PART II LABORATORY
11 ENERGY LOSS OF ALPHA PARTICLES PASSING
THROUGH MATTER
11.1 MOTIVATION
The purpose of this practical is twofold. On the first day the energy loss of alpha particles
(helium nuclei) passing through matter will be investigated experimentally, and the energy loss
relationship will be used to measure the thickness of various commercial aluminium foils. On
the second day you will gain experience with the use of ultra high vacuum (UHV) equipment,
and use this equipment to manufacture your own thin aluminium foil. UHV equipment is
important in many areas of experimental physics, and this section is designed to give you an
appreciation of the practical issues involved in producing and maintaining UHV equipment.
11.2 BACKGROUND
As alpha particles pass through matter they loose energy due to both electrostatic interactions
with electrons in the matter and excitation of electrons into unoccupied energy levels, and it can
be shown that the energy lost per unit distance due to such interactions with the matter is given
by1
2
dE  1   2 NZe4 3   me v 2 


 ln

 
dx  4 o   me v 2   I 
Eq. 11.1
where I is the mean excitation and ionisation energy of matter of atomic number Z , me is the
mass of an electron, v is the velocity of the alpha particle, and all other symbols have their
usual meaning. Noting that the majority of the terms in Eq. 11.1 are simply constants we can
simplify this expression to

dE  c1 
   ln c2 E 
dx  E 
Eq. 11.2
where we have introduced the variable E  m v 2 denoting the incident energy of the alpha
particle (the me term having been subsumed into the constants c1 and c2 ). If the material is
sufficiently thin that the energy loss is small compared to the total energy (as is the case for a
thin foil) the log term in Eq. 11.2 is almost constant over the foil thickness and Eq. 11.2 can be
approximated as
E
k
Eq. 11.3
 m
T
E
where E is the energy lost and E the incident energy of the  particle passing through the
foil, T is the foil thickness, and both k and m are constants which are a property of the foil
material. Taking the logarithm of both sides of Eq. 11.3 we get
logE   log k   logT   m log E 
Eq. 11.4
thus if we plot a graph of E as a function of E on a log-log graph for a foil of given thickness
T we get a straight line (recall that the constants k and m are properties of the material).
Reversing this argument, we can work out the foil thickness T from a log-log graph of E as a
function of E provided we know the constants k and m for the foil material. This is the
technique used here for determining the thickness of unknown foils.
1
A detailed theoretical derivation of the energy lost passing through matter is not important to this
practical.
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ENERGY LOSS OF ALPHA PARTICLES PASSING THROUGH MATTER
11.3 MEASUREMENT OF UNKNOWN FOIL THICKNESS
Figure 11.1 Schematic layout of detector electronics
In this section you will use the relationship relating foil thickness to energy loss, Eq. 11.4 of
section 11.2, to measure the thickness of several aluminium foils.
The basic concept behind this experiment is fairly simple: the schematic layout of the
experiment is shown in Figure 11.1 with a detail of the detector chamber shown in Figure 11.2.
Alpha particles from a radioactive source, in this case 226Ra, are pass through a foil before
striking a solid state energy sensitive detector, the geometry of this system being such that all 
particles incident on detector must have passed through the foil 2. The charge pulses from the
detector are amplified first by a preamplifier then a linear amplifier before being passed to a
multi-channel analyser card located in a desktop PC. Because of the short range of alpha
particles in air it is necessary to conduct the experiment in an evacuated chamber at a pressure
of 10-3 torr or less.
In order to measure the energy lost by alpha particles passing though the aluminium foils it is
first necessary to calibrate the relationship between alpha particle energy and channel number
on the multi-channel analyser (MCA). We can then use this information to determine the
thickness of the unknown foils.
2
The detector used here is of the same type as the solid state detector used in the Rutherford experiment,
to which students are referred for details of the how the detector works.
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PART II LABORATORY
Figure 11.2 Detail of detector chamber
11.3.1 DETECTOR CALIBRATION
a)
Setting up the equipment
 Look around your bench. Identify all the equipment shown Figure 11.1 and Figure 11.2, and
follow the cables to see what is connected to what.
 Turn on mains power to all equipment except the vacuum pump one by one: this includes the
NIM bin containing the amplifier modules, the CRO, and the PC. Let the equipment warm up
for a few minutes (this enables the electronics to stabilise and helps make sure your
readings don’t drift during the experiment).
 Open up the detector chamber by lifting off the lid using the two brass handles and inspect
the inside, making sure that the 226Ra source is in
place. (If the lid is hard to remove you may have to
Emitted Particle
Energy (keV)
loosen one of the air inlet valves first, making sure
7687.1

that the vacuum pump is switched off first). Identify
6002.6

5489.7
the source, detector, and the slot for the foil holder.

