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Shape of the random sum photo-peak in scintillation spectrometry
N U C L E A R I N S T R U M E N T S AND METHODS 3 t ( I 9 6 4 ) 9 0 - 9 2 ;
©
NORTH-HOLLAND
PUBLISHING
CO.
S H A P E OF T H E R A N D O M S U M P H O T O - P E A K IN S C I N T I L L A T I O N S P E C T R O M E T R Y A. JASI1KISKI, J. L U D Z I E J E W S K I and J. B I A L K O W S K I
Institute for Nuclear Research, Polish Academy of Sciences, Poland, Swierk Received 11 May 1964
The pulse-height distribution of the r a n d o m s u m photo peak is studied with a scintillation spectrometer. It is shown that the shape of this peak is strongly dependent on that of the
analyzed pulses and on the opening time, z, of the input circuit of the analyzer. The experimental pulse-height distribution is compared with the calculated one.
1. Introduction The random summing effect of two pulses in integrating circuits of detectors or amplifiers takes place at all measurements in scintillation spectrometry, and in most cases it is neglected because of its small value. When this effect, however, is comparable with the measured one, as it may be the case in a study of internal bremsstrahlung or weak y-transitions and in many other experiments, the random sum peaks make the analysis of the experimental results more difficult. This sum peak, if it is in coincidence with other y-lines, cannot be removed by measuring the random coincidences and lack of knowledge with regard to the shape of that peak can lead in the in-
terpretation of the experimental results to incorrect conclusions. The aim of this paper has been to study the shape of the spectrum in the random summing of two photopeaks in the case of scintillation spectrometry. The authors were faced with the above problem in measuring the high-energy region of the coincidence spectrum of internal bremsstrahlung 1) accompanying the K-electron capture decay of HgZg?--+ Au 197. The two peaks at 356 and 470 keV (fig. 1) are caused by the random summing of the 279 keV y-ray due to the Hg 2°3 isotope with the 77 and 191 keV y-rays, respectively (see inset in fig. 1). Naturally, these peaks cannot be removed by measuring random coincidences, since the 77 and 191 keV y-lines are in coincidence with the KX-ray. The knowledge of the shape of those sum peaks made possible the correct analysis of this spectrum.
r
Hgt#~ \
H9 cg?
46,gd
2?9 keV
\
1
.......7.7-. 6 6 h
2. Theoretical considerations Spectra in nuclear spectrometry are usually studied by means of multichannel pulse height analyzers. To measure correctly the amplitudes, the input circuit of the analyzer must be open for a time 3, larger than the rise-time of the input pulses. Hence, it should be added that there is always a definite probability that two or more pulses enter the analyzer during this time interval. As is well known, the rate of recording chance coincidences is Nr = N 2 ~ ,
tgf ! /
i
..... l cos toga
- ~N
40(
Z~
Igl*2?gkeV o
°
40
50
n n ~
60
70
r
BO
CHANNEL NUMOER
Fig. 1. The high energy part of the coincidence internal bremsstrahlung spectrum accompanying the electron capture decay of Hg 197. The background and random coincidences are subtracted.
where N is the counting rate of unrelated events at the analyzer input. In this case, the pulse height distribution is dependent on the shapes of the single pulses, as well as on the interval z of the gate of the analyzer circuits. z) A. Jasiflski, J. Kownacki, H. Lancman, J. Ludziejewski, Intern. Conf. on the Role of Atomic Electrons in Nuclear Transformations, Warsaw 24-28 September 1963.
90
S H A P E OF T H E R A N D O M
SUM P H O T O - P E A K
The sum photo-peak consisting of two Gaussian ones, with a strictly determined time delay t between them, is also recorded as a Gaussian with a half width equal to the root of the sum of squares of the width of the single photo-peaks. In the case of r a n d o m coincidences, the time delay t, between two pulses varies in a continuous manner in the region (0, 0 , and the resultant mean amplitude of this pulse will be a function of that time shift. The probability of occurrence of any amplitude z, will be given by the product of probabilities due to the Gaussian distribution of the sum pulse, and to the time shift t of the two summing pulses. The total probability will be the sum of those individual probabilities, and the sum is to be extended over the whole time interval [0, ~]. I f T ~ Tin, while I'm is defined as the mean time interval between pulses at the analyzer input, which is usually encountered in practice, one can assume that the probability of recording of chance coincidences with any time shift t, is constant in the whole time interval [0, T]. Taking into account all the above for the pulse height distribution of the random sum photo-peak one can write :
Nr
--
N2 f~ e - -[A(t)-Z]2--" - - ~ ctt ~/ :~D o
(1)
where Nr is the counting rate of the random coincidences, A(t) is the mean amplitude of the two randomly summed pulses, and D = Dz q- D2 (~/½ D1, ~/½ D2 are standard deviations of the distributions of the single pulses). As one can see from the above equation, the shape of that sum photo-peak remains no more Gaussian, and in becoming asymmetric, it extends from the amplitude value which corresponds to the smaller photo-peak up to the summed value of both photo-peaks.
