Oslo Cyclotron Laboratory
Laboratory Excercise in FYS3180 - Experimental
Methods in Physics
Morten A. Salvesen
University of Oslo, Oslo, Norway
2007-09-24 to 2007-11-15
Contents
1 Abstract
1
2 Oslo Cyclotrone Laboratory
1
3 Singles
2
3.1
NaI- and Ge-detectors
. . . . . . . . . . . . . . . . . . . . . . . .
3.2
Calibration
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
3.3
Pair Production - Single and Double Escape . . . . . . . . . . . .
5
3.4
Unfolding
6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Coincidence
2
8
4.1
Basic Coincidence Technique
. . . . . . . . . . . . . . . . . . . .
8
4.2
TDC Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
4.3
NaI Eciency at 511keV and 1275keV
. . . . . . . . . . . . . . .
11
4.4
Multiplicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
5 Summary
13
6 Appendix
14
6.1
Partial Decay Schemes . . . . . . . . . . . . . . . . . . . . . . . .
14
1
Abstract
Over the course of 9 weeks spent at the Oslo Cyclotrone Lab working with the
CACTUS - a sum of 29 detectors - measuring various radioactive sources, we
were to gain an introductory understanding in the use of detectors, their advantages and disadvantages; the use of programs/software; and dierent methods
used in experimental nuclear physics.
2
Oslo Cyclotrone Laboratory
Built in 1979 the Oslo Cyclotron Laboratory (OCL) has since then formed the
basis for experimental nuclear physics in Norway.
Outtted with the MC-35
Scanditronix cyclotron it's the only accelerator in Norway for ionized atoms,
and is for this reason used in various elds of research and applications.
The main focus at OCL is investigation of level densities and radiative
strength functions; quantities that are important for understanding of thermodynamic and electromagnetic properties of atomic nucleus, as well as for
understanding stellar evolution and accelerator-driven transmutation of nuclear
waste.
The cyclotron at OCL is also used in medicine for production of radioactive
isotopes.
Particularly it's been used by the Norwegian Radium Hospital in
Oslo for the production of
Production of
18
18
F used in positron emission tomography (PET).
F has since been taken over by the Radium Hospital itself, and
the production of radioactive isotopes these days is mainly for research purposes.
Figure 2 shows the layout of the OCL. The MC-35 cyclotron is able to
accelerate protons to a velocity of 83 000km/s - 28% of lightspeed, which gives
a relativistic mass increase of 4%.
Table 1 shows the four available types of
particle beams from the cyclotron. Although the MC-35 is the main attraction
at the OCL, our studies where only concerned with the CACTUS, g 1, which
consists of 26 5x5 NaI detectors and one Ge detector, and the use of software
used with the CACTUS.
Particle type
Energy (MeV)
Beam intensity (uA)
Proton
2-35
100
Deuteron
4-18
100
3
He
6-47
50
4
He
8-35
50
Table 1: Available MC-35 cyclotron beams
1
Figure 1: The OCL CACTUS: 26 NaI and one Ge detectors
Figure 2: General layout of the OCL
3
Singles
3.1 NaI- and Ge-detectors
The OCL CACTUS utlizies NaI scintillation detectors and Ge semiconduction
detectors. Scintillators work by absorbing high energy electromagnetic radiation
which causes the detector to emit (uoresce) photons at visible or near visible
light energies, thus releasing the previously absorbed energy, which is detected
2
and measured by a photomultiplier tube (PMT).
In semiconductor detectors the radiation is measured by looking at the
amount of charge carriers that are set free in the detector by the absorbed
radiation.
The amount of energy required to create an electron-hole pair is
known, and is independent of incoming radiation, so measuring the amount of
electron-hole pairs gives the energy of the incident radiation.
