Cosmic Rain:
Investigating Particles from Space
Holly Batchelor
Supervised by Peter Reid and Alan Walker
School of Physics
University of Edinburgh
Abstract
This project consisted of three experiments, each investigating different aspects of cosmic rays.
The main aim was to investigate the angular distribution of cosmic rays at sea level and to compare it
to modern day theories. This was done by constructing and using a cosmic ray hodoscope (based on a
design from Berkeley) which measured cosmic ray flux. The hodoscope consisted of two scintillator
paddles, each coupled to a photomultiplier tube; the pulses from the photomultiplier tubes were sent to
a circuit board designed to count coincident pulses. These paddles were positioned far apart to create a
cosmic ray ‘telescope’ which would only count a small angular range of cosmic rays. The hodoscope
was angled at varying degrees from the zenith angle and cosmic ray flux was investigated.
Theoretical calculations were first carried out to estimate the flux at various angles from the zenith
using stated vertical flux measurements and the cos2.16θ rule discovered by Crookes and Rastin in 1972.
These results were compared with the flux count obtained from our hodoscope. It was found that our
results correlated with the expected cos2.16θ curve for angles less than 75º. For larger angles the
estimated flux is lower than the actual result as cosmic rays can enter both sides of the hodoscope,
increasing the count.
A secondary investigation involved using the Teach Spin muon lifetime apparatus to determine the
energy spectrum of muons at sea level. This apparatus counts muon decays by turning the double
scintillation caused by a muon decay into an electrical pulse which can be sent to a computer. For a
muon to have reached the scintillator then decayed, it must have had a certain energy, which was
calculated using known formulae. Muons with different energy levels were selected by placing
moderating layers of steel above the detector. Only muons with a low energy of <1GeV could be
investigated as only 48cm of steel could be obtained. Every 72 hours, 3cm of steel was removed and
the number of muons (for each energy) decaying in the scintillator counted. Finally, a graph of the
results was constructed. As expected for muons with low energy levels, the flux was evenly distributed
for all energies.
The third task was to design and construct a diffusion cloud chamber for viewing particle tracks made
by cosmic rays. One of the aims for this investigation was to make a reliable chamber for a reasonable
amount of money so that it could be copied by schools. The chamber was constructed from a plastic
aquarium, sheet aluminium and felt, all for under £40. When a temperature gradient was established in
the chamber by cooling the base with dry ice, particle tracks could be seen clearly in the layer of supersaturated mist.
Contents
1
Introduction
1
2
Methodology
5
3
Results
7
4
Conclusions
10
5
Further Developments
10
6
References
11
7
Acknowledgements
11
8
Appendix
12
muons is approximately 2.2μs, the majority survive
travelling through the atmosphere to sea level even though
this would take an approximate time of 50μs as a result of
time dilation, making them the most numerous charged
particles at sea level. Some muons do decay, producing
electrons and neutrinos:
1 Introduction
1.1 Cosmic Rays
Although the source of cosmic rays is still not completely
known, possible sources have been identified. Supernovae
are known to provide many charged, high energy particles
and we know that similar particles come from the Sun.
   e   e  
   e   e  
Primary cosmic rays consist of the nuclei of elements
produced by events elsewhere in the universe. Around
90% are single protons, the nuclei of hydrogen atoms
[URL Ref 1]. They are accelerated through magnetic
fields in space, but when trapped by the magnetic field of
the Earth, hit the upper atmosphere where high energy
strong interactions (as well as electromagnetic processes)
with protons in the atmosphere lead to showers of
secondary particles:
1.3 Energy Spectrum
Muons arrive at sea level with different velocities and
therefore with a spread of different energy levels. The
number of muons arriving per unit area per unit time is
called the flux. Over a long period of time, only few
measurements have been made to determine the flux and
the energy spectrum of muons in the atmosphere. Part of
this project was to determine whether there was a
connection between flux and energy level of muons at sea
level and whether previous assumptions – namely that
there are similar fluxes of muons of different energy levels
at sea level – were correct.
p  p      0  K  K
The most abundant of these secondary cosmic rays are
pions (  ), with other mesons (kaons (K) etc) and
nucleons also being produced. Charged pions decay
through the weak interaction into muons and muonneutrinos and the neutral pion decays through the
electromagnetic interaction to produce gamma rays:
1.4 Angular Distribution
This investigation was centred on the angular distribution
of cosmic rays at sea level. When doing energy spectrum
experiments, amongst others, it is assumed that the
majority of cosmic rays come through the atmosphere
vertically. In actual fact, cosmic rays travel through the
atmosphere at all angles. Cosmic rays arriving at some
angle  from the vertical will have travelled further.
Assuming that all particles are created at the same height
and neglecting the curvature of the Earth’s atmosphere, it
can be said that their path length increases as 1/cos().