IN SCINTILLATION
[
x ~URCE
3.1. COINCIDENCE MEASUREMENTS In order to obtain the correct and pure pulse height distribution of the random sum photo-peak, the experimental arrangement shown in fig. 2 was used. As a
I CIR :ulr I~ [ ~ = t ,~6,c.j
Fig. 2. The block
diagram of a r a n d o m analyzer.
sum-photo-peak
source 661 keV y-line of Cs t37 was used. The single channel pulse height analyzers select pulses from photomultipliers, due to photo-peaks only. These pulses are fed to the coincidence circuit, whose resolving time was chosen to be equal to the opening time of the analyzer gate. The pulses from amplifiers are summed in a summing circuit and are analysed by a multichannel pulse-height analyzer. The two additional delay circuits and gate circuits shown in fig. 2 were utilized to compensate for all time shifting introduced by electronic systems, as well as to secure the correct amplitude measurements of the sum pulses. A pulse height distribution of the random sum photo-peak of the Cs 137 661 keV y-ray is shown in
51N~L £J" PEA K
i//"
- "-
RANDOM JUM PEAX
Ji
To check the above considerations, two independent experiments described in sec. 3 were carried out. The source of y-rays as well as the manner of performing all measurements were chosen so as to obtain the shape of the random sum photo-peak without any distortion.
3. Experimental results
91
SPECTROMETRY
r
I J
7
'
, 'k
40
50
7#
CHAHNEL
80
NUMBER
Fig. 3. The pulse height distribution o f the r a n d o m s u m photopeak of the Cs 137 661 keV ~,-ray. The solid curve represents the calculated distribution.
A. J A S I N S K I et al.
92
fig. 3. Experimental points are denoted by open circles. The solid curve shows the calculated distribution obtained by numerical integration of eq. (1), see appendix. As one can see the agreement between the calculated and experimental results is very good. 3.2. MEASUREMENTSWITH A SINGLE CRYSTAL This experiment was carried out using a 1¼" × 2 " NaI(T1) well-type crystal spectrometer. The Cd l°a source was placed in the well of the crystal. An absorber consisting of thin cadmium and copper foils, was inserted between the source and the crystal in order to supress the characteristic KX-radiation of silver. In this case the experimental high-energy portion spectrum, shown in fig. 4 consists of three components due to the following sums : peak q- peak, peak q- escape peak and escape peak q- peak. The experimental points obtained with the 1.2/~s and 2.3 #s gates of the analyzer are shown in fig. 4 as open and full circles, respectively. The shapes of these two sum peaks, in agreement with the expected ones, are the same in the high energy range, and differ consi-
derably in the low-energy range. This difference is caused by a change of the function A(t) which depends on the time interval, z, of the gate. The solid curve shown in fig. 4, being the sum of the above mentioned three components obtained by nummerical integration of eq. (1), is in good agreement with the experiment. The authors wish to thank Mgr. H. Lancman and Dr. Z. Sujkowski for helpful discussions.
Appendix The pulse shape measured on the analyzer input is shown in inset in fig. 4. The sum amplitude A(t) also shown in that figure has been obtained by means of the graphical methods, by shifting the pulse shape curve for each given t. To calculate the integral of eq. (1), the time interval [0, ~] was divided into ten parts so that one could assume, with good approximation, that the amplitude A(t) would be a linear function of time t in each interval, i.e. A(t) = Ao (1 -r et). Owing to that approximation, the integral (1) reduces to a simple sum of the well known and tabulated Gaussian integrals.
7
89k~eVP!EAK
X0|310
X|0310
l I
,
t
•
~2~ A
K ~ p~ULSEHAPE
.< ESCAPP~EP' E*'A~K n5
~~
o.5
o'5
~
i f us]
~
z ffp:
L
f s
4
;
RANOOM ~UH PEA• 89*89keV
~t
Io
to
30
4o
5o 60 CHANNEL NUhIBER
7o
80
9o
Fig. 4. The high energy part of the random sum peak spectrum obtained with a single well-type cristal. The dashed line represents the singles T-ray spectrum of Cd 1°9. The open and full circles correspond to the experimental points obtained with 1.2/~s and 2.3 #s gates of the analyzer, respectively. The solid curve represents the calculated spectrum. (The KX-ray peak was not taken into account.)
