Lab KF6: GAMMA SPECTROSCOPY I

Transcription

1 Lab KF6: GAMMA SPECTROSCOPY I Reworked by Martin Karlsson, Reworked by Rickard du Rietz, 2004 (the procedure). Translated by Martin Ljunggren, 2011.

2 1 INTRODUCTION Gamma spectroscopy is a very important part of nuclear physics. Many (if not all) nuclear processes are accompanied by the emission of gamma radiation. A useful feature of gamma radiation is the absence of charge, which gives a high probability for the radiation to make it out of a sample. It is therefore suitable as a probe. In all large laboratories where research is conducted in nuclear or elementary particle physics there are many different gamma ray detectors of varying size and complexity. Thus, to be able to interpret the results from research at such facilities, it is very important to have a good understanding of the interactions of gamma radiation with matter and the principles of detection. In this laboration exercise, we shall study two different detector systems (NaI(Tl) and HPGe), as they represent the two dominating detector types: scintillation detectors and semiconductor detectors. We aim to to gain insight in the field of gamma spectroscopy by performing a series of measurements with the two detector systems and compare the properties of the detectors. We will: Determine the relative strength of the two strongest photo peaks from 22 Na. Determine the internal conversion coefficient for the K-shell in 203 Tl. Identify gamma transitions in the thorium series. Determine the resolution as a function of energy for both detectors. Determine the binding energy of the deuteron. This manual starts with a theory section presenting the relevant physics topics. Following that is a section about the detectors and the electronics. Finally, there is a section concerning the different concepts used within the field of gamma spectroscopy. Along with this manual, a small appendix (titled KF6 Bilaga ) which contains important figures and tables, should be distributed. Some chapters start with a reference to literature. They refer to relevant chapters in Kenneth Krane: Introductory Nuclear Physics. If anything should be unclear it might be worthwhile to follow these references. 2

3 2 THEORY 2.1 Emission of gamma quanta and internal conversion Literature: Chapters 10.1, 10.4, 10.6 and Like the atom, the atomic nucleus can be excited to discrete energy levels above the ground state. The excitation energy, E n, goes into rotational or vibrational states of the nucleus or excitations of one or more nucleons to higher energy orbits. The magnitude of E n is on the order of MeV. The mean lifetime, τ, of an excited state is in most cases too small, i.e. less than s, to be measured directly. Large differences in spin between the initial and final states can, however, give rise to long lived isomeric (or metastable) states with τ s. If E n is less than the threshold for particle emission, the nucleus will deexcite through gamma emission or internal conversion Gamma emission The emission of gamma radiation means that the nucleus is getting rid of excess energy by emitting a gamma quantum with the energy E n 1, or by emitting several quanta in a cascade. The latter involves gradual transitions between different levels until the ground state is reached. The sum of the cascade energies is E n (ignoring the recoil energy) Internal conversion In the process of internal conversion, the nucleus transfers its excess energy to an electron in one of the inner electron shells, in most cases from the K-shell. The electron is thereby emitted with the energy T e = E n B e (1) where B e is the binding energy of the electron. Internal conversion is a one step process, which means that the nucleus transfers the energy to the electron directly and not through the emission of a gamma photon and subsequent photoemission. The internal conversion coefficient, α x, for the electron shell x, is defined as α x = λ e,x λ γ ; x = K, L, M,... (2) 1 If we take the recoil energy into account, we can write the gamma energy as E γ = En (En)2 2Mc 2. Here, M is the rest mass of the recoiling nucleus and c is the speed of light. 3

4 where λ e,x is the decay constant for internal conversion from shell x and λ γ is the decay constant for gamma emission. By summing the coefficients we get the total internal conversion coefficient, α: α = x α x. (3) Since the activity, n (decays per second), of a radioactive material in general can be written as n = dn dt = Nλ, (4) where N is number of nuclei and t is time, the internal conversion coefficient can be written as α x = n e,x n γ (5) where n e,x is the number of internal conversion electrons from shell x per unit of time and n γ is the number of gamma photons per unit of time. Internal conversion can be demonstrated by detecting the internal conversion electron or the x-ray photon that is emitted when the vacancy left by the conversion electron is filled by another electron (a radiative process). However, the number of conversion electrons emitted is not necessarily equal to the number of x-ray photons. A process competing with x-ray emission is the emission of Auger electrons. In the Auger effect, an electron of low energy is emitted instead of an x-ray photon when a vacancy in an atomic shell is filled. The Auger electron is an atomic electron that receives enough energy to be emitted, in most cases from the L-shell, when another electron makes a transition from the same shell to fill a vacancy in the K-shell. In our case, the vacancy arose due to an internal conversion. The proportion of vacancies in the K-shell that are filled with electrons through radiative processes is called K-fluorescence yield and is usually denoted by ω K. Since the mean lifetime, τ, is short in most cases, excited nuclides must be produced continuously during the measurements. This can for example be achieved by irradiating a suitable nuclide with a suitable projectile using an accelerator, which will place the nuclide in an excited state. In this exercise, we will use radioactive samples that will decay, through alpha or beta decay, to an excited state of the daughter nucleus that can be studied with gamma spectroscopy through its subsequent deexcitations through gamma decay. 4

