- Email: [email protected]
Study of the background characteristics by means of a high efficiency liquid scintillation counter
S
S T U D Y OF T H E B A C K G R O U N D C H A R A C T E R I S T I C S BY M E A N S OF A H I G H EFFICIENCY LIQUID SCINTILLATION COUNTER M. ALESSIO, L. ALLEGRI, F. BELLA and S. IMPROTA Istituto di Fisica dell' Universitd di Roma, Centro lnterdisciplinare per le Datazioni col Metodo del t4C, Rome, Italy
Received 10 May 1976 A high efficiencyliquid scintillation counter used for studying the characteristics of the background of a counter is described. Measurements have also been carried out in underground laboratories. An asymptotic formula for the evaluation of the intrinsic background of the counter is proposed. I. Introduction
2. The counter and its characteristics
The problem of increasing the figure of merit E 2 / B of a counter, where E is the efficiency and B the background, involves specifically its background when the activity of low intensity, low energy sources is to be measured. The background of a counter can be considered as due to three different components, namely: (1) the cosmic radiation, (2) the room radioactivity, (3) the inner activity due to the materials used for the con,;truction of the counter, to cross-talk effects, etc.1). In order to evaluate the contribution of every single component, a systematic study of the characteristics of each of them was undertaken. A liquid scintillation counter, normally used in this laboratory for 14C dating, was employed in this experiment.
2.1. DESCRIPTIONOF THE COUNTER
Fig. 1. Sample vial.
The detecting system consists of a sealed cylindrical glass counting vial, 10cm a in volume (see fig. 1), inserted in a light-guide (fig. 2) which is placed between two photomultipliers working in coincidence. The samples whose activity is usually measured in this laboratory are made of benzene and are mixed in the counting vial with commercial liquid scintillator (NE 216) supplied by Nuclear Enterprises Limited having paraxylene as a solvent. The detector-photomultipliers unit is held together by a PVC cylinder (fig. 3) which is placed inside a
Fig. 2. Light-guide.
538
M. A L E S S I O et al.
plastic scintillator viewed by a third photomultiplier in anticoincidence with the first two (fig. 4). The whole apparatus is enclosed in a box at the controlled temperature of 12°C and is shielded by 27 cm of iron. 2.2.
EFFICIENCY CURVE AND FIGURE OF MERrI'
As the radioactive species is a liquid other than the solvent of the added scintillator, the efficiency varies with the concentration of the liquid scintillator in the mixture. As is known2), this is due to two different reasons: 1) The conversion factor s of the solvent can be considerably different for the different solvents, as is the case for paraxylene and benzene. 2) The solvent-solute energy transfer quantum efficiencyfis affected by the presence of the radioactive
TABLE l Variation of efficiency and background with concentration.
Concentration c
Efficiency E(%)
Background B (cpm) a = 0 . 1 6 cpm
Figure of merit
0.98 0.95 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10
97 94 95 94 93 92 91 90 88 84 74
7.02 6.98 7.19 6,87 6,79 6,90 7,00 6.59 6.69 6.85 6.69
1340 1270 1240 1270 1280 1210 1180 1220 1170 1030 820
E2/B
species, owing to the dependence of f on both the solvent nature and the solute concentration. The radioactive species used in this laboratory to determine the efficiency curve was a standard F-source consisting of l gC in the chemical form of n-hexadecane, supplied by The Radiochemical Centre (Amersham, England), diluted in different proportions. The curve thus obtained is shown in fig. 5. Each of the points in fig. 5 is derived from the integral of the B-spectrum at the corresponding concentration measured with a multichannel analyzer. In fig. 6 several such spectra are shown in order to clarify the variation of shape with varying concentration. These spectra have been obtained by subtracting the background which, as follows from table 1, remains practically constant when the concentration is varied. Furthermore, the differential spectrum of the background does not vary appreciably with varying concentration. A typical spectrum is shown in fig. 7b. It follows that also the figure of merit E2/B depends on concentration. 3. Characteristics of the background
Fig. 3. PVC cylinder for assembling the photomultipliers.