This longer path length causes more particles to decay in
the atmosphere than those travelling vertically and we
would expect the cosmic ray flux to decrease as cos(θ).
However, the variation of cosmic ray flux with angles of
less than 75º from zenith, obtained by Crooke and Rastin,
has been shown to be adequately represented by the
expression:
      
      
 0  
These gamma rays go on to produce electron-positron pairs
which subsequently undergo bremsstrahlung, which can
again produce electron-positron pairs, and so on as long as
the photon energy exceeds 1.02 MeV [Greider] – this
repetitive process leads to an electromagnetic shower in
the atmosphere.
This ever-changing shower of electrons, gamma rays,
neutrinos and muons moves through the atmosphere at the
speed of light (see Figure 1 below).
F ( )  F cos 2.16 
For angles greater than 75º, count rate does not follow this
trend as horizontal cosmic rays can be measured from both
directions, increasing the expected rate.
1.5 Equipment
This project was made up of three different experiments,
each investigating different aspects of cosmic rays. The
main aim was a numerically-orientated investigation to
measure the angular distribution of cosmic rays by
constructing a hodoscope (see Section 2.1.1). A secondary
experiment was to check a previous Nuffield project
(Ingrid Burt, Beeslack Community High School) by
investigating the energy spectrum of muons at sea level
with equipment which was already available. The last
component involved the design and building of a diffusion
cloud chamber from scratch which would allow you to see
particle tracks left by cosmic rays.
Figure 1. Cosmic Ray Shower
1.2 Muons
Cosmic ray muons are the decay products of charged pions
and have similar properties to electrons but are about 207
times more massive. Although the average lifetime of
1
1.5.1 Angular Distribution Investigation
A cosmic ray hodoscope was constructed (with assistance
from the project supervisors) from commercially available
components and was used to measure the angular
distribution of cosmic rays at sea level.
The design for the cosmic ray hodoscope was based on the
Berkeley Cosmic Ray Detector [URL Ref 5] (see Figure
4). This device counts the number of cosmic rays which
pass through both of its two scintillator panels. The
hodoscope consists of a pair of polyvinyltoluene
scintillator paddles (with surface area of 199cm) coupled
with a pair of photo multiplier tubes (PMTs), all connected
to a circuit board with a three-digit LED display (see
Figure 2).
Figure 2. Schematic circuit diagram
When a charged particle passes through one of the
scintillator paddles, it emits a small flash of light. This is a
result of the organic scintillator solution in the plastic
solvent absorbing and reemitting energy in the form of
visible light. The light output of the scintillator is directly
proportional to the exciting energy of the cosmic ray. This
reemission occurs within 10ns and the flashes last for 3ns.
This fast response and fast recovery time allows the
scintillator panels to accept high count rates, since the dead
time (when pulses could overlap) is reduced.
Figure 3. Schematic diagram of a PMT
The light produced by the scintillator is transmitted to the
PMT by means of total internal reflection with the
scintillator panel, where it is incident on a cathode. The
light signal is transformed to an electrical signal and
further amplified by an electron multiplier system (see
Figure 3) – electrons released from the cathode are
accelerated towards the first dynode and multiplied with
each successive dynode at a higher potential than the
previous one, which means that at each stage the number
of electrons increases by a factor of the order of five.
1.5.2 Energy Spectrum Investigation
A secondary experiment used the Muon Physics apparatus
(MP1-A) from Teach Spin Inc to count the flux of different
energy levels of muons (see figure 5). It consists of a
cylindrical block of scintillator coupled with a PMT
encased in an aluminium tube. When a cosmic ray passes
through the scintillator, a small flash of light is emitted in
the same way as in the hodoscope’s scintillator paddles.
The PMT works in the same way as the PMTs in the
hodoscope, turning the scintillations into electrical signals
which are then sent to the electronics box. Here, the output
signal from the PMT feeds into a two stage amplifier and
then to a voltage discriminator which produces a TTL
output pulse. The number of pulses is the data sent to a PC
via a communications module. A computer program then
counts the flux and time elapsed for each run of the
experiment.
The electrical signals produced by the PMTs are further
amplified by op-amps in the circuit. When both PMTs are
connected and a cosmic ray passes through both of them,
the board registers coincident signals and there is an output
pulse from the AND gate, as it has received two high logic
inputs. These pulses cause the seven segment displays to
change, counting the flux of comic rays. The coincidence
technique allows us to ignore random electrical noise
within each PMT (as long as it is not too severe).
Although this equipment has similar components to the
hodoscope, the muon detector works in a different way.
The hodoscope has two paddles and counts coincident
outputs whereas the muon detector has only one scintillator
block. This single scintillator can be used to count
scintillations caused by charged particles passing through
2
or can count muon decays by the double flash caused by
their entry, halting in the chamber and then decaying (the
electron release in decay causes the second flash). In this
investigation, muon decays were counted as the energy
range for these decaying muons could then be calculated.