5 2.2 Interactions of gamma radiation with matter Literature: Chapter 7.1. Gamma photons interact with matter in one of three main processes: photoelectric effect, Compton scattering and pair production, see Fig. 1. E γ 1 - e E γ 2 E γ E γ - e 3 e + - e 511 kev 511 kev Figur 1: The three main interaction processes. 1: Photoelectric effect. 2: Compton scattering. 3: Pair production Photoelectric effect A photon can not be absorbed by a free electron since it would be impossible to satisfy both momentum and energy conservation in such a process. If the electron is bound in an atom however, the photon can transfer all of its energy to the electron which will be emitted from the atom. (We neglect here the energy transferred to the atom since the mass of the atom is considerably larger than the electron mass.) In this case, momentum and energy conservation is satisfied since the atom absorbs excess momentum. The electron will leave the atom with the energy T e according to T e = E γ B e (6) where E γ is the photon energy and B e is the binding energy of the electron. The probability for photoelectric effect is larger the more tightly bound the electron is and is therefore largest for K-electrons. Furthermore, the cross section increases with the nuclear charge Z of the absorbant. It turns out that the cross section for photoelectric effect, σ f, goes approximately as σ f Z 4.5 E 3.5 γ. (7) 5

6 Thus, the cross section decreases with the photon energy and is only relevant up to a few MeV Compton scattering Compton scattering can be described as a collision between a photon and a nearly free electron, i.e. the theory is valid when the electron binding energy is low compared to E γ. Since this is almost always the case, and since the cross section for photoelectric effect generally is considerably larger than the cross section for Compton scattering when E γ is on the order of the binding energy (see Fig.B1 in the appendix) this is not a serious restriction. The photon will change its direction of motion in the collision and transfer part of its energy and momentum to the electron. Conservation of energy and momentum gives E γ = E γ 1 + Eγ m ec 2 (1 cos θ) where E γ is the energy of the scattered photon, θ is the angle between the photon s direction of motion before and after the collision and m e is the rest mass of the electron. The kinetic energy of the electron becomes T e = E γ E γ. Using (8), this can be written as T e = E γ 1 + mec2 E γ(1 cos θ) (8). (9) Thus, the energy of the electron ranges from T emin to = 0 at θ = 0 (no scattering) for θ = 180 (back scattering). T emax = E γ 1 + mec2 2E γ (10) The cross section for Compton scattering, σ c, can be approximated as σ c Z. (11) Intuitively, this should make sense since the number of electrons per atom is Z. The cross section decreases with the photon energy and is relevant up to a few tens of MeVs. 6

7 2.2.3 Par production If a photon passing through matter has an energy exceeding 2m e c 2 = 1.02 MeV, the following reaction can occur: γ e + + e The gamma photon is absorbed and an electron-positron pair is produced. Pair production can not occur in vacuum since energy and momentum conservation can not be satisfied simultaneously in this case. The reaction has to occur in the vicinity of an atomic nucleus, or an electron, that can absorb some of the photon momentum. If T e + and T e are the kinetic energies of the positron and the electron respectively, we get E γ = 2m e c 2 + T e + + T e (12) where we have neglected the energy transferred to the nucleus 2. The cross section of pair production, σ p, is only larger than zero above a photon energy of 1.02 MeV, after which it increases with the photon energy. It turns out that σ p Z 2. (13) The reverse reaction, i.e. a positron and an electron becomes a photon, is called annihilation. When a positron encounters an electron in the medium, the reaction e + + e γ 1 + γ 2 occurs, where γ 1 and γ 2 are two gamma photons. Generally, annihilation occurs when the positron has lost most of its kinetic energy. Two gamma photons, with an energy of MeV each, will be emitted. Since momentum has to be conserved they will be emitted back to back. Fig. B1 in the appendix shows how the three effects depend on E γ in a NaI crystal. 2 We can do this since the mass, M(Z, A), of a nucleus with atomic number Z and mass number A is much larger than the electron mass m e. 7

