Experiment 23. Nuclear Lifetimes
Updated MD July 15, 2016
1
Safety First
During this experiment we are using radioactive sources. All sources are well shielded or are of
low intensity, nevertheless you should avoid any unnecessary exposure by keeping away from
the sources (r −2 dependence) and limit the time of being in proximity to them. If not in use,
radioactive sources should stay in a lead container provided.
Another safety concern is the high voltage power supply used to power on detectors. Under
any circumstances do not switch on the high voltage power supply if high voltage cables are
not connected to the detector. Do not disconnect high voltage cables if the high voltage power
supply is active.
If you notice any exposed or damaged electrical wires, please notify laboratory staff immediately.
23–2
2
S ENIOR P HYSICS L ABORATORY
Objectives
The build-up and decay of radioactivity in silver caused by reaction with slow neutrons will be
studied. In particular, you will be able to measure two separate radioisotope lifetimes, within
the same sample, using a computer function fitting procedure on the decay of radioactivity
data. You will also carry out measurements on the growth of radioactivity as a function of
time when the sample is irradiated by a slow neutron flux. In particular you will show that the
activity level will reach an asymptotic value. You will also be able to separate the activity of
two radioactive isotopes. In addition, you will examine a method used to chemically separate
a daughter radionuclide from its parent.
3
Introduction
Radioactivity can be regarded as a particular form of nuclear reaction where the emission of
the decay product(s) takes a much longer time in comparison with the time taken for a particle
of typical energy to move a large distance from the nucleus.
In the first part of this experiment you will study radioactivity resulting from bombardment
with slow neutrons. “Slow” means with energies comparable with the Boltzmann energy kT ,
i.e. around 0.03 eV.
The neutrons are produced in an americium-beryllium source. In this source
into beryllium powder. The following reactions occur
241 Am
is mixed
241 Am
→237 Np + α (a source of 1 Curie i.e. 37 GBq)
α +9 Be →12 C + n (5.75 MeV)
One in 20000 of the alphas produce a neutron so that the yield of neutrons is about 2 million per
second. Neutrons ejected with this energy can cause nuclear reactions but the cross-section is
small. They can be slowed down by putting them into a medium containing light nuclei which
does not contain nuclei that absorb them. Such a medium is called a moderator; the neutrons
elastically scatter from the light nuclei, losing a portion of their energy at each collision. After
a small number of collisions their energy becomes comparable with the thermal energy of the
scattering nuclei and they are said to be thermalised.
Suitable moderator nuclei are protons, deuterons, beryllium and all the stable nuclei of carbon,
nitrogen and oxygen. All have very low cross-sections for neutron capture except the proton.
This disadvantage is partly compensated for by the proton’s small mass and by the fact that
suitable hydrogen containing chemical compounds are freely available: water, plastics, wax,
etc.
With a source of slow neutrons we can cause nuclear reactions to occur by processes such as
A
Z + n → A+1 Z + γ
In the present experiment we are limited to the study of slow neutron capture reactions where
A+1 Z is radioactive with a ‘reasonable’ half life and where the slow neutron capture crosssection is large. By ‘reasonable’ we mean that the half life is much greater than the time
required to take the irradiated sample from the neutron source to the counter, but not longer
N UCLEAR L IFETIMES
23–3
than few hours. Silver, dysprosium, and indium being investigated in the experiment fits well
to these criteria.
Question 1: Why use light nuclei to thermalise neutrons?
Question 2: Why can very low energy neutrons cause nuclear reactions and low energy alphas
can’t?
4
Measurement of dead time of a Geiger-Müller counter
A Geiger-Müller (GM) counter is a cylinder filled with a mixture of gases. There are two
electrodes in it: An anode in the form of a thin wire placed along the axis and a cathode that is
usually the cylinder itself. The front of the cylinder is closed with very thin window that allows
energetic particles such as electrons, protons or muons to go through. When such a charged
particle enters the gas it ionises molecules and an electric current will go from the anode to the
cathode. This will produce an electric pulse that can be detected and analysed in a variety of
electronic instruments such as simple counters or more sophisticated data acquisition systems.