As has been already said in sect. 1, the background of a counter is due to three difl'erent causes, i.e. the cosmic radiation, the room radioactivity and the inner activity. The contribution of each of the above-mentioned factors cannot be evaluated by the usual techniques for discriminating the heights of the pulses, as these appear superimposed in the differential spectrum of the background. Nor is it possible to eliminate the unwanted components resorting to techniques such as anticoin-
BACKGROUND
539
CHARACTERISTICS
Fig. 4. T h e w h o l e a p p a r a t u s w i t h the plastic s c i n t i l l a t o r a n d the t h i r d p h o t o m u l t i p l i e r .
cidence shielding; these, in fact, though eliminating the penetrating component of the cosmic radiation, are partly efficient even as far as the room radioactivity is concerned. Examples of this behaviour are given[in curves a and b of fig. 7, which show the background spectrum
,ttI
0.96 b
0.92! o.~-I
without and with the anticoincidence shielding. These spectra were obtained by using the counter described in sect. 2, according to the block diagram reported in fig. 8 in the arrangement IA; the last one with the connection (2 2 inserted.
chmn 24O
oN~ 0.7f
~o
O.T,
0001
02
0.4
0.6
0.8
1. C
Fig. 5. V a r i a t i o n o f the efficiency as a f u n c t i o n o f the v o l u m e c o n c e n t r a t i o n c o f the l i q u i d s c i n t i l l a t o r in the s o l u t i o n .
20
40
60
80
ch~nd
Fig. 6. C o n f i g u r a t i o n s o f f l - s p e c t r u m for different c o n c e n t r a t i o n s c o f the l i q u i d s c i n t i l l a t o r : c u r v e 1 c = 0.10; c u r v e 2 e = 0.20; curve 3 c=0.30; curve 4 c=0.40; curve 5 c=0.60; curve 6 c = 0.90; c u r v e 7 c = 0.98. T h e a c c u m u l a t i o n t i m e is 22 h for all the s p e c t r a o f figs. 6, 7, 9, 10, 11, 12, 13a, 13b. ( P u l s e s / c h a n n e l x 10-3.)
540
M. A L E S S I O et al.
The spectrum of the pulses from the photomultiplier connected to the plastic scintillator obtained with the arrangement 2B of fig. 8 is particularly interesting as it is possible to note the presence of a peak, indicated with # in fig. 9, situated in the region of higher energy; the area of this peak amounts to about 80% of the integral of the spectrum.
4. Background variations with shielding; effect of the cosmic radiation In order to study how the background is affected by the variation of the shielding from all the external agents, an experiment was carried out in which the counter was shielded with different Pb thicknesses. Measurements have shown that the shape and the area of the #-peak remain unchanged when the thickness is varied slightly (fig. 10). On the basis of these results, the appearance of this peak has been considered as due to the penetrating component of the cosmic radiation. This assumption has been confirmed by measurements carried out in a
tunnel under Mont Blanc, with a thickness of overlying rock of about 5000 mwe. In these conditions the #-peak disappeared completely, as shown in fig. 11. Similar measurements were carried out at the underground laboratory under Monte dei Cappuccini, in Turin, with an overlying thickness of sandy ground of about 70 rowe. It is to be noted that the #-peak reappears in the spectra with an intensity definitely less than that of the peak of fig. 10, relative to the Rome laboratory, in agreement with the different attenuation of the mesonic component (fig. 12)3). A study of the local radioactivity in different shielding conditions was also carried out in the two above
~r cham 24~
! i 2~
,
\ \
0
40
80
120
160
200
240
280
320
360 channel
Fig. 9. Spectrum from the photomultiplier connected to the plastic scintillator (arrangement 2B in fig. 8). (Pulses/channel x 10-23
I i
0
40
80
120
160
200
240
280
320 channel
Fig. 7. Curve a: b a c k g r o u n d spectrum without anticoincidence shielding. Curve b: b a c k g r o u n d s p e c t r u m with anticoincidence shielding. C o n c e n t r a t i o n o f the sample c = 0.90.
