition to the change in their intensity, that of the counter efficiency and of the response function was taken into account.
NaI(T1) A N D CsI(T1) C R Y S T A L S
313
these lines have the same intensity, the resulting surface was divided according to the ratio of the total efficiencies of the crystal for the energies 1.38 MeV and 2.76 MeV.
5.43 MeV
ZOO0
,ooo
"..,-/
--_ --
=
'/
-
= ~ _ -
.
.
.
.
"4
~
8'0
I
.
.
I00
t
.
.
.
...
L~_=E___-..~
t 120 Pulse height
Fig. 1. M e a s u r e d s p e c t r u m of p u l s e h e i g h t , for s u p l h u r t a r g e t , o b t a i n e d w i t h a 3" × 3~ NaI(T1) c r y s t a l , t o g e t h e r w i t h a n a l y s i s C u r v e 1 : r e a c t o r b a c k g r o u n d ; c u r v e s 2 - 8 : a s s o c i a t e d lines.
This is exemplified in fig. 1, where the experimental spectrum as obtained for sulphur with the 3" x 3" NaI(TI) crystal is shown. Graph 1 is that of the reactor background, and graphs 2-8 are those of the shape of the various associated lines. On summation of all the corrections and subtraction from the measurements, new points were obtained determining the response function for a given crystal and gamma energy. The response function could not be determined for small pulses owing to increasingly large inaccuracy as a result of the increasing reactor background and summation of error in correcting for associated lines. Consequently the measured tail for all energies and crystals was extended horizontally to pulse height zero. For the Na 2. source, separation of the 1.38 and 2.76 MeV lines was effected as follows: As both
For each crystal and each w a y of irradiation the curves for the various energies were assembled in one diagram. The system was normalized so that the maxima of the photolines coincided. This causes, b y various accounts, the zero points of the spectra for different lines to be displaced. Such representation admits of a better comparison of the results and reveals regularities in the changes of the response function for different gamma energies. In particular, the changes in height of both escape peaks can be determined as a function of the energy, thus permitting an easy interpolation for all intermediary gamma energies. Two examples of such diagrams are shown in figs. 2 and 3t. Furthermore, for illustration, the response functions for one energy each, in function of the crystal dimensions and of the diameter of the gamma ray beam, are also outlined (figs. 4 and 5). 2.3. E V A L U A T I O N O F T H E P H O T O P E A K
t A n a l o g o u s figures for t h e o t h e r c r y s t a l s a n d for f u r t h e r b e a m g e o m e t r i e s (r/R = 0.6 a n d r/R = 1) as well a s m o r e a c c u r a t e c u r v e s of t h e p h o t o p e a k efficiency ~ (E) a r e a v a i l a b l e on r e q u e s t .
EFFICIENCY
In the case of a collimated beam, the photopeak efficiency was determined b y three methods. The first consisted in applying the results derived in the
L. J A R C Z Y K gt al.
314
Gamma I 2
3 4 ,5
Energies 10.03 MeV 7.38 ,, s.4a ,
,5.43 4.s3
i xA /l\ /" \
. .
/
\
/
E'g- 2.0 MeV
\
E¥-1.0 MeV
Elf
Fig. 2. Pulse height distribution for narrow parallel beam of gamma rays of energy ranging between 1.38 MeV and 10.83 MeV, obtained with the 3" × 3" NaI(T1) crystal.
Gamma Energies I 2 3 4 ,5 6
~ T . ~
10.83 IVleV 7.38 ,, 8.42 ,, `5.43 , 4.93 " ~.,54 ,,
---:--~
I
----- - - - - - - " ~ I
E~-2MeV
/1\ /
\
/ /
....
,,~
\
/
\ .c.
.~l!~ "'/,'J !~
......
i
i
E ~ - IMeV
8
i
,
E~
Fig. 3. Pulse height d i s t r i b u t i o n for n a r r o w parallel beam of gamma rays of energy r a n g i n g between 1.38 M e V and 10.83 MeV, obt ai ned w i t h the 5= × 4 ~ NaI(T1) crystal.
PHOTOPEAK
I
EFFICIENCY
NaI(TI) A N D CsI(Tl) C R Y S T A L S
2"X 2" NOI
315
/~
J ...........
OF VARIOUS
/
~
t
,,A,
/.-7"-~.k.'/i 1,7,
_
\\
I 5.0 MeV
I 6.0 MeV
\ \'-,. £1 (MeV)
Fig. 4. R e s p o n s e f u n c t i o n for different scintillation crystals for n a r r o w parallel beam, E r = 6.42 MeV.
