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Nuclear Measurements Sainati Giacomo June 26, 2023 2 Contents 1 Radiation interactions 7 1.1 Interaction of gamma-rays...................... 7 1.1.1 Interaction mechanism.............

Nuclear Measurements Sainati Giacomo June 26, 2023 2 Contents 1 Radiation interactions 7 1.1 Interaction of gamma-rays...................... 7 1.1.1 Interaction mechanism.................... 7 1.1.2 Gamma ray attenuation................... 14 1.2 Heavy charged particle interactions................. 17 1.3 Interactions of fast electrons..................... 21 2 Characteristic quantities of radiation field 25 2.0.1 Particle fluence (Φ)...................... 25 2.1 Dosimetric quantities......................... 27 2.1.1 Absorbed dose D....................... 27 2.1.2 Kerma (Kinetic Energy Released in Matter)........ 28 2.2 Quantities for radiological protection................ 29 2.2.1 Organ absorbed dose (DT )................. 30 2.2.2 Organ equivalent dose HT.................. 31 2.2.3 Effective dose (E)...................... 32 2.2.4 Internal exposure....................... 34 2.2.5 Collective exposure...................... 34 2.3 Operational quantities........................ 35 2.3.1 Ambient dose equivalent (H ∗ (d)).............. 36 2.3.2 Directional dose equivalent (H ′ (d, Σ))........... 36 2.3.3 Personal dose equivalent (HP (d)).............. 36 3 Neutron calibration field 37 3.1 Calibration.............................. 37 3.2 Sources................................ 38 3.2.1 Radionuclide sources..................... 38 3.2.2 Manganese bath system................... 41 3.2.3 Thermal neutrons...................... 42 3.2.4 Fast neutrons......................... 44 3.2.5 High-energy neutrons.................... 46 3.3 Simulated work place fields..................... 47 4 Detector generalities 49 4.1 Types of detector........................... 49 4.2 General properties.......................... 50 4.2.1 Simplified detector model.................. 50 4.2.2 Modes of detector operation................. 51 3 4 CONTENTS 4.2.3 Pulse height spectra..................... 54 4.2.4 Counting curves and plateaus................ 55 4.2.5 Energy resolution....................... 55 4.2.6 Detection efficiency...................... 58 4.2.7 Dead time........................... 59 5 Gas filled detectors 61 5.1 General properties of gas filled detectors.............. 61 5.2 Ionization chamber.......................... 65 5.2.1 Current mode of operation................. 65 5.2.2 Integrating mode of operation................ 67 5.2.3 Pulse mode operation.................... 67 5.3 Proportional counter......................... 74 5.3.1 Gas multiplication...................... 74 5.3.2 Gas multiplication factor.................. 76 5.3.3 Counting curve........................ 78 5.4 Geiger-Muller counter........................ 80 5.4.1 Time behavior........................ 83 5.4.2 Fill gases........................... 86 5.4.3 Behavior and counting efficiency.............. 88 6 Scintillators 91 6.1 Operation of the scintillator..................... 92 6.2 Scintillator material......................... 94 6.2.1 Organic............................ 94 6.2.2 Inorganic........................... 99 6.3 Scintillator properties........................ 101 6.3.1 Response to various radiations............... 102 6.4 Photomultiplier tube......................... 103 6.5 Pulses comparison between gas detectors and scintillators.... 105 6.6 Detected spectra........................... 106 6.6.1 General spectral features.................. 108 6.7 Scintillator set-up and event-types................. 111 6.7.1 Scintillator set-up...................... 111 6.7.2 Shield event-types...................... 111 6.7.3 Detector event-types..................... 114 6.7.4 Various Spectra........................ 118 6.7.5 Detector geometry...................... 120 6.8 Detector performance........................ 124 6.8.1 Detector efficiency...................... 124 6.8.2 Linearity of energy dependence............... 125 6.8.3 Pulse pile-up......................... 126 6.8.4 Baseline shift......................... 127 6.9 Uranium and plutonium assay.................... 128 6.9.1 Uranium assay with lower resolution............ 128 6.9.2 Plutonium isotopic assay.................. 129 CONTENTS 5 7 Semiconductors 131 7.1 General properties.......................... 131 7.1.1 Intrinsic ad extrinsic semiconductors............ 132 7.2 Semiconductor detector structure and properties......... 135 7.2.1 PN junction.......................... 135 7.2.2 Detector properties...................... 136 7.3 Semiconductor detector types.................... 137 8 TLD, OSLD and RPLD 139 8.0.1 Luminescence......................... 139 8.1 Thermoluminescence (TL)...................... 139 8.1.1 Luminescence emission process............... 140 8.1.2 Important parameters.................... 142 8.1.3 Summary........................... 144 8.2 Optically stimulated luminescence (OSL)............. 145 8.3 Radio-photo luminescence (RPL).................. 146 9 Neutrons 147 9.1 Introduction.............................. 147 9.2 Neutron dosimetry fundamentals.................. 147 9.2.1 Neutron radiation protection dosimetry.......... 148 9.3 Thermal neutrons detection..................... 151 9.3.1 Thermal neutron significant interactions.......... 151 9.3.2 BF3 proportional tube.................... 154 9.3.3 Boron-lined proportional counter.............. 157 9.3.4 3He proportional counter.................. 158 9.3.5 6Li detector.......................... 158 9.4 Reactor instrumentation....................... 159 9.4.1 Self-powered neutron detectors............... 159 9.4.2 Fission chambers....................... 161 9.5 Neutron spectroscopy........................ 163 9.5.1 Sandwich detector...................... 163 9.5.2 3He proportional counter.................. 165 9.5.3 6Li scintillator........................ 166 9.5.4 Detector based on (n,p) scattering reactions........ 166 9.6 Neutron dosimetry.......................... 168 9.6.1 Spherical moderated detector................ 168 9.6.2 Albedo neutron dosimetry.................. 170 9.6.3 Long counter......................... 172 9.6.4 Nuclear emulsion dosimeter................. 173 9.6.5 Track etch detector...................... 173 9.6.6 Superheated emulsion dedtector.............. 175 9.6.7 Practical dosimetry with silicon based semiconductors.. 177 9.6.8 Tissue equivalent proportional counter........... 177 9.7 Neutron activation detectors..................... 178 9.7.1 Material selection....................... 179 9.7.2 Materials for 1/v and resonance detectors......... 180 9.7.3 1/v detectors with cadmium difference method...... 182 9.7.4 Resonance detectors with sandwich method........ 182 9.7.5 Threshold detectors..................... 