The diffusion cloud chamber design was taken from that of
the cloud chamber built for the CERN open day in October
2004 (see Figure 6). It consists of a plastic aquarium with
a sheet of felt/sponge that is soaked in isopropyl alcohol
attached to the inside of the base. This is then placed
upside down on a sheet of aluminium on top of an
insulated box filled with dry ice. A trough was milled in
the base plate and filled with isopropyl alcohol to produce
an airtight seal. Alternatively, Vaseline can be spread
around the edge if a milling machine is not available. A
steep temperature gradient is established as the metal base
cools to -78ºC and the felt at the top remains at room
temperature. When the alcohol in the felt evaporates, the
vapour falls towards the cold base of the chamber but is
unable to condense as it lacks nucleation sites and thus
forms a layer of super saturated vapour near the base of the
chamber. When a cosmic ray passes through this super
saturated layer, it leaves behind ions on which droplets can
form. This produces a visible trail of droplets in the path
taken by the cosmic ray.
1.5.3 Cloud Chamber
The third task was to design and construct a diffusion
cloud chamber. A cloud chamber allows you to physically
see particle tracks and was used, in this case, to view the
tracks left by cosmic rays. One aim of this experiment was
to investigate whether a reliable cloud chamber could be
made cheaply and easily to be taken on tour with the
Particle Physics for Scottish Schools project (PP4SS, URL
Ref 8). It needed to be suitably simple to construct and run
so that it could be copied by schools, to allow pupils to see
particle tracks.
Power supply
Scintillator paddles
Circuit board
PMTs
Figure 4. The hodoscope mounted in its display case
3
Figure 5. Muon lifetime apparatus
Felt soaked with IPA
Plastic aquarium
30ºC
Evaporated
vapour falls
from felt
Anodised
aluminium plate
-70ºC
Insulated box filled with dry ice
Figure 6. The cloud chamber
4
difficult part of construction as it was very hard to tell
whether the pulses the PMTs were emitting were a result
of a scintillation or just electrical noise. In an attempt to
combat this problem, the PMTs were calibrated
simultaneously with both plugged into the circuit board,
which was set to register coincidences. This meant that the
paddles could be placed at opposite ends of the room, each
mounted with the paddles vertically orientated, so that no
(or at least very few) coincidences caused by cosmic rays
could occur. The PMTs were then calibrated so that the
coincident count rate was zero. In effect, this should have
limited the sensitivity of the PMTs to only be triggered by
coincident scintillations caused by cosmic rays.
2 Methodology
Firstly, all background information had to be understood,
including: radioactive decay law; uncertainties in
radioactive decay; particle interaction probability and
mean free path; energy loss in atomic collisions, calculated
using the Bethe-Bloch equation; organic scintillators and
their output response; basic construction and operation of
photomultiplier tubes; how to mount and operate a
scintillation detector; the origin of cosmic rays; the
production of secondary cosmic rays and decay
mechanisms of pions and kaons.
2.1.3 Operation
Once everything was set up, the paddles were held over a
metre apart and placed parallel to the ground. This created
a cosmic ray ‘telescope’ as only a small range of cosmic
rays from different directions would cause a coincident
signal (see Figure 7). Cosmic ray flux results were taken
over long periods of time at the zenith angle and then at
varying angles from the zenith angle to investigate the
angular distribution. The average expected cosmic ray flux
at sea level was calculated for this hodoscope and
compared with the results.
2.1 Angular Distribution Investigation
2.1.1 Construction
The cosmic ray hodoscope had to first be constructed with
the assistance of the project supervisors. The scintillator
paddles were wrapped in aluminium foil to reflect any
escaping photons back into the scintillator. They were
covered in black card and black tape to ensure they were
light tight. They were coupled with the PMTs and then
further wrapped in black tape.
As a result of the windows for the cathode in the PMTs
being on the side rather than end on, various ways of
holding the scintillator paddles to the PMTs without the
need of optical glue were tried. As a result of the PMT’s
curved face attaching to the flat scintillator paddle end,
there was too large a gap between each surface to be filled
with optical glue. This proved not to be a problem as the
paddles worked well even without the glue.
In the first (prototype) hodoscope, nylon pipe with
machined holes and slots was used to hold the paddle
against the side of the PMT prior to and during taping.
This was effective at holding the two pieces together but
was found to put too much stress on the glass of the PMT
(one of which was broken), making it unsuitable for
repeated use in experiments. This hodoscope was mounted
in a display case for use as an exhibit and display model
for PP4SS (see Figure 4).
