The effect of dead times
M. C. Moxon
January 2003
1 Introduction
The intrinsic dead time of a detector system is the time after an event during which other
events seen by a detector are not recorded due mainly to the amplitude of the event being above
the bias level of the discriminator unit. These missed counts are usually accounted for by a
simple formalism assuming that the system is open to record events for the time of the
measurement minus the product of the number of events recorded and the average dead time.
As the intrinsic dead time varies with pulse shape and amplitude, a fixed dead time is
usually applied to the discriminator output pulse. The use of a fixed dead time simplifies the
corrections for the missed counts, making it almost independent of the pulse height distribution.
Ideally the fixed "dead time" should be longer than the longest pulse observed by the detector but
much shorter than the average time between events. The longest dead time associated with the
detection equipment should also be as close electronically to the detector as possible. If longer
dead times are encountered in later units the final dead time is no longer fixed and will be
extended by other events occurring between the end of the detector dead time and the units longer
dead time. The corrections for extended dead times become difficult to determine and are count
rate dependent.
An idealized output from a detector is shown in Figure 1. The larger signals cross the bias
level and return below it at a later time. Any other event occurring during this period will not be
recorded by the detector system, when using a discriminator with a fixed bias level. Events that
are not large enough to cross the bias level are not counted. However events that would normally
be below the bias level can trigger the discriminator if they occur after a large signal during the
period when it has returned below the bias and before it has return to zero.
1
120
100
Amplitude
80
Bias level
Signal
Intrinsic dead time
Intrinsic output
Fixed dead time output
60
40
20
0
0
20
40
60
80
100
Time
Figure 1 Idealized detector output
The setting of the bias level has to be a compromise between detecting all the true events
and cutting off as much as possible of the underlying background and noise. A fixed dead time
that extends out to a time where the amplitude of a signal is much lower than the bias level
reduces the effect of the noise events raised above the bias by the tails from previous events. The
effect of after pulsing associated with detectors using some types of photo-multipliers can also be
greatly reduced by the use of a dead time that extends out beyond the time of the after pulses.
2 The measurement of the dead time.
(a) Detector
The usual and simplest technique for determining the required dead time is to view an
oscilloscope display of the signals from the detector and the output from the discriminator. The
length of the dead time can then be adjusted until it is longer than the longest input pulse. The
disadvantage of this technique is that the fluctuations in the underlying noise make it difficult to
judge the time when the amplitude of an event has dropped far enough below the bias.
The second method is to observe the count rate from a single source of radiation as a
function of distance from the detector. In the analysis of the data it is assumed that the true count
rate is inversely proportional to the square of the distance R from the centre of the detector to the
centre of the source
a(R)
A0 =
2
R (1 - a(R)  )
2
1
Where A0 is the effective source strength,  the dead time of the detector and the observed count
rate at distance R is a(R). A least square fit to the observed count rate a(R), at several distances
can be used to solve for the effective source strength A0 and the dead time . Correction to the
observed count rate have to be carried out for any reactions that the radiation has with the air
between and surrounding the detector and source as well as near by objects. It also does not take
into account the fact that the dead time does depend on the observed count rate. A modification
to this technique is to use at least two almost identical sources and measure the count rate
observed with each individually in given but separate positions and with both sources in place.
This technique does not require corrections for the reactions of the radiations in the media and
A1 =
a1
(1 - a1  )
a2
(1 - a 2  )
a12
A1 + A2 =
(1 - a12  )
A2 =
2
objects surrounding the source and detector but does require good statistics.
Where A1 and A2 are the effective source strengths, a1 and a2 are the observed individual count
rates and a12 the observed count rate from both sources together. The above equations can be
solved to give the dead time and the effective source strength.
=
a1 a 2 
2
2
a1 a 2 - ( a1 + a 2 - a12 ) a1 a 2 a12
( a1 a 2 a12 )
3
Measurements carried out at different distances between the source and detector can then
be used to determine the dependence of the dead time  on the observed count rate.
A better technique is to feed the signals from the detector into a fast discriminator with a
dead time a lot less then the width of the narrowest pulse. The digital signal from this