4e~
i
4o[
I' t
• without Pb shielding . with 10cm Pb ~hiekiing with 15cm Ph shelding
21k 0
40
eo
~
'
~ 2~0
~GATE IN IN
L ~ J
Fig. 8. D r , D2, Da: discriminators; C1C2: coincidences; (2z: anticoincidence o u t p u t o f C2 ; T1 Tz : triggers.
Fig. 10. Spectra from the photomultiplier connected to the plastic scintillator (arrangement 2B in fig. 8) for different Pb thicknesses. T h e s h a p e and position o f the p-peak are not comparable to those o f fig. 9, as in the present experiment a different integrator was used. (Pulses/channel x 10-2.)
BACKGROUND
541
CHARACTERISTICS
c~
• without Pb shielding t~ with lOon Pb shielding
4E
4~
4(
o with 15cm Pb shiel~mg
4O
3;
32
2~
24
I
0
40 80 12fl channel Fig. 1. Spectra f r o m photomultiplier connected to the plastic scintillator ( a r r a n g e m e n t 2B in fig. 8) at the laboratory u n d e r M o n t Bhmc: curve a: w i t h o u t Pb shielding, curve b: with 10 cm Pb shielding, curve c: with 15 c m Pb shielding. (Pulses/channel × I0-2.)
40
80
120
160
200 channel
Fig. 12. Spectra f r o m photomultiplier connected to the plastic scintillator (arrangement 2B in fig. 8) at the laboratory u n d e r M o n t e dei Cappuccini in Turin. (Pulses/channel × 10-2.)
r
oulses charm 18ff
!
,°i/1 Ii',l/
1 I! I/
40
\
\
I
20~-
\\\
0 ~ ~ - ~ ~~ -~ 0 40 80 120 160 200 240 channel Fig. 13. (a) Spectra obtained without Pb shielding using the anticoincidence shielding: curve a: in R o m e , curve b: at the laboratory u n d e r M o n t Blanc, curve c: at T u r i n laboratory. (Pulses/channel × 10-3.)
40
80
120
160
200
240 d~nel
(b) Spectra obtained with anticoincidence shielding. Curves a, a': R o m e laboratory, curves b, b': M o n t Blanc laboratory, curves c, c': T u r i n laboratory. T h e curves a, b, c were obtained with 10 c m Pb shielding; the curves a', b', c' with 15 c m Pb shielding.
542
M. A L E S S I O et al.
TABLE 2 Experimental results f o r / ~ ( x ) in three different laboratories, and values of 7p. Laboratory
/~(x~) (cpm)
/~(x2) (cpm)
/t(x3) (cpm)
~. (cpm) extrapol, value integral of the /t-peak
Rome
477.2±0.5
20.144-0.06
16.93±0.06
Mont Blanc
254.9±0.4
3.28±0.03
2.00:t:0.02
- 0 . 1 ±0.8
Turin
159.1 ± 0.2
3.52 4- 0.03
2.67 4- 0.03
1.3 ± 0.6
12
±2
13.8 ±0.1 /t-peak absent 0.97 ± 0.03
a Xl=Xo; X2__Xo=(13± 1)cm; xa--Xo=(21 ± 1 ) c m ; mean calculated thicknesses of the lead shielding. The errors quoted in the extrapolated value of ~. are overall uncertainties.
mentioned uderground laboratories, as well as in Rome, thus obtaining a useful comparison. In figs. 13a and 13b the differential spectra obtained using the ant±coincidence shielding are shown.