A new design was developed using a wooden block to hold
the PMT securely in place by its powerbase (without
touching the glass). The paddle was then pushed through a
slot until it just touched the PMT’s surface. This ensured
that no unnecessary pressure was acting on the glass of the
PMT, making this design more suitable for use in the
angular distribution experiments. A further hodoscope was
made with the same ‘block’ design but this time the wood
was tapered towards the end with the paddle to make
taping easier, therefore making the hodoscope more light
tight.
Figure 7. Cosmic ray telescope, showing the two
scintillators mounted vertically and the range of cosmic
rays which can be detected
2.1.4 Further Developments
The mounted hodoscope and spare hodoscope will be used
for demonstrating this project and cosmic ray physics at
the Particle Physics in the Universe Today (PPUT, URL
Ref 9) exhibit at St Andrews University on 21st August,
2006. The mounted hodoscope will be used as a
2.1.2 Calibration
All calibration was undertaken with assistance from the
project supervisors.
The cables from the PMT’s
powerbase were wired and connected to the circuit board.
The board also had to be checked for continuity to ensure
nothing would short circuit. Then both photomultiplier
tubes had to be calibrated, using their internal
potentiometers, for sensitivity. This proved to be the most
5
demonstration model of how cosmic rays can be detected
and the other hodoscope will be part of a ‘cosmic ray
doorway’ exhibit, designed and built during and after this
project. The hodoscope will sit on top of a doorway with a
strip of LEDs down the side and a pressure pad underneath
which acts as the trigger for the circuit which runs the
LEDs. When someone stands in the doorway and a
coincidence is registered by the hodoscope, the LEDs will
flash from the top of the doorway to the bottom, signalling
that a cosmic ray must have passed through the person.
Circuitry for this purpose has had to be designed (by one of
the supervisors) and a track board design with a master
board and two slaves was laid out on a PC. Each board
had a PIC chip which was programmed to run 33 I/O pins one input pulse pin and 32 outputs, which ran 32 LEDs, the
last of which was used as the pulse that triggered the PIC
chip on the next board to run its LEDs. The necessary
components for these boards had to be sourced and the
boards then needed to be wired and checked for continuity
(this was carried out by the Nuffield student).
2.3 Cloud Chamber
The cloud chamber was assembled and the base plate
cooled on top of dry ice. Isopropyl alcohol (IPA) was
poured over the felt and into the trough and the aquarium
was placed on top of the plate to set up a temperature
gradient with a corresponding layer of super saturated
vapour. The depth of the layer of vapour is highly
dependant on the temperature gradient and keeping the felt
warm was found to help – in this instance, a hot water
bottle was used. This gave a temperature gradient of
approximately 30ºC to -60ºC from top to bottom of the
tank.
It was discovered that in order to make the tracks more
easily visible, the aluminium base plate would need to be
black. It could not be painted however as the IPA would
strip this off, so instead it was anodised black. (A cheaper
option would have been to cover the base in Gaffer tape
but anodising the metal is more permanent.) It also helped
to view the chamber in a darkened room and to surround it
with black card too, thus blocking off any extra, unwanted
light.
2.2 Energy Spectrum Investigation
The muon lifetime apparatus was set up at the beginning of
the project and ran for several weeks. Muon flux for
different energy levels was investigated by slowing down
the muons with varying moderating layers of steel placed
above the scintillator. If a muon decayed in the scintillator
then it must have had a minimum energy level to have
made it through all of the steel. The School Of Physics
was able to offer 96 sheets of steel, each 5mm thick,
weighing 1/3 tonne in total.
A point light source was used to illuminate a section of the
chamber for viewing particle tracks – an LED torch or
standard torch was found to work best, although the LED
torch did not work for taking photographs of the tracks.
After trying many angles for the light source,
approximately 20º from the horizontal was found to be the
best. Cutting a gap in the surrounding card through which
the light source could be pointed through helped stop the
chamber being flooded with light, and making the tracks
easier to see. (Images of some of the tracks which were
seen can be found in Appendix.)
The first decay rate measurement was taken over 72 hours
with the full 48cm of steel. The experiment was then
repeated over a time scale of six weeks, removing 3cm of
steel every 72 hours. The average decay rate per hour for
each depth of steel was then calculated.
By using a spreadsheet constructed with the Bethe-Bloch
equation (using the muon’s relativistic momentum), the
muon energy losses for different depths of iron (as steel is
composed primarily of iron) were calculated. The energy
losses for the muons entering the scintillator and decaying
at the top, middle or bottom were calculated using a similar
spreadsheet – when these values were subtracted from the
muon’s rest energy, the minimum amount of energy
required for a muon to reach the scintillator, decay and be
counted was given. Using these calculated values, the
minimum energies of muons reaching the scintillator after
travelling through different depths of steel were found.
See Appendix for table of calculated values and Section 3
for a graph of results.