5305

 Replace the lid on the chamber, close the air inlet
4748.5

valve, and turn on the vacuum pump. When the
3280

pressure in the chamber has dropped below 10-1
1161

Torr slowly raise the detector bias to 90V.
690

 We now have to set the gain on the amplifier so that
170

the amplifier output falls within a useful detection
Table 11.1  and  particle energies
range of the MCA card. The MCA card digitises
emitted by 226Ra.
voltages in the range from 0 volts to 10V into 1024
channels, and from the table of alpha particle
energies in Table 11.1 we know that we have to be
able to detect alpha particles of at least 7700keV. To ensure enough dynamic range you
should therefore adjust the amplifier gain set so that the 7687keV peak falls at about 9V
when viewed on the CRO. Note your final amplifier settings.
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ENERGY LOSS OF ALPHA PARTICLES PASSING THROUGH MATTER
Signals from
electronics
Start acquire: <Alt-1>
Stop acquire: <Alt-2>
Clear MCA: <Alt-3>
Swap view: <F4>
MCA card
Save: <Alt-F><Alt-S>
PC memory
Move data from MCA to PC: <Alt-5>
<Print Screen>
<Print Screen>
Restore: <Alt-F><Alt-R>
Move cursor: Left/Right arrows
Fast movement: PageUp/PageDown
Toggle expanded view: <F3>
Change expanded view region: Keypad +/Change vertical scale: Up/Down arrows
Figure 11.3 Summary of MCA commands
b)
Setting up the data acquisition software
 Make sure the PC with the MCA card is switched on and start the MCA program by typing
mca at the command prompt. (yes, this is a DOS based program but it works as well as its
modern counterparts. Who needs a graphical interface anyway?)
 Review the MCA command list (see Figure 11.3) and try the following:
- Start collecting a test spectrum (Alt-1). You should see a series of dots creeping up
on the screen - let this run for about 1 minute or so.
- Stop acquisition (Alt-2) and transfer your data from the MCA card into the computer’s
buffer memory (Alt-5), then save the data (Alt-F, Alt-S) into a temporary file. You
can only save data in the buffer, but can only acquire data from the MCA card, thus
you must always transfer the data from the MCA to the buffer (Alt-5) before saving.
Many a student has wasted hours by saving the wrong spectrum in the wrong file, so
be careful.
- Move the cursor using the left and right arrow keys. Note that a counter at the bottom
of the screen changes as you do this: this indicates which channel number the central
line is located over. Note that Page-up and Page-down move the cursor quickly from
one place to another.
- Adjust the vertical scale from logarithmic to linear (Up arrow): at first the spectrum
will disappear, but keep going until the spectrum reappears. To return to a
logarithmic scale keep hitting the down arrow key.
- Change to expanded view (F3) and move the cursor around again. Now change the
size of the expansion region using Keypad +/- and note that you can get the cursor
resolution down to single channel units.
 Note the counter on the left indicating the detector dead time. It takes the MCA card a few
milliseconds to digitise the incoming pulse during which time no further incoming pulses can
be measured. The dead time measures the amount of time the MCA is digitising data
relative to the amount of time it is waiting for incoming data. Check that the is less than 10%
and, if not, adjust your experimental parameters.
 Briefly inspect your spectrum with reference to the alpha particle tabulated in Table 11.1 and
check that it looks like what you would expect. If you are at all unsure about whether your
spectrum looks OK check with your demonstrator now.
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PART II LABORATORY
c)
Calibrating the detector
We are now in a position to calibrate the relationship between MCA channel number and
energy. First, collect a spectrum for about 10 minutes. There is nothing magical about
this figure: the longer the count time the better the spectrum, but the more time you have
to spend waiting for data collection. 10 minutes is a reasonable compromise, but feel free
to choose some other time if you think it appropriate. After the spectrum has been
collected save the file, print one copy for each member of your group by pressing the
<print screen> key, and record the channel numbers of all features using the MCA
program.
Question (a)
Identify which features are due to the alpha particles and which are
due to the beta particles (where do the beta particle peaks appear?) and, using only