The energy that is required for electron-hole pairs is fairly low, which leads
to a higher energy resolution in the Ge semiconduction detectors than in the NaI
scintillator. By resolution is meant the ability of the detector to separate gamma
rays of dierent energy. It's most common to express the resolution in terms
of the Full Width at Half Maximum (FWHM) value; the width of the gamma
ray peak at half of it's highest point. The relative resolution is also sometimes
used; the FWHM divided by the energy of the gamma ray. As the resolution of
detectors varies for dierent energies it's usual to give a reference energy. See
gure 3 for a spectrum of a
137
Cs source taken with a Ge detector. Photons
of energy 662keV are released as
137
Cs decays to
137
Ba, this is represented by
the peak in the spectrum. The FWHM was measured to 4.2keV, which gives a
relative resolution of
0.63%
gave a relative resolution of
at 662keV. In comparison one of our NaI detectors
9.60%
at the same energy.
Figure 3: Counts vs energy (keV) of
137
Cs measured with Ge detector
Earlier the problem with Ge detectors has been the relatively small size,
which gives a lower eciency than NaI detectors which have generally been
larger. Eciency is the probability that emitted gamma rays will interact with
the detector. The eciency of a scintillator is dependent on the relatively slow
uorescence decay time of the substance used as detector, whereas in semiconductors it's governed by the fast travel time of the electrons/holes. Techniques
3
for growing Ge crystals have improved over the years, so that todays Ge detectors can be made at equal or larger size than the available NaI detectors. The
Ge detectors however have a much higher cost than NaI detectors, and larger
size consequently gives a very high price. Another disadvantage to the Ge detectors is the requirement that they be cooled down to about liquid nitrogen
temperatures (77K) to work.
3.2 Calibration
The detectors used all had to be calibrated for the software we used for our
measurements, so precise information could be gleaned from the results given
by the detectors. In addition, calibrating all the NaI detectors allows us to use
all the 26 detectors as one large detector. Calibration for the Ge detector was
done by measuring gamma rays with known energy, from
40
K and
228
Th, which
have peaks at 1460.8keV and 2614.6keV respectively. These isotopes are found
in surrounding walls and similar in the OCL, and this background radiation is
cause of unexpected peaks when doing experiments. A
and
40
137
Cs (662keV) source
K background radiation was used for calibration of the NaI detectors.
Figure 4 shows the spectrum from the Ge detector.
The peaks are found
at channels 1387.6 and 2489.7 corresponding to 1460.8keV and 2614.6keV. This
gives a calibration factor of 1.0469keV/ch, and an energy of 8.1085keV at ch0.
This calibration isn't perfect, as the spectrum can't properly be dened by a
linear function such as this.
Figure 4: Spectrum gained from measuring background radiation from
228
Th
40
K and
Calibrating the NaI detectors was done by measuring gamma rays from
4
137
Cs
and
40
K, gure 5. The peaks from each is 662keV and 1460.8keV which gives
approximately an 800keV dierence. We wanted the NaI detectors calibrated
with 10keV/ch; giving 80ch between the two peaks. This was acomplished by
changing the voltage on the PMTs for each detector. In addition, all detectors
should be aligned, by making ch0 equal 0keV, thus giving the
ch66 for all detectors; gure 6.
Recording radiation from
137
137
Cs peak at
Cs using all the
NaI detectors as one then gave us a FWHM of 5.9keV, and the peak at ch65.45,
giving us a relative resolution of 9.01% at 662keV.
Figure 5: Matrix for selection of NaI
Figure 6: Matrix for calibrated and
detectors.
aligned NaI detectors.
662keV and 1460.8keV
peaks at red/white and orange concentration respectively.
3.3 Pair Production - Single and Double Escape
It's important to note that not all interactions with the detectors create peaks
at the desired energies, as can be seen by the blurring and the non-zero peaks
and background peaks in our spectra.
The distinct energy peaks are full en-
ergy absorption peaks due to photoelectric eect. Background radiation from
elements in our surroundings also cause peaks such as those to appear in our
spectra, as we saw in section 3.2. There's also counts of photons of most energies
up to the maximum full energy peak of the source due to compton scattering.
And we have peaks due to pair production.