discriminator is then passed into a fan out unit; one output is then used to start a fast timing scaler
and the next signal to stop the scaler. The scaler being run in the single shot mode i.e. only one
event per start is recorded. The time between the start pulse and the next pulse is stored and a
distribution of the time between adjacent pulses generated. The observed count rate as a function
of time should at first be near zero then increase, reach a maximum and then decay in an
exponential form (see fig. 2). For a constant input count rate the decay constant of the
exponential part and its amplitude extrapolated to zero time being proportional to the true count
rate. The dead time should be set at a time when the observed count rate follows the expected
exponential decaying form. Observation in the time distribution of any deviation from the
exponential form are generally an indication of the enhancement of noise pulses or after pulsing
in a detector and/or it's electronics (see fig.9 and 15).
3
1.0E+05
Fitted curve
Intrinsic dead time
Fixed dead time
Count rate
8.0E+04
6.0E+04
4.0E+04
2.0E+04
0.0E+00
0
1
2
3
4
5
6
7
8
9
10
Time
Figure 2 The time distribution of adjacent events
Black curve is an exponential fit to the data points at times greater than 2.5 -second. The green points denote
the intrinsic dead time and the red ones denote the fixed dead time of 2.5 -second.
(b) Time of flight scaler
In time of flight measurements the input of the scaler will not accept another event for the
period of time while it is being processed. This does not cause a problem with the dead time
correction for a single detector as long as the dead time of the detector is the longer. For
measurements that are using more than one detector feeding into a single time scaler, correction
may have to be made to each spectrum for the dead time caused by all the other detector inputs.
This correction must be carried out first, followed by correction to the data from the individual
detectors.
As standard pulses are use as input to most multi-input time of flight scalars, the dead
time can be measured by feeding the processed signals from a detector into several inputs via a
fan out and delay units. The dead time for a given input is then, the time difference between it
and any other input when its count rate increases from zero.
(c) Gated random count
A technique developed by a group at CERN uses the dead time from the signals to gate a
fast random pulse generator, recording the resultant counts on a separate input to the time of
flight scaler. The advantage of this technique is that it measures the dead time during the actual
experiment. The main disadvantage of this technique is that if it is using the same time of flight
4
scaler as the counts from the detector it adds the additional dead time of the scaler. The delays
have to be introduced into the various signals pathways to ensure that the signals arrive at the
time of flight scaler in the correct time order.
3 Correcting for dead time
(a) Correction algorithms
If Co counts are observed in an elapsed time of t, the true counting time is t -  t(i)
where the summation is over all the observed events and t(i) is the dead time of event C(i). The
total counts C that should have been observed in time t is given by equation 4.
C=
Co
(1 -  0 )
4
Where  0 =  t(i) / t  C0 t t , where t is the average dead time.
However equation 4 is only true at low constant count rates times the average dead time i.e.
 t (i) t is not greater than a few percent. At higher count rates the dead time t will be
extended by events occurring during that period. Various algorithms have been developed over
the years to correct the dead time for these events, Muller [Rapport BIPM-75/6 ] from the BIPM
in Paris has compiled a bibliography of papers on dead time effects.
An algorithm similar to equation 4 was used at Harwell in the latter years to correct the
Co
C=
(1 -
0
)
(1 -   1 )
5
time of flight capture yield data. Where 0 is given above and 1 can be set equal to 0 if the
count rate is constant or is proportional to the count rate at times prior to the start of the dead
time. From the analysis of the results of the earlier Monte Carlo,  was found to be
approximately equal to loge2 = 0.693. The presently modified Monte Carlo program gives a
minimum value of ~0.5 and a maximum of ~0.65
The latest Monte Carlo calculations indicate that equation 4 underestimated the true count
rate by approximately half the square of the correction i.e. an observed count rate times the fixed
dead time (CR*DT) of ~0.1 gave values ~0.006 lower than the true rate. This observation is
consistent with equations and comments by Muller in his paper title Generalised dead times
(Nuc. Inst. and Methods A301 (1991) 543) and indicates that the Monte Carlo program is
carrying out the calculations in the expected manner. Using equation 4 with CR*DT greater
than~0.15 underestimated the true count rate by several percent. Correction using equation 5
were better than 1/500 up to an observed CR*DT of ~0.15 but rapidly became less accurate for
5
values of CR*DT in excess of 0.25.
The latest version has been used to develop another algorithm for correction of observed
data on a similar line to equation 5.
C=
Co
6
1 
(1 )
2 
(1 )
3 
(1 )