8 2.3 Determining the binding energy of the deuteron Literature: Chapters 4.1, 12.1 and In the last exercise of this laboration, we will determine the binding energy of the deuteron. This is an example of a very simple and straight forward application which contains a lot of physics. A neutron source producing fast neutrons (neutrons with a kinetic energy of 100 kev or above) is placed in a hydrogenous material, e.g. water. At these energies, the cross section for elastic scattering of the neutrons dominates. Therefore, they will rapidly lose energy, mainly through scattering against hydrogen nuclei since they have approximately the same mass as the neutron. When the neutrons have reached thermal energies (kinetic energy: ev) and are in thermal equilibrium with its surroundings, the reaction H + n γ + 2 H can compete with elastic scattering. By studying this reaction with a HPGedetector, the energy of the gamma radiation can be determined with great accuracy. If the proton and deuteron masses are known (the masses of these particles can be determined very accurately using a mass spectrometer since both particles are charged), the binding energy of the deuteron can be determined. The energy balance for the reaction gives M H c 2 + m n c 2 + T n = M D c 2 + E γ + T D, (14) where M H, m n and M D are the mass of the hydrogenatom, the neutron and the deuterium atom respectively. T n and T D denotes the kinetic energy of the neutron and the recoil energy of the deuteron. The binding energy can be calculated using equation (14). 3 The scintillation detector Literature: Chapter 7.3. Detecting ionizing radiation (charged particles, neutrons, gamma rays and x- rays) through scintillations 3 is one of the oldest detection methods. The scintillation process is still one of the best for measuring intensity and energy of the studied radiation. 3 A scintillation is a flash of light emitted by certain materials when irradiated. 8

9 There are many materials available for use in scintillation detectors. For detection of gamma radiation however, the NaI detector is dominating. Other examples include different kinds of plastic (for charged particles) and organic liquids (for detection of neutrons through proton recoil and pulse shape discrimination). Recently, Bi 4 Ge 3 O 12 (BGO) has become popular for certain applications due to its high density (high detection efficiency), high Z (83) and manageability (non hygroscopic). 3.1 The NaI detector The discovery of sodium iodide activated with thallium in the begin of the 1950s gave birth to a new branch of nuclear physics: modern gamma spectroscopy. Despite certain disadvantages (NaI is hygroscopic, i.e. it absorbs water, which means that the crystal has to be encapsulated in an airtight casing) NaI(Tl)-detectors dominates applications where simplicity and detection efficiency are more important than energy resolution. Fig. 2 shows a schematic drawing of a NaI(Tl)-detector. Fotokatod NaI(Tl)-kristall Fotomultiplikator Figur 2: Simple schematic over the important parts of a NaI(Tl)-detector. NaI is a crystal and its energy levels therefore exhibit the characteristics of a crystal band structure with a valence band and a conduction band. The size of the band gap between the valence band and the conduction band determines the crystal s electrical properties. For NaI the band gap is about 4 ev and it is therefore considered to be an insulator. The process of detecting gamma rays with the scintillation detector is rather complicated. Let s begin with a schematic overview: 1. A gamma ray hits the detector (NaI (Tl)-crystal). 2. One (or two) primary electrons are produced (through one of the interaction processes described above). 9

10 3. These primary electrons are slowed down by exciting electrons in the crystal from the valence band to the conduction band. 4. The excited atoms deexcite by the emission of light (scintillation photons). 5. Some of the light hits the photocathode of the photomultiplier and a certain percentage of the photons knock out electrons from the photocathode. 6. The shower of electrons from the photocathode is amplified in the photomultiplier to a detectable pulse. Let us now study the different processes in some more detail: Through interactions with the crystal, the gamma photon will form one (or possibly two) primary electrons moving at high speed. Here, high speed means that they have energies of the same magnitude as the incident photons, i.e., in our case around 100 kev 3 MeV. The primary electrons slow down as they collide with electrons in the crystal s valence band, leading to the excitation of said electrons into the conduction band. As the electrons deexcite back to the valence band, light (scintillations) will be emitted. For this to be as efficient as possible and to make sure that the scintillation photone does not have an energy that fits into the band gap, activation atoms are added to the crystal Activation For NaI, thallium (Tl) atoms are added during activation. These atoms will create energy levels between the valence band and the conduction band. Both the ground state and excited states of thallium will end up in the band gap, see Fig. 3. Energi Ledningsband Exiterade nivåer i tallium Bandgap Grundnivå i tallium Valensband Figur 3: The energy levels of a thallium activated NaI crystal. The band gap is about 4 ev. What happens is thus as follows: after excitation, a hole has been formed in the valence band (and there is one electron in the conduction band). The positively 10