Pair production occurs when a photon interacts with a nucleus inside the
detector and creates an electron-positron pair. Electron-positron annihilation is
then common, where the particles annihilate to produce two (or more, but this
is less likely) photons, with energy 511keV (rest energy of electron/positron). If
one of the 511keV photons escapes from the detector, you'll get the single escape
peak, which will have an energy 511keV lower than the expected photoelectric
peak, likewise if both photons escape the energy will be 1022keV lower.
Taking the spectrum from the Ge detector in section 3.2, gure 4, and enhancing the area between ch1900 to ch2500, gure 7, we see a peak at ch2003,
5
which equals an energy of 2105keV. This is due to single escape from pair production of the
228
Th 2614.6keV gamma ray.
Double escape is rarer and we
were not able to detect any satisfactory peak at the desired energy; the counts
registered could just as well be due to noise.
Figure 7: Single escape at ch2003 (2105keV) due to pair production from
228
Th
2614.6keV gamma ray interaction in Ge detector.
3.4 Unfolding
As we've seen in our spectra so far, there's a lot of unwanted noise: We have
the full energy photoelectric peaks, the single- and double escape peaks, as
well as the Compton background, and more. Therefore we need methods that
correct our spectra to better represent the full energy spectra we want.
One
such method is unfolding of a broad energy distributed spectrum into a true
full energry spectrum. We will use a folding iteration method [2] to unfold a
background reduced spectrum of
152
Eu.
The background reduced spectrum, gure 8, was made by running the NaI
detectors for equal amounts of time rst with the
152
Eu and then without. Then
the background spectrum was subtracted from the original
152
Eu spectrum. The
reduced spectrum was then used to create a response matrix, gure 9, required
for the folding operation.
6
Figure 8:
Spectrum of
152
Eu with
Figure
background radiation subtracted.
9:
Response
matrix
ated from bacground reduced
cre152
Eu
spectrum, g 8.
Ri,j as response in channel i when a
j
interacts with a detector. Normalization
P
of each response function is then
i Ri,j = 1, and so folding is given by f = Ru,
where f is the folded and u is the unfolded spectra. The folding iteration method
In the folding iteration method we dene
photon with energy equalling channel
then follows four steps:
We use
r
u0 = r
as the rst trial function for the unfolded spectrum
u0 , where
is the observed spectrum. Then the rst folded spectrum is calculated:
f 0 = Ru 0
Then we use the dierence spectrum
u
0
r − f0
and the original trial function,
, to nd the next trial function:
u1 = u0 + (r − f 0 )
We fold and get a new
f1
which is then used to obtain the next trial function:
u2 = u1 + (r − f 1 )
And so on until the folded spectrum
equal to
f i,
where
i
is the iteration index, is
r.
Using this method on our reduced
152
Eu spectrum gives us gure 10, which
now looks more like a full energy spectrum.
Taking a look at the peaks at
ch32, ch77, ch96 and ch141, we see that these correspond to the expected full
energy peaks of
152
Eu at energies 344.3keV, 778.9keV, 964.13keV and 1408.01keV
respectively. The spectrum isn't entirely correct however, as can be seen by the
lower than zero parts of the graph. Uncertainties occur due to our assumption
in our calculations that there are only 8 full energy peaks, where there are in
fact more than this. There's also bound to be some systematic error throughout
the process.
7
Figure 10:
152
Eu spectrum unfolded to closer resemblance to true full energy
spectrum.
4
Coincidence
4.1 Basic Coincidence Technique
Often with decay of nucleus two or more photons will be emitted at the same
time, f.ex.
when an unstable nucleus is created and immediately decays and
emits several photons, or, as we shall see with
22
Na; two photons can be pro-
duced when a product of the original decay annihilates inside the source. For
incidents like these we need measurement methods to separate them from simple single photon occurences; coincidence techniques. Figure 11 shows a simple
system for measuring coincidence.
The system works by recording all signals
that overlap (within a minimum timeframe) as coincidence events. We use the
Ge detector as the starter for the timeframe, and the NaI detectors as stop.
The curled
T
in the diagram represents a time delay; as the photon emissions
are simultaneous (or very close to) we don't want the stop detector to register
before start has occured.