, ~/R = ,.oo ~/~ .o.~, ~,~ : o.~
/,\ /
6.0
Fig. 5. Variation of t h e pulse h e i g h t d i s t r i b u t i o n according to t h e value of of 7.38 M e ¥ ,
\
7.0
E~' (MeV)
r/R, for t h e 3" × 3" NaI(TI) c r y s t a l a n d an energy
316
L. J A R C Z Y K e t a/.
preceding section. From the known shape of the response function, the photofraction p* was determined as follows: A Gaussian curve was inscribed into the photopeak; the ratio of the area of the Gaussian curve to the total area yielded the photofraction p* for a given gamma energy. The photopeak efficiency was obtained on multiplying the photofraction p*(E) b y the total efficiency e(E). The latter quantity was calculated from the expression s(E) = 1 - e -~(E)'L with the values of the attenuation coefficient given b y Grodstein 22) and Bell et al.2a). The second method is based on a comparison of the photopeak efficiency of the scintillation counter with the efficiency of a magnetic pair spectrometer. This implied determining the absolute efficiency of the pair spectrometer, which was done in two steps. First, the relative shape of the efficiency curve of the magnetic spectrometer was determined. This was done b y using targets of two homogenously mixed substances. The ratio of the number of coincidences in the maximum of line nl relating to the first substance and that of line n2 of the second is given b y the f o r m u l a nA = Nt n2
" ffl
"
qtT(E1) " %(El)
(2)
N 2 " 0"2 " q2 T ( E 2 ) " ep(E2) '
where a is the cross section for thermal neutron capture, q - intensityin gamma-quanta per neutron capture, T ( E ) - the total attenuation of gamma rays of energy E in the target and along the path leading from the spectrometer to the target, ep(E) the efficiency of the magnetic spectrometer for the energy E, and N - the number of atoms of the isotope in the sample. Na, Pb and C were chosen for calibration. The q-values for these substances are known. For the 7.38 MeV line of Pb, q = 1 2o), for the 2.76 MeV activation line of Na 24, q = 1, and for the 4.95MeV and 3.68 MeV lines of carbon 0.69 and 0.31 respectively I s). In the measurements, targets were used, con32) G. W. Grodstein, X - R a y Attenuation Coefficients from 10 keV to 100 Me¥, National Bureau of Standard Circ. No. 583 (1957). 29) p. R. Bell, R. C. Davis, D. S. Hughes, W. H. Jordan and C. A. Randall, Oak Ridge National Laboratory Report No. 1415 (1953).
taining 700 g N a F and 300 g of graphite, mixed respectively with 600 g PbO and 170 g PbO. The following values were obtained: %(7.38) _- 7 0 . 2 ,
%(2.76) %(7.38) = 19.3, %(3.68) %(7.38) -- 5.2. %(4.95) Absolute calibration of the pair spectrometer was then carried out in measuring the gamma ray flux emerging from the reactor with the three NaI(T1) crystals. For this, the values of the photopeak efficiency as obtained b y the first method for the same crystals and an energy of 2.76 MeV were used. B y comparing the gamma ray flux of energy 2.76 MeV with the number of coincidences recorded b y the pair spectrometer, the absolute efficiency for energy 2.76 was obtained. The results from the three NaI crystals were in good agreement, maximum deviations from the average are less then 3 %. The mean value from several measurements yielded %(2.76) = 4.87 x 10 -9. Comparison with the absolute efficiency, obtained from integration of the Bethe-Heitlerformula for 4 different energies, proved good agreement. Above 7.4 MeV theoretical curves were used, as no test elements with exactly determined q-value are known. With the calibrated pair spectrometer, for gamma energies above 2.76 MeV, the photopeak efficiency of the various crystals could then be determined, using the following formula:
it(e) =
Ns(E ) • %(E). ap .¢p Np(E). as" d?s
(3)
Ns(E) is the number of pulses per photopeak per second, as given by the area of the inscribed Gaussian curve, N p ( E ) - the number of coincidences of the pair spectrometer, Op- the solid angle of collimationof the magnetic spectrometer, and ~ that of the crystal spectrometer.~bp/$, is the ratio of the neutron fluxes corresponding to measurement with the pair and crystal spectrometers.