the alpha particle data, determine the relationship between channel number and
energy for your electronic settings. Remember to include uncertainties for all
measurements.
11.3.2 MEASUREMENT OF THE THICKNESS OF ALUMINIUM FOILS.
At this point we would usually get you to determine the relationship between energy loss and foil
thickness, m and k from Eq. 11.4, for a given material. However this is a tedious and timeconsuming process so instead we will give you the relationship, determined from previous
experimental data collected using your equipment, and let you use it to determine the thickness
of a number of aluminium foils. A calibration plot obtained from previous experimental data for a
12m thick aluminium foil is shown in Figure 11.4. Note how, when plotted on log-log axes, the
data appears as a straight line, and that fitting a straight line to this data enables us to
determine m and k 3.
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Figure 11.4 Calibration of energy loss vs energy for 12m thick aluminium foil
3
Note that if we let x  log 10 E  and y  log 10 E  we can recast Eq. 11.4 in the form
where c  log 10 k   log 10 T  . For a given material
will be manifested as differences in the value of
y  mx  c
k and m are constant, thus differences in thickness
c.
104
ENERGY LOSS OF ALPHA PARTICLES PASSING THROUGH MATTER
Armed with this information we are in a position to determine the thickness of unknown foils by
measuring the energy lost by the alpha particles as they pass through the foil. On your bench
you will find a selection of aluminium foils of different thickness, a small sample of which can be
located in the foil holder mount between the 226Ra source and the detector. Table 11.1 you
know the energy of the alpha particles incident on this foil and, by measuring the spectrum with
the foil in place, you can determine the energy lost by the alpha particles as they pass through
the foil (simply Ein – Eout). By plotting these two on log-log scales you can work out the
thickness of the foil by comparing the gradient and intercept values with those of a 12m foil
presented in Figure 11.4.
11.4 MANUFACTURING A THIN FOIL
The purpose of this section is to introduce you to the operation of ultra-high vacuum (UHV)
equipment through the manufacture of a thin aluminium foil by evaporation. UHV systems are
commonly used in experimental physics thus it is essential that you have an appreciation of how
they work – your report should therefore aim to demonstrate an understanding of UHV
technology and how to use it.
Manufacturing the thin foil and measuring its thickness takes up all of today’s lab session so it is
essential that you start on the foil manufacture as soon as you get into the lab. There are
lengthy periods of waiting during the foil manufacture process which you might like to use to
answer some of the questions if you have not had time to do so already. Feel free to discuss the
questions on vacuum technology with your demonstrator.
11.4.1 INTRODUCTORY READING
The book Vacuum Technology by Roth is available from the part 2 office and answers many of
the questions in this section. You might like to sit down in comfortable location and quickly read
the following sections. This is not meant to be an arduous task and there is much more detail in
the text than you need. In particular DO NOT transcribe large slabs of the book, in fact don’t
even bother sitting down and taking slabs of notes – rather, skim read the text and briefly
answer the questions (no more than one paragraph per point). If you have any questions do not
hesitate to discuss them with your demonstrator.
a)
Sections 7.1 and 7.2: Materials and cleaning techniques
b)
Chapter 5: Pumping techniques
Read Section 5.1: Introduction, pp. 200-203; Section 5.2.4: Rotating vane pumps, pp. 206-212;
Section 5.2.8: Molecular pumps, pp. 217-220; Section 5.3.3: Diffusion pumps, pp. 223-232;
Section 5.6: Cryopumping, pp. 248-263
c)
Chapter 6: Measuring low pressures
Read Section 6.1: Classification of vacuum gauges, pp.280-282; Section 6.3.1: Manometers,
pp. 285-287; Section 6.6: Thermal conductivity gauges, pp. 304-310; Section 6.7: Ionisation
gauges, pp. 310-325.
The section on sealing techniques is also particularly interesting if you have time to read it.
11.4.2 FOIL MANUFACTURE
We will use the technique of evaporation to manufacture a thin foil. To do this the source
material (aluminium) is placed on a metallic boat made of heat resistant material such as
105
PART II LABORATORY
Basic rules for operating a high vacuum system