11 charged hole will quickly move to an activator atom that will then be ionized (the electron in the ground state of the thallium atom will fall into the hole in the valence band). Meanwhile, the electron moves freely (in the conduction band) until it reaches an ionized thallium atom, there it is caught by the thallium atom and ends up in one of the excited levels of thallium. The above processes (migration of the hole and electron to the activator atom) is very fast: the following process takes place during a considerably longer time span, i.e. the deexcitation of the thallium atom. The mean time that the electron spends in the excited state is, for NaI (Tl), about 200 ns 4. During deexcitation, scintillation photons will now be emitted with high efficiency (so-called fluorescence). These scintillation photons have a mean energy of about 3 ev (wavelength 415 nm), which is less than the band gap. Thus, the crystal is transparent to these scintillation photons. To summarize: The NaI(Tl) crystal and the activation atoms converts the energy deposited by the incoming photon into a flash of light by fluorescence Photocathode and photomultiplier Scintillation detectors would not have been useful without a device that can enhance the extraordinarily weak light flashes to a sufficiently large electrical signal. The photomultiplier is suitable for this task: a few hundred scintillation photons are enough to get a measurable pulse. For a schematic figure of a photomultiplier, see Fig. 4. Scintillationsfotoner Fokuseringselektroder 2:a dynoden 10:e dynoden Anod Utpuls Fotokatod 1:a dynoden Figur 4: Schematic of a photocathode and a photomultiplier. The figure also shows the beginning of the path for a few electrons. 4 It is actually closer to 230 ns. This can be compared to plastic scintillators which are considerably faster with mean times of about 2ns. 11

12 The light from the NaI(Tl) crystal hits the semi-transparent photocathode, which consists of a layer of an alkali metal on the inside of the photomultiplier tube. Since the photocathode is connected to a negative potential (relative to the first dynode), the electrons that have been emitted at the cathode through photoelectric effect are accelerated to ev towards the first dynode. There, each electron will, due to their high kinetic energy, knock out a number of electrons, which in turn are accelerated towards the next dynode. This process then continues through the chain of dynodes. If each electron knocks out, for example, seven electrons, the gain would be be 7 10 or about after ten steps. At the anode, a pulse of will arise due to these electrons. To provide the photocathode and dynodes with the appropriate voltage, one uses a resistor chain,a so-called a photomultiplier base (see Fig. 5). The signal is usually extracted over a resistor (R L ) at the anode. In the system in Fig. 5, there will be a voltage drop when the electron pulse passes through R L. Thus, we will get a negative pulse from the PM tube that we can pass on to the various electronic modules. fotokatod till 1:a dynoden till 2:a dynoden anod Utpuls R L +HV Figur 5: Schematic of the resistor chain in the photomultiplier base which provides the voltage for the dynodes. In the resistor chain, positive high voltage is supposed to be used (+ HV). The essential assumption made for the entire NaI(Tl) system is: The output pulse is proportional to the energy deposited in the detector. This means, that the number of scintillation photons is proportional to the energy that the primary charged particles obtain through the interaction, the number of photoelectrons at the photocathode is proportional to the number of scintillation photons and that the number of electrons in the output pulse is proportional to the number of electrons from the photocathode. As we will see during the lab, this assumption is very reasonable and is also fulfilled for many other detector systems. 12

13 4 Electronics 4.1 The single channel analyzer According to the above, the output signal from the photomultiplier is proportional to the energy deposited in the detector. By analyzing the pulse height spectrum from the photomultiplier we get information about the energy spectrum of the radiation absorbed in the detector. The simplest form of pulse height analyzer is the so-called single channel analyzer. The single channel analyzer basically consists of two discriminators and an anticoincidence circuit. A discriminator is a circuit that provides a standardized output pulse if an input pulse exceeds a certain (adjustable) level. The single channel analyzer can be used in two ways, integral-mode or differential mode. In the integral mode, only one discriminator is used: a standard output pulse is obtained if the adjustable level (this can be set with a potentiometer and is usually labeled lower level ) is exceeded. In differential mode, both discriminators are active, and by using an anticoincidence circuit (XOR circuit) an output pulse is obtained only for pulses within an adjustable window (usually labeled upper level or window ). Thus, with a single channel analyzer one can count the number of pulses within a window in the pulse height distribution. In spectroscopic applications, the window is usually set over a full absorption peak (photo peak). It is also possible, with a narrower window that moves over the pulse height distribution, to record a full spectrum (number of pulses as a function of pulse height) with a single channel analyzer. For this purpose, however, the multichannel analyzer is a much more efficient instrument. 4.2 The multi channel analyzer The Multi Channel Analyzer (MCA) is basically a pulse height sorting machine. In most cases, pulses in the range 0 10 V are accepted. If the analyzer has, for example, 1024 channels, the first channel corresponds to very small pulses ( 0 V), channel 512 corresponds to 5 V pulses and channel 1024 corresponds to 10 V pulses. A multichannel analyzer consists of three main parts, an Analog to Digital Converter (ADC), a memory and some kind of display. We will use a MCA card which is mounted in a standard PC. The computer will thus account for the interface to the MCA and for the display. 13