PHOTOPEAK
EFFICIENCY
The third method was applied at the energies 7.38 MeV and 10.83 MeV only. It consisted in comparing the efficiency of the scintillation counter for a given value of the energy and that for 2.76 MeV. For this, a target containing 10 g N a F and 700 g PbO and one containing 10 g N a F and 600 g melamine were used. The substances were mixed homogeneously. Subsequently, the number of pulses in the photoline for gamma quanta of energy 7.38 MeV resp. 10.83 MeV was measured. The same measurements were carried out for the Na 2. activation line of energy 2.76 MeV with the reactor shut down. From the known time of activation and photopeak efficiency for 2.76 MeV, the photopeak efficiency for the energies of 7.38 MeV and 10.83 MeV, respectively, was determined, The resulting values of the photopeak efficiency obtained by these three methods are illustrated in The errors in the determination of the photopeak efficiency come from different sources, varying according to the method of measurement. With few exceptions they do, however, not exceed 8-12 %. On determination of the peak to total ratio [ Z(E)
0.7
~
0.6
I
I I 2 3 4
0.3
0.2
5"x4" Nal 2S//4"xZl/4" Ctl
3"x3" No! 2"x2" Nat
\
~
\
0.1
~
2
4
"-~t)....,~..~
6
- ~
8
317
OF V A R I O U S NaI(T1) AND CsI(T1) C R Y S T A L S
~ ,
I0 E~r (MW)
Fig. 6. Photopeak efficiency for narrow beam. • E v a l u a t e d from peak to t o t a l ratio (method 1). O Obtained b y comparison with t h e pair spectrometer-efficiency (method 2). [] F r o m measurements w i t h t a r g e t s of two mixed substances (method 3) t.
(method 1) errors up to 10 % are possible on deduction of associated lines with not sufficiently known q-values; furthermore an uncertitude occurs from the completion of the spectrum for small x (E) 0.7 5"x4" NaI z zW~zWc, t 3 3"x3"NaI 4 2"x2" Not
0.6
o.5 0.4 ~ \ oz \ ~ o.2 ~,.~
OA
2
4
6
8
I0 E~ (MIV)
Fig. 7. Photopeak efficiency for broad parallel beam. • Evaluated from peak to t o t a l ratio. [] Obtained b y comparison with narrow beam measurementst.
pulses. A better accuracy of approx. 3 % is obtained with Na 24 (2.76 MeV). This error is also transmitted to the results of the other methods. Furthermore, the measurements with the pair spectrometer (method 2) m a y cause inaccuracy in the curve of efficiency with errors of 5 % at 7.38 MeV and 10 % for other energies. The mixed target method (method 3) brings for gamma energy 7.38 MeV an accuracy of approx. 5 %, whereas at 10.83 MeV the accuracy is not more than 15 % in view of the divergence in the q-values. It should be noted that in all cases the experimental photopeaks extend to higher energies than the Gaussian curves inscribed therein. The difference in the area varies with gamma energy, ranging from 3 % for the lower energies to 8 % for higher energies. In calibrating the scintillation counters, the area of the Gaussian curve as inscribed into the experimental curve was always employed. t cf. foot note p. 52.
L. J A R C Z Y K et al.
318
Further measurements in order to determine the photopeak efficiency for a broad parallel beam were made using gamma rays having energies of 661 keV, 2.76 MeV, 5.43 MeV, 7.38 MeV and 10.83 MeV respectively. The measurement procedure was similar to the method 1 used for the narrow beam: From the given shape of the response function, the photofraction p*(E) and hence ~(E) were determined (fig. 7). Moreover the variation of the photofraction in function of the value of the r/R was determined. For this, lead blocks with apertures of radii r such as to yield an r/R ratio of 0.1, 0.3, 0.6 or 1.0 were placed in the path of the parallel beam irradiating the crystal. The Gaussian curve was inscribed into the photopeak of the response function. With the so-determined q u a n t i t y N, and the radius r of the beam incident upon the crystal, the ratio Nd=r 2 yields the variation of the photopeak efficiency ~(E) with r/R. In particular, the values were obtained for the beam irradiating the whole crystal. Fig. 8 depicts a curve of p*/p* versus r/R for the 3" x 3" NaI crystal and gamma quanta of 7.38 MeV. In a further run of measurements the scintil-
lators were irradiated with a narrow beam parallel to its axis. The point of incidence of the beam on the crystal was moved along the radius from the centre towards the edge, with gamma ray intensity constant. This procedure yielded the function p*(E,r') for a collimated beam ($ = 6 mm), with r' denoting the distance of the beam's axis from that of the crystal. The p*(E,r) values for different r]R were derived from the formula
f" p "(E, r')2nr' dr' p'(E,r) =
o
(4)
f
" 2~r' dr' 0
The points thus obtained for the 3" x 3" NaI crystal and 7.38 MeV are also given in fig. 8. The average values for the beam irradiating the entire scintillator, as obtained by the two last methods, are also included in fig. 7. The results obtained served also for determining the percentage variation of the photopeak efficiency for the broad as compared with that of the narrow beam; this is :
~/a.