183 6 CONTENTS Chapter 1 Radiation interactions The operation of any radiation detector depends on the manner in which the radiation to be detected interacts with the material of the detector. It is con- venient to arrange the four major categories of radiations into the following matrix: Charged Particle Radiations Uncharged Radiations Heavy charged particles Neutrons (characteristic distance 10−5 m) (characteristic length 10−1 m) Fast electrons X-rays and γ-rays (characteristic distance 10−3 m) (characteristic length 10−1 m) The entries in the left column represent the charged particle radiations that, because of the electric charge, continuously interact through the coulomb force. The radiations in the right column are uncharged, so they are not subject to coulomb force. Instead, they must first undergo a “catastrophic” interaction that radically alters the properties of the incident radiation in a single encounter. If the interaction does not occur within the detector, these uncharged radiations can pass completely through the detector volume without revealing themselves. 1.1 Interaction of gamma-rays Three are the most important interactions in radiation measurements: photo- electric absorption, Compton scattering and pair production. All these interactions lead to the partial or complete transfer of the gamma-ray photon energy to electron energy. This behavior is in marked contrast to the charged particle, which slows down gradually. 1.1.1 Interaction mechanism Photoelectric absorption A photon undergoes an interaction with an absorber atom in which the photon completely disappears. In its place, an energetic photo-electron is ejected by the atom from one of its bound shells. The interaction can not take place with 7 8 CHAPTER 1. RADIATION INTERACTIONS free electrons. For gamma-rays of sufficient energy, the most probable origin of the photo-electron is the K shell of the atom. The photo-electron appears with an energy: Ee− = hν − Eb (1.1) For gamma-ray energies of more than a few hundred keV , the photo-electron carries off the majority of the original photon energy. In addition to the photo-electron, the interaction also creates an ionized absorber atom, with a vacancy in one of its bound shells. This vacancy is filled with an electron captured from the medium, or with a rearrangement of the other electrons. Therefore, one or more characteristic X-ray photons may be generated. Most of the time these X-rays give rise to other photoelectric absorption involving less tightly bound shells. In this way there is a cascade of interactions that takes all the energy from the initial photon. There is also a little probability, for the X-ray to escape. In some fraction of the cases, an Auger electron may be emitted in place of a characteristic X-rays. The photoelectric absorption is the predominant interaction for gamma or X-rays of relatively low energy. The probability of interaction is also enhanced for high atomic number Z. As an approximation we can see: Zn τ∼ = constant × 3.5 (1.2) Eγ where we can assume a probabil- ity dependence on Z 3. Such a severe dependence on the atomic number is the reason for the preponderance of high-Z material (Pb) in gamma shield. A plot of the photoelectric absorption cross section for a popular gamma- ray detection material, sodium iodide, is shown in Figure 1.1. In the low- energy region, discontinuities in the curve or ”absorption edges” appear at gamma-ray energies that correspond to the binding energies of electrons in the various shells of the absorber atom. The edge lying highest in energy therefore corresponds to the binding energy of the K-shell electron. For gamma-ray energies slightly above the edge, the photon energy is just sufficient to undergo a photoelectric interaction in which a K-electron is ejected from the atom. For gamma- Figure 1.1: Energy dependence of the ray energies slightly below the edge, various gamma-ray interaction this process is no longer energetically possible and therefore the interaction probability drops abruptly. Similar ab- 1.1. INTERACTION OF GAMMA-RAYS 9 sorption edges occur at lower energies for the L, M,...electron shells of the atom. Other detail on this interaction: ˆ Typical interaction for the Iodine (Z=53) ˆ The vacancy is filled mainly by L-shell electron ˆ Nearly always the cascade of absorption is too fast to be appreciable We can say something also on the emitted electron, which, being the pho- toelectric absorption a low energy photon interaction, is ejected approximately at a right angle (forward). As the energy of the photon increases, the angle decreases. The plot for lead has discontinuities at about 15 and 88 keV. These corre- spond to the L and K shell binding energies. There is the highest probability of interaction when the photon energy is exactly the electron binding energy. Note that water has a Zef f ≃ 7.4, lead has Z = 82 and the ratio between the two plots is about 1000. This because it depends on Z 3 (roughly) and (82/7.4)3 ≃ 1300. Figure 1.2: Absorption edges of lead Compton scattering It takes place between the incident gamma-ray photon and an electron in the absorbing material. It is most often the predominant interaction mechanism for gamma-ray energies typical of radioisotope sources. In Compton scattering, the incoming gamma-ray photon is deflected through an angle θ with respect to its 10 CHAPTER 1. RADIATION INTERACTIONS Figure 1.3 original direction. The photon transfers a portion of its energy to the electron (assumed to be initially at rest), which is then known as recoil electron. Because all angles of scattering are possible, the energy transferred to the electron can vary from zero to a large fraction of the gamma-ray energy. The expressions that relates the energy transfer and the scattering angle for any given interaction, using the symbols defined in Figure 1.3, is: hν hν ′ = (1.3) hν 1+ (1 − cos θ) m0 c2 Eel = hν − hν ′ (1.4) hν hν α= 2 = (1.5) m0 c 0.511 2α Emax = hν (1.6) 1 + 2α ′ 1 hνmin = hν (1.7) 1 + 2α If a photon makes a direct hit with the electron, the electron will travel forward (ϕ = 0) and the scattered photon will travel backward (θ = π), with the reported value of energy. In the case of a low-energy photon direct hit most of the energy is kept by the photon, on the contrary most of the energy is transferred to the recoil electron. As the photon energy increases beyond the binding energy of the K-electron, the photoelectric effect decrease rapidly with energy and the Compton effect becomes more and more important. However, the Compton effect also decreases with increasing photon energy. The Compton interaction involves essentially free electrons in the absorbing material, therefore it is independent on Z. It follows that the Compton mass attenuation coefficient is independent on Z and depends only on the number of electrons per gram ( Z∗NA ) ˆ Hydrogen Z A = 1 (For the hydrogen the Compton effect is much more relevant) ˆ Light elements (C, N, O) Z A = 0.5 ˆ Heavier elements Z A ≪1 1.1. INTERACTION OF GAMMA-RAYS 11 Material Density Atomic Number Number of Electrons (g/cm3 ) per Gram Hydrogen 0.0000899 1 6.00 ∗ 1023 Carbon 2.25 6 3.01 ∗ 1023 Oxygen 0.001429 8 3.01 ∗ 1023 Aluminum 2.7 13 2.90 ∗ 1023 Copper 8.9 29 2.75 ∗ 1023 Lead 11.3 82 2.38 ∗ 1023 Effective Atomic Number Fat 0.916 5.92 3.48 ∗ 1023 Muscle 