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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:

AZ X

X: Element symbol

A: Number of nucleons (P+N)

Z: Number of protons

Isotope Z =const. Isobare A = const.

Isotone N = const. Isomere A, Z = const.

Then nuclear reactions can be described as follows: 31 2

1 2 31 2 3 ..AA AZ Z ZX X X→ + +

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

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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: 226 222 488 86 2Ra Rn He→ + or also written as 226 222Ra 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 (anti-)neutrino, have a high cross section and interaction with matter, can be stopped by matter without problems (sheet of PMMA)

Beta minus: 0en p e ν+ −→ + +

with n0 as neutron, p+ as proton, e- as electron and eν as anti-neutrino.

Example: 137 137 055 56 1Cs Ba e−→ +

Beta plus: 0ep n e ν+ +→ + +

with n0 as neutron, p+ as proton, e+ as positron and eν as neutrino.

Example: 22 22 011 10 1Na Ne e+→ +

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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 60 60 *27 28 eCo Ni e ν−→ + + (beta decay)

60 * 6028 28Ni Ni γ→ + (gamma decay)

Figure 3-4: Decay Schematic of 60Co

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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.

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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: 1/ 2ln(2) ln(2)t τλ

= = ⋅ with λ decay constant and τ as mean lifetime

Decay law: ( )

( )1/ 21/ 2

ln 2

0 0( ) e 1/ 2t t

tt toI t I I e Iλ

⎛ ⎞⎛ ⎞− ⋅⎜ ⎟⎜ ⎟− ⎝ ⎠⎝ ⎠= ⋅ = ⋅ = ⋅

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:

QmJ = 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 60Co 34 37 37 35

Table 3-1: Factor f to calculate the absorbed dose

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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

xeIxI µρ−= 0)(

Quantities:

ρ = density

µ = material specific absorption constant (for γ- radiation 33Zλµ ∝ , 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 r- Hence, for a given Area A the activity decreases with increasing distance.

20)(

rIrI =

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

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xeIxI µρ−= 0)(

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

33Zλµ ≈

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 Ge-Counter.

3.4.2 Geiger-Müller

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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 gamma-rays 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€.

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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.

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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

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c) for increasing distance source, detector

5 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

6 Literature: 1. M. F. L’Annunziata; Handbook of Radioactivity Analysis; Academic Press; 2003

2. Gerthsen, Kneser, Vogel, Physik Springer Verlag

3. www.wikipedia.org