4 
(1 )

(1 -  5
)
(1 -  6  )
where  is the same as in equation 4 and 1=1.0, 2= 3=4=5=6=0.5.
Using the latest version of the Monte Carlo program with an idealised pulse height
spectrum i.e. all the pulses are above the bias level. The pulse rises vertically from zero to a
maximum and is followed by an exponential decay.
Table 1 and figure 3 shows the difference between the corrected "observed" counts and
the "true" input counts using correction equations 4, 5 and 6. Equations 5 and 6 give slightly
better agreement than equation 4 for these idealised conditions, being better than 1 in 500 for
observed CR*DT of less than ~0.15 and within ~1% of the true value up to CR*DT values of
~0.2. The fixed dead time correction factors appear to be almost independent of the pulse decay
time as long as the average pulse width at the bias level is at least a factor of three less than the
fixed dead time imposed on each pulse.
a (%)
b(%)
c (%)
d (%)
e (%)
f (%)
0.481
0.481
-0.000747
0.00042
0.00042
0.00042
0.680
0.679
-0.00296
-0.000626
-0.000623
-0.000627
0.962
0.958
-0.00577
-0.00111
-0.00110
-0.00111
1.360
1.35
-0.00804
0.00125
0.00128
0.00125
1.924
1.90
-0.0184
0.000139
0.000222
0.000132
2.721
2.66
-0.0369
-0.000018
0.000222
-0.000003
3.848
3.72
-0.0777
-0.00431
-0.00363
-0.00434
5.442
5.18
-0.139
0.00676
0.00869
0.000669
7.696
7.16
-0.309
-0.0224
-0.0171
-0.0227
10.884
9.81
-0.614
-0.0531
-0.0380
-0.00534
15.392
13.3
-1.25
-0.163
-0.120
-0.162
21.768
17.7
-2.56
-0.474
-0.359
-0.475
30.784
22.8
-5.13
-1.36
-1.07
-1.37
43.535
28.3
-10.1
-3.85
-3.19
-3.85
61.568
33.4
-19.3
-10.3
-9.06
-10.3
Table 1 Differences between "observed" count rates corrected for a fixed dead time and input true count rates
versus count rate times the dead time for the various correction algorithms.
Bias level =15, pulse amplitude =47, decay half-life = 0.5 -seconds, intrinsic dead time = 0.82 -seconds
6
Column a
The true count rate multiplied by the dead time of 2.5 μ-seconds.
Column b
Observed count rate multiplied by the dead time of 2.5 μ-seconds
Column c, d, and e
The observed corrected counts minus the true count divided by true counts, using equations 4, 5, and 6
respectively.
Column f
Uses equation 5 with  1 proportional to the sum of observed events in the second dead time region.
1.0E-01
Equ. 5
Equ. 6
Equ. 4
-Difference ratio
1.0E-02
1.0E-03
1.0E-04
1.0E-05
0.00
0.20
0.10
0.30
Observed count rate times fixed dead time
Figure 3 The ratio of the corrected “observed counts” minus the true counts divided by the true counts
using equation 4, 5 and 6.
(b) Correcting the neutron time of flight data
In neutron time of flight measurements the time of arrival of an event after the start of the
scaler is digitised and the contents of the appropriate time of flight channel are increased by one
count. The timing channels used in the measurements can vary from one nano-second to as long
as several milli-seconds depending on the neutron energy range of interest, flight path length and
the width of the initial neutron burst. The dead time corrections to the observed counts in a given
channel are carried out using the counts in that channel together with those observed in the time
equivalent to the detector/scaler dead time prior to the channel.
In a time of flight measurement the counts Co are observed at time t for M neutron bursts.
However the true number of bursts Mo(t) that the time interval can record an event is M minus
the number of events that occur in the time equivalent to the dead time  of the detector prior to
the event.
7
 y -t 
y=t
y=t -
 y
M o (t) = M -  y=t - C o (y) y -  y=-infinity C o (y) F 
  