14 4.2.1 ADC An analog-to-digital converter (ADC) converts an analog pulse height to a digital number. The incoming pulse is detected by a low-set discriminator, at which point a clock is started. At the same time, a capacitor is charged with a constant current. The incoming pulse is stretched, so that the maximum pulse height is preserved. A circuit constantly compares the voltage across the capacitor U(t) with the maximum value V of the input pulse. When U(t) = V, the clock is stopped, and the number of clock pulses immediately gives a measure of the pulse height. The number of clock pulses is thus a number between 0 and 1023 and is the address of a memory cell, this memory cell is updated and we get a count in the channel. 4.3 NIM electronics The electronics used in the lab is standardized according to the so-called NIM (Nuclear Instrument Module) standard. This standard has been used for many years, mainly in nuclear physics applications. The advantage of a standard is that one readily can mix modules from different manufacturers. The physical size and the connectors on the back of the voltage supply has been standardized, that is, all modules can be placed in the same kind of support structure (NIM-bin). Furthermore, the size of the linear signals (0 10V) and logic pulses are standardized. 5 The semiconductor detector Literature: Chapter 7.4. If NaI(Tl) can be called an old detector type, the opposite has to be said about semiconductor detectors. The principle of semiconductor detectors is not particularly new (early 60s) but the development of increasingly sophisticated techniques for producing different semiconductor materials is moving at a fast pace. Thus, there are many different kinds of semiconductor detectors that work in different ways and are used in different applications. The different terms are used in a somewhat chaotic manner, here we shall make an attempt to clarify this a bit. 5.1 Silicon and germanium The dominant semiconductor materials are silicon and germanium. In solid form, they form a crystalline structure that causes the individual, discrete, energy levels to form a band structure. Silicon and germanium have four valence electrons and in a crystal, these four pairs of electrons will form covalent bonds with their nearest 14

15 neighbours. For the energy levels, this means that they form a valence band. Higher levels form the so-called conduction band, see Fig. 6. Energi Si Ledningsband Ge Ledningsband E g E g Valensband Valensband Figur 6: The band structure in silicon and germanium. The band gap, E g, is 1.1 ev for silicon and 0.7 ev for germanium Charge carriers The electrons in the valence band participate in covalent bonds between two atoms (the atoms share a pair of electrons). Thus, they are localized between two atoms and can not move freely in the crystal. Electrons in the conduction band are not involved in any bonds and can move freely in the crystal (they are known as free charge carriers). Electrons will spontaneously be excited to the conduction band, the higher the temperature the greater the probability of excitation. At a temperature of 0 K, all valence electrons will be in the valence band. When an electron is excited to the conduction band, a hole is left in the valence band. This hole can be filled by another electron from the valence band, i.e. the hole can move in the valence band. Thus, holes in the valence band are also free charge carriers. To summarize: electrons in the conduction band and holes in the valence band are charge carriers Doping If we have an absolutely pure crystal (of Si or Ge), its conductivity depends only on temperature since the number of free charge carriers determines the conductivity. However, there are other ways to change the number of free charge carriers: the crystal can be doped. N-Doping N-doping is the intentional introduction of atoms ( impurities ) from Group V of the periodic table, such as phosphorus and arsenic, in the otherwi- 15

16 se pure crystal where they will replace some of the silicon or germanium atoms. These atoms have five valence electrons which means that there are four electrons to participate in covalent bonds while the fifth will be left over. This fifth wheel electron will be very loosely bound and therefore, the atom can easily be ionized. In other words, the electron can easily end up in the conduction band and move away from the parent atom. For the energy levels, this means that the impurity atom produces a level just below the conduction band, called a donor level. Electrons in this level are easily excited into the conduction band. P-Doping For p-doping, impurities from group III, such as boron or aluminum, that are added. They have three valence electrons, which means there are only enough electrons to form three covalent bonds. The impurity atom can easily bind an electron 5 from a silicon or germaniumatom. We have therefore introduced a hole in the valence band. For the energy levels, this means that an impurity atom forms an acceptor level just above the valence band. When the impurity atom binds a fourth electron, the acceptor level is filled. Fig. 7 illustrates the concepts. p-dopning Ledningsband n-dopning Ledningsband Donatornivå Acceptornivå Valensband Valensband Figur 7: The effects of doping. The acceptor and donor levels lie about 0.01 ev from the valence band and the conduction band respectively 5.2 Detector What is required for a material to function as a detector? First of all, there must be some kind of material where detection (interaction) can take place. If we want to detect photons, more material is required than for the detection of heavy charged particles. The purpose of the material is to somehow convert the incoming radiation to an electronic signal, since an electronic pulse is very easy to analyze and modify. Thus, we need some way of turning electrons (and holes) into an electronic pulse. 5 This electron will be bound, but not as tight as the other valence electrons. 16