1.00 7.42 3.36 ∗ 1023 Water 1.00 7.42 3.34 ∗ 1023 Air 0.001293 7.64 3.01 ∗ 1023 Bone 1.85 13.8 3.00 ∗ 1023 For the hydrogen we do not have an Avogadro’s number of electron per gram due to the presence of its isotopes deuterium and tritium. Total mass attenuation coefficient µ/ρ = σcoh /ρ + τ /ρ + σc /ρ + π/ρ When diagnostic energy photons interact with materials of low atomic num- ber (soft tissue), the Compton effect dominates. We can see in lead the fast reduction of the photoelectric absorption after 88 keV (K-shell electron binding energy). For soft tissue and bone, since their effective atomic number is lower than the atomic number of the lead, the photoelectric effect decays before. Figure 1.4: Percentage of photoelectric absorption and Compton scattering in differ- ent materials 12 CHAPTER 1. RADIATION INTERACTIONS Pair production If the gamma-ray energy exceeds twice the rest-mass energy of an electron (1.02 M eV ), the process of pair production is energetically possible. At gamma-ray energies that are only a few hundred keV above this threshold, the probabil- ity for pair production is small. However, this interaction mechanism becomes predominant as the energy increases into the many-M eV range. In the interac- tion (which must take place in the coulomb field of a nucleus), the gamma-ray photon disappears and is replaced by a negatron-positron pair. All the excess energy carried in by the photon above the 1.02 M eV required to create the pair goes into kinetic energy shared by the positron and the electron. Because the positron will subsequently annihilate after slowing down in the absorbing medium, two annihilation photons are normally produced as secondary prod- ucts of the interaction. The subsequent fate of this annihilation radiation has an important effect on the response of gamma-ray detectors. In this process we have at the beginning production of matter (negatron-positron) and then the disappearance of matter, through the annihilation of the positron, while the negatron will remain in the medium. The line at the left of Figure 1.5 represents the energy at which pho- toelectric absorption and Compton scattering are equally probable as a function of the absorber atomic number. The line at the right represents the energy at which Compton scattering and pair pro- duction are equally prob- able. Three areas are thus defined on the plot within which photoelec- Figure 1.5: Prevalence region for photon interactions tric absorption, Compton scattering, and pair pro- duction predominate. Coherent (or Rayleigh) scattering This process neither excites nor ionizes the atom, and the gamma-ray photon maintain its original energy after the scattering event (in first approximation). However, the direction of the photon is changed. The probability of scattering is significant only for low photon energies (below a few hundred keV for common materials) and is most prominent in high-Z absorbers. The average deflection angle decreases with increasing energy. 1.1. INTERACTION OF GAMMA-RAYS 13 Summary of photon interaction µ/ρ Dependence Mechanism E Z Energy Range in Soft Tissue Simple Scatter 1/E 3 Z2 1-20 keV Photoelectric 1/E 3 Z3 1-30 keV Compton Falls slowly with E Independent 30 keV - 20 M eV Pair Production Rises slowly with E Z2 Above 20 M ev Photon Energy Relative Interactions (M eV ) τ σ Φ 0.01 95 5 0 0.026 50 50 0 0.060 7 93 0 0.150 0 100 0 4.00 0 94 6 10.00 0 77 23 24.00 0 50 50 100.00 0 16 84 Figure 1.6 14 CHAPTER 1. RADIATION INTERACTIONS Effective atomic number (Zef f ) Zef f is the atomic number of an element with which photons interact the same way as with the given composite material. For photoelectric interactions, Mayenord has defined the effective atomic number of a compound as follows:
1/2.94 Zef f = a1 Z12.94 + a2 Z22.94 +... + an Zn2.94 (1.8) Where the coefficient a are the fractional contributions of each element to the total number of electrons in the mixture. Figure 1.7 Muscle composition is very similar to water composition, in term of com- ponent, effective Z and density. Therefore, water is a good approximation of muscle for photon interaction. Also air is very similar to water, but there is a difference in the density of about 3 order of magnitude and this aspect affect the efficiency of a detector. Bones have a wide range of effective Z, depending on the type of bone considered. Air, due to the lack of hydrogen, is not a good approximation of any soft tissue in the case of neutrons. 1.1.2 Gamma ray attenuation Attenuation coefficient If we perform a transmission experiment (with a good geometry), in which mono-energetic gamma-rays are collimated into a narrow beam and allowed to strike a detector after passing through an absorber of variable thickness, the result should be a simple exponential attenuation of the gamma-rays. Each interaction removes the gamma-ray photon from the beam either by absorption or by scattering away from the detector direction and can be characterized by a fixed probability of occurrence per unit path length in the absorber. The sum of these probabilities is simply the probability per unit path length that the gamma-ray photon is removed from the beam: 1.1. INTERACTION OF GAMMA-RAYS 15 Figure 1.8: Transmission of gamma-rays through lead absorbers µ = τ (photoelectric) + σ(compton) + π(pair) + σcoh (1.9) I = I0 e−µt (1.10) R ∞ −µx xe dx 1 λ = R0 ∞ −µx = (1.11) 0 e dx µ µ (1.12) ρ ((1.9) Linear attenuation coefficient, (1.10) Number of transmitted photons, (1.11) Mean free path and (1.12) Mass attenuation coefficient.) Since the linear attenuation coefficient varies with the density of the ab- sorber, its use is limited. Therefore, the mass attenuation coefficient is much more widely used (it is the same for any physical state of the absorber). It can be defined also for a compound or mixture of elements and it is simply a weighted sum of the mass attenuation coefficient of the elements, with the weight fraction of the correspondent element as weight. Absorber mass thickness The attenuation law for gamma-rays takes the form: I = I0 e(−µ/ρ)ρt (1.13) 16 CHAPTER 1. RADIATION INTERACTIONS The product (ρt), known as the mass thickness of the absorber, is now the significant parameter that determines its de- gree of attenuation. The thickness of absorbers used in radiation measurements is therefore often mea- sured in mass thickness rather than physical thick- ness, because it is a more fundamental physi- Figure 1.9 cal quantity. The mass thickness is also an useful concept when discussing the energy loss of charged particles and fast electrons. For absorber materials with similar neutron/proton ratios, a particle will en- counter about the same number of electrons passing through absorbers of equal mass thickness. Therefore, the stopping power and range, when expressed in units of (ρt), are roughly the same for materials that do not differ greatly in Z. ln(2) HV L = (1.14) µ Figure 1.10: Attenuation of a broad spectrum HVL (half-value layer) is the thickness of an absorber required to attenuate the intensity of the beam to half its original value. As