7
The first integral of equation 7 is the sum of events occurring in the time interval t to t-. The
second integral in equation 7 is due to the extension of the dead time for events prior to initial
dead time and in most time of flight data is assumed to be small and is ignored. F[(y-t)/] being
equivalent the s in equation 5 and 6. Using equation 7 with only the first integral algorithms for
time of flight data can be derived in similar manner to that of equation 5.
The variables used in the equations are described as follows:C(i,j)---are the corrected counts in channel i for detector j, recorded for M neutron
bursts i.e. the number of starts for the timing scaler.
Cs(i,j)---are the counts corrected for the dead time of the timing scaler.
Co(x,i)---are the observed counts at time x for detector i
Co(y,k)---are the observed counts for detector k at time y.
Co(i,j)---are the observed counts for channel i for detector j.
ti -------is the width of the timing channel i which starts at time ti.
ts-------is the dead time of the scaler.
td-------is the dead time of the detector and its electronics.
n---------is set such that the time interval from the end of channel i to the start of
channel i-n is equal to or slightly greater than the dead time of the timing scaler ts or the
detector tj.
nn-------is set such that the time interval from the end of channel i to the start of
channel i-nn is equal to or slightly greater than the n times dead time of the timing scaler ts or
the detector tj.
(c) Time of flight scaler
In measurements using a single time of flight with inputs from several detectors the
correction for the dead time of the scaler must be carried out first and then the corrections to the
counts of the individual detectors. The type of correction depends on the arrangement of the
scaler.
First assuming that all inputs have equal weight, the first input with a signal is recorded,
any latter inputs that occur within the dead time are rejected.
x=t i+t
C s (i, j)=  x=ti
C o (x, j)
1 

y= x
k= N
 1 - k=1,k  j  y= x- t s C o (y, k)y 
M

x
8
If the count rate does not vary greatly from channel to channel and the correction is small,
8
equation 8 can be reduced to the following simpler form.
C s (i, j)=
C o (i, j)

 
 1
 1 - kk==1,Nk  j mm==ii - n C o (m, k)  m=i t s 

 m=i -n  t m  M

9




For a correction greater than a few percent, equation 5 or 6 can be used with values of 0
given by equation 10 and 1 is given by equation 11.

 1
 ts

 t m  M

 0 = kk==1,N k  j mm=ii -n C o (m,k)

 1

 m i  n t (m)  M
 m i  nn

 1  k 1,k  j m i  nn C 0 (m, k )
kN
10
m=i
m=i - n
m i  n
t s
11
If the inputs are listed in priority i.e. a signal from detector i occurring within the dead
C o (x, j)
x=t i+ t i
C s (i, j)=  x=ti
1 

k =i -1 y= x
 1 -  k=1  y= x - t s C o (y, k)y 
M

x
12
time from a higher numbered detector j will be attributed to detector i not j.
As for equation 8, equation 12 can be reduced to the following simpler form.
C s (i, j)=
C o (i, j)