5. Limiting background of a counter; asymptotic determination Measurements carried out in the three abovementioned laboratories under different shielding conditions have demonstrated that the background decreases as a function of the shielding thickness tending to a limiting value representing the contribution of the inner activity alone. This limiting background can, therefore, be evaluated by extrapolating the measurements corresponding to shieldings of increasing thickness; in the absence of a sufficiently high number of measurements, the limiting background can be estimated using a convenient asymptotic formula connecting the background B(x) to the thickness of the corresponding shielding, as viewed from the centre of the detector. This thickness is unambiguously defined for a spherical geometry; but in the commonest cases in which different geometries are employed, this evaluation is difficult and a calculation of an average thickness must be resorted to. An empirical formula having the wanted characteristics and seeming to describe the asymptotic behaviour suggested by the experimental results to a reasonable approximation is the following B (x) = c~i +
7
1 + (X-Xo)/6' where cq
(1)
TABLE 3 Resulting values for ~.?'. Laboratory
Rome Mont Blanc Turin
B(xz) (cpm)
B(x2) (cpm)
651.0±0.9 363.2±0.9 229.7±0.4
13.97:t:0.09 7.11 ±0.06 9.16±0.07
:ti
(cpm)
(cpm)
10.23±0.09 4 4-2 5.44-t:0.04 3 ± I 7.4 -I-0.3 4.5±2.5
xl =Xo; x z - X o = ( 1 3 4 - 1 ) cm; x 3 - X o = ( 2 1 ± l ) cm; mean calculated thicknesses of the lead shielding. The errors quoted on the extrapolated value of c~i are overall uncertainties. The considerable error on B(xs) for the measurements at Turin Laboratory is due to some misfunctioning of the apparatus which gave rise to irregularities in the counting rates in the case of the arrangement 1A in fig. 8.
X-Xo
= calculated average thickness of the added shieldings, x0 = average value of the unavoidable shielding effect on the detector of all the materials necessary for the assembling and for the regular functioning of the counter. 7 and 6 = constants typical of the particular room radioactivity and of the shielding material; determined experimentally. If the counter has no ant±coincidence shielding, the previous formula can still be used, provided the thicknesses of the shieldings are not large enough to give rise to an appreciable attenuation of the muonic component of cosmic radiation. In this case the limiting background is increased by the contribution of the muonic component ct~, and the formula can be written as follows
B'(x) = ~i+cg + = limiting background,
B(xj
1 + ~X-Xo)/~'
.
(2)
BACKGROUND CHARACTERISTICS
By extending these considerations to that component
B(x) of the radiation which can be suppressed by means of the anticoincidence, one has
B(x) = % +
7' I + (X-Xo)/6'
7 1 + (X-Xo)/6
If follows that, for x ~ oo, the limiting value of B(x) is %. 6. Comparison with the experimental results and conclusions It is possible to check experimentally that % is the limiting value orB(x) for x--, oo. This test can be carried out independently through evaluations of ~. based on the area of the/~-peak in figs. 10, 11 and 12. In table 2 the experimental results for B(x) obtained in the three different laboratories are reported and the values of e, calculated with the formula are compared to those obtained graphically according to what was explained above. The results reported in the last two columns of table 2 show an excellent agreement which enables one to think that the type of dependence indicated in eq. (1) represents a convenient description of the phenomenon under consideration, thus allowing an evaluation of the limiting background. Therefore, using the values of B(x) obtained in the three laboratories, the values of 7~ are derived, resulting in table 3.
543
As is seen, the values of ~i obtained show a satisfactory agreement. However, a further elaboration to obtain the average value to be taken as the limiting background of the counter would be meaningless from a probability point of view, owing to the nature of the errors. These, in fact, have been calculated as overall uncertainties on the basis of the calculated thickness and of the statistical fluctuations in the counting rates; they are probably overestimated, as indicated by the relatively small dispersion in the value of cq. We express our thanks to Prof. C. Castagnoli, Director of Mont Blanc and Turin Laboratories of Cosmogeophysics for his kind hospitality, and Ing. F. Cuaz, Director of the Gestione ed Esercizio del Tunnel del Monte Bianco, for his help. The assistance of Mr M. Canonico, A. Giuliano, A. Romero and R. Saba is gratefully acknowledged• We thank Consiglio Nazionale delle Ricerche for financial support• References 1) D. L. Horrocks, Applications of liquid scintillation counting (Academic Press, New York and London, 1974). z) j. B. Birks, The theory and practice of scintillation counting (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfurt, 1964). 3) G. Bertolini, F. Cappellani, G. ResteUi, E. Fiorini and A. Pullia, IEEE Nucl. Sci. Syrup. on Nuclear science (1972) vol. 19, p. 135.