reported in Figure 1.9, the transmitted intensity can also be reported in function of the HVL. Another important aspect of the attenuation phenomena is the attenuation of a broad spectrum. In the case of Figure 1.10 is considered the spectrum of 1.2. HEAVY CHARGED PARTICLE INTERACTIONS 17 X-rays, that shows the characteristic line and we imagine to have subsequent penetration in absorber sample. The spectrum of the low energy part disappears first, since the X-rays with lower energy have a lower penetrating power. The characteristic lines are not attenuated in the same way since they do not have the same energy and there is a shift of their origin due to the attenuation of the spectrum. The ratio between the subsequent HVL give an indication of the spectra at the different stages. In particular the thickness needed to have half of the initial intensity of the incident radiation increases, because the spectra after some stages will be constituted mainly of high intensity X-rays. 1.2 Heavy charged particle interactions Heavy charged particles, such as alpha particles, interact with matter primarily through coulomb forces between their positive charge and the negative charge of the orbital electrons within the absorber atoms. Although interactions of the particle with nuclei (as in Rutherford scat- tering or alpha-particle-induced reactions) are also possible, such encounters occur only rarely. Upon entering any absorbing medium, the charged particle immediately interacts simul- taneously with many electrons. In any one such encounter, the electron feels an impulse from the attractive coulomb force as the particle passes its vicinity. Depending on the proximity of the encounter, this impulse may be sufficient Figure 1.11: Generic track either to raise the electron to a higher-lying shell structure schematic within the absorber atom (excitation) or to re- move completely the electron from the atom (ionization). The energy that is transferred to the electron must come at the expense of the charged particle, and its velocity is therefore decreased as a result of the encounter. Using the conservation of momentum and kinetic energy we can find an approximation of the maximum energy that can be transferred from a charged particle (alpha particle) to an electron: Em E Qmax = 4 = (Head on collision) with M = 8000m M 2000 Because this is a small fraction of the total energy, the primary particle must lose its energy in many such interactions during its passage through an absorber. At any given time, the particle is interacting with many electrons, so the net effect is to decrease its velocity continuously until the particle is stopped. Except at their very end, the tracks tend to be quite straight because the particle is not greatly deflected by any one encounter, and interactions occur in all directions simultaneously. The products of these encounters in the absorber are either excited atoms or ion pairs. Each ion pair is made up of a free electron and the correspond- ing positive ion of an absorber atom from which an electron has been totally removed. The ion pairs have a natural tendency to recombine in order to form 18 CHAPTER 1. RADIATION INTERACTIONS neutral atoms but, in some types of detectors, this recombination is suppressed so that the ion pairs may be used as the basis of detector response. In particularly close encounters, an electron may undergo a large enough impulse that after having left its parent atom, it still may have sufficient kinetic energy to create further ions. These energetic electrons are sometimes called delta rays and represent an indirect means by which the charged particle energy is transferred to the absorbing medium. Under typical conditions, the majority of the energy loss of the charged particle occurs via these delta rays. The range of delta rays is always small compared with the range of the incident energetic particle, so the ionization is still formed close to the primary track. On a microscopic scale, one effect of this process is that the ion pairs normally do not appear as randomly spaced single ionization, but there is a tendency to form many ”clusters” of multiple ion pairs distributed along the track of the particle. Stopping power The linear stopping power S for charged particles in a given absorber is simply defined as the differential energy loss for that particle within the material divided by the corresponding differential path length: dE 4πq 4 z 2 mv 2 v2 v2 S=− =− 2 N Z[ln( ) − ln(1 − 2 − 2 )] (1.15) ds mv I c c For v 15 keV and beta rays with energy > 2 M eV ) with the recommended value d=10 mm. The unit of measurement is [Sv]. H ∗ (10) is used for area monitoring of strongly penetrating radiations. 2.3.2 Directional dose equivalent (H ′ (d, Σ)) The directional dose equivalent, H ′ (d, Σ), at a point in a radiation field, is the dose equivalent that would be produced by the corresponding expanded field, in the ICRU sphere at depth, d, on the sphere radius in a specified direction, Ω, with respect to the reference direction. It is only used for area monitoring for weakly penetrating radiation (alpha particles, photons with energy ¡ 15 keV , beta rays with energy ¡ 2 M eV )with d = 0.07 mm if referred to the skin or d = 3 mm for the eye. The unit of measurement is [Sv]. 2.3.3 Personal dose equivalent (HP (d)) The personal dose equivalent, HP (d), is the dose equivalent in soft tissue, at an appropriate depth, d, below a specified point on the human body surface. It is used for strongly penetrating radiation with d =10 mm (estimation of the effective dose E) and for weakly penetrating radiation with d = 0.07 mm (estimation of the skin equivalent dose HT ). The unit of measurement is the [Sv]. Chapter 3 Neutron calibration field What promotes a radiation field to become a calibration field? The characteri- zation of the field. We concentrate now on the neutron fields, which are the most difficult to obtain for a calibration, since most of the time we have a broad neutron spec- trum. For gamma and alpha radiations is easier to obtain a mono-energetic source. Neutrons can be produced by means of a radionuclide source, a particle accelerator or a reactor. The last will certainly be a broad spectrum source, but it can be used with a filter. The other need in order to characterize a radi- ation field is neutron metrology, in particular, it is needed to determine energy and number of neutrons produced. With these two, it is possible to obtain a well-characterized radiation field, i.e. to know field quantities and dosimetric quantities related to the field. Field quantities: total fluence, differential fluence and double differential fluence, where the last one is the most complete quantity, because are known energy and angular distribution. Dosimetric quantities: kerma and dose. They are calculated using con- version coefficients. Then the operational quantities, that hopefully the detector resemble. 