17 Furthermore, the relationship between signal and noise must be high enough since too much noise will drown the signal. A simple detector would be an ionization chamber, i.e. a chamber containing a gas (material) and two electrodes held at a potential difference. Ionizing radiation will produce electron-ion pairs in the gas which leads to a current as they move towards the anode and the cathode respectively. If there is no interaction in the gas, no current will flow since the gas is nonconducting (unless the electric field is very strong). Because of this, a good signal-to-noise ratio is obtained. Fig. 8 shows a schematic of an ionization chamber. Elektroder Signal Joniserande Strålning Gasvolym Figur 8: Schematic of an ionization chamber. The voltage across the electrodes results in an electric field. The field will collect the charges that are produced when ionizing radiation interacts with the gas. A disadvantage of the ionization chamber, when it comes to the detection of photons, is the gaseous form of the material. The number of atoms in the material that can interact with the photon is not very large. In a solid material, there would be about 1000 times more atoms in the material 6. This means that the probability for photon interaction in a solid material will be approximately 1000 times greater than in a gas. The material must fulfill two requirements: No current must flow when there is no ionizing radiation in the material (noise). When ionizing radiation interacts with the material, the produced charges must be collected in an efficient way (signal). It turns out that semiconductors in some configurations satisfy both requirements 7. 6 The density of a gas at atmospheric pressure is of the order g/cm 3 while solids have densities of the order 1g/cm 3. 7 Semiconductors also has other advantages as we will see. 17

18 5.3 Semiconductors as detectors If a piece of (unaffected) semiconductor is placed between two electrodes and a potential difference is applied, current will flow through the semiconductor which is not what we want. To prevent this, a so-called p n junction can be formed by joining one p-doped and one n-doped piece of semiconductor, e.g. silicon 8. The electrons from the n-side will diffuse into the p-material and build up a net spacecharge: positive on the n-side and negative on the p-side. This net charge generates an electric field between the p-side and n-side which eventually counteracts further diffusion of electrons and holes, forming an equilibrium state. This volume is called the depletion region since it is almost depleted of free charge carriers. The p-n junction will essentially behave like a diode: if the positive terminal of voltage source is connected to the p-side, current will flow. If, on the other hand, the negative terminal is connected to the p-side (so-called reverse bias), the depletion region will grow and only a very small current can flow through the junction. A p-n junction in reverse bias serves as the current reducing unit in a semiconductor detector. A mathematical description of p-n junctions will be given in the solid state physics course (see for example, Solid State Physics, Hook & Hall). In the following, some examples of detectors using the p-n junction are discussed Surface barrier detectors A common detector type is the surface barrier detector. They are usually made from n-doped silicon. By etching gold on one of its surfaces, a p-n junction 9 is formed. A reverse bias will expand the depletion region which will then act as a detector material. It works like this: since there are very few free charge carriers, the area will have a high resistivity. This means that the voltage drop from the reverse bias will occur across the depletion region and a strong electric field is formed over the depletion region, see Fig. 9. When a heavy charged particle, such as a proton, enters the depletion region, electrons will be excited to the conduction band and subsequently swept away by the strong electric field. This produces a pulse whose total charge is proportional to the energy deposited in the detector. Unfortunately, it is not possible to produce large surface barrier detectors, the maximum size is a few millimeters. Furthermore, silicon has a low atomic number (Z = 14). This means that they are not suitable for detecting photons. Nowadays, 8 Technically, creating a p-n junction is quite complicated. 9 Actually, this is no p-n junction but rather a so-called Schottky barrier. It works in the same way however. 18

