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Cyclic activation flux monitor
NUCLEAR
INSTRUMENTS
AND
METHODS
I34 (I976) 2 5 7 - 2 5 9 ;
©
NORTH-HOLLAND
PUBLISHING
CO.
CYCLIC A C T I V A T I O N FLUX M O N I T O R G.C. MEGGITT
Rutherford Laboratory, Royal Military College of Science, Shrivenham, Swindon, Wilts SN6 8LA, England Received 23 J a n u a r y 1976 A simple circuit has been designed which accurately determines the effective flux in cyclic activation analysis, allowing for fluctuations in n e u t r o n flux a n d variations in activation sequence. Theoretical analysis o f the cyclic process is also given.
1. Introduction
2.1. VARIATION DURING SINGLE CYCLE
A number of authors ~-3) have evaluated the possibility of using very short half-life neutron irradiation products as a means of quantitative analysis. The approach seems to offer useful sensitivities for several otherwise difficult elements if a cyclic technique is used. In cycling the procedure is to irradiate the sample with a burst of neutrons and then, after a short delay, count the induced activity. This cycle is then repeated many times, counts being accumulated in each cycle. A limitation upon the accuracy obtainable derives from the difficulty in making a proper measurement of the effective neutron flux when this does not remain constant during each irradiation period and from cycle to cycle.
When a target is bombarded with a neutron flux ~b(t) for a period t = 0 to tb, the activity induced at t = t b by the flux incident in t to t + dt is
Na~(t)
dt" 2 e -~(tb-t),
(1)
where N is the number of target nuclei, a the crosssection for the production of the radiation of interest and 2 is the decay constant of the activity ( = in 2/z~). The activity induced at tb by all the flux is then: Na2
I 'b q~(t) e -~(tb-') dl.
(2)
jo
The factor
2. Cyclic activation with varying flux
F = 2
qS(t) e -a('u-~) dt
Expressions for the accumulated induced counts have been derived on the assumption that the flux is constant during each irradiation period and also from cycle to cycle. In the following analysis this condition has been relaxed.
is the effective flux for activity of decay constant 2. If the induced activity is counted for a period tc beginning a time t w after the end of the irradiation then the number of counts accumulated will be:
o
NEUTRON FLUX CYCLE TIME T
T
T
TIME
tb
tb
irradiate
Fig. 1. T h e timing sequence for the activation analysis s h o w n on a d i a g r a m o f n e u t r o n flux received by the sample as a function o f time.
258
G. C. M E G G I T T
e -at dt
(3)
The total counts caused by all the irradiation periods is then
Na~ -aIw ( 1 - e -ac) F , 2
(4)
D.
C = N a g e -atw F
-
-
f
ie
0
N a e e -aw ( 1 - e -at°)
e
=
2., .,=,
d.,
=
- -
2
1-e -at
x
where e is the detection efficiency of the counting system. 2.2. VARIATION DURING ENTIRE RUN
If the sample is submitted to the irradiate-waitcount sequence many times with a cycle time T as shown in fig. 1, the activity induced during a cycle will be counted not only in that cycle but in all subsequent ones also. Considering the cycle number n', it has already been shown that the counts induced and counted in this cycle will be C,. = -N-a e e -atw (1--e -a'°) F . , ,
(5)
2 where, in the evaluation of F~, the time origin has been taken as the beginning of the n'th irradiation period. Thus the total counts in the run due to the n'th irradiation will be (6)
d,, = C , , + C , , e - a t + ... + C,, e - ~ ' - " ' ) a r ,
where n is the total number of cycles in the run. d,,
=
C,,(1 - e -("-"'+ 1) at) 1-e -at
(7)
GATE IRRADIATION PERIOD a
RATENETER
If it is assumed that the flux has the same value during each irradiation then this expression reduces to that derived by Givens et al.*). The result shows the complex relationship which exists, in general, between incident flux and counts recorded. It should be noted that a direct measurement of total incident flux will cause errors not only because F is not measured but also because of the second term in the brackets. 3. Cyclic flux monitor A simple electronic circuit, fig. 2, has been designed which simulates the response of a target nucleus producing, after activation, radiation of a particular half-life. The pulse signals from a neutron detector, here an NE451 scintillator system, are input, through a gate opened during the irradiation period, to a ratemeter with a time constant equal to that of the activity of interest. With this choice of time constant the ratemeter voltage is proportional to the activity of interest at all times. After a buffer stage, the output signal is gated with a field effect transistor which conducts only during the counting period of the multichannel
LINEAR GATE
BUFFER
INTEGRATOR
+ 15
47K
* 15
swt
~BCIO~
NV~f, o
-~r~_5
~o
3.3K
,.