©
NORTH-HOLLAND
PUBLISHING
CO.
S H A P E OF T H E R A N D O M S U M P H O T O - P E A K IN S C I N T I L L A T I O N S P E C T R O M E T R Y A. JASI1KISKI, J. L U D Z I E J E W S K I and J. B I A L K O W S K I
Institute for Nuclear Research, Polish Academy of Sciences, Poland, Swierk Received 11 May 1964
The pulse-height distribution of the r a n d o m s u m photo peak is studied with a scintillation spectrometer. It is shown that the shape of this peak is strongly dependent on that of the
analyzed pulses and on the opening time, z, of the input circuit of the analyzer. The experimental pulse-height distribution is compared with the calculated one.
1. Introduction The random summing effect of two pulses in integrating circuits of detectors or amplifiers takes place at all measurements in scintillation spectrometry, and in most cases it is neglected because of its small value. When this effect, however, is comparable with the measured one, as it may be the case in a study of internal bremsstrahlung or weak y-transitions and in many other experiments, the random sum peaks make the analysis of the experimental results more difficult. This sum peak, if it is in coincidence with other y-lines, cannot be removed by measuring the random coincidences and lack of knowledge with regard to the shape of that peak can lead in the in-
terpretation of the experimental results to incorrect conclusions. The aim of this paper has been to study the shape of the spectrum in the random summing of two photopeaks in the case of scintillation spectrometry. The authors were faced with the above problem in measuring the high-energy region of the coincidence spectrum of internal bremsstrahlung 1) accompanying the K-electron capture decay of HgZg?--+ Au 197. The two peaks at 356 and 470 keV (fig. 1) are caused by the random summing of the 279 keV y-ray due to the Hg 2°3 isotope with the 77 and 191 keV y-rays, respectively (see inset in fig. 1). Naturally, these peaks cannot be removed by measuring random coincidences, since the 77 and 191 keV y-lines are in coincidence with the KX-ray. The knowledge of the shape of those sum peaks made possible the correct analysis of this spectrum.
r
Hgt#~ \
H9 cg?
46,gd
2?9 keV
\
1
.......7.7-. 6 6 h
2. Theoretical considerations Spectra in nuclear spectrometry are usually studied by means of multichannel pulse height analyzers. To measure correctly the amplitudes, the input circuit of the analyzer must be open for a time 3, larger than the rise-time of the input pulses. Hence, it should be added that there is always a definite probability that two or more pulses enter the analyzer during this time interval. As is well known, the rate of recording chance coincidences is Nr = N 2 ~ ,
tgf ! /
i
..... l cos toga
- ~N
40(
Z~
Igl*2?gkeV o
°
40
50
n n ~
60
70
r
BO
CHANNEL NUMOER
Fig. 1. The high energy part of the coincidence internal bremsstrahlung spectrum accompanying the electron capture decay of Hg 197. The background and random coincidences are subtracted.
where N is the counting rate of unrelated events at the analyzer input. In this case, the pulse height distribution is dependent on the shapes of the single pulses, as well as on the interval z of the gate of the analyzer circuits. z) A. Jasiflski, J. Kownacki, H. Lancman, J. Ludziejewski, Intern. Conf. on the Role of Atomic Electrons in Nuclear Transformations, Warsaw 24-28 September 1963.
90
S H A P E OF T H E R A N D O M
SUM P H O T O - P E A K
The sum photo-peak consisting of two Gaussian ones, with a strictly determined time delay t between them, is also recorded as a Gaussian with a half width equal to the root of the sum of squares of the width of the single photo-peaks. In the case of r a n d o m coincidences, the time delay t, between two pulses varies in a continuous manner in the region (0, 0 , and the resultant mean amplitude of this pulse will be a function of that time shift. The probability of occurrence of any amplitude z, will be given by the product of probabilities due to the Gaussian distribution of the sum pulse, and to the time shift t of the two summing pulses. The total probability will be the sum of those individual probabilities, and the sum is to be extended over the whole time interval [0, ~]. I f T ~ Tin, while I'm is defined as the mean time interval between pulses at the analyzer input, which is usually encountered in practice, one can assume that the probability of recording of chance coincidences with any time shift t, is constant in the whole time interval [0, T]. Taking into account all the above for the pulse height distribution of the random sum photo-peak one can write :
Nr
--
N2 f~ e - -[A(t)-Z]2--" - - ~ ctt ~/ :~D o
(1)
where Nr is the counting rate of the random coincidences, A(t) is the mean amplitude of the two randomly summed pulses, and D = Dz q- D2 (~/½ D1, ~/½ D2 are standard deviations of the distributions of the single pulses). As one can see from the above equation, the shape of that sum photo-peak remains no more Gaussian, and in becoming asymmetric, it extends from the amplitude value which corresponds to the smaller photo-peak up to the summed value of both photo-peaks.