19 Signal Kisel/Utarmningsområde Joniserande Strålning Schottky barriär Elektriskt fält Hållare Figur 9: Simple schematic of a surface barrier detector. High Purity Germanium detectors are instead used for this purpose High Purity Germanium (HPGe) To be suitable for photon detection, a detector must be large enough for the task. One way to make large detectors is to use high-purity germanium. Simply put, the germanium crystal is made as free from contaminants as possible (since it is the contaminants that cause doping). This is called intrinsic germanium. In this type of germanium, the amount of impurity atoms is too low to have a great effect on the conductivity. This means that a strong electric field can be be applied over the material without causing the flow of a current. We still need to have some kind of p-n junction to get a non-conducting contact. This can for example be accomplished by diffusing a thin layer of lithium atoms 10 into one side of the crystal. The concepts are illustrated in Fig. 10. The semiconductor detector used in this laboration exercise is a HPGe detector Ge(Li) and Si(Li) These two detector types are only mentioned to prevent confusion with HPGe. In Ge(Li) and Si(Li) detectors, the concentrations of p-doping and n-doping atoms are the same, which means that the acceptor and donor levels will cancel each other. This results in a so-called compensated material. A compensated material has, like intrinsic germanium, a very low concentration of free charge carriers. Ge(Li) and Si(Li) detectors are not used very much nowadays, mainly due of the 10 This should not be confused with the manufacturing of a compensated material where Li atoms are allowed to drift into the entire crystal. 19

20 Signal High Purity Germanium n-dopat (m.h.a. Li) Elektriskt fält Hållare Figur 10: Schematic of a HPGe detector. After the cleaning process, the germanium crystal is usually lightly p-doped. Thus, a p-n junction is obtained when n-doping atoms are introduced in the crystal. In this case, this is accomplished with a very high concentration of lithium atoms at the surface. fact that lithium atoms high diffusion rate at room temperature means that the detectors has to be kept at a very low temperature at all times. 6 Gamma spectroscopy Literature: Chapter 7.6. In the following, some concepts useful in gamma spectroscopy (and in this laboration) will be discussed. When a photon traverses the sensitive volume of a detector, its total energy is either absorbed, partially absorbed or not absorbed at all, in which case the photon passes through the sensitive volume without interacting. It is important to remember that the detector only records the energy transferred by the photon to electrons and positrons, possibly after many sub-processes, in the sensitive volume. We refer here to the figures B2 and B3 in the appendix, where many of the possible processes are shown. We will soon discuss the figures in somewhat more detail. 6.1 Energy resolution If reality were as simple as described in Section 2.2, a spectrum from a monoenergetic gamma source would in principle look like the one shown in Fig. 11. If more than one of these processes can take place for a given energy, the resulting spectrum would look like a combination of each spectrum. A real spectrum, however, will be smeared out, since the different detector systems will have a 20

21 Antal Counts Fotoprocessen Antal Counts Comtonprocessen Antal Counts Parbildningsprocessen (per kanal) (per kanal) (per kanal) Energi Energi Energi Figur 11: Theoretical spectra from the different interactions. The radiation is presumed to originate from a monoenergetic gamma source. certain resolution. The resolution, R, is defined using the full absorption peak according to equation (15), R = F W HM H 0 (15) where F W HM is the Full Width at Half Maximum of the full absorption peak and H 0 is the pulse height of the full absorption peak. Thus, a detector system with a good resolution has a small value of R. There are in principle two contributions to the width of the peak: the statistical nature of the processes occuring in the detector and the noise of the electronics. These contributions are added in quadrature according to: (F W HM) 2 (F W HM) 2 statistical + (F W HM) 2 noise. (16) (F W HM) statistical The statistical contribution to the FWHM is caused by the statistical fluctuations in the number of information carriers that are created for a certain amount of energy deposited in the detector. Here, information carrier means: NaI(Tl): photoelectrons released from the photocathode. HPGe: electron-hole pairs. These numbers have been chosen since they are the smallest in the chains that build up the detector systems. In a simple model for the statistical fluctuations, the creation of information carriers can be assumed to follow Poisson statistics. That is, in the creation of N information carriers, the standard deviation, σ, is equal to N. Furthermore, 21

22 assuming that the photo peak has a Gaussian shape, the following relation is valid 11 : F W HM 2.35 σ. NaI(Tl) Since the statistical distribution depends on the number of electrons released at the photocathode, it is important to maximize this number. This is done by using scintillator materials, with a reflecting layer (such as magnesium oxide) on all surfaces except where the photomultiplier sits and a good optical contact between the crystal and the photomultiplier (silicone grease). It turns out that it takes about 25 ev to create a scintillation photon in the crystal and the efficiency at the photocathode is around % (i.e % of the scintillation photons that hit the photocathode will generate photoelectrons). HPGe An advantage of HPGe compared to NaI(Tl) is that information carriers are cheap to produce. It only takes about 2.96 ev to create an electron-hole pair in germanium. This means that it is mainly electronics noise that gives major contributions to the FWHM (F W HM) noise Electronics noise simply refers to noise that arises in the various electronics components one uses. NaI(Tl) For NaI(Tl), it is mainly the so-called dark current of the photomultiplier that contributes to the noise: even if no photon hits the photocathode, occasional electrons will be released due to thermal emission (some electrons have much higher energy than the average; the tail on the Maxwell distribution). These electrons will, after amplification in the photomultiplier, give rise to small pulses at the anode. These small pulses will then be superimposed on the proper pulses and thus increase the fluctuation in the number of true electrons. This becomes especially problematic when one wants to be able to detect low energies (small pulses). To reduce the dark current, the photocathode can be cooled. HPGe As mentioned above, the resolution of a HPGe detector is mostly determined by the electronics noise. The noise is generated by various processes, especially in the preamplifier, such as thermal variations in the resistors. 11 See the literature reference. 22