6
3 Results
3.2 Energy Spectrum Investigation
Due to constraints in the equipment (a maximum of 48cm
of steel), only low energy muons with an energy level of
less than 1GeV could be investigated. The muon flux for
each energy level was noted and plotted (see Figure). The
spreadsheets showing energy losses in the scintillator and
steel can be found in the appendix. Uncertainties were
calculated in both values, calculating the error for count
rate using Poisson statistics. With these error bars
included in a graph of my results, it can be seen that muons
with varying energy levels are almost evenly distributed at
ground level.
3.1 Angular Distribution Investigation
The estimated cosmic ray flux for any hodoscope is
dependent on the distance between the paddles and on the
area of the scintillator. The subtended solid angle (the
‘cone’ above the detector in which cosmic rays will pass
through both paddles) was calculated using 4  -geometry:
 
A paddle
4R 2
4 ,
Where R=107.3cm, the distance from the centre of the
bottom paddle to a corner of the top paddle.
A check of muon lifetime was also undertaken for each
energy level. Data were collected from the muon lifetime
software that is coupled with the muon lifetime apparatus
and these results were then plotted (see Appendix).
  0.0173 steradians
To calculate the estimated vertical flux for this hodoscope,
the published value for flux (muons and electron-positron
pairs) at sea level per unit are per unit time about the
vertical direction [Review of Particle Physics], Fv, was
used:
3.3 Cloud Chamber
Many different tracks were seen each time the cloud
chamber was set up. By using a digital camera set with a
long exposure time, photographs of many different tracks
were taken, some of which can be seen below (for more
detailed photographs, see Appendix). Some of these tracks
were characteristic of muons interacting with electrons in
the vapour. A track which bends at an angle shows a muon
decaying into an electron and neutrinos, the electron’s
track is still visible (see Figure 8). Occasionally a track
that appears to split in two was seen – this is evidence of a
muon knocking-on an electron (see Figure 9). Tracks
which zigzag show the multiple scattering of low energy
muons which are bounced off many atoms (see Figure 10).
F  110 m-2s-1sr-1
 0.66 -2
cm min-1sr-1
flux    F  A paddle
 2.281 min 1
Flux distribution is proportional to cos2.16θ [Crookes and
Rastin, 1972] where θ is the angle measured from the
zenith. Using this, theoretical estimates for flux at
different angles were calculated and compared to my
results:
Figures below: Cropped cloud chamber photographs:
F ( )  Fv cos 2.16 
Figure 8. Muon decay

A graph of the average results was plotted (see Figure 11).
On the same graph, the theoretical estimates for flux were
also plotted as a comparison, along with the cos2.16θ curve
which corresponds to the results. As can be seen on the
graph, the results correlate with the cos2.16θ rule until the
hodoscope nears the more horizontal angles. The results
do not tend towards zero, instead levelling off at around 20
counts per hour. This is because as the angle from the
zenith tends towards 90º, cosmic rays begin to enter the
hodoscope from both sides – the count rate at these angles
is higher than the estimated flux as a result. The results for
vertical flux are very close to the average flux expected at
sea level. Discrepancies in the results could have been as
a result of the hodoscope being too sensitive by the PMTs
amplifying electrical noise as well as scintillations.
Although coincidences of electrical noise are unlikely,
their occurrence may also account for the higher vertical
flux results.
e


Figure 9. Knock-on
electron


e
Figure 10. Low energy muon, travelling slowly
The statistical Poisson error in the count rate was
calculated to be very small, whereas the error in the angle
from the zenith was considerably larger. This is a result of
not using precise equipment which made it very difficult to
properly adjust the angle of the hodoscope. (To be
improved at a later date, see Section 5.)
7
Average Angular Distribution
180.0
This cos2.16θ curve was extrapolated from the vertical flux result. It
shows how well the results follow the curve and also helps to illustrate
how the flux levels off at angles above 75º.
Average Count Rate (counts h
-1
)
160.0
140.0
These are the data points gathered during the project. Each
point is averaged over 5 counts. The measured data
matches the theoretical curve closely until about 70º or so.
120.0
100.0
Theoretical
Average
80.0
This is the theoretical cos2.16θ curve
constructed from the published
value of flux at sea level.
60.0
The measured data here is higher than the curve
because at nearly horizontal angles, cosmic rays
can enter the hodoscope from both sides.
40.0
20.0
0.0
0
10
20
30
40
50
60
Angle From Zenith (º)
Figure 11. Angular distribution of cosmic rays, showing the match between theory and experiment
8
70
80
90
100
Muon Energy Spectrum
70
60
Muon flux (decays per hour)
50
40
30
20
10
0
0
100
200
300
400
500
Minumum energy of muon leaving Fe (MeV)
Figure 12. Muon energy spectrum
9
600
700
800
4 Conclusions
5 Further Developments
4.1 Angular Distribution Investigation
5.1 Angular Distribution Investigation
Even with the highly inaccurate method of angling the
hodoscope, the results obtained from many experiments
follow the cos2.16θ curve as discovered by Crooke and
Rastin and level off at around 75º. It is to be expected that
more accurate results will be derived from longer runs (see
Section 5.1).