 
 1
 1 - kk==1i -1 mm==ii - n C o (m, k)  m=i t s 



 m=i - n  t m  M





13
For correction greater than of a few percent equation 5 or 6 can be used with values of 0
and 1 given by equation 14 and 15 respectively
9

 1
 ts

 t m  M

 0 = kk==1i-1 mm==ii-n C o (m, k) 
14
m=i
m=i - n

 ts
m
=
i
n
 m=i -nn  t (m)

 1 = kk==1i -1 mm=ii--nnn C 0 (m,k)
 1

M

15
(d) Detector
In calculating the dead time correction, it is assumed that the longest dead time of the
system is fixed by the first discriminator encountered by the signal and is longer than any of the
x= + t i
C(i, j)=  x=tt ii
C os (x, j)

 1
y= x
 1 -  y= x- t d C os (y, j)y 
M


 

x
16
signals from the detector.
If the count rate does not vary greatly from channel to channel and the correction is small,
C(i, j)=
C os (i, j)

 
 1
 1 - kk==ii -n C os (k, j)  k=i t d 

  k =i - n  t k  M





17
equation 16 can be reduced to the following simple form.
For correction greater than of a few percent equation 5 or 6 can be used with values of 0
and 1 are given by equation 18 and 19 respectively

 td  1

 t k  M
 
 0 = kk==ii-n C os (k, j) 
k=i
k=i - n

 1 = kk==ii--nnn C os (k, j) 