0-~ ~- FLUX v IINPUT
-10 -5
ANALYSERCOUNT PERIOD ,,6
-Uo
--[o 5
•
J-
~
.FW',
*5 15K
0
IC 107 ~5.1V .15 • "I
f ~56K
.~fK ~ ' ~ B C
I07 -5
-70 Fig. 2. T h e m o n i t o r circuitry. T h e operational amplifiers are RS C o m p o n e n t s F E T - M O P A .
C Y C L I C A C T I V A T I O N FLUX MONITOR
analyser counting the activity in the cycling run. The output from the gate is then integrated on the 1 p F capacitor by the operational amplifier. If the switch SWl is closed momentarily before a run is commenced, to discharge the integrating capacitor, then the voltage II, measured at the output by a digital voltmeter after a cycling run is V,=
k e -a''~ (1 - e -a'°) x 2 1 - e -~r
x{~ Fn'-e-t~+l)ar ,'=1 ~ F~'e~'~r}
259
total cycle time was maintained at a constant value while the 2 wait times were varied. With a constant pulse raie input from a pulse generator the response after 20 cycles was then measured as a function of the delay between irradiating and counting. In terms of equation (9) this is equivalent to keeping T, tb, and t c constant and varying tw. The result obtained was a simple exponential relation between V, and t w from which 2 could be found. The value of the ratemeter resistor (R in fig. 2) was adjusted until the correct value of 2 was obtained.
(9) 5. Conclusions
where k is a factor depending upon, for example, circuit components and the efficiency of the flux monitor. So, for the time constant chosen
D,,/Vn = Nae/k.
(10)
Hence not only is the flux accurately accounted for but so is any variation in the timing sequence: after one measurement of a standard to calibrate the system the sequence could be modified at will. The irradiation period gate is provided so the monitor can be used where the cycling is performed by repeated pneumatic transport of the sample. While the counting is being performed in a neutron-free environment the input to the ratemeter can be made zero also. The gate would be held open continuously if the cycling were performed by pulsing neutrons onto a stationary sample. The stability of the circuit is such that the output to the digital voltmeter drifts by approximately I mV/min. With a signal output in the range 5-10 V this means the device can operate accurately for a run of many minutes. 4. Measurement of ratemeter time constant
The monitor has been used in conjunction with the sequence controller previously described4). This latter provides accurately timed sequences, for a predetermined number of cycles, of irradiation and counting times with a range of wait times between each. To measure the time constant of the ratemeter the
The monitor is being used in determinations of lead by 14 MeV neutron activation analysis by means of the 0.8 s activity of 2°7mpb. The need for regular running of standards has not been eliminated since these correct for other factor such as variation in accelerator beam spot drift in addition to checking the calibration of the monitor. However it is now possible to use results where the cycling conditions varied from those pertaining during the standardisation with some confidence. Clearly it is necessary to have a separate ratemeter, FET gate and integrator for each half life of interest. However these components are not expensive and such systems could be constructed quite easily. If several such channels were employed and calibrated for known half-lives then it might prove possible to interpolate accurately for other half-life activities. The ratemeter input and FET gate drive circuitry would be common to all channels while the same DVM could be used for all outputs. The author would like to thank Mr N. P. W. Martyn for his help in constructing the unit. The work was financed by the Ministry of Defence as part of a research contract. References 1) W. W. Givens, W. R. Mills and R. L. Caldwell, Nucl. Instr. and Meth. 80 (1970) 95. 2) A. Golanski, J. Radioanal. Chem. 3 (1969) 161. 3) A. Tani, Y. Matsuda, Y. Yuasa and N. Kawai, Radiochem. Radioanal. Lett. 1 (1969) 155. 4) G. C. Meggitt, Nucl. Instr. and Meth. 124 (1975) 455.