For more accurate and detailed results, a continually
running mechanical hodoscope that sent data to a PC with
appropriate software could be used. This could be
achieved by attaching the paddles to either end of a metal
pole which was attached to an electric motor at its centre.
This motor would rotate the cosmic ray telescope
(hodoscope with panels far apart) by 360º, alternating the
direction of rotation so as not to tangle the wires. The
angular position of the hodoscope would be measured
using a potentiometer attached where the pole joins the
motor. The pulses from the board and the voltage across
the potentiometer would be analysed by a PIC chip which
would translate the voltage to an angle and send all the
data to the serial port of a PC. Software would then be
used which would allow a graph of count rate against angle
from zenith to be constructed. The fact that this hodoscope
is controlled by a motor and all outputs go to a PC would
allow it to be left running for weeks at a time, providing
more accurate results. This project will be undertaken at a
future date.
4.2 Energy Spectrum Investigation
From the graph of the results, it can be seen that the small
range of energies investigated seem to be fairly evenly
distributed. A flat spectrum is expected at low energy
levels (less than 1GeV) which includes the results, which
range from around 370 to 720 MeV (see spreadsheet in
Appendix). At higher energy levels, variations from the
flat spectrum are expected.
4.3 Cloud Chamber
Our cloud chamber cost under £40 to manufacture and ran
for around two hours at a time without needing to be
refilled with IPA. The chamber was simple to construct,
simple to set and up very reliable. With a steep
temperature gradient (aided by the hot water bottle) I was
able to see and photograph tracks for hours each time the
chamber was set up.
5.2 Energy Spectrum Investigation
The muon detector could be used at a future date to
investigate the charge ratio of muons arriving at sea level.
If the apparatus could be left running for very long periods
of time (much longer than this project allowed) then the
charge ratio of μ+ and μ- at sea level could be calculated.
Equal numbers of μ+ and μ- are created in the upper
atmosphere and in a vacuum, equal amounts would travel
equal distances. The charge ratio occurs because μ - have a
much shorter lifetime than μ+ as a result of μ- being
susceptible to muon capture so fewer μ- reach sea level.
This investigation has shown that it is feasible for schools
to construct their own cloud chamber, and it will be
possible to take our cloud chamber out on tour with
PP4SS.
Summary of what I did and learned during
the project:









Researched all about cosmic rays, their origin,
radioactive decay theory, decay reactions for
particles in the upper atmosphere, angular
distribution theory, energy spectra
Researched previous investigations similar to
mine for comparison of results and derivation of
equations
Designed and was involved in the construction of
a diffusion cloud chamber
Learned how to operate our cloud chamber and
worked out how to keep it running with a good
layer of mist for hours at a time
Constructed a cosmic ray hodoscope and used it
to investigate the angular distribution of cosmic
rays by creating a cosmic ray telescope
Learned to solder and make cables
Introduction to basic circuit board testing
(continuity, power, track board lay out) and basic
electronic components
Learned how to design, wire and check a circuit
board when constructing the hodoscope
Laid out, checked and populated a track board for
the cosmic ray doorway from a design laid out on
a PC
5.3 Cloud Chamber
As a result of having a working and reliable chamber, it
will be possible to take it out with PP4SS more often. To
make the tracks even easier to see, the cloud chamber
would need to be in dark conditions with a point source
illuminating the tracks. To achieve this, a light tight
container with fixed light sources inside should be
designed and manufactured.
10
6 References
1.
Frank Close, Particle Physics: A Very Short Introduction, OUP, ISBN 0192804340 (2004)
2.
Michael W. Frielander, A Thin Cosmic Rain, Harvard University Press, ISBN 0674002881 (2000)
3.
Peter K.F. Grieder, Cosmic Rays At Earth, Elsevier, ISBN 04444507108 (2001)
4.
W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer-Verlag, ISBN 0387572805 (1994)
5.
Krane, Introductory Nuclear Physics
6.
J.N. Crookes and B.C. Rastin, An Investigation of the Absolute Intensity of Muons at Sea Level, Nucl Phys B
Vol 39 page 493 (1972)
7.