8
Figure 11: A diagram for a simple coincidence measurement system.
Measuring a
60
Co source and recording both singles and coincidence gave
an interesting observation; the NaI detectors closest to the Ge detector had a
much higher count of coincidence events than the other NaI detectors which had
a more uniform spread. This is most likely due to an eect called cross-talk,
where a gamma ray is created by interaction between the incident gamma ray
and the Ge detector, the new gamma ray then escapes the Ge detector and
interacts with one of the nearby NaI detectors, causing a coincidence event.
This also works for NaI to Ge or even NaI to NaI detector. Thus we decided
to use six non-neighbouring NaI detectors, as these oered results closer to a
true full energy spectrum. Another source of accidental coincidence is random
coincidence, where background events arrive within the resolving time of the
coincidence circuit.
Figure 12 shows singles and coincidence for the
60
Co.
trum contains three peaks; the 1.17MeV and 1.33MeV from
1460keV peak from background
40
K. Since the
40
The singles spec60
Co, as well as the
K peak is a single incident it
won't be registered as a coincidence event (unless an accidental coincidence happens). If we assume that
NCGe (Eγ1 ) = ΩN aI (Eγ2 )NSGe (Eγ1 );
coincidence count
rate for the Ge detector equals the eectiveness of the NaI detector multiplied
with the singels count rate of the Ge detector, when the source has gamma
multiplicity
Mγ = 2,
we can use this to nd the solid angle for a typical NaI
detector (or the combined solid angle for six typical NaI detectors in our case).
And since all the NaI detectors are identical, we can multiply the solid angle
with the number of detectors to get the eciency of the combined NaI detectors.
9
Figure 12: Singles and coincidence measurements for a
60
Co source using the
Ge detector
Rearranging the equation above we get:
ω(Eγ2 ) =
NCGe (Eγ1 )
NSGe (Eγ1 )
Which we can use to nd the total eectiveness of the combined NaI detectors:
ΩN aI (Eγ ) =
26
· ω(Eγ )
6
From the spectra in gure 12 we nd:
NSGe (1.17M eV )
NCGe (1.17M eV )
NSGe (1.33M eV )
NCGe (1.33M eV )
=
=
=
=
0.8986 · 104
0.2708 · 103
0.8244 · 104
0.2801 · 103
And we get the solid angle of a typical NaI detector and the total eciency
for the combined NaI detectors respectively:
ω(1.17M eV ) = 0.03398
ω(1.33M eV ) = 0.03013
Ω(1.17M eV ) = 0.1472
Ω(1.33M eV ) = 0.1306
10
4.2 TDC Calibration
A TDC (Time to Digital Converter) spectrum shows the number of coincidences
as a function of time delay.
Figure 13 shows a TDC spectrum for a
22
Na
source, with the Ge detector as start. We add a 16ns delay to the Ge detector,
shortening the timespan between start and stop and expecting the TDC graph
to shift to the left, as shows in gure 14. The amount of channels the peak has
shifted from gure 13 to gure 14 is 33. With a 16ns delay that gives us a factor
of
a1 = 0.48ns/ch.
We want the spectrum to show the peak of the graph as
time zero, meaning channel 345.7 (centroid of unshifted spectrum) corresponds
to time zero, and we have a calibration constant
a0 = −a1 · 345.7 = −166.
The
FWHM of this spectrum is then found to be 35ns, this is the resolving time of
our system.
Figure 13: TDC spectrum for
22
Na
Figure 14: TDC spectrum for
with Ge detector as start
22
Na
with 16ns delay on Ge detector
4.3 NaI Eciency at 511keV and 1275keV
Using the CACTUS to measure a
22
Na source gives us singles and coincidence
spectra for the Ge detector seen in gure 15.
with
β+
22
Na decays in 90.5% of the cases
emission; this positron is annihilated in the source resulting in the
emission of two 511keV photons with an angle of
180◦
between them. In the
remaining 9.5% events electron capture occurs, emitting a photon at 1275keV.