INSTRUMENTS
AND
METHODS
I34 (I976) 2 5 7 - 2 5 9 ;
©
NORTH-HOLLAND
PUBLISHING
CO.
CYCLIC A C T I V A T I O N FLUX M O N I T O R G.C. MEGGITT
Rutherford Laboratory, Royal Military College of Science, Shrivenham, Swindon, Wilts SN6 8LA, England Received 23 J a n u a r y 1976 A simple circuit has been designed which accurately determines the effective flux in cyclic activation analysis, allowing for fluctuations in n e u t r o n flux a n d variations in activation sequence. Theoretical analysis o f the cyclic process is also given.
1. Introduction
2.1. VARIATION DURING SINGLE CYCLE
A number of authors ~-3) have evaluated the possibility of using very short half-life neutron irradiation products as a means of quantitative analysis. The approach seems to offer useful sensitivities for several otherwise difficult elements if a cyclic technique is used. In cycling the procedure is to irradiate the sample with a burst of neutrons and then, after a short delay, count the induced activity. This cycle is then repeated many times, counts being accumulated in each cycle. A limitation upon the accuracy obtainable derives from the difficulty in making a proper measurement of the effective neutron flux when this does not remain constant during each irradiation period and from cycle to cycle.
When a target is bombarded with a neutron flux ~b(t) for a period t = 0 to tb, the activity induced at t = t b by the flux incident in t to t + dt is
Na~(t)
dt" 2 e -~(tb-t),
(1)
where N is the number of target nuclei, a the crosssection for the production of the radiation of interest and 2 is the decay constant of the activity ( = in 2/z~). The activity induced at tb by all the flux is then: Na2
I 'b q~(t) e -~(tb-') dl.
(2)
jo
The factor
2. Cyclic activation with varying flux
F = 2
qS(t) e -a('u-~) dt
Expressions for the accumulated induced counts have been derived on the assumption that the flux is constant during each irradiation period and also from cycle to cycle. In the following analysis this condition has been relaxed.
is the effective flux for activity of decay constant 2. If the induced activity is counted for a period tc beginning a time t w after the end of the irradiation then the number of counts accumulated will be:
o
NEUTRON FLUX CYCLE TIME T
T
T
TIME
tb
tb
irradiate
Fig. 1. T h e timing sequence for the activation analysis s h o w n on a d i a g r a m o f n e u t r o n flux received by the sample as a function o f time.
258
G. C. M E G G I T T
e -at dt
(3)
The total counts caused by all the irradiation periods is then
Na~ -aIw ( 1 - e -ac) F , 2
(4)
D.
C = N a g e -atw F
-
-
f
ie
0
N a e e -aw ( 1 - e -at°)
e
=
2., .,=,
d.,
=
- -
2
1-e -at
x
where e is the detection efficiency of the counting system. 2.2. VARIATION DURING ENTIRE RUN
If the sample is submitted to the irradiate-waitcount sequence many times with a cycle time T as shown in fig. 1, the activity induced during a cycle will be counted not only in that cycle but in all subsequent ones also. Considering the cycle number n', it has already been shown that the counts induced and counted in this cycle will be C,. = -N-a e e -atw (1--e -a'°) F . , ,
(5)
2 where, in the evaluation of F~, the time origin has been taken as the beginning of the n'th irradiation period. Thus the total counts in the run due to the n'th irradiation will be (6)
d,, = C , , + C , , e - a t + ... + C,, e - ~ ' - " ' ) a r ,
where n is the total number of cycles in the run. d,,
=
C,,(1 - e -("-"'+ 1) at) 1-e -at
(7)
GATE IRRADIATION PERIOD a
RATENETER
If it is assumed that the flux has the same value during each irradiation then this expression reduces to that derived by Givens et al.*). The result shows the complex relationship which exists, in general, between incident flux and counts recorded. It should be noted that a direct measurement of total incident flux will cause errors not only because F is not measured but also because of the second term in the brackets. 3. Cyclic flux monitor A simple electronic circuit, fig. 2, has been designed which simulates the response of a target nucleus producing, after activation, radiation of a particular half-life. The pulse signals from a neutron detector, here an NE451 scintillator system, are input, through a gate opened during the irradiation period, to a ratemeter with a time constant equal to that of the activity of interest. With this choice of time constant the ratemeter voltage is proportional to the activity of interest at all times. After a buffer stage, the output signal is gated with a field effect transistor which conducts only during the counting period of the multichannel
LINEAR GATE
BUFFER
INTEGRATOR
+ 15
47K
* 15
swt
~BCIO~
NV~f, o
-~r~_5
~o
3.3K
,.
