F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
1
Title of the experiment:
Gamma-ray spectroscopy
2
Aim of the experiment:
Learning and practicing the basics of gamma-ray spectroscopy. Operating a typical apparatus
and doing simple experiments in connection with basics of radioactivity.
3
Keywords for theory:
3.1 Radioactive decay modes
Assumption: the reader/student is familiar with elementary nuclear physics. Expressions like,
neutron, proton, electron and elementary models of nuclear physics (Bohr) should be known.
3.1.1 Nomenclature
In nuclar physics, elements are described as follows:
A
Z
X: Element symbol
X
A: Number of nucleons (P+N)
Z: Number of protons
Isotope Æ Z =const.
Isobare Æ A = const.
Isotone Æ N = const.
Isomere Æ A, Z = const.
Then nuclear reactions can be described as follows:
A1
Z1
X1 →
A2
Z2
X 2 + ZA33 X 3 + ..
where Ai, Zi etc have to fulfill sum rules and ... stands for further “particles” like neutrinos
etc.
Definition: radioactive decay is the property of instable nuclei to transform and decay. Energy
will be set free by emission of particles, ionization or gamma rays. Typical decay modes are
described in the following:
3.1.2 Alpha decay
Figure 3-1: Schematic on an alpha-decay
1/11
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
Alpha particles have high mass and energy compared to other particles, high interaction cross
section, hence dangerous for human body, but can be easily stopped by matter (sheet of paper
is sufficient) Detection can be done e.g. in Wilson fog chamber.
Example:
226
88
Ra →
222
86
Rn + 24 He or also written as
226
Ra →
222
Rn + α
where α is the alpha-particle consisting of two protons and two neutrons (like the helium
nucleus)
3.1.3 Beta decay
Figure 3-2: Schematic on a beta-decay
Beta particles, e.g. electrons or positrons are charged particles, continuous energy spectrum Æ
(anti-)neutrino, have a high cross section and interaction with matter, can be stopped by
matter without problems (sheet of PMMA)
Beta minus: n0 → p + + e− + ν e
with n0 as neutron, p+ as proton, e- as electron and ν e as anti-neutrino.
Example:
137
55
0
Cs → 137
56 Ba + −1 e
Beta plus: p + → n 0 + e + +ν e
with n0 as neutron, p+ as proton, e+ as positron and ν e as neutrino.
Example:
2/11
22
11
Na → 1022 Ne + +10 e
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
3.1.4 Gamma decay
Figure 3-3: Schematic of a gamma-decay
Gamma „particles“ are not charged, they possess a small cross section of interaction with
matter. And can be described like high energetic electromagnetic waves. They cannot be
stopped easily (e.g. 1 cm of lead reduces Intensity only by factor of two)
Example: 60Co decay
Co →
60
27
60
28
Ni* →
60
28
Ni* + e − + ν e (beta decay)
60
28
Ni + γ (gamma decay)
Figure 3-4: Decay Schematic of 60Co
3/11
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
3.1.5 Wilson Fog Chamber
In order to “see” different decay modes and to visualize radioactivity, a Wilson Fog chamber
is a useful device.
Fig. 3-4 left: scematic of Wilson chamber, right: Alpha source, note the short and equal distance of traces
In the supersaturated vapour atmosphere in this chamber the particles and gamma-rays will
give clear traces. Hence average length, stopping power, energy and charge (if the particle is
charged, the trace will be bent if a magnet is used) can be detected. Typical pictures are
shown in the next figure.
Fig. 3-5 typical pictures from Wilson Fog Chamber. a) alpha particle + proton, b) two alpha particles c)
alpha particle + flurorine atom.
4/11
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
3.2
Basic quantities and units and laws of radioactivity
3.2.1 Becquerel
Definition: one Becquerel is one decay per second, no matter, which kind of decay. It
specifies the activity of a sample independent of the energy transferred.
Nuclear decay is a statistical process. It follows an exponential decay law, i.e. from a given
activity I0 after the so called „half life time“ 50 % have decayed.