From section 4.1 we recall how we found the solid angle of a typical NaI detector,
and total eciency of our combined NaI detectors. Using the same method now
we nd:
NSGe (511keV )
NCGe (511keV )
NSGe (1275keV )
NCGe (1275keV )
11
=
=
=
=
17396
497
5528
236
Figure 15: Singles and coincidence spectra for
22
Na with Ge detector.
Which gives:
ω(511keV )
ω(1275keV )
Ω(511keV )
Ω(1275keV )
=
=
=
=
0.04269
0.02857
0.1850
0.1238
The reason for the larger eciency at 511keV might stem from the fact that
when there's a
β + decay
it always results in two 511keV photons, so even if one
of the photons escapes detection there's still a chance the other one will register.
We notice as well that the results we got from measuring
60
Co correspond to
what looks like a decrease in detector eciency for higher energies.
4.4 Multiplicity
We'll be looking at something called
n-fold Ge spectra. n-fold means that n NaI
detectors have to be in coincidence with the Ge detector. Specically we'll be
looking at 0, 1 and 2 fold spectra; i.e. 0, 1 and 2 NaI detectors in coincidence
with Ge detector, for
MγN aI =
22
for
Na.
1
N aI
and Mγ
137
Cs,
=2
60
Co and
22
Na, with multiplicities of
respectively. Figure 16 shows us the
MγN aI = 0,
n-fold
spectra
In the lower left panel (0-fold) we recognize the 511keV, 1275keV and the
1460keV line from
2-fold.
40
K. The potassium line is expected to disappear for 1-, and
Examining the 1-fold spectrum, however, shows us a count of about
400 1460keV photons. These are most likely due to random coincidence. And
12
Figure 16: Lower left, lower right and upper left contain 0-, 1- and 2-fold spectra
for
22
Na respectively.
indeed, the 1460keV line has a count
≤ 20
in the 2-fold spectrum; that there's
any count at all is probably because of chance interactions with background
radiation or compton scattering.
The results for
60
Co were as expected, with negligible counts for 2-fold.
However, the detectors registered a count of 456 for 1-fold for
137
Cs, where we
should be expecting none; we would expect the counts to be proportional with
the relation
fold
i.
fi = Ωi
for
i ≤ MγN aI ,
and
fi = 0
for
i ≥ MγN aI ,
where
fi
is
Though the ratio of counts for the 662keV line in 0-fold (212882) and
1-fold (456) makes it likely that the unexpected counts are just a consequence
of random coincidence.
5
Summary
Through the course of this laboratory excercise in nuclear physics we've learned
about detectors - particularly NaI scintillators and Ge semiconduction detectors;
their advantages and disadvantages, and the appropriate use of the detectors;
13
when one needs higher resolution or better eciency, as well as the more technical aspect of using the detectors; calibration f.ex., and nding and calculating
eciency and resolution, among other things. We've seen the eects of photoelectric eect, pair production and compton spread, as well as studied methods
to reduce unwanted interference from these incidents.
We learned the basics of coincidence techniques and
n-fold
measurements.
Their applications for determining decay events in sources, as well as their use
in nding eciency of single or multiple detectors. We also learned about the
gamma multiplicity of isotopes.
The excercise has also taught us about general lab work; keeping logs, writing
reports and doing presentations, and proper conduct within a laboratory.
6
Appendix
6.1 Partial Decay Schemes
14
References
[1] Magne Guttormsen, Hilde Nyhus -
Guidance, counselling and advice
[2] M. Guttormsen, T.S. Tveter, L. Bergholt, F. Ingebretsen, J. Rekstad -
Unfolding of Continuum γ -ray Spectra
[3] W. R. Leo -
Techniques for Nuclear and Particle Physics Experiments
[4] K. S. Krane -
Introductory Nuclear Physics
[5] Oslo Cyclotron Laboratory webpage [6] Wikipedia.org -
·
·
·
·
·
·
·
http://ocl.uio.no
http://www.wikipedia.org
Compton scattering
Electron-positron annihilation
Gamma spectroscopy
Pair production
Photoelectric eect
Scintillator
Semiconductor detector
15
The