0-~ ~- FLUX v IINPUT
-10 -5
ANALYSERCOUNT PERIOD ,,6
-Uo
--[o 5
•
J-
~
.FW',
*5 15K
0
IC 107 ~5.1V .15 • "I
f ~56K
.~fK ~ ' ~ B C
I07 -5
-70 Fig. 2. T h e m o n i t o r circuitry. T h e operational amplifiers are RS C o m p o n e n t s F E T - M O P A .
C Y C L I C A C T I V A T I O N FLUX MONITOR
analyser counting the activity in the cycling run. The output from the gate is then integrated on the 1 p F capacitor by the operational amplifier. If the switch SWl is closed momentarily before a run is commenced, to discharge the integrating capacitor, then the voltage II, measured at the output by a digital voltmeter after a cycling run is V,=
k e -a''~ (1 - e -a'°) x 2 1 - e -~r
x{~ Fn'-e-t~+l)ar ,'=1 ~ F~'e~'~r}
259
total cycle time was maintained at a constant value while the 2 wait times were varied. With a constant pulse raie input from a pulse generator the response after 20 cycles was then measured as a function of the delay between irradiating and counting. In terms of equation (9) this is equivalent to keeping T, tb, and t c constant and varying tw. The result obtained was a simple exponential relation between V, and t w from which 2 could be found. The value of the ratemeter resistor (R in fig. 2) was adjusted until the correct value of 2 was obtained.
(9) 5. Conclusions
where k is a factor depending upon, for example, circuit components and the efficiency of the flux monitor. So, for the time constant chosen
D,,/Vn = Nae/k.
(10)
Hence not only is the flux accurately accounted for but so is any variation in the timing sequence: after one measurement of a standard to calibrate the system the sequence could be modified at will. The irradiation period gate is provided so the monitor can be used where the cycling is performed by repeated pneumatic transport of the sample. While the counting is being performed in a neutron-free environment the input to the ratemeter can be made zero also. The gate would be held open continuously if the cycling were performed by pulsing neutrons onto a stationary sample. The stability of the circuit is such that the output to the digital voltmeter drifts by approximately I mV/min. With a signal output in the range 5-10 V this means the device can operate accurately for a run of many minutes. 4. Measurement of ratemeter time constant
The monitor has been used in conjunction with the sequence controller previously described4). This latter provides accurately timed sequences, for a predetermined number of cycles, of irradiation and counting times with a range of wait times between each. To measure the time constant of the ratemeter the
The monitor is being used in determinations of lead by 14 MeV neutron activation analysis by means of the 0.8 s activity of 2°7mpb. The need for regular running of standards has not been eliminated since these correct for other factor such as variation in accelerator beam spot drift in addition to checking the calibration of the monitor. However it is now possible to use results where the cycling conditions varied from those pertaining during the standardisation with some confidence. Clearly it is necessary to have a separate ratemeter, FET gate and integrator for each half life of interest. However these components are not expensive and such systems could be constructed quite easily. If several such channels were employed and calibrated for known half-lives then it might prove possible to interpolate accurately for other half-life activities. The ratemeter input and FET gate drive circuitry would be common to all channels while the same DVM could be used for all outputs. The author would like to thank Mr N. P. W. Martyn for his help in constructing the unit. The work was financed by the Ministry of Defence as part of a research contract. References 1) W. W. Givens, W. R. Mills and R. L. Caldwell, Nucl. Instr. and Meth. 80 (1970) 95. 2) A. Golanski, J. Radioanal. Chem. 3 (1969) 161. 3) A. Tani, Y. Matsuda, Y. Yuasa and N. Kawai, Radiochem. Radioanal. Lett. 1 (1969) 155. 4) G. C. Meggitt, Nucl. Instr. and Meth. 124 (1975) 455.