S T U D Y OF T H E B A C K G R O U N D C H A R A C T E R I S T I C S BY M E A N S OF A H I G H EFFICIENCY LIQUID SCINTILLATION COUNTER M. ALESSIO, L. ALLEGRI, F. BELLA and S. IMPROTA Istituto di Fisica dell' Universitd di Roma, Centro lnterdisciplinare per le Datazioni col Metodo del t4C, Rome, Italy
Received 10 May 1976 A high efficiencyliquid scintillation counter used for studying the characteristics of the background of a counter is described. Measurements have also been carried out in underground laboratories. An asymptotic formula for the evaluation of the intrinsic background of the counter is proposed. I. Introduction
2. The counter and its characteristics
The problem of increasing the figure of merit E 2 / B of a counter, where E is the efficiency and B the background, involves specifically its background when the activity of low intensity, low energy sources is to be measured. The background of a counter can be considered as due to three different components, namely: (1) the cosmic radiation, (2) the room radioactivity, (3) the inner activity due to the materials used for the con,;truction of the counter, to cross-talk effects, etc.1). In order to evaluate the contribution of every single component, a systematic study of the characteristics of each of them was undertaken. A liquid scintillation counter, normally used in this laboratory for 14C dating, was employed in this experiment.
2.1. DESCRIPTIONOF THE COUNTER
Fig. 1. Sample vial.
The detecting system consists of a sealed cylindrical glass counting vial, 10cm a in volume (see fig. 1), inserted in a light-guide (fig. 2) which is placed between two photomultipliers working in coincidence. The samples whose activity is usually measured in this laboratory are made of benzene and are mixed in the counting vial with commercial liquid scintillator (NE 216) supplied by Nuclear Enterprises Limited having paraxylene as a solvent. The detector-photomultipliers unit is held together by a PVC cylinder (fig. 3) which is placed inside a
Fig. 2. Light-guide.
538
M. A L E S S I O et al.
plastic scintillator viewed by a third photomultiplier in anticoincidence with the first two (fig. 4). The whole apparatus is enclosed in a box at the controlled temperature of 12°C and is shielded by 27 cm of iron. 2.2.
EFFICIENCY CURVE AND FIGURE OF MERrI'
As the radioactive species is a liquid other than the solvent of the added scintillator, the efficiency varies with the concentration of the liquid scintillator in the mixture. As is known2), this is due to two different reasons: 1) The conversion factor s of the solvent can be considerably different for the different solvents, as is the case for paraxylene and benzene. 2) The solvent-solute energy transfer quantum efficiencyfis affected by the presence of the radioactive
TABLE l Variation of efficiency and background with concentration.
Concentration c
Efficiency E(%)
Background B (cpm) a = 0 . 1 6 cpm
Figure of merit
0.98 0.95 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10
97 94 95 94 93 92 91 90 88 84 74
7.02 6.98 7.19 6,87 6,79 6,90 7,00 6.59 6.69 6.85 6.69
1340 1270 1240 1270 1280 1210 1180 1220 1170 1030 820
E2/B
species, owing to the dependence of f on both the solvent nature and the solute concentration. The radioactive species used in this laboratory to determine the efficiency curve was a standard F-source consisting of l gC in the chemical form of n-hexadecane, supplied by The Radiochemical Centre (Amersham, England), diluted in different proportions. The curve thus obtained is shown in fig. 5. Each of the points in fig. 5 is derived from the integral of the B-spectrum at the corresponding concentration measured with a multichannel analyzer. In fig. 6 several such spectra are shown in order to clarify the variation of shape with varying concentration. These spectra have been obtained by subtracting the background which, as follows from table 1, remains practically constant when the concentration is varied. Furthermore, the differential spectrum of the background does not vary appreciably with varying concentration. A typical spectrum is shown in fig. 7b. It follows that also the figure of merit E2/B depends on concentration. 3. Characteristics of the background
Fig. 3. PVC cylinder for assembling the photomultipliers.