We use a computer’s sound card to capture a signal from the detector and the “Pulse Recorder
and Analyser (PRA)”[2] application to analyse the pulses. After each pulse occurs, a certain
time is required for all ions in the gas chamber to be collected. During this time, called the dead
time, the GM counter will not respond to any charged particle which enters the detector. The
simple model for dead time behaviour is called a nonparalyzable response. (See [3] p.120).
The “Pulse Recorder and Analyser” application collects beginning of each pulse as well as
its width and height. This data is analysed by the “PRA” and results of different statistical
histograms can be displayed in separate windows. The different options of the data acquisition
and parameters of the analysis can be adjusted using the Settings window. All the windows in
the application (except the main window) can be opened from the View menu. Here is a short
description of each window:
• The main window displays collected pulses vs time. You can use up and down arrow
keys to decrease or increase the time scale.
• The “Counting Rate vs Time” window shows how the number of pulses detected during
a certain period changes with time (e.g. it shows changes of the activity of the radioactive
material monitored by the detector).
• The “Counting Rate Histogram” window displays the variation of the counting rate. This
information is not used in our experiment.
• The “Interval Histogram” shows statistics on the time interval between the two successive
pulses (fold = 1). The height of each bin corresponds to the number of occurrences of
the time interval. The bins with zero counts at the beginning of the histogram illustrate
dead time phenomenon. If dead time is very short compare to the bin size, then we should
observe the largest number of the occurrences in the first bin. From this histogram “PRA”
calculates approximate dead time which value is displayed.
• The “Pulse Width Histogram” represents frequency of the occurrence of the pulses with
a certain width.
• The “Pulse Height Histogram” shows how many pulses of a certain height occur in our
data. In the case of the GM counter the height of the pulse does not depend on the energy
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S ENIOR P HYSICS L ABORATORY
of the particle and is almost constant. The height of the pulse from the N aI scintillation
detector depends on the energy of the particle deposited in the detector. In this case pulse
height histogram is also called energy spectrum if is callibrated in energy units.
• The “Audio Input” window is like an oscilloscope. It displays digitised electric signal at
the input of the sound interface of the computer.
Let us assume we observe X pulses during time T seconds. If a dead time of the counter is W
seconds then XW seconds will be excluded from the detector activity. The effective live time
will be T − XW . Let X ′ be the expected number of pulses during live time T . Assuming a
constant average counting rate we can write:
X
XT
X′
=
⇒ X′ =
T
T − XW
T − XW
(1)
In this experiment we will use the special twin carbon 14 C source. In this source you can
install the left half or the right half separately, together or none. Let XL , XR , XLR and XB are
numbers of pulses counted during the same period of time using left, right, both and none of
the sources.
′ − X ′ = (X ′ − X ′ ) + (X ′ − X ′ ) leading
Subtracting background counts we must have XLR
B
L
B
R
B
to the formula for W , namely
W =
√
AT
(1 − 1 − C)
B
(2)
where
A = XL XR − XB XLR
B = XL XR (XLR + XB ) − XB XLR (XL + XR )
C = B(XL + XR − XLR − XB )/A2
To determine the dead time of the GM counter use the following procedure:
1. Run the “PRA” application.1
2. Open “Audio Input” window (use V iew → Audio Input) and start acquiring data (use
Action → Start Data Acquisiton). You should see two lines; red and blue representing correspondingly samples from left and right channel of the sound interface. Left
(red) channel is connected to the signal from the Geiger counter placed below the neutron source in the room’s corner. Right (blue) channel is connected to the scintillation
detector placed on the bench top. You should see infrequent pulses produced by a background radiation caused by the naturally occurring radioactive isotopes and cosmic rays.
Signal pulses from the GM counter are positive and all approximately of the same height
and pulses from the NaI scintillator are negative of different height from very small to so
large that clipped by the electronics.
3. Select “Settings → Data Acquisition and Analysis” menu to open dialogue box window
and check if pulse threshold is set correctly for both channels. Ensure that the left channel
is selected to analyse signal from the GM counter.
4. Place a 14 C source at the GM counter (you do not need to irradiate it in the neutron
source, just slide it down the plastic conduit).