3.1 Calibration Figure 3.1 There are mainly four components of the initial source that hit a detector besides the direct radiation coming from the source. The most important in 37 38 CHAPTER 3. NEUTRON CALIBRATION FIELD terms of intensity is the room scatter, i.e. radiations scattered by the wall which are added to the direct radiation. There are also air in-scatter and air out-scatter radiations, which are less important due to the density effect. The last component is mainly a problem of characterization of the source and it is the source scatter. It can be either a positive or negative contribution. It comes without saying that the calibration result should not depend on the facility (it should not depend on the size, the wall and in general on the pecu- liarity of the facility). Therefore, in order to determine the reference value for direct neutrons, experimental methods to subtract the reading due to scattered neutrons are used. If not possible or feasible, we have to determine the reference value including scattered neutrons, with spectrometry or transport calculations. Shadow-cone technique In this procedure, first it is per- formed a measure without the shadow-cone, then the shadow- cone is placed between the source and the detector in order to elimi- nate the direct and source scatter. We assume a point source and a larger detector and the shadow object can be either a cylinder or a cone (with the base facing the detector). This technique allows to eliminate the room scatter and Figure 3.2 the air scatter and, with a good characterization of the source, also the source scatter can be eliminated. The shadow object is made of (at least) two materials, in order to cover a larger range of neutron energy, and, the most common, uses iron and polyethylene. Distance variation technique This technique makes use of the different distance variation of different compo- nents, performing some measure with the detector placed in different positions. A system of equation in which we have to determine the constant that mul- tiply the different contribution is obtained. Distance-variation of the different components: ˆ Direct radiation = 1/r2 ˆ Air in-scatter radiation = 1/r ˆ Room scatter radiation = constant 3.2 Sources 3.2.1 Radionuclide sources There are several facilities world-wide (at primary and secondary labs). The neutron sources recommended by ISO 8529-1 are the following: 3.2. SOURCES 39 ˆ 252 Cf that is an artificial radionuclide with a spectrum which is similar to that of 235U ˆ 252 Cf, heavy water moderated (different neutron energy) ˆ Am-Be (α, n) ˆ Am-B (α, n) 252 Cf Figure 3.3 It is a good source, but the principal limitation is the low half-life (2.65 years). It is a single peak source. 252 Cf, heavy water moderated Figure 3.4 It is used heavy water due to the better neutron economy. There are lower energy neutrons but still no thermal neutrons. The “hole” between the 2 peaks 40 CHAPTER 3. NEUTRON CALIBRATION FIELD is caused by the material that surround the source. The dominant decay mech- anism is alpha decay, and the alpha emission rate is about 32 times that for spontaneous fission. The neutron yield is 0.116 n/s per Bq, where the activity is the combined alpha and spontaneous fission decay rate. On a unit mass basis, 2.30 x 106 n/s are produced per microgram of the sample. (α,n) sources Some combination of radionuclides and sources are available, even if the most widely used are the two previously mentioned. Radionuclides: ˆ 238 Pu and 239Pu are quite good, because they have not short half-life, a decent neutron yield and a low gamma ray exposure, but because of proliferation and possible misuse, they were abandoned. ˆ 226 Ra long half-life, the better neutron yield but an enormous gamma-ray exposure rate ˆ 241 Am is a good compromise among all the possibilities The targets are several and they should be chosen on the basis of the energy of principal neutron peak primarily. As it can be seen from Figure 3.5, Be shows many peaks, while the others have a dominant peak in terms of neutron energy. 241 241 (a) Am-Be(α,n) neutron spectrum (b) Am-B(α,n) neutron spectrum (c) Comparison of the different spectra Figure 3.5 3.2. SOURCES 41 3.2.2 Manganese bath system The manganese sulfate (M nSO4 ) bath facility provides a method for accurately measuring the rate of neutron emissions from a ra- dioactive neutron source of in- terest. These measurements can then be used to accurately cali- brate neutron sources for various applications in science and indus- try. In this facility, a neutron source (often a sphere-shaped ob- Figure 3.6 ject) is surrounded by a liquid bath of pure manganese sulfate. The bath absorbs neutrons, making some of the manganese atoms radioactive (emission of gamma rays). The radioactive solution is pumped in the detec- tor assembly, where two detectors measure the radioactive emission from the manganese. This is an indication of the strength of the neutron source. Some precautions have to be taken in order to avoid errors: ˆ The manganese bath has to be large enough in order to have a high prob- ability of interaction between neutron and manganese ˆ A long counter is used with the purpose of detecting how many neutrons escape from the bath De Pangher long counter Long counter (LC) is one of the standard instruments in neutron source flux measurements. Its counting efficiency is independent on the neutron energy and can be useful device in many neutron physics applications. Fast neutron flux measure- ment by thermal neutron detec- tor requires moderating materials such as paraffin and polyethylene. When a cylindrical thermal neu- tron detector is in moderator, ef- Figure 3.7 fective center of this detector is changed. Effective center is a differential volume of detector that is assumed point detector for different distances from radioactive (neutron) source. Effec- tive center is dependent on neutron energy. If neutron field is generated with energetic neutron, effective center is deeper into front surface of the detector. On the other hand, penetration length of energetic neutron is greater compared to low energy neutron. Measurement of neutron flux in laboratory requires a detec- tor with characteristics properties such as independent response on wide range 42 CHAPTER 3. NEUTRON CALIBRATION FIELD of neutron energy, directional response and insensitive to gamma ray response. Such detectors are generally called long counter (LC) and sensitive minimum neutron energy is cut off of cadmium. In neutron laboratory, due to neutron scattering from environment (such as walls and the air in the exposure environ- ment), elimination of scattered neutrons is one of the important requirements for neutron flux measurements. Furthermore, in mixed fields of neutron and gamma-ray, neutron separation from gamma-ray will be helpful for net neutron flux measurement in the laboratory. This kind of counter can be applicable in neutron flux monitoring for neutron generators, calibration of neutron sources and neutron fields in neutron secondary standard dosimeter laboratory. The De Pangher LC takes advantage of the reaction of boron-10 with thermal neutrons and use polyethylene as moderator. Most neutron detector sys- tems suffer from the disad- vantage that the counting ef- ficiency depends strongly on the energy of the neutrons to be detected. The LC avoid that disadvantage. Be- cause of the nearly energy- independent response of this type of counting tube, the arrangement is also called a “flat response” detector. We can compare the effective cen- Figure 3.8 ter of the LC with the neu- tron energy distribution of the radionuclide sources. 