As has been already said in sect. 1, the background of a counter is due to three difl'erent causes, i.e. the cosmic radiation, the room radioactivity and the inner activity. The contribution of each of the above-mentioned factors cannot be evaluated by the usual techniques for discriminating the heights of the pulses, as these appear superimposed in the differential spectrum of the background. Nor is it possible to eliminate the unwanted components resorting to techniques such as anticoin-
BACKGROUND
539
CHARACTERISTICS
Fig. 4. T h e w h o l e a p p a r a t u s w i t h the plastic s c i n t i l l a t o r a n d the t h i r d p h o t o m u l t i p l i e r .
cidence shielding; these, in fact, though eliminating the penetrating component of the cosmic radiation, are partly efficient even as far as the room radioactivity is concerned. Examples of this behaviour are given[in curves a and b of fig. 7, which show the background spectrum
,ttI
0.96 b
0.92! o.~-I
without and with the anticoincidence shielding. These spectra were obtained by using the counter described in sect. 2, according to the block diagram reported in fig. 8 in the arrangement IA; the last one with the connection (2 2 inserted.
chmn 24O
oN~ 0.7f
~o
O.T,
0001
02
0.4
0.6
0.8
1. C
Fig. 5. V a r i a t i o n o f the efficiency as a f u n c t i o n o f the v o l u m e c o n c e n t r a t i o n c o f the l i q u i d s c i n t i l l a t o r in the s o l u t i o n .
20
40
60
80
ch~nd
Fig. 6. C o n f i g u r a t i o n s o f f l - s p e c t r u m for different c o n c e n t r a t i o n s c o f the l i q u i d s c i n t i l l a t o r : c u r v e 1 c = 0.10; c u r v e 2 e = 0.20; curve 3 c=0.30; curve 4 c=0.40; curve 5 c=0.60; curve 6 c = 0.90; c u r v e 7 c = 0.98. T h e a c c u m u l a t i o n t i m e is 22 h for all the s p e c t r a o f figs. 6, 7, 9, 10, 11, 12, 13a, 13b. ( P u l s e s / c h a n n e l x 10-3.)
540
M. A L E S S I O et al.
The spectrum of the pulses from the photomultiplier connected to the plastic scintillator obtained with the arrangement 2B of fig. 8 is particularly interesting as it is possible to note the presence of a peak, indicated with # in fig. 9, situated in the region of higher energy; the area of this peak amounts to about 80% of the integral of the spectrum.
4. Background variations with shielding; effect of the cosmic radiation In order to study how the background is affected by the variation of the shielding from all the external agents, an experiment was carried out in which the counter was shielded with different Pb thicknesses. Measurements have shown that the shape and the area of the #-peak remain unchanged when the thickness is varied slightly (fig. 10). On the basis of these results, the appearance of this peak has been considered as due to the penetrating component of the cosmic radiation. This assumption has been confirmed by measurements carried out in a
tunnel under Mont Blanc, with a thickness of overlying rock of about 5000 mwe. In these conditions the #-peak disappeared completely, as shown in fig. 11. Similar measurements were carried out at the underground laboratory under Monte dei Cappuccini, in Turin, with an overlying thickness of sandy ground of about 70 rowe. It is to be noted that the #-peak reappears in the spectra with an intensity definitely less than that of the peak of fig. 10, relative to the Rome laboratory, in agreement with the different attenuation of the mesonic component (fig. 12)3). A study of the local radioactivity in different shielding conditions was also carried out in the two above
~r cham 24~
! i 2~
,
\ \
0
40
80
120
160
200
240
280
320
360 channel
Fig. 9. Spectrum from the photomultiplier connected to the plastic scintillator (arrangement 2B in fig. 8). (Pulses/channel x 10-23
I i
0
40
80
120
160
200
240
280
320 channel
Fig. 7. Curve a: b a c k g r o u n d spectrum without anticoincidence shielding. Curve b: b a c k g r o u n d s p e c t r u m with anticoincidence shielding. C o n c e n t r a t i o n o f the sample c = 0.90.