Phys Rev D54 July 1996, Review of Particle Physics
URL References:
1. http://www.cosmicrays.org
2. http://www.pdg.lbl.gov
3. http://www2.slac.stanford.edu/vvc/cosmicrays/default.htm
4. http://physics.msuiit.edu.ph/spvm/papers/2001/terio.pdf
5. http://www.lbl.gov/abc/cosmic/documentation/CosmicDetector2-0.pdf
6. http://www.lbl.gov/abc/cosmic/SKliewer/Cosmic_Rays/Muons.htm
7. http://www.eljentechnology.com
8. www.scifun.ed.ac.uk/pages/pp4ss.html
9. www.ph.ed.ac.uk/sussp61 see PPUT
7 Acknowledgements
I would like to thank the Nuffield Foundation for funding this project and Frances Chapman for its organisation. Thanks
to Mark Reynolds for helping me with construction, Peter Clarke for triple-checking my calculations and SCI-FUN for
giving me space to work. Special thanks go to Peter Reid and Alan Walker, my supervisors, for hours of help and
patience.
All work in this project was my own, unless otherwise stated.
11
Appendix
For brevity some intermediate rows in the following tables, necessary for accurate calculations, have been hidden.
Table 1, page 13: Cosmic ray flux counts for varying angles from zenith and calculations for angular distribution
investigation
Table 2, page 14: Energy loss calculations in scintillator and varying depths of steel using simplified Bethe-Bloch
equation for muons
Graph 1, page 16: Muon lifetime for varying energy levels of muons
Images, page 17: Photographs of particle tracks seen in the cloud chamber
12
Table 1
Cosmic ray flux counts for varying angles from zenith (θ) and theoretical calculations for investigating angular distribution of cosmic rays.
Paddles 106.5cm apart, I hour runs
θ
0
10
20
30
40
50
60
70
80
90
162
150
151
100
87
73
32
20
18
11
count rate per hour
134
166
134
128
123
146
105
99
73
91
53
70
42
37
29
25
22
30
16
16
156
153
121
108
74
61
43
34
13
9
158
154
115
104
104
69
32
26
16
17
average
155.20
143.80
131.20
103.20
85.80
65.20
37.20
26.80
19.80
13.80
13
cos2.16θ
1.000
0.967
0.874
0.733
0.562
0.385
0.224
0.099
0.023
0.000
theoretical
count
136.6
132.2
119.4
100.1
76.8
52.6
30.6
13.5
3.1
0.0
extrapolated
count
154.500
149.475
135.076
113.239
86.879
59.478
34.570
15.222
3.521
0.000
error in
count rate
12.46
11.99
11.45
10.16
9.26
8.07
6.10
5.18
4.45
3.71
Table 2
Energy loss calculations for muons in the scintillator and varying depths of steel, using simplified Bethe-Bloch equation.
BB
Coeff.
1.1257
muon
mass
MeV
105.6584
electron
mass
MeV
0.5110
Z/A
I
eV
0.46556
286.0000
density
hnup
gm/cm^3
eV
7.874
55.1720
rho
2.5040
-C
4.2911
Energy at the top of scintillator required to reach Top/Middle/Bottom of Scintillator:Using
Total
Kinetic
Gamma
Beta
p
p/mc
BBv2
Energy
Energy
Top
105.6584
0.0000
1.0000
0.0000
0.0000
0.0000
Middle
140.2530
34.5946
1.3274
0.6576
92.2345
0.8730
Bottom
159.1389
53.4805
1.5062
0.7478
119.0021
1.1263
Energy at the top of iron required to reach Top/Middle/Bottom of Scintillator:Using
Total
Kinetic
Energy at
Gamma Beta
p
BBv2
Energy
Energy
bottom of Fe
1.3cm Fe
Top
141.3430
35.6846
105.6589
1.3377 0.6642
93.8837
Middle
161.2502
55.5918
140.2531
1.5261 0.7554 121.8110
Bottom
177.4043
71.7459
159.1389
1.6790 0.8033 142.5082
4.3cm Fe
Top
185.3294
79.6710
105.6589
1.7540 0.8216 152.2606
Middle
200.9839
95.3255
140.2531
1.9022 0.8507 170.9703
Bottom
215.0315 109.3731
159.1389
2.0352 0.8710 187.2828
7.3cm Fe
Top
222.1921 116.5337
105.6589
2.1029 0.8797 195.4626
Middle
236.6942 131.0358
140.2531
2.2402 0.8948 211.8028
Bottom
250.0002 144.3418
159.1389
2.3661 0.9063 226.5754
10.3cm
Fe
Top
256.8612 151.2028
105.6589
2.4311 0.9115 234.1239
