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Coincident summing effects in Ge(Li)-detectors
NUCLEAR
INSTRUMENTS
65 (1968) I 2 I - I 2 2 ;
AND METHODS
©
NORTH-HOLLAND
PUBLISHING
CO.
C O I N C I D E N T S U M M I N G EFFECTS IN G e ( L i ) - D E T E C T O R S A. L U U K K O and P. H O L M B E R G
University of Helsinki, Finland* Received 16 August 1968
The advent of the Ge(Li)-spectroscopy technique also enabled detection of very weak transitions in the gamma-ray decay of nuclei. With further development of measurement techniques, the lower limit for intensity has been diminished. One consequence of this is that with a decreasing intensity limit, the effects of sumpulses will become disturbing. This effect is of course reduced, for example, if weak sources and large distances between source and detector are used, but this will influence intensity measurements in an undesirable direction. The literature contains little information on summing effects in Ge(Li)-detectors. However, in principle this effect should be similar to that in NaI(T1)-detectors. In the following, consideration is given to nuclei which emit two g a m m a rays in cascade. The nunlbers of pulses in the two photopeaks are denoted by N~(~I) and Np(72). The notations 51 and e2 are used to indicate the efficiency values for g a m m a rays one and two, to produce a pulse in the corresponding photopeaks. The number of g a m m a rays emitted by a sample of radioactive nuclei can now be expressed as
N(Tt) =Np(71)/r5,{1 - 52 W(0°)q12}],
(1)
N(Tz) =Np(72)/[52{1 - ~1 W(0°)qzt}] •
(2)
The expressions resemble those given by Heath~), valid for NaI(Tl)-detectors. Often, an angular dependence exists between the two g a m m a rays, and this is taken into account by the factor W(0°); q12 is the fraction of ?~ in coincidence with 72- The two g a m m a rays may add up to a sum-pulse, and the area under the sumpeak is expressed by N~ =Np(Tt)e2q,2 W(0°)/[1 - 52 W(0°)q,2]. Usually, for Ge(Li)-detectors leads to
52
(3)
W(0°)qa2< 1, which
N~ -- Np(71)52 W(0°)q12 =Np(72)51 W(O°)q21.
(4)
Eq. (4) can be applied to find out the number of pulses caused by the coincident summing effects of two photopeaks. I f the decay scheme is constructed, q~2 and q2 t are obtainable. As a rule, when the sum effects are observable, the source-to-detector distance is so
511 keY o
1274 keY
o
10~
................. .......
10~ 8
(D
10 ~
°%,,,
.Sum:
%~o./,o peak
oo °0'
I
100
I
200 Channel n u m b e r
I
300
I
400
Fig. 1. Singles spectrum of ~2Na.
small that the solid angle correction leads to a rather close approximation: W(0 °) = 1. The absolute gammaray efficiencies e 1 and 52 for a given geometry are obtainable by the use of standard sources with known activities. Another method for efficiency calibration is that of measuring the number of photo-peak sum pulses in a decay of a known radio-nucleus, which emits two (or more) g a m m a rays in cascade with no cross-over transitions observable. The efficiency of the g a m m a energy concerned can now be calculated by means of eq. (4). If the form of the response function for the detector is known, then the efficiency for different gamma-ray energies is attainable. In this method, it is worthy to note that the decay rate of the source need not be known. Fig. 1 depicts a singles spectrum from a 22Na source, of which the strength was ~ 5 #Ci. A 2 cm 3 Ge(Li)-erystal with a depletion depth of 5 m m was * Department of Physics, Siltavuorenpenger 20 C, Helsinki 17, Finland.
121
122
a . L U U K K O AND P. H O L M B E R G
used as detector. The source-to-detector distance was 12 m m (front face of detector), and the 1024-channel spectrum was recorded on a Nuclear D a t a N D 160 analyser. In the decay of 22Na, the 1.274 MeV level is fed to 100%. T h e / / + - b r a n c h of the decay is 90%, which means that coincidences are obtained between the annihilation radiation and the 1.274 MeV g a m m a rays. These coincidences may add up to a sum-pulse
with an energy of (0.511 + 1.274) MeV. The effect of the sum-pulses is clearly discernible in fig. 1. The present experimental data well agree with eq. (4), which thus provides a possibility for calculation of the summing effects in g a m m a ray spectra. Reference *) R. L. Heath, AEC Report, IDO 16880 (1964).