4e~
i
4o[
I' t
• without Pb shielding . with 10cm Pb ~hiekiing with 15cm Ph shelding
21k 0
40
eo
~
'
~ 2~0
~GATE IN IN
L ~ J
Fig. 8. D r , D2, Da: discriminators; C1C2: coincidences; (2z: anticoincidence o u t p u t o f C2 ; T1 Tz : triggers.
Fig. 10. Spectra from the photomultiplier connected to the plastic scintillator (arrangement 2B in fig. 8) for different Pb thicknesses. T h e s h a p e and position o f the p-peak are not comparable to those o f fig. 9, as in the present experiment a different integrator was used. (Pulses/channel x 10-2.)
BACKGROUND
541
CHARACTERISTICS
c~
• without Pb shielding t~ with lOon Pb shielding
4E
4~
4(
o with 15cm Pb shiel~mg
4O
3;
32
2~
24
I
0
40 80 12fl channel Fig. 1. Spectra f r o m photomultiplier connected to the plastic scintillator ( a r r a n g e m e n t 2B in fig. 8) at the laboratory u n d e r M o n t Bhmc: curve a: w i t h o u t Pb shielding, curve b: with 10 cm Pb shielding, curve c: with 15 c m Pb shielding. (Pulses/channel × I0-2.)
40
80
120
160
200 channel
Fig. 12. Spectra f r o m photomultiplier connected to the plastic scintillator (arrangement 2B in fig. 8) at the laboratory u n d e r M o n t e dei Cappuccini in Turin. (Pulses/channel × 10-2.)
r
oulses charm 18ff
!
,°i/1 Ii',l/
1 I! I/
40
\
\
I
20~-
\\\
0 ~ ~ - ~ ~~ -~ 0 40 80 120 160 200 240 channel Fig. 13. (a) Spectra obtained without Pb shielding using the anticoincidence shielding: curve a: in R o m e , curve b: at the laboratory u n d e r M o n t Blanc, curve c: at T u r i n laboratory. (Pulses/channel × 10-3.)
40
80
120
160
200
240 d~nel
(b) Spectra obtained with anticoincidence shielding. Curves a, a': R o m e laboratory, curves b, b': M o n t Blanc laboratory, curves c, c': T u r i n laboratory. T h e curves a, b, c were obtained with 10 c m Pb shielding; the curves a', b', c' with 15 c m Pb shielding.
542
M. A L E S S I O et al.
TABLE 2 Experimental results f o r / ~ ( x ) in three different laboratories, and values of 7p. Laboratory
/~(x~) (cpm)
/~(x2) (cpm)
/t(x3) (cpm)
~. (cpm) extrapol, value integral of the /t-peak
Rome
477.2±0.5
20.144-0.06
16.93±0.06
Mont Blanc
254.9±0.4
3.28±0.03
2.00:t:0.02
- 0 . 1 ±0.8
Turin
159.1 ± 0.2
3.52 4- 0.03
2.67 4- 0.03
1.3 ± 0.6
12
±2
13.8 ±0.1 /t-peak absent 0.97 ± 0.03
a Xl=Xo; X2__Xo=(13± 1)cm; xa--Xo=(21 ± 1 ) c m ; mean calculated thicknesses of the lead shielding. The errors quoted in the extrapolated value of ~. are overall uncertainties.
mentioned uderground laboratories, as well as in Rome, thus obtaining a useful comparison. In figs. 13a and 13b the differential spectra obtained using the ant±coincidence shielding are shown.