Middle
270.8798 165.2214
140.2531
2.5637 0.9208 249.4237
Bottom
283.8556 178.1972
159.1389
2.6865 0.9281 263.4584
13.3cm
Fe
Top
290.5797 184.9213
105.6589
2.7502 0.9316 270.6896
Middle
304.3747 198.7163
140.2531
2.8807 0.9378 285.4475
Bottom
317.1983 211.5399
159.1389
3.0021 0.9429 299.0837
16.3cm
Fe
Top
323.8603 218.2019
105.6589
3.0652 0.9453 306.1402
Middle
337.5577 231.8993
140.2531
3.1948 0.9498 320.5955
Bottom
350.3201 244.6617
159.1389
3.3156 0.9534 334.0067
19.3cm
Fe
Top
356.9597 251.3013
105.6589
3.3784 0.9552 340.9641
Middle
370.6280 264.9696
140.2531
3.5078 0.9585 355.2484
Bottom
383.3805 277.7221
159.1389
3.6285 0.9613 368.5335
22.3cm
Fe
Top
390.0205 284.3621
105.6589
3.6913 0.9626 375.4361
Middle
403.6997 298.0413
140.2531
3.8208 0.9651 389.6277
14
p/mc
0.8886
1.1529
1.3488
1.4411
1.6181
1.7725
1.8499
2.0046
2.1444
2.2159
2.3607
2.4935
2.5619
2.7016
2.8307
2.8975
3.0343
3.1612
3.2270
3.3622
3.4880
3.5533
3.6876
X0
-0.0012
X1
a
m
3.1531
0.1468
2.9632
Bottom
25.3cm
Fe
Top
Middle
Bottom
28.3cm
Fe
Top
Middle
Bottom
31.3cm
Fe
Top
Middle
Bottom
34.3cm
Fe
Top
Middle
Bottom
37.3cm
Fe
Top
Middle
Bottom
40.3cm
Fe
Top
Middle
Bottom
43.3cm
Fe
Top
Middle
Bottom
46.3cm
Fe
Top
Middle
Bottom
49.3cm
Fe
Top
Middle
Bottom
416.4728
310.8144
159.1389
3.9417
0.9673
402.8472
3.8127
423.1269
436.8414
449.6539
317.4685
331.1830
343.9955
105.6589
140.2531
159.1389
4.0047
4.1345
4.2557
0.9683
0.9703
0.9720
409.7227
423.8711
437.0640
3.8778
4.0117
4.1366
456.3306
470.0956
482.9593
350.6722
364.4372
377.3009
105.6589
140.2531
159.1389
4.3189
4.4492
4.5710
0.9728
0.9744
0.9758
443.9301
458.0679
471.2600
4.2016
4.3354
4.4602
489.6639
503.4888
516.4110
384.0055
397.8304
410.7526
105.6585
140.2531
159.1385
4.6344
4.7653
4.8876
0.9764
0.9777
0.9788
478.1287
492.2776
505.4865
4.5252
4.6591
4.7842
523.1468
537.0376
550.0226
417.4884
431.3792
444.3642
105.6584
140.2530
159.1390
4.9513
5.0828
5.2057
0.9794
0.9805
0.9814
512.3660
526.5412
539.7788
4.8493
4.9834
5.1087
556.7918
570.7518
583.8022
451.1334
465.0934
478.1438
105.6588
140.2531
159.1390
5.2697
5.4019
5.5254
0.9818
0.9827
0.9835
546.6749
560.8867
574.1614
5.1740
5.3085
5.4341
590.6057
604.6368
617.7540
484.9473
498.9784
512.0956
105.6585
140.2531
159.1389
5.5898
5.7226
5.8467
0.9839
0.9846
0.9853
581.0778
595.3335
608.6512
5.4996
5.6345
5.7606
624.5924
638.6954
651.8796
518.9340
533.0370
546.2212
105.6580
140.2535
159.1385
5.9114
6.0449
6.1697
0.9856
0.9862
0.9868
615.5907
629.8953
643.2599
5.8262
5.9616
6.0881
658.7528
672.9277
686.1789
553.0944
567.2693
580.5205
105.6584
140.2534
159.1390
6.2347
6.3689
6.4943
0.9871
0.9876
0.9881
650.2242
664.5811
677.9954
6.1540
6.2899
6.4169
693.0868
707.3330
720.6505
587.4284
601.6746
614.9921
105.6585
140.2534
159.1385
6.5597
6.6945
6.8206
0.9883
0.9888
0.9892
684.9859
699.3971
712.8629
6.4830
6.6194
6.7469
15
Graph 1
Graph of muon lifetime for muons with various energy levels.
Muon Lifetime
2.000
Lifetime (µs)
1.500
As expected, the muon lifetime does not vary for muons
with different energies, as can be seen by the flat spectrum
of results.
Power supply
1.000
0.500
0.000
0
100
200
300
400
500
Minimum energy of muon leaving Fe (MeV)
16
600
700
800
Images
Plastic wall of chamber
1
2
Anodised base of chamber
This image of the inside of our cloud chamber shows the black plate and layer of super saturated mist forming near the base.
Many particle tracks are shown including a muon decay (1) and a knock-on electron (2).
1
2
3
This image of the inside of our cloud chamber shows a muon decay (1) and a knock-on electrons (2 & 3).
17