1
See PRA’s help for more information about using the program.
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5. Acquire the data for T = 100 s for each configuration of the 14 C source and record the
values of XL , XR , XLR , and XB .
6. Calculate the dead time using the formula (2). Hint: Use “Libre Office Calc” or “Microsoft Excel”. 2
7. Compare the result with the time interval histogram. The dead time phenomenon is
represented in the time interval histogram by a few empty bins at the beginning and its
value calculated by PRA is also displayed.3
C1 ⊲
5
Activation of silver
Elemental silver consist of two isotopes: 107 Ag (52% abundance) and 109 Ag (48% abundance).
Neutron bombardment leads to two short lived activities and a composite decay curve can be
drawn when the count rate of a GM counter is plotted against time.
The reactions produced by the neutrons are:
n+
n+
107 Ag
47
60
109 Ag
62
47
→
→
108 Ag + γ → 108 Cd + e− + νe (E
60
e
max = 1.65 MeV, t1/2 = 2.382 min)
48
47
61
110 Ag + γ → 110 Cd + e− + νe (E
4
62
e
max = 2.89 MeV, t1/2 = 24.56 s)
63
47
48
To investigate above reactions, use the following procedure:
1. Place the silver foil labelled Ag6 in the neutron source by letting it slide down the plastic
conduit into the neutron source and irradiate it for 16 minutes. There is a rod at the front
of the neutron source that must be pushed in to stop the sample inside the box. Place
your sample in the conduit with a silver side (not a perspex) facing you (GM counter).
2. Start the data acquisition before the end of the activation time and then release the silver
foil (by pulling on the rod) to fall down to the GM counter. Collect the data for at least
30 minutes.
3. Save the collected data to a file. This data will be reused in the next section.
4. The data to be analysed should start at the point where there is a clearly visible increase in
GM counter activity as shown in the PRA’s main window or in the counting rate versus
time plot. Adjust the beginning of the analysed data with accuracy at least of 0.1 s.
Increase the “ Bin size in seconds” of the “Counting rate vs Time” . Usually sampling
time 4 s to 8 s is suitable.5 Export the counting rate versus time data as a text file.
5. Open the “QtiPlot” application and import saved file as an text (ASCII) file into your
worksheet. Set the “Time” column as X. Add one column and set its values to the corrected counts taking into account the GM counter dead time (formula (1)). Set this
column as Y. Add another column
and set its values to the error of the number of counts
√
(use formula: error = σ = N umberOf Counts + 1). Set this column as Y error.
2
The template document named “DeadTime Calculation” is on the computer’s desktop.
For more information about dead time see [3, Knoll, p 121, 122]
4
For more information about neutron activation of silver see Appendix 9.
5
Sampling time should be few times shorter than the expected lifetime of the radioactive isotope, but not to short.
For example, sampling time 1 s is too short if you expect that the isotope has the lifetime in a range of hours. Using
short sampling time will lead to many data bins, each of a very small number of counts which does not represent
well statistical data.
3
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S ENIOR P HYSICS L ABORATORY
6. Select the X,Y and Y error columns and make a scatter plot of your data.
7. Click on the Analysis → F it W izard . . . menu to open the “QtiPlot - Fit Wizard” window. Select the Exp2Decay function from the User defined category. This is the second
order exponential decay function (it means, there are two superimposed exponentials).
Check the “Fit with selected user function” checkbox.
8. Click on the ⇒ button to move to the next function fitting step. Set the “Weighting
Method” to instrumental (this means the fitting procedure will weight the data using the
Y error column). Click on the Fit button to finish fitting procedure and close the Fit
Wizard.
9. Compare your results with the tabulated values of the lifetimes and comment.
Note:
There are two definition of the lifetime of the nuclei:
• A half lifetime t1/2 defined as the time needed for the number of not decayed nuclei to
decrease by a factor of 2.
• A mean lifetime τ where the decrease factor is e = 2.78....
A half lifetime occurs more frequently in the tables containing numerical data of the radioactive
isotopes. Mean lifetime is used more often in radioactive decay theory. Both lifetimes are
related by the formula:
t1/2 = τ ln 2
(3)
C2 ⊲
6
Activity build-up in the neutron source
In order to observe the build-up of foil activity when irradiated by the neutron source, we have
supplied six identical foils of silver labelled “Ag1” to “Ag6”.