5. Limiting background of a counter; asymptotic determination Measurements carried out in the three abovementioned laboratories under different shielding conditions have demonstrated that the background decreases as a function of the shielding thickness tending to a limiting value representing the contribution of the inner activity alone. This limiting background can, therefore, be evaluated by extrapolating the measurements corresponding to shieldings of increasing thickness; in the absence of a sufficiently high number of measurements, the limiting background can be estimated using a convenient asymptotic formula connecting the background B(x) to the thickness of the corresponding shielding, as viewed from the centre of the detector. This thickness is unambiguously defined for a spherical geometry; but in the commonest cases in which different geometries are employed, this evaluation is difficult and a calculation of an average thickness must be resorted to. An empirical formula having the wanted characteristics and seeming to describe the asymptotic behaviour suggested by the experimental results to a reasonable approximation is the following B (x) = c~i +
7
1 + (X-Xo)/6' where cq
(1)
TABLE 3 Resulting values for ~.?'. Laboratory
Rome Mont Blanc Turin
B(xz) (cpm)
B(x2) (cpm)
651.0±0.9 363.2±0.9 229.7±0.4
13.97:t:0.09 7.11 ±0.06 9.16±0.07
:ti
(cpm)
(cpm)
10.23±0.09 4 4-2 5.44-t:0.04 3 ± I 7.4 -I-0.3 4.5±2.5
xl =Xo; x z - X o = ( 1 3 4 - 1 ) cm; x 3 - X o = ( 2 1 ± l ) cm; mean calculated thicknesses of the lead shielding. The errors quoted on the extrapolated value of c~i are overall uncertainties. The considerable error on B(xs) for the measurements at Turin Laboratory is due to some misfunctioning of the apparatus which gave rise to irregularities in the counting rates in the case of the arrangement 1A in fig. 8.
X-Xo
= calculated average thickness of the added shieldings, x0 = average value of the unavoidable shielding effect on the detector of all the materials necessary for the assembling and for the regular functioning of the counter. 7 and 6 = constants typical of the particular room radioactivity and of the shielding material; determined experimentally. If the counter has no ant±coincidence shielding, the previous formula can still be used, provided the thicknesses of the shieldings are not large enough to give rise to an appreciable attenuation of the muonic component of cosmic radiation. In this case the limiting background is increased by the contribution of the muonic component ct~, and the formula can be written as follows
B'(x) = ~i+cg + = limiting background,
B(xj
1 + ~X-Xo)/~'
.
(2)
BACKGROUND CHARACTERISTICS
By extending these considerations to that component
B(x) of the radiation which can be suppressed by means of the anticoincidence, one has
B(x) = % +
7' I + (X-Xo)/6'
7 1 + (X-Xo)/6
If follows that, for x ~ oo, the limiting value of B(x) is %. 6. Comparison with the experimental results and conclusions It is possible to check experimentally that % is the limiting value orB(x) for x--, oo. This test can be carried out independently through evaluations of ~. based on the area of the/~-peak in figs. 10, 11 and 12. In table 2 the experimental results for B(x) obtained in the three different laboratories are reported and the values of e, calculated with the formula are compared to those obtained graphically according to what was explained above. The results reported in the last two columns of table 2 show an excellent agreement which enables one to think that the type of dependence indicated in eq. (1) represents a convenient description of the phenomenon under consideration, thus allowing an evaluation of the limiting background. Therefore, using the values of B(x) obtained in the three laboratories, the values of 7~ are derived, resulting in table 3.
543
As is seen, the values of ~i obtained show a satisfactory agreement. However, a further elaboration to obtain the average value to be taken as the limiting background of the counter would be meaningless from a probability point of view, owing to the nature of the errors. These, in fact, have been calculated as overall uncertainties on the basis of the calculated thickness and of the statistical fluctuations in the counting rates; they are probably overestimated, as indicated by the relatively small dispersion in the value of cq. We express our thanks to Prof. C. Castagnoli, Director of Mont Blanc and Turin Laboratories of Cosmogeophysics for his kind hospitality, and Ing. F. Cuaz, Director of the Gestione ed Esercizio del Tunnel del Monte Bianco, for his help. The assistance of Mr M. Canonico, A. Giuliano, A. Romero and R. Saba is gratefully acknowledged• We thank Consiglio Nazionale delle Ricerche for financial support• References 1) D. L. Horrocks, Applications of liquid scintillation counting (Academic Press, New York and London, 1974). z) j. B. Birks, The theory and practice of scintillation counting (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfurt, 1964). 3) G. Bertolini, F. Cappellani, G. ResteUi, E. Fiorini and A. Pullia, IEEE Nucl. Sci. Syrup. on Nuclear science (1972) vol. 19, p. 135.