IN SCINTILLATION
[
x ~URCE
3.1. COINCIDENCE MEASUREMENTS In order to obtain the correct and pure pulse height distribution of the random sum photo-peak, the experimental arrangement shown in fig. 2 was used. As a
I CIR :ulr I~ [ ~ = t ,~6,c.j
Fig. 2. The block
diagram of a r a n d o m analyzer.
sum-photo-peak
source 661 keV y-line of Cs t37 was used. The single channel pulse height analyzers select pulses from photomultipliers, due to photo-peaks only. These pulses are fed to the coincidence circuit, whose resolving time was chosen to be equal to the opening time of the analyzer gate. The pulses from amplifiers are summed in a summing circuit and are analysed by a multichannel pulse-height analyzer. The two additional delay circuits and gate circuits shown in fig. 2 were utilized to compensate for all time shifting introduced by electronic systems, as well as to secure the correct amplitude measurements of the sum pulses. A pulse height distribution of the random sum photo-peak of the Cs 137 661 keV y-ray is shown in
51N~L £J" PEA K
i//"
- "-
RANDOM JUM PEAX
Ji
To check the above considerations, two independent experiments described in sec. 3 were carried out. The source of y-rays as well as the manner of performing all measurements were chosen so as to obtain the shape of the random sum photo-peak without any distortion.
3. Experimental results
91
SPECTROMETRY
r
I J
7
'
, 'k
40
50
7#
CHAHNEL
80
NUMBER
Fig. 3. The pulse height distribution o f the r a n d o m s u m photopeak of the Cs 137 661 keV ~,-ray. The solid curve represents the calculated distribution.
A. J A S I N S K I et al.
92
fig. 3. Experimental points are denoted by open circles. The solid curve shows the calculated distribution obtained by numerical integration of eq. (1), see appendix. As one can see the agreement between the calculated and experimental results is very good. 3.2. MEASUREMENTSWITH A SINGLE CRYSTAL This experiment was carried out using a 1¼" × 2 " NaI(T1) well-type crystal spectrometer. The Cd l°a source was placed in the well of the crystal. An absorber consisting of thin cadmium and copper foils, was inserted between the source and the crystal in order to supress the characteristic KX-radiation of silver. In this case the experimental high-energy portion spectrum, shown in fig. 4 consists of three components due to the following sums : peak q- peak, peak q- escape peak and escape peak q- peak. The experimental points obtained with the 1.2/~s and 2.3 #s gates of the analyzer are shown in fig. 4 as open and full circles, respectively. The shapes of these two sum peaks, in agreement with the expected ones, are the same in the high energy range, and differ consi-
derably in the low-energy range. This difference is caused by a change of the function A(t) which depends on the time interval, z, of the gate. The solid curve shown in fig. 4, being the sum of the above mentioned three components obtained by nummerical integration of eq. (1), is in good agreement with the experiment. The authors wish to thank Mgr. H. Lancman and Dr. Z. Sujkowski for helpful discussions.
Appendix The pulse shape measured on the analyzer input is shown in inset in fig. 4. The sum amplitude A(t) also shown in that figure has been obtained by means of the graphical methods, by shifting the pulse shape curve for each given t. To calculate the integral of eq. (1), the time interval [0, ~] was divided into ten parts so that one could assume, with good approximation, that the amplitude A(t) would be a linear function of time t in each interval, i.e. A(t) = Ao (1 -r et). Owing to that approximation, the integral (1) reduces to a simple sum of the well known and tabulated Gaussian integrals.
7
89k~eVP!EAK
X0|310
X|0310
l I
,
t
•
~2~ A
K ~ p~ULSEHAPE
.< ESCAPP~EP' E*'A~K n5
~~
o.5
o'5
~
i f us]
~
z ffp:
L
f s
4
;
RANOOM ~UH PEA• 89*89keV
~t
Io
to
30
4o
5o 60 CHANNEL NUhIBER
7o
80
9o
Fig. 4. The high energy part of the random sum peak spectrum obtained with a single well-type cristal. The dashed line represents the singles T-ray spectrum of Cd 1°9. The open and full circles correspond to the experimental points obtained with 1.2/~s and 2.3 #s gates of the analyzer, respectively. The solid curve represents the calculated spectrum. (The KX-ray peak was not taken into account.)