3.2.3 Thermal neutrons Neutron sources with moderator (JAERI facility) Thermal neutron fields were established at FRS using moderated neutrons from a graphite pile with a Cf-252 neutron source. The graphite pile has a dimen- sion of 1.50 m (W) Ö 1.64 m (L) Ö 1.50 m (H). The neutron source (100 g) is settled in the center of the pile. There are two calibration points, in front of two different faces of the pile. The calibration points are set at 40 cm from each surface and 75 cm above the floor. The distances from the Cf-252 source to the calibration points are 122 cm and 115 cm for the calibration points. Then the neutron fluence rates and spectra are a little different at between the two points. Because epithermal and fast neutrons mixed in thermal neutrons may affect the calibration of the dosimeters, it is necessary to evaluate these neu- trons. Then the neutron spectra at the calibration points were measured with a Bonner multi-sphere spectrometer system and calculated with the MCNP-4C code. The Bonner multi-sphere spectrometer system consists of eight spherical moderators with a spherical BF3 proportional counter. The moderators are made of polyethylene and the thicknesses are different for each spectrometer. Their outer surfaces were covered with 1mm thick cadmium shells to measure neutrons above 0.5 eV. Additionally, thermal and epithermal neutrons were 3.2. SOURCES 43 measured with the BF3 counter without a moderator in conditions of being covered with and without a 1 mm cadmium shield. Time off light technique (GKSS Geesthacht) Figure 3.9 The target is hit directly by the neutrons coming from the reactor (which are not mono-energetic). The neutron beam encounter the chopper device: it is a rotating switch that interrupts intermittently the continuous neutron beam, producing very short neutron pulses. Neutrons can cross the chopper only when the chopper layers (made of Cd) are (quasi) parallel to the incident beam direc- tion. At the exit of the chopper, the neutron are forced to cross a long vacuum tube before reaching the detector: the arrival time of the neutrons depends on their energy. By using a suitable counting electronics, the detector response is recorded only for a very short time interval, and with a delay compared to the chopper pulse. The chopper is typically applied for slow neutrons (< 1 eV ), even if some very fast choppers can be used for neutron energies up to 1 keV. At the GKSS they have a Fourier chopper with 1024 slits, that can rotate up to 1760 rpm. The wavelength range goes to 0.1 nm to 0.4 nm. Figure 3.10 44 CHAPTER 3. NEUTRON CALIBRATION FIELD 3.2.4 Fast neutrons Mono-energetic neutrons can be obtained accelerating protons or deuterons onto target of lithium, beryllium, deuterium or tritium, by means of accelerators, exploiting different threshold reactions. Neutron energy range (M eV ) Reaction 0.002 to 0.050 Sc-45(p,n)Ti-45 0.05 to 0.63 Li-7(p,n)Be-7 0.60 to 2.8 T(p,n)He-3 2.8 to 6.0 D(d,n)He-3 13 to 20 T(d,n)He-4 The neutrons emitted by these reactions at a certain deflection angle with respect to the incident particle direction, have practically the same energy. By properly choosing the reaction, the energy of the projectile particle and the neutron emission angle, it is possible to obtain mono-energetic neutrons with energies about the interval 100 keV - 20 M eV. Van De Graaff accelerator A Van de Graaff generator is an elec- trostatic generator which uses a mov- ing belt to accumulate electric charge on a hollow metal globe on the top of an insulated column, creating very high electric potentials. The potential difference achieved by modern Van de Graaff generators can be as much as 5 M V. A tabletop version can pro- duce on the order of 100 kV. The larger the sphere and the farther it is from ground, the higher its peak po- tential. The sign of the charge (posi- tive or negative) can be controlled by the selection of materials for the belt and rollers. Higher potentials on the sphere can also be achieved by using a voltage source to charge the belt di- Figure 3.11 rectly. The initial motivation for the de- velopment of the Van de Graaff generator was as a source of high voltage to accelerate particles for nuclear physics experiments. The high potential differ- ence between the surface of the terminal and ground results in a corresponding electric field. When an ion source is placed near the surface of the sphere (typically within the sphere itself) the field will accelerate charged particles of the appropriate sign away from the sphere. By insulating the generator with pressurized gas, the breakdown voltage can be raised, increasing the maximum energy of accelerated particles. Once the charged projectile particle (proton or 3.2. SOURCES 45 Item Problem Remedy Beam current Not steady and often subject to Very stable accelerator opera- wild fluctuations tion is required but is very dif- ficult to obtain Beam energy Variation causes change in the Usually capable of very stable neutron yield and energy control Beam movement Neutron yields change because Beam collimation to a small of target non-uniformity and size, use of thin target holder because of changes in the atten- uation in the target holder as a function of the angle of observa- tion Target deterioration Occurs if the beam is too in- Air jet, beam sweeping, beam tense and cooling is not em- defocussing, target gyration, ployed use of low beam currents Room scattering Energy and direction of scat- Free-air scattering geometry, tered neutrons are incorrect. e.q., example, a 10-ft deep pit Scattered intensity changes covered with a light metal grat- when positions of scatterers are ing floor changed External sources C(d,n) and D(d,n) neutrons Periodic replacement of beam from carbon and deuterium de- stops and apertures, careful ac- position at beam stops and celerator alignment apertures Competing targets C(d,n) and D(d,n) neutrons Reduction of organic vapors in from carbon deposition on the the vacuum system, periodic surface of the target and deu- replacement of targets, use of terium deposition in the target high-Z backing materials like backing platinum and tantalum, use of deuterium and tritium gas targets for D(d,n) and T(d,n) sources deuteron) have been accelerated, it hits the target and we have neutron emission due to the previous reactions. Characteristics of typical targets used to produce neutrons: Reaction Target material Backing material Target thickness Energy loss Li(p,n) lithium fluoride 0.25 mm silver 60 µg cm2 6 keV for 2.3 M eV (565 keV neutrons) T(p,n) 50 Gbq tritium in 0.2 mm gold 350 µg cm2 (es- 28 keV for 3.3 5 cm2 titanium sentially the tita- M eV (2.5 M eV layer nium) neutrons) D(d,n) 1 cm3 deuterium 0.25 mm silver µg cm2 110 keV for 1.8 in 5 cm2 tritium M eV (5 M eV layer neutrons) The backing material has to be such to do not give additional neutrons and, in order to achieve this, the thickness is indicated. The neutron spectrum has to remain unchanged, as well. The last column (energy loss) represent, for the first row for example, the energy that 2.3 M eV protons must lose (6 keV ) to give 565 keV neutrons. 