(ei) Gated random count
10
t
 1

 t k  M
d
k=i - n
k=i - nn
18
19
The dead time correction using this technique is much simpler than the previous methods.
The observed counts have to first corrected for the time of flight scaler dead time. The fraction of
time channel I is operative is given by 1 - C rs (i)/CR where Crs is the random observed count rate
after the scaler dead time correction in channel i and CR the count rate from the random count
C(i) =
C os (i)
(1 - C rs (i)/CR)
generator. The true counts C(i) in channel i are given by equation 20.
11
20
Monte Carlo calculations
A Monte Carlo program has been used to simulate the effects of the detector and scaler
dead times on the measurements. The time dependence of a signal from an event is assumed to
have a vertical rise followed by an exponential decay. The number of events occurring per start of
the recording interval is first selected assuming a Poisson distribution about mean input count
rate. The amplitude of an event is selected from the pulse height distribution. The time of arrival
of an event after the start is selected from one of the three distributions, constant, or an
exponential decay or time to a given power. A transmission or yield curve as a function of energy
or time can also be included. An event is accepted if the value of the random number is below the
transmission/yield curve.
At the end of each cycle the events are stored and tagged as function of the time of arrival
and the time to the next pulse according to the following.
(a) Is the amplitude of the event greater than the bias level?
(b) Does the event occur within the dead time from a previous event?
(c) For events below the bias level, is the amplitude plus the tails of previous events greater
than the bias level?
(d) For events now above the bias level that where below it, is the amplitude of the tails of
previous events lower than the bias level just prior to the noise event?
(e) Does the event occur within the fixed dead time?
(f) Does the event occur within the dead time of the scaler from a previous event in another
detector?
The initial calculation was carried out using a pulse height spectrum similar to that from a
lithium glass scintillator. The interpretation of the results proved difficult and a simple spectrum
of a delta pulse height distribution with the pulse height about twice the bias level was
introduced. Figure 2 shows the results of such a Monte Carlo calculation of the time to the next
event for a constant count rate. The solid line is the count rate, assuming no dead time, using a
decay constant and amplitude deduced from a fit to the "data" points at times greater than the
fixed dead time. The other two sets of "data" points are for an intrinsic dead time and for the
fixed dead time.
shows the accumulated calculated counts for 8106 starts with a count rate of 8
events per start. The bias level was set at channel 15 the single pulse height at channel 48, with a
decay time of 0.5 -second. 1024 timing channels were used each of width 0.1 -second. The
count rate in the regions from 50 -seconds to 55 -seconds and 75 -seconds to 102.4 -seconds
was set at a level of 0.01 and that in the region 55 -seconds to 75 -seconds set to unity. The
dark blue curve is the true counts with no dead time. The data assuming an intrinsic dead time is
shown in red and the data with a fixed dead time of 2.5 -second is shown in green.
Figure 4
In Figure 5 and Figure 6 it can be seen that the discrepancies between the true counts and the
corrected counts increases in the region where there are changes in count rate for all the
correction equations.
12
1.4E+05
1.2E+05
Counts
1.0E+05
8.0E+04
No dead time
Intrinsic dead time
Fixed dead time
6.0E+04
4.0E+04
2.0E+04
0.0E+00
50
60
70
80
Time
Figure 4 Calculated counts
1.0E-01
8.0E-02
Ratio
6.0E-02
Equation 4
Equation 5
Equation 6
Correction factor, equation 4
4.0E-02
2.0E-02
0.0E+00
-2.0E-02
50
60
70
80
90
Time
Figure 5 Fractional discrepancies between true counts and corrected observed counts.
13
100
2.0E-02
Ratio
1.0E-02
0.0E+00
Equation 4
Equation 5
Equation 6
Correction factor, equation 4
-1.0E-02
-2.0E-02
50
60
70
80
90
100
Time
Figure 6 Fractional discrepancies between true counts and corrected observed counts.
Ratio equals the corrected observed counts minus the true counts divided by the true counts.
Figures 7, 8, 9 and 10 show the effect of adding a “noise” pulse height spectrum to
the calculation. The first spectrum the pulse is in channel 47 as previously, in the second the
pulse is in channel 8 and as before the bias level is equivalent to channel 15. For the first
pulse height spectrum the amplitude in the time of flight regions from 50 to 55 -second and
75 to 102.4 -second are set to unity and the region from 55 to 75 has a count rate of 0.01.
The observed time of flight spectrum for the second pulse height should be zero as the pulse
height is below the bias level but counts are observed and these are due to tails of previous
pulses increasing the amplitude of the “noise” pulses. The noise contribution is seen as a
decaying count rate starting at the steep decrease in count rate at 55 -seconds and a rising
count rate starting at the steep increase in count rate at 75-seconds. The shape and amplitude
of this changing “noise” contribution depends on the shape of the pulses, the count rate and
the length of the dead time relative to the decay of the pulse. The “noise” contribution to