When starting a mechanical pump first ensure that the rotor moves in the correct direction and that the
oil level is correct.

Always vent a mechanical pump to atmospheric pressure when the power is off. The presence of a
residual vacuum in the pump frequently causes oil to be drawn into the casing or vacuum system.

Do not permit a mechanical pump to exhaust a high-vacuum system below a pressure of a few
hundred microns unless the pump is separated from the high-vacuum chamber with a trap stopping
the oil vapour from entering the chamber.

Always keep the inside of a high vacuum system clean. In particular, grease from fingers can result in
considerable contamination and gloves should always be used when handling anything destined for
the inside of high vacuum equipment.

Do not run a mechanical pump at high pressures for long periods of time. The motors are not
generally designed for long term use with the additional load, and the pump will eject much oil in
addition to gas.

Diffusion pumps should be cooled to a safe intermediate temperature before being vented to
atmosphere. Venting at too high a temperature results in oxidation of the pump fluid and excessive
carryover of the fluid into the mechanical pump.

Always check that the cooling water supply to diffusion and turbomolecular pumps is turned on prior to
operation. It is also a good idea to have thermal protection to guard against interruption to the cooling
water supply.

In liquid nitrogen trapped systems the trap should be cool enough to condense the diffusion pump oil
prior to turning on the diffusion pump. Maximum backstreaming of pump oil occurs during startup and
shutdown of the diffusion pump.

Do not vent a liquid nitrogen trap to air whilst cold.

When the chamber is vented to atmospheric pressure it is advisable to use a dry, inert gas such as
nitrogen to minimise moisture adsorption on the surface of the vacuum system. Never vent from the
foreline of a diffusion pump.

Ionisation gauges, in particular hot cathode gauges, should not be turned on until the pressure is
below 10-3 Torr.
titanium which is heated by passing an electric current through it. The source material itself sits
within a depression in the boat which is thinner than the surrounding material – it thus has a
higher resistance relative to the rest of the circuit and heats up the fastest. This heats the
source material to boiling, at which point the vapour expands in a hemisphere above the boat
condensing on whatever surfaces it first strikes. Because the material is heated to boiling point
it is essential that this procedure be conducted under high vacuum so that the source material
does not oxidise.
A schematic diagram of the evaporation chamber is shown in
Figure 11.5. The evaporation takes place inside a glass bell jar which is evacuated by a
diffusion pump and a rotary pump. Next to the evaporation chamber is a high-current power
supply consisting of a variable 240V, 10A to 3V, 80A step down transformer connected to the
boat clamps via 150A cables. Note that the bell jar is very expensive (˜$2600) and should
only be handled by your demonstrator, and that the perspex shield should always be
placed around the bell jar when it is evacuated to guard against shrapnel in the unlikely
event of an implosion.


Inspect the vacuum chamber and identify all components. If the bell jar has not already
been removed get your demonstrator to remove it now. Also locate the titanium boat,
aluminium sample, and the foil holder with a thin mylar film in it.
The titanium boat will have been handled by hand, therefore it is necessary for you to clean
it prior to placing it in the vacuum chamber. After putting on one of the latex gloves
provided gently clean the boat using isopropyl alcohol and one of the lint free tissues
106
ENERGY LOSS OF ALPHA PARTICLES PASSING THROUGH MATTER
provided. The titanium is quite brittle and will easily snap, so be careful whilst doing this.
Once clean carefully place the titanium boat in its holder in the evaporation chamber being
careful not to touch it with bare hands.
Pre-lab Question (a) Why is it important to keep the inside of a high vacuum system clean?
What is the effect of contaminants such as sweat and grease from hands on the vacuum
system, and how can contamination from such sources be minimised?
Pre-lab Question (b) What are the desirable properties of the material from which a vacuum
chamber should be made? What sort of materials have these properties?
Pre-lab Question (c) What is outgassing and how can the outgassing rate of a vacuum
chamber be reduced?



Locate the 0.5g aluminium slug and place it in the boat, once again making sure that it is
clean of all grease.
Find and locate the holder with the mylar foil, on which the aluminium will be deposited.
This will also have been handled by hand so you will have to clean it with isopropyl alcohol
before placing it in the vacuum chamber as you did for the titanium boat. Once clean,
mount the foil holder in the clamp approximately 7cm above the boat: if you place it too
close (<6cm) the mylar will melt during evaporation whilst if it is too far away (>9cm) the
aluminium layer will be too thin to be interesting.
Inspect the inside of the vacuum chamber for any accidental fingerprints. If you find any,
clean them away with alcohol before replacing the bell jar. (Also remember to make sure
that the perspex implosion shield is in place before pumping down the system).
Pre-lab Question (d) Note the rubber seal on the bell jar. Briefly describe the main means of
sealing a vacuum chamber. What are the most common types of vacuum seal, and what
are the main parameters which define the useful range of a particular vacuum seal?
Figure 11.5 Schematic diagram of
vacuum system