46 CHAPTER 3. NEUTRON CALIBRATION FIELD Ranges of neutron energies (a) Ranges of neutron energies avail- (b) Neutron energy as a function of able from five most common neutron- angle for five most common neutron- producing reactions producing reactions Figure 3.12 In Figure 3.12 (a) are reported the range of neutron energy as a function of the bombarding energy. The energy of the neutrons depends on the angle with which they come out from the target. The minimum neutron energy with a given bombarding energy is achieved with an angle of 180 degree, while the maximum energy with an angle of 0 degree. As can be seen, there is the possibility to obtain a wide span of neutron energy, adjusting bombarding energy, target, projectile and angle. In figure 3.12 (b) is crucial to remark the importance to have a flat neutron energies with respect to the angle. This aspect is fundamental when we are dealing with large detector. Making reference at the diagram it can be stated that the reaction T(d,n)He-4 and C-12(d,n)N-13 are quite good, because they have a flat energy behavior. 3.2.5 High-energy neutrons Quasi-mono-energetic neutron beams are typically produced at the iThemba LABS fast neutron beam facility by the Li-7(p,xn) or Be-9(p,xn) reactions. With the proton beams available from the separated sector cyclotron, the neu- tron energy range from about 30 M eV to 200 M eV can be covered almost continuously with varying thicknesses of Li and Be targets. In order to simulate a quasi-mono-energetic neutron energy distribution via Li-7(p,xn), the energy spectra of neutron beams generated by the Li + p reaction at neutron emission angles of 0° and 16° are simultaneously measured. The neutron energy distri- butions from these emission angles feature a prominent peak and a continuum. The prominent peak is associated with direct reaction transitions mainly to the ground state and to the unresolved first excited state of Be-7. The continuum 3.3. SIMULATED WORK PLACE FIELDS 47 at lower energies is associated primarily with the three-body break up process; Li-7(p,n He-3)He-4. The intensity of the prominent peak in the 0° spectrum is high and rapidly decreases with increasing neutron emission angle. For the low energy continuum, the intensity is almost independent of the neutron emission angle for angles up to 16°. The yield produced by irradiation with the neutron beam in the 0°emission angle includes components due to reactions initiated by both the high energy peak neutrons (prominent peak) and the continuum. On the other hand, the yield resulting from irradiation with the neutron beam in the 16° emission angle is dominated by reactions initiated by the low energy continuum alone. Therefore, a yield determined for the quasi-mono-energetic neutron energy is obtained through a “difference spectrum”, by subtracting the yield produced in the 16° beam from that simultaneously produced in the 0°. The energy of the peak coincide with the proton energy. (a) Neutron beams generated by the (b) Difference spectrum Li + p reaction at neutron emission angles of 0 and 16 degree (c) Examples of energy distributions at reference position Figure 3.13 3.3 Simulated work place fields Nuclear industry In France (IRSN) there is a facility (CANEL) where a field, which represent the field of the work place in a nuclear industry, is reproduced without a reactor. With an accelerator 3.3 M eV neutrons are produced thanks to the D(d,n) re- action. With a U-238 shell (converter) fission neutrons are produced and the neutron spectra of interest is produced with a particular shielding: iron, water 48 CHAPTER 3. NEUTRON CALIBRATION FIELD and polyethylene. Than, the spectra in the figure come out, with a little peak at 3.3 M eV , which corresponds to the primary neutrons escaped. Figure 3.14: Energy distribution of the CANEL field (IRSN) Flight altitude The facility CERF simulate the distribution at the commercial flight’s altitude (10 km). This is not easy to reproduce, because, as it can be seen from the figure on the right, it shows two peak: ˆ The peak at lower energy is called evaporation peak ˆ The peak at higher energy is called spallation peak In the facility a beam of 120 GeV /c of hadrons strikes a copper target, producing a lot of radiations (neutrons, muons etc), but we are only interested to neutrons. Two radiation field are measured: one behind 80 cm concrete and the other behind 40 cm iron, with the two separated distribution showed in the left figure (while the overall distribution is compared with that of the aircraft). Figure 3.15: Energy distributions at CERF and comparison with spectrum at flight altitudes Chapter 4 Detector generalities 4.1 Types of detector Based on structure Gas-filled: they are among the most commonly used. There are several types of gas-filled detector, and while they have various differences in how they work, they all are based on similar principles. When the gas in the detector comes in contact with the radiation, it reacts, with the gas becoming ionized and the resulting electronic charge being measured by a meter. The different types of gas-filled detectors are: ionization chambers, proportional counters, and Geiger- Mueller (G-M) tubes. The major difference between these types is the applied voltage across the detector, which determines the type of response that the detector will register from an ionization event. Solid-state: Generally using a semiconductor material such as silicon, they operate much like an ion chamber, simply at a much smaller scale, and at a much lower voltage. Semiconductors are materials that have a high resistance to electronic current, but not as high resistance as an insulator. They are composed of a lattice of atoms that contain “charge carriers”, these being either electrons available to attach to another atom, or electron “holes”, or atoms with an empty place where an electron could be. Silicon solid state detectors are composed of two layers of silicon semiconductor material, one “n-type” (which means that it contains a greater number of electrons compared to holes) and one “p-type” (it has a greater number of holes than electrons). Electrons from the n-type migrate across the junction between the two layers to fill the holes in the p- type, creating what’s called a depletion zone. The depletion zone acts like the detection area of an ion chamber. Radiation interacting with the atoms inside the depletion zone causes them to re-ionize, and create an electronic pulse which can be measured. The small scale of the detector and of the depletion zone itself means that the ion pairs can be collected quickly, meaning that the instruments utilizing this type of detector can have a particularly quick response time. This, when coupled with their small size, makes this type of solid state detector very useful for electronic dosimetric applications. They are also able to withstand a much higher amount of radiation over their lifetime than other detectors types such as G-M tubes, meaning that they are also useful for instruments operating in areas with particularly strong radiation fields. 