23 6.2 Efficiency The extent to which a photon is absorbed is determined by its energy (i.e. the cross section for the different ways of interaction), the detector material and dimensions of the detector. The efficiency ɛ eff for a detector is defined as ɛ eff = V (E γ) I(E γ ) where V (E γ ) is the number of photons with energy E γ that interacts with the crystal and I(E γ ) is the total number of incoming photons with energy E γ. The attenuation coeffiecient is often when discussing efficiency. The attenuation coefficient is a measure of the probability that a photon with a certain energy will interact. During the laboration exercise we shall see how the ɛ eff is related to the attenuation coefficient. 6.3 Peak-to-total ratio A photon can be fully absorbed in the following ways: 1. Through photoabsorption (photoelectric effect). 2. Through one or several Compton scatterings followed by photoabsorption. (17) 3. Pair production and subsequent full absorption (through 1 or 2) of the annihilation radiation. Photons that have been fully absorbed in the detector gives rise to a peak in the MCA spectrum, the so-called full absorption peak (or photo peak as photoabsorption usually is the dominant process), which is often denoted FE (Full Energy). The peak-to-total ratio, ɛ P/T, is defined as ɛ P/T = F (E γ) V (E γ ) where F (E γ ) is the number of fully absorbed photons with energy E γ. Fig. B4 in the appendix shows how ɛ P/T depends energy and detector size. 6.4 Response function A spectrum from a monoenergetic gamma source is called the response function of the detector system.the response function is a function of photon energy, detector material, and geometry and size of the detector. 23 (18)

24 6.4.1 The small detector Fig. B2 in the appendix shows the expected response of a small gamma-ray detector. Small means that the probability of secondary photons to interact in the detector is negligible. We see that if E γ < 2m e c 2, we get a continuous Compton distribution from 0 to T emax (see equation 10) and a full energy peak corresponding to photoabsorption of the photon. The binding energy, B e, of the emitted electron is also absorbed in the detector since the x-ray photon, which follows the emission of the electron, has a very high probability to be absorbed even in a small detector (see Fig. B1 in the appendix). When E γ > 2m e c 2, the process of pair production is added to the possible interactions. In a small detector, where annihilation photons are not absorbed, this leads to a peak with energy E γ 2m e c 2. This is called the double escape peak and is often abbreviated as DE Medium size detector Figure B3 in the appendix shows the response of a medium-sized detector. If E γ < 2m e c 2 we get, as before, a full energy peak followed by a Compton distribution. Note that the FE peak is now much higher than the Compton distribution since the probability for secondary photons to interact in the detector has risen sharply, giving a substantial contribution of multiple events to the FE peak. The probability of multiple Compton scattering also gives events in the area between the FE peak and the Compton edge. If E γ > 2m e c 2, the possibility of pair production is present once again. There is still a certain probability that both annihilation photons leave the detector without interacting, which would give a DE peak. Since the detector is larger, there is now also a probablility that one of the annihilation photons is fully absorbed, resulting in the so-called single escape peak (SE) with energy E γ m e c Effects of surrounding material In a real setup for gamma spectroscopy, the detector is in most cases surrounded by a shielding material, e.g. lead, in order to reduce the amount of background radiation impinging on the detector. Gamma radiation from the investigated source will also hit the shielding, and can therefore give rise to secondary radiation that is absorbed in the detector. Figure B5 in the appendix shows the main effects of this irradiation of the shielding materials. Photoabsorption in the shielding gives rise to one or more characteristic X-ray peaks in the spectrum and pair production gives rise to an annihilation peak. Photons that have been Compton scattered in the shielding gives rise to a broad 24

25 so-called backscattering peak. Fig. B6 in the appendix shows how the energy of Compton scattered photons depends on the beam angle for different energies of the incident radiation. The figure shows that for scattering angles of approximately 120, photons with different initial energies (in the range 0.5 to 3 MeV) get about the same energy, which is the reason why this effect gives a diffuse peak in the spectrum. 25