Let us activate (theoretically) one of those foils in the neutron source. If we suppose that the
activation rate is R (the number of target nuclei activated per second) and number of active
nuclei after time t is N (t) then we have:
N (t)
dN (t)
=R−
dt
τ
If N (0) = 0 then solution to this equation is:
N (t) = Rτ (1 − e−t/τ )
Activation rate R = φnσ so we can write it in a final form as:
N (t) = φnστ (1 − e−t/τ )
where:
(4)
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φ is the neutron flux through the foil,
n is the number of target nuclei in the foil,
σ is the cross-section for neutron capture,
τ is the mean life of the activated state, and
t is the time the foil was irradiated by the neutron source.
We now transfer such irradiated foil to the GM counter. Suppose we assume a constant delay
of d seconds in taking the foil from the source to the counter and c seconds to be the counting
time. We expect the resulting counts from each isotope 108 Ag and 110 Ag to be expressed by
the formula:
C(t, d, c) = ηN (t)e−d/τ (1 − e−c/τ )
where:
d is the delay time needed to move the sample from the neutron source to the detector,
c is a counting time,
η is the efficiency of the GM counter detector (i.e. fraction of pulses registered by the
counter divided by the number of all emitted betas),
C(t, d, c) is number of pulses counted in the detector.
For both isotopes together the number of counts is equal to:
X
C(t, d, c) =
φηi σi ni τi e−d/τi (1 − e−c/τi )(1 − e−t/τi )
i=1,2
We will keep the delay and counting times constant. In this case, the above formula can be
simplified by substituting constant values as ki = φηi σi ni τi e−d/τi (1 − e−c/τi ). The result is
simply:
C(t) = k1 (1 − e−t/τ1 ) + k2 (1 − e−t/τ2 )
(5)
Let us compare this result to the experimental data:
1. Start the data acquisition in the “PRA” application.
2. Place the silver foil sample in the neutron source. Using a stopwatch, activate the foils:
Ag1 for 0 s (just drop it down without stopping in the neutron source), Ag1 for 15 s, Ag2
for 30 s, Ag3 for 1 min, Ag4 for 2 min, Ag5 for 4 min and Ag6 for 8 min. Record the
activity of each sample for at least 100 s.
3. Calculate the delay needed for the foil to drop from the neutron source to the GM counter.
Assume there is no friction with the conduit and the distance from the neutron source to
the GM counter is 1.2 m.
4. Find the number of counts during the first c = 100 s of each foil by adjusting the beginning and the duration of the analysed data with accuracy of at least 0.1 s.
5. Re-use previously collected data from the t = 16 min activation time to obtain an additional data point.
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S ENIOR P HYSICS L ABORATORY
6. In the “QtiPlot” application type your data in the table (irradiation time in the first column
and number of counts during 100 s in the second column).
7. Correct the number of counts using known value of the dead time of the GM counter and
then subtract the background (the number of counts in the first row).
8. Add new column and calculate errors of the number of counts. Corrected number of
counts is calculated as a difference of two values and both their errors should be included
in the result.
9. Plot the number of counts, C(t), versus activation time, t, for the 8 measurements (the
first should be C(0) = 0 as we subtracted the background) and note the value of the final
plateau. This represents the sum of the saturated contributions from both, the long and
the short lifetimes (i.e. k1 + k2 ).
10. Fit a second order exponential function to the data to obtain values for k1 , k2 , τ1 and
τ2 . To do this repeat the previous fitting procedure but this time use the Exp2Saturation
function from the User defined category. Usually 8 data points is not enough to calculate
all 4 parameters accurately. In such a case, set the values of τ1 and τ2 ( known from the
previous measurement or table ) as constant and find k1 and k2 .