observed count for zero dead time is found to be proportional to the square of the true count
rate. The intrinsic dead time reduces this contribution to the observed counts by about a factor
of three and the fixed dead time of five times the pulse decay time reduces its contribution to
a negligible amount. Figure 10 shows that only the noise pulses that occurred within the first
part of the dead time of the large pulse are registered. The sharp drop in the count rate at ~1.4
-seconds is due to the fact that the amplitude of the noise pulses plus the tails from previous
ones do not cross the bias level.
Figure 12 shows the time of flight spectrum similar to the above but using a pulse
height spectrum similar to that of a Li-glass scintillator (see Fig. 11) but with no noise or
background contribution. The effect of adding a background and noise pulse height spectrum
14
is shown in figures 13 and 14. Figure 15 show the contribution of the background and noise
to the spectra in figures 13 and 14. Figure 16 is the distribution of the time to the next pulse.
The rise above the fitted curve in the first few -seconds is due to the background and noise
pulses and indicates that the fixed dead time should extend out to at least five times the decay
time of the pulses (0.5 -seconds).
9.0E+04
Counts
8.0E+04
No dead time
Intrinsic dead time
Fixed dead time
No dead time and no noise events
7.0E+04
6.0E+04
5.0E+04
50
55
60
65
70
75
80
Time
Figure 7 Observed counts showing the inclusion of a noise pulse below the bias level
1.0E+05
1.0E+04
Counts
No dead time
Intrinsic dead time
Fixed dead time
No dead time and no noise events
1.0E+03
1.0E+02
50
55
60
65
70
75
80
Time
Figure 8 Observed counts showing the effect of a noise pulse below the bias in the minima count region.
15
10000
No dead time
Intrinsic dead time
Fixed dead time
Counts
1000
100
10
1
50
55
60
65
70
75
80
Time
Figure 9 The observed counts due to noise pulses being raised above the bias level by the tails of previous
pulses.
1.0E+05
1.0E+04
Counts
Fitted curve
No dead time
Intrinsic dead time
Fixed dead time
1.0E+03
1.0E+02
0
1
2
3
4
5
6
7
8
Time
Figure 10 The observed time to the next pulse including the effect of noise pulses.
16
9
10
6.0E+00
Relative probability
5.0E+00
4.0E+00
Signal
Background
3.0E+00
2.0E+00
1.0E+00
0.0E+00
0
10
20
30
40
50
60
70
80
90
100
Amplitude
Figure 11 Pulse height spectrum similar to that from a Li-glass scintillator for neutrons
1.0E+05
No dead time
Intrinsic dead time
Fixed dead time
Counts
1.0E+04
1.0E+03
1.0E+02
50
55
60
65
70
75
Time
Figure 12 Counts for Li-glass pulse height spectrum, with no noise pulses with 32 counts per start.
17
80
1.5E+05
No dead time
Intrinsic dead time
Fixed dead time
No dead time, no noise
Counts
1.0E+05
5.0E+04
0.0E+00
50
55
60
65
70
75
80
Time
Figure 13 Counts from a Li-glass pulse height spectrum plus some background and noise contribution.
2.0E+04
1.8E+04
Counts
1.6E+04
1.4E+04
No dead time
Intrinsic dead time
Fixed dead time
No dead time, no noise
1.2E+04
1.0E+04
50
55
60
65
70
Time
Figure 14 An expanded version of figure 11 showing the region of the minima.
18
75
80
2.0E+04
1.8E+04
Counts
1.6E+04
1.4E+04
1.2E+04
No dead time
Intrinsic dead time
Fixed dead time
No dead time, no noise
1.0E+04
8.0E+03
50
55
60
65
70
75
80
Time
Figure 15 The background and noise contribution to the data shown in figure 11.
5.0E+05
4.0E+05
Fitted curve
No dead time
Intrinsic dead time
Fixed dead time
Counts
3.0E+05
2.0E+05
1.0E+05
0.0E+00
0
1
2
3
4
5
6
7
8
Time
Figure 16 Distribution of the time to the next pulse for the data shown in figure 11
19
9
10
Conclusions?
If the output from the program DTIME is a good representation of experimental data,
then the main conclusion is that most of the algorithms used in the correction of dead time
effects underestimate the true count rate and that this underestimate increases with increasing
count rate.
The effect on activation measurements is to underestimate the source strength and if
the measurement is followed over several half-lives is also an underestimate of the half-life.
With an initial count loss of ~10% decreasing down to ~2.5% after about two half-lives,
corrections using equation 4 give a source strength and the half-life ~0.5% low, Equation 5 is
slightly better being only ~0.15% low. The addition of a background and noise pulses to the
calculations enhances these effects and its magnitude depends on the signal to background
ratio.
In time of flight measurements again the effect is to under estimate the true count rate.
In transmission measurements this will cause a slight decease in the observed cross-sections,
as the effect is proportional to the difference between the corrections for the sample in the
neutron beam and no sample in the neutron beam. If during the period of the dead time there
are large changes in the count rate the equation given in this paper do not appear to give an
adequate correction factor.
The addition of a background and noise to the time of flight spectra showed that the
background is not a simple function of time as used in most time of flight measurements. If
the dead time does not extend out beyond the longest/largest pulses seen in the experiment
then there will probably be a component that depends on the square of the count rate as can
be seen in figures 12, 13 and 14.
If these effects are present in time of flight data they may go some way in explaining
the small discrepancies often encounter when comparing measurements from different
laboratories.
20