Half-life: t1/ 2 =
ln(2)
λ
= ln(2) ⋅τ
Decay law: I (t ) = I o ⋅ e
− λt
= I0 ⋅ e
with λ decay constant and τ as mean lifetime
⎛ t
⎞
⋅ln ( 2 ) ⎟
⎜−
⎝ t1/ 2
⎠
⎛ t ⎞
⎜
⎟
= I 0 ⋅ (1/ 2 )⎝ t1/ 2 ⎠
3.2.2 Sievert
As different decay modes and the corresponding „particles“ have different interaction
possibilities with the cells of the human body, hence the conversion from Becquerel to a
human body relevant quantity is not straightforward, but can be done for all isotopes and
exposition possibilities.
First one has to measure the ion dose J of a radioactive source. The ion dose describes the
amount of ionizing radiation which is necessary to create a certain amount of electrical
charging in a certain amount of gas. It is given as:
J=
Q
m
in units
C ( Coulomb )
kg
Now one can calculate the absorbed dose E by multiplying the ion dose with the factor f as
given in Table 3-1. The factor f is depending on the energy of the radiation as well as the
absorbing matter. The absorbed dose E is given in Gray (Gy) or in SI units J/kg. This unit also
makes the quantity Gray easy to understand and to measure. It is just the total energy set free
during decay => in principle can be measured by putting source into thermally isolated water
bath and measuring temperature increase.
Absorbed dose [Gy] = Ion dose [C/kg] * f [J/C]
Energy [keV]
Air [J/C]
Water [J/C]
Muscle [J/C]
Bone [J/C]
50
34
34
36
163
100
34
35
36
140
150
34
37
36
89
60
34
37
37
35
Co
Table 3-1: Factor f to calculate the absorbed dose
5/11
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
The equivalent dose H to a tissue is found then by multiplying the absorbed dose by a
dimensionless "quality factor" Q, dependent upon radiation type. These quality factors are
given in Table 3-2.
Radiation type
Q
X-ray, beta- and gamma- rays
1
Neutrons (depending of energy)
5-20
Alpha-rays
20
Table 3-2: Quality factors Q
The equivalent dose is usually given in Sievert (Sv), which is a measure for the dose a human
body is exposed to by radiation. (formally rem = radiation equivalent men). The natural
background is about 1 mSv per year.
3.2.3 Lambert Beer law
As particles and photons interact with matter, the radiation and energy of a given source of
Intensity I0 will be reduced
I ( x) = I 0 e − µρx
Quantities:
ρ = density
µ = material specific absorption constant (for γ- radiation µ ∝ λ3 Z 3 , see below)
x = thickness of absorber
3.3 Basics of protection against radioactivity
In particular in Germany there are strict rule handling radioactive material.
(Strahlenschutzverordnung). In this practical course we only use samples with an activity
below the „Freigrenze“ which can be handled without restrictions. For general protection, the
following rules („vier A’s”, only useful for germans) are used and discussed.
3.3.1 Abstand = distance
W assume a point like activity source. This one emits isotropically into a sphere of radius rHence, for a given Area A the activity decreases with increasing distance.
I (r ) =
I0
r2
Rule of Thumb: keep away
3.3.2 Aktivität = activity
Obvious, see above
Rule of Thumb: Use low activity
3.3.3 Abschirmung = shielding
Obvious, the Lambert-Beer law
6/11
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
I ( x) = I 0 e − µρx
means, a high thickness of shielding x, with a high density and a high specific absorption µ
will help. From nuclear physics one can learn, that the specific absorption µ scales as follows
µ ≈ λ3 Z 3
where λ is the wavelength and Z the number of protons. Hence, for a given wavelength lead
will be a good shielding material.