R(E) = ~°(E) - ~cR(E) r0(E )
x 100%,
(5)
I.{2
0.8
with w0(E) denoting the photopeak efficiency for the collimated beam, and rR(E) -- t h a t for the wide beam irradiating the entire crystal. Table 2 summarises the results. The latter are correct to within
\
5%.
o,
0.2
0.4
0.6
0.8
3. Discussion of the Results
r/R
Fig. 8. Dependence of the photofraction on the ratio r/R, for the 3 " × 3" NaI(T1) crystal and an energy of 7.38 MeV.
In spite of the amount of work put into research on the scintillation counter, the essential point of
TABLE 2
Reduction R(E) of the photopeak efficiency, comparing broad beam with narrow beam measurements. Energy (MeV) Crystal
NaI 2" NaI 3" NaI 5" CsI 2~"
× X X ×
2" 3" 4" 2~~
0.661
1.38
2.76
5.43
21% 22% 22%
27% 26%
30%
42% 42% 42%
28% 27%
32% 32% 32%
39%
7.38
10.83
45%
53%
44% 43 % 44%
52%
50% 50%
P t I O T O P E A K E F F I C I E N C Y O F V A R I O U S NaI(T1) A N D
difficulty in the w a y of comparing the results resides in the diverging conditions of irradiation of the crystals with gamma rays. A comparison of the response function between ctf= 4.45 MeV
/l),/l \ A
CsI(T1) C R Y S T A L S
319
TABLI~ 3 Photofraction results compared 2" × 2" NaI(T1) crystal, broad beam Gamma energy (MeV)
Results of Miller
2.68 4.49 6.13 7.10 8.00
0.189 0.II0 0.069 0.056 0.045
Results of present work
et al. 13)
4
'
0.156 0.075 0.049 0.042 0.035
Table 4 Photofraction results compared 5 " × 4" NaI(T1) crystal, narrow beam Pulse h~ht
Gamma I energy
g~= 6.13 MeV
(MeV)
iI
Pulse height
Fig. 9. Response function obtained experimentally (dashed line) and the one calculated by Miller 12) (continuous line).
our results and those calculated b y Miller and Snow 13) is possible for the 2" x 2" NaI crystal and broad beam. Fig. 9 gives the response function obtained from Miller's results extended to finite resolution, together with those interpolated from the experimental curves of the present investigation. The agreement in the area of escape peaks is considerable; yet for the higher energies the calculations yield somewhat too great values. More important, however, is the discrepancy in the tail, where the calculated results are lower throughout. This explains also the difference in the values of the photofraction as illustrated in table 3 for the same crystal, or in table 4 for a 4" x 5" NaI crystal with narrow parallel beam. Errors in the experimentally determined response function might occur on account of beam scattering from source, collimator, etc. This can, however, in no case completely explain the dis-
0.661 1.33 2.62 4.45
Results due t o : present Miller x2) Berger n) Schmidt~) F°°teS) I work 0.819 0.651 0.510 0.447
0.821 0.667 0.531 0.491
0.71
0.46 0.29
0.8
0.74 0.55 0.41 0.31
crepancy, since then the photofractions obtained b y methods 2 and 3, for the determination of which the tail was not required, would not agree with those of method 1. The Monte-Carlo calculations contain simplifications, the influence of which cannot be estimated easily. To mention only the assumption that with pair production positron and electron should obtain the same energy, wherefore the escape of bremsstrahlung is underestimated. Zerby and Moran 14) mention that their calculations show considerably lower values in the photofraction than those of Miller and Snow. Unfortunately, these authors have not calculated a case that can be compared with the present experimental results. Moreover, measurements dealing with the variations of the photofraction as a function of beam width can also be compared: Berger and Doggett t i) calculated that, at 0.661 MeV, the variation of the photofraction lies between 18 % and 20%, according to the size of the crystal. Kreger*) obtained 2 4 % at 661 keV and 2 7 % at 1.11 MeV for a 4 " x 4" NaI crystal. The present investigation yielded, for all crystals utilized, 22 % at an energy of 0.661 MeV, and 26 % at 1.38 MeV.
320
L. J A R C Z Y K a a / .
Acknowledgements The authors wish to thank Prof. P. Scherrer and Prof. P. Marmier for their kind interest in the present investigation and Mr. R. Boesch for his experimental assistance. The authors are also in-
debted to the staff of the Saphir reactor, in particular to Dr. P. Schmid. One of us (L. J.) expresses his very sincere thanks to the Schweizerische Schulrat, for the grant of a scholarship which enabled him to participate in the present investigation.