11. Derive a formula for the ratio η1 /η2 and calculate it.
Tabulated values for silver isotopes:
τ1 = 35.43 s
τ2 = 206.19 s
n1 = 48 %
n2 = 52 %
σ1 = 86.3 b
σ2 = 37 b
E1 = 2.89 MeV
E2 = 1.65 MeV
η1 /η2 can also be calculated from the analysis of the counting rate versus time distribution as we already did in the previous section. Counting rate versus counting time is a
partial derivative ∂C(t, d, c)/∂c.
R(c) = ∂C(t, d, c)/∂c =
X
i=1,2
φηi σi ni e−d/τi (1 − e−t/τi )e−c/τi
Since the values of t, d, τi are constant, substitute ai = φηi σi ni e−d/τi (1 − e−t/τi ). The
result is:
R(c) = a1 e−c/τ1 + a2 e−c/τ2
(6)
12. Use the previously obtained values of a1 and a2 (coefficients in the second order exponential decay function fit to the data from the 16 min irradiation case) to calculate η1 /η2
again. Both results should be very close to each other.
Question 3: Why is it that electrons emitted from different isotopes are detected by the GM
counter with different efficiency? Hint: Consider the thickness of the silver foil, thickness of
the GM counter window and energy of the electrons emitted by each isotope.
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23–9
The chemical separation of a daughter radionuclide from its parent
For this part of the experiment the radionuclide to be studied 137 Bam will be separated from its
parent 137 Cs by a chemical method. The parent nuclide was originally produced in a nuclear reactor by fission. It was then incorporated into a “Isotope Generator” which allows the daughter
nuclide to be eluded (separated out) by passing a HCl/saline solution through the device.
The decay scheme for 137 Cs:
137 Cs
137 Bam
→
→
137 Bam
+ e− + ν˜e
137 Ba + γ
7/2+ 0 keV
137
Cs
55 82
(t1/2 = 30.05 a)
(Eγ = 661.659 keV, t1/2 = 2.552 min)
30.05 a
β- 100%
94.36 %
11/2-
661.659 keV
2.552 min
137 m
Ba
81
56
1/2+
283.5 keV
3/2+
0 keV
0.00061 %
5.64 %
137
Ba81
56
Fig. 23-1 Decay of caesium 137
55 Cs82 .
Follow this procedure:
1. The gammas are recorded in a scintillation detector. In the “Data Acquisition and Analysis” settings window change the “Channel selection” to “Right All”.
2. Place the “Isotope Generator” into the lead castle, as a source of 137 Cs.
3. Collect some data and analyse the time interval histograms. The “PRA” application has
a feature to calculate dead time from the time interval histogram. Write down the result.
4. Remove the isotope generator from the lead castle. Take the syringe supplied with the
generator and fill it up with approximately 1 ml of the eluting solution (0.9 % NaCl in
0.04 M HCl). Remove the stoppers from the generator. Insert the syringe firmly into
the hole on top of the generator and while holding the generator verticaly, force eluting
solution through the generator onto the planchet. After use, remove the syringe from the
generator, replace the stoppers and empty any unused solution back into the bottle.
5. Place the planchet containing the elutriate in the lead castle and collect data for 20 min.
6. Export the counting rate versus time distribution to the “QtiPlot”. Apply correction for
dead time and find the lifetime of 137 Bam (using Exp1Decay fit function).
7. Compare the result with the accepted value and comment.
Question 4: Why is a scintillation detector more effective in detecting gamma radiation than
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S ENIOR P HYSICS L ABORATORY
GM counter?
C4 ⊲
8
Metastable states - nuclear isomerism (Optional)
The term nuclear isomer refers to cases where distinctly different nuclei have the same atomic
number Z and the same mass number A. If there are two isomers, one will have lower energy
and usually a different spin/parity to its ‘brother’ at higher energy. Examples abound in the
Appendix 9, in particular 108 Ag has two isomers. The level at 109.440 keV with a spin/parity
of 6+ has a half life of 438 years. This level is called a metastable state and a superscript m is
put after the nuclide symbol to denote this. These states decay in a variety of ways as shown in
the diagrams in the Appendix 9. Note that the states half life has to be long compare with the
other nucleus’ exited states before the term metastable can be used.