Thumb rule: use shielding
3.3.4 Ausdauer = Exposure time
Obvious
3.4
Detectors
3.4.1 General principle
Usually, detectors look for gamma-radiation. They consist of an insulating material (e.g. gas
for Geiger-Müller counter, Ge for solid state detector) and high voltage applied (usually some
kV). Gamma-quantum interacts with gas or solid matter, generates number of charge carriers
which are amplified. For the Geiger-Müller Counter this current pulse is used for the “sound”
of the Counter. Detailed analysis of the energy is done and hence discussed for the GeCounter.
3.4.2 Geiger-Müller
7/11
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
3.4.3 NaJ + Ge Detectors
In a Ge-Gamma-quantum counter the gamma-quantum interacts with solid matter, generates
number of charge carriers being proportional to energy of the gamma quantum. Due to the
applied voltage a current pulse is generated and used as a measure for energy of the particular
gamma quantum. This pulse can be further analyzed (the area of a current pulse is a measure
for the energy of the gamma particle) and a Multi-Channel Analyser is used to count the in the
appropriate energy windows..
Important parameters for a Ge detector are the energy resolution, i.e. how good two gammarays with different energies can be resolved or differentiated. This is mainly related to the
purity of the detector material and the reduction in noise, usually done by cooling to liquid
nitrogen temperature. Another key parameter is the efficiency, i.e. the ratio of incoming
number of gamma quanta to the number of detected gamma events. Also important is the
background, which is reduced by cooling and by appropriate shielding.
All this has significant influence on the price. Detectors like the ones used in the present
experiment cost about 10 k€.
8/11
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
3.5 Details of present experiment
A complete setup for gamma ray detection consists at least of
•
High voltage supply for the high voltage for the detector
•
The detector (+ cooling unit + shielding)
•
A preamplifier for the signal, usually directly mounted at the cooled detector base
•
An amplifier to adjust the out coming voltage-current pulses
•
An analyzing module to select only events that are within a given energy window
The last two units are summarized in the present experiment in a spectroscopic amplifier
Multichannel Analyzer (MCA). In this counter unit the pulses are selected according to their
energy and number of counts within given (small) energy windows are increased and stored.
The common power supply for the high voltage, the amplifier and analyzer are usually within
the so called NIM power support module, a standard module delivering stabilized Voltage and
current.
PC: Data from the MCA are transferred to a PC to be treated with, data treatment includes
start and stop of counting, evaluation of certain energy windows and long-term data storage.
Spectrum: A typical spectrum in such a measurement then looks like this one.
9/11
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
4
Experimental part:
4.1 The laboratory
Students will be introduced into the laboratory. Geiger Müller Counter will be made
availiable. Students should check laboratory, identify radioactive places and become familiar
with lab and security measures.
4.2
Using of the apparatus
4.2.1 Sample identification
Several simple sample with small activity (below the in German so called “Freigrenze”) will
be given. The spectrum should be identified. The isotopes should be named. The activity or
efficiency of detector should be estimated.
Further samples will be given to play around with.
4.2.2 Physics of radiation protection
For a given sample, the students should determine the reduction of counting rate
a)
for different shielding materials
b)
for one shielding material with different thickness
10/11
F:\temp internet\Temporary Internet Files\Content.IE5\MTM49VNY\Anleitung-Praktikumgammastrahlen-revised.doc
c)
5
6
for increasing distance source, detector
Ideas for evaluation (some of them even during experiment)
•
Identification of isotopes
•
Estimation of background
•
Correcting counting rates for background
•
Comparison of different detectors (Geiger-Müller vs. Ge detector) with respect to
price, efficiency and reliability
•
Determination of counting rates for different distances source, detector, explanation of
deviations from theory
•
Determination of counting rates for different thickness of shielding / and or different
thickness of one shielding material should be used for determination of absorption
quantities (Lambert – Beer law)
•
Comparison with theory, i.e. absorption for fixed thickness increases with Z of
absorber material
Literature:
1. M. F. L’Annunziata; Handbook of Radioactivity Analysis; Academic Press; 2003
2. Gerthsen, Kneser, Vogel, Physik Springer Verlag
3. www.wikipedia.org
11/11