INSTRUMENTS
65 (1968) I 2 I - I 2 2 ;
AND METHODS
©
NORTH-HOLLAND
PUBLISHING
CO.
C O I N C I D E N T S U M M I N G EFFECTS IN G e ( L i ) - D E T E C T O R S A. L U U K K O and P. H O L M B E R G
University of Helsinki, Finland* Received 16 August 1968
The advent of the Ge(Li)-spectroscopy technique also enabled detection of very weak transitions in the gamma-ray decay of nuclei. With further development of measurement techniques, the lower limit for intensity has been diminished. One consequence of this is that with a decreasing intensity limit, the effects of sumpulses will become disturbing. This effect is of course reduced, for example, if weak sources and large distances between source and detector are used, but this will influence intensity measurements in an undesirable direction. The literature contains little information on summing effects in Ge(Li)-detectors. However, in principle this effect should be similar to that in NaI(T1)-detectors. In the following, consideration is given to nuclei which emit two g a m m a rays in cascade. The nunlbers of pulses in the two photopeaks are denoted by N~(~I) and Np(72). The notations 51 and e2 are used to indicate the efficiency values for g a m m a rays one and two, to produce a pulse in the corresponding photopeaks. The number of g a m m a rays emitted by a sample of radioactive nuclei can now be expressed as
N(Tt) =Np(71)/r5,{1 - 52 W(0°)q12}],
(1)
N(Tz) =Np(72)/[52{1 - ~1 W(0°)qzt}] •
(2)
The expressions resemble those given by Heath~), valid for NaI(Tl)-detectors. Often, an angular dependence exists between the two g a m m a rays, and this is taken into account by the factor W(0°); q12 is the fraction of ?~ in coincidence with 72- The two g a m m a rays may add up to a sum-pulse, and the area under the sumpeak is expressed by N~ =Np(Tt)e2q,2 W(0°)/[1 - 52 W(0°)q,2]. Usually, for Ge(Li)-detectors leads to
52
(3)
W(0°)qa2< 1, which
N~ -- Np(71)52 W(0°)q12 =Np(72)51 W(O°)q21.
(4)
Eq. (4) can be applied to find out the number of pulses caused by the coincident summing effects of two photopeaks. I f the decay scheme is constructed, q~2 and q2 t are obtainable. As a rule, when the sum effects are observable, the source-to-detector distance is so
511 keY o
1274 keY
o
10~
................. .......
10~ 8
(D
10 ~
°%,,,
.Sum:
%~o./,o peak
oo °0'
I
100
I
200 Channel n u m b e r
I
300
I
400
Fig. 1. Singles spectrum of ~2Na.
small that the solid angle correction leads to a rather close approximation: W(0 °) = 1. The absolute gammaray efficiencies e 1 and 52 for a given geometry are obtainable by the use of standard sources with known activities. Another method for efficiency calibration is that of measuring the number of photo-peak sum pulses in a decay of a known radio-nucleus, which emits two (or more) g a m m a rays in cascade with no cross-over transitions observable. The efficiency of the g a m m a energy concerned can now be calculated by means of eq. (4). If the form of the response function for the detector is known, then the efficiency for different gamma-ray energies is attainable. In this method, it is worthy to note that the decay rate of the source need not be known. Fig. 1 depicts a singles spectrum from a 22Na source, of which the strength was ~ 5 #Ci. A 2 cm 3 Ge(Li)-erystal with a depletion depth of 5 m m was * Department of Physics, Siltavuorenpenger 20 C, Helsinki 17, Finland.
121
122
a . L U U K K O AND P. H O L M B E R G
used as detector. The source-to-detector distance was 12 m m (front face of detector), and the 1024-channel spectrum was recorded on a Nuclear D a t a N D 160 analyser. In the decay of 22Na, the 1.274 MeV level is fed to 100%. T h e / / + - b r a n c h of the decay is 90%, which means that coincidences are obtained between the annihilation radiation and the 1.274 MeV g a m m a rays. These coincidences may add up to a sum-pulse
with an energy of (0.511 + 1.274) MeV. The effect of the sum-pulses is clearly discernible in fig. 1. The present experimental data well agree with eq. (4), which thus provides a possibility for calculation of the summing effects in g a m m a ray spectra. Reference *) R. L. Heath, AEC Report, IDO 16880 (1964).