In order to reduce the pressure to <10-4 Torr we have to use the diffusion pump, which
requires us to first pump the bell jar down to 10-2 Torr. To do this first close all of the air
inlet valves, check that both the baffle and backing vales are closed, then open the roughing
valve. Switch on the rotary pump and wait until the pressure in the bell jar has dropped
below 10-2 Torr, then open the backing valve and turn on the diffusion pump heater.
Pre-lab Question (e) Describe the operation of a rotating vane pump (otherwise known as a
rotary pump, which is the main type of vacuum pump used in the nuclear labs). What
defines the lowest pressure at which a rotary pump can operate? What is the function of gas
ballast in a rotary pump? Is there any advantage to be gained from connecting two pumps in
series and, if so, why?
107
PART II LABORATORY
Pre-lab Question (f)
Briefly describe the principle behind the diffusion pump (the second
type of vacuum pump you will use today). What is meant by roughing and backing, and why
are these necessary when using a diffusion pump? Why is it necessary to cool a diffusion
pump? What is the effect of having no cooling? What is a cold trap and why might it be
useful in combination with a diffusion pump?
Pre-lab Question (g) Briefly describe the principle behind the turbo-molecular pump (a
common pump used in experimental laboratories). What limits the ultimate pressure to
which a turbo pump can operate? Do turbo pumps require backing by another pump and, if
so, why?
Pre-lab Question (h) Describe the process by which cryopumping operates. How is its
action different that of mechanical and diffusion pumps? What is the useful range of
pressures over which cryopumping can be used?
Pre-lab Question (i)
vacuum pump?

What are the main parameters which define the useful range of a
Once the diffusion pump has heated up (about 15 minutes) close the roughing valve, open
the baffle valve (think about what would happen if you forgot to close the roughing valve
first!), and watch the pressure drop below what could be achieved with the rotary pump
alone. Comment on any rapid fluctuations in pressure during this pumping procedure.
Pre-lab Question (j)
How does a thermistor gauge measure vacuum pressure? What is the
difference between a Pirani and thermistor gauge (both of which are commonly used in
modern laboratories)? Over what range of pressures can thermal conductivity gauges be
used?
Pre-lab Question (k) On what principle does an ionisation gauge work (these are also
commonly used in modern laboratories)? In particular what is the difference between hot
and cold cathode gauges? Over what pressure range are ionisation gauges useful?
Pre-lab Question (l)
What is the definition of a Torr, the most commonly used unit of
pressure measurement in vacuum systems? (The term Torr originates from the Torricelli
vacuum above a column of mercury in a sealed glass tube.)



When the pressure has dropped below 10-5 Torr you can start the evaporation. First turn on
the evaporation power supply and raise the current until the boat glows bright red (about 5070A). When the aluminium has melted slowly increase the current until the boat glows
white hot and you can see the bell jar being coated with aluminium. Continue evaporation
until you can see that all of the aluminium has been evaporated (about 2 minutes).
You have now made the foil and can proceed to bring the bell jar back up to atmospheric
pressure. First close the baffle valve, then turn off the diffusion pump heater. The bell jar is
now isolated from all pumps so you can use the air inlet closest to the bell jar to bring the
chamber back up to atmospheric pressure.
When the diffusion pump has cooled (about 20 minutes) you can close the backing valve,
turn off the rotary pump, and bring the vacuum side of the rotary pump to atmospheric
pressure using the right most air inlet valve.
Question (b)
Comment on why you have to let the diffusion pump cool before turning
off the backing pump, and on why you should leave the inlet of the rotary pump at
atmospheric pressure. What would happen if you failed to do this?
11.4.3 MEASUREMENT OF FOIL THICKNESS
Congratulations – you now have a thin aluminium foil of your own making. All that remains to
be done is to measure its thickness. To do this repeat the procedure used yesterday to
measure the foil thickness, section 11.3.2 above, making sure that the mylar side of the foil is
towards the 226Ra source. Compare your measured value with what you would expect if all of
the 0.5g aluminium slug had been evaporated – Aluminium has a density of 2.7g/cm3 and
during the evaporation this uniformly coats a hemisphere of radius equal to the boat-mylar
distance, from which you can calculate the expected foil thickness.
108
ENERGY LOSS OF ALPHA PARTICLES PASSING THROUGH MATTER
But there is a catch – the alpha particles have passed through both the aluminium and the
mylar, not just the aluminium. The energy lost by alpha particles passing through the mylar is
small but measurable and can be taken into account.
Question (c)
Work out how you could take the effect of the mylar into account and, if
you have time, perform the necessary experiments. (Hint: there is a second, identical
mylar foil available should that be of any use.) Also remember to quote uncertainties
on all results so that you can properly assess whether your measured thickness is in
agreement with what you would expect from the mass of aluminium evaporated.
11.5 REFERENCES
Roth, A., Vacuum Technology, 3rd Edition, (Elsevier Science B. V., Amsterdam, 1990)
109