We have two targets where the neutron bombardment produces isomeric pairs of radionuclide,
namely indium and dysprosium. Indium has one stable isotope with a mass number of 113 and
an abundance of 4% and the other 96% of atoms in an indium sample are 115 In which is beta
active with a half life of 6 × 1014 years.
Neutron irradiation produces 116 In, 116 Inm and 116 Inm2 . You will probably not see the third
nuclide’s decay; its lifetime is too short and it decays through γ emission. 116 Inm is interesting
in that it does not decay (either by gamma emission or internal conversion) to 116 In. It decays
exclusively by β particle emission to 116 Sn, a fact that makes it possible to record its activity
with a GM counter. (Recall that the GM counter is very inefficient at recording γ photons; most
go straight through the tube without interaction).
Neutron irradiation of 164 Dy produces the pair of isomers 165 Dy and 165 Dym and in this case
we have the more ‘conventional’ decay of the metastable state 165 Dym : 97.76% via gamma
emission and internal conversion to 165 Dy and only 2.24% by beta decay to 165 Ho. The decay
of 165 Dym to 165 Dy has a large internal conversion coefficient i.e. most decays are by emission
of an orbital electron rather than the 108.16 keV γ photon. It is because of this fact that the
165 Dym activity can be recorded with a GM counter.
Experimental procedure:
1. Choose either the Indium target or the Dysprosium target for irradiation. The technique
for this part of the experiment is the same for both.
2. We suggest the following order for your measurements:
(a) Irradiate the target for a short period to induce a reasonable activity of the shorter
lifetime isomer (Indium 20 s, Dysprosium 2 min).
(b) Acquire the decay data for at least 10 times longer than the irradiation time.
(c) Irradiate the same target for at least 1 hour to induce a reasonable activity of the
longer lifetime isotope.
(d) Set the Acquisition time and Maximum number of pulses to their maximum values.
Close all windows except the main window. Acquire the decay data overnight.
3. As before, use “QtiPlot” to estimate the lifetimes and compare the result with the tabulated values.
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S ENIOR P HYSICS L ABORATORY
References
[1] Bureau International Des Poids et Mesures, Pavillon de Breteuil, F-92310 Sèvres. Table
of Radionuclides. http://www.nucleide.org/DDEP_WG/DDEPdata.htm
[2] M. Dolleiser. PRA, v. 15, 2016.
http://www.physics.usyd.edu.au/˜marek/pra/
[3] Glenn F. Knoll. Radiation detection and measurement. John Wiley & Sons, 1989.
[4] I. Vasilief. QtiPlot, v. 0.9.9, 2016.
http://soft.proindependent.com/qtiplot.html
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9
23–13
Appendix
0.33 barn
90.9 %
6+ 109.440 keV
438 a
m
108
Ag
9.1 %
61
47
1+
2.19 %
+
0.283 %
(n, )
37.6 barn
0 keV
108
Ag61
47
108
Pd62
46
2.382 min
-
97.53 %
108
Cd60
48
107
Ag 60
47
6+ 117.59 keV
249.78 d
m
110
Ag
63
98.64 %
47
1.36 %
4.7 barn
86.3 barn
0.30 %
1+
0 keV
24.56 s
110
Ag
47
63
99.70 %
(n, )
110
Pd64
46
110
Cd62
48
109
Ag 62
47
109
Fig. 23-2 Neutron activation and simplified decay scheme of silver 107
47 Ag60 and 47 Ag62 .
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S ENIOR P HYSICS L ABORATORY
81 barn
8- 289.660 keV
2.18 s
116 m2
In
100 %
49 67
162.3 barn
5+ 127.267 keV
54.29 min
116 m
In
100 %
49 67
40 barn
1+
0 keV
14.10 s
116
In
49 67
99.98 %
0.02 %
(n, )
116
Cd68
48
116
Sn66
50
115
In
49 66
1610 barn
1040 barn
1/2- 108.16 keV
1.257 min
m
165
Dy
97.76 % 66
99
2.24 %
7/2+
0 keV
2.334 h
165
Dy
66
99
99.70 %
(n, )
165
Ho98
67
164
Dy98
66
164
Fig. 23-3 Neutron activation and simplified decay scheme of indium 115
49 In66 and dysprosium 66 Dy98 .