49 50 CHAPTER 4. DETECTOR GENERALITIES In scintillation detectors, the interaction of ionizing radiation produces UV and/or visible light. Liquid phase: Also in this case there can be scintillators and ion chambers with a liquid between the plates. The biggest advantage is being able to put the source directly inside the detector, without problems with positioning. There are also super-heated emulsions detectors, which consist of uniform dispersion of over-expanded halocarbon and/or hydrocarbon droplets suspended in a compliant material such as a polymeric or an aqueous gel. Super-heated emulsions operate like the bubble chamber, long used in high energy particle physics. Charged particles liberated by radiation interactions nucleate the phase transition of the super-heated liquid and generate detectable bubbles. They are continuously sensitive since the liquid is kept in steady-state superheated conditions. Based on output Detectors may also be classified by the type of information produced: ˆ Counters, such as Geiger-Mueller (GM) detectors, that indicate the num- ber of interactions occurring in the detector ˆ Dosimeters, which indicate the net amount of energy deposited in the detector by multiple interactions ˆ Spectrometers, which yield information about the energy distribution of the incident radiation, such as NaI scintillation detectors 4.2 General properties 4.2.1 Simplified detector model We begin with a hypothetical detector that is subject to some type of irradiation. Attention is first focused on the interaction of a single particle or quantum of radiation in the detector, which might, for example, be a single alpha particle or an individual gamma-ray photon. In order for the detector to respond at all, the radiation must undergo interaction through one of the mechanisms discussed in Chapter 1. The interaction or stopping time is very small (typically a few nanoseconds in gases or a few picoseconds in solids). In most practical situations, these times are so short that the deposition of the radiation energy can be considered in- stantaneous. The net result of the radiation interaction in a wide category of detectors is the appearance of a given amount of electric charge within the de- tector active volume. Our simplified detector model thus assumes that a charge Q appears within the detector at time t = 0 resulting from the interaction of a single particle or quantum of radiation. Next, this charge must be collected to form the basic electrical signal. Typically, collection of the charge is accom- plished through the imposition of an electric field within the detector, which causes the positive and negative charges created by the radiation to flow in op- posite directions. The time required to fully collect the charge varies greatly from one detector to another. For example, in ion chambers the collection time can be as long as a few milliseconds, whereas in semiconductor diode detectors 4.2. GENERAL PROPERTIES 51 the time is a few nanoseconds. These times reflect both the mobility of the charge carriers within the detector active volume and the average distance that must be traveled before arrival at the collection electrodes. We therefore begin with a model of a detector, whose response to a sin- gle particle or quantum of radiation will be a current that flows for a time equal to the charge collection time. The sketch below illustrates one ex- ample for the time dependence the de- tector current might assume, where tc represents the charge collection time. Z tc i(t) dt = Q (4.1) Figure 4.1 0 The time integral over the duration of the current must simply be equal to Q, the total amount of charge generated in that specific interaction. In any real situation, many quanta of radiation will interact over a period of time. If the irradiation rate is high, situations can arise in which current is flowing in the detector from more than one interaction at a given time. For purposes of the present discussion, we assume that the rate is low enough so that each individual interaction gives rise to a current that is distinguish able from all others. The magnitude and duration of each current pulse may vary depending on the type of interaction. 4.2.2 Modes of detector operation We can now introduce a fundamental distinction between two general modes of operation of radiation detectors. The two are called pulse mode and cur- rent mode. Pulse mode is easily the most commonly applied of these, but current mode also finds many applications. Although the two modes are opera- tionally distinct, they are interrelated through their common dependence on the sequence of current pulses that are the output of our simplified detector model. In pulse mode operation, the measurement instrumentation is designed to record each individual quantum of radiation that interacts in the detector. In most common applications, the time integral of each burst of current, or the total charge Q, is recorded since the energy deposited in the detector is directly related to Q. All detectors used to measure the energy of individual radiation quanta must be operated in pulse mode. Such applications are categorized as radiation spectroscopy. In other circumstances, a simpler approach may suit the needs of the mea- surement: All pulses above a low-level threshold are registered from the detector, regardless of the value of Q. This approach is often called pulse counting. It can be useful in many applications in which only the intensity of the radiation is of interest, rather than the incident energy distribution of the radiation. At very high event rates, pulse mode operation becomes impractical or even impossi- ble. The time between adjacent events may become too short to carry out an adequate analysis, or the current pulses from successive events may overlap in time. In such cases, one can revert to alternative measurement techniques that 52 CHAPTER 4. DETECTOR GENERALITIES respond to the time average taken over many individual events. This approach leads to the remaining mode of operation. Current mode Figure 4.2 If we assume that the measuring device has a fixed response time T, then the recorded signal from a sequence of events will be a time-dependent current given by Z T 1 I(t) = i(t′ )dt′ (4.2) T t−T Because the response time T is typically long compared with the average time between individual current pulses from the detector, the effect is to average out many of the fluctuations in the intervals between individual radiation in- teractions and to record an average current that depends on the product of the interaction rate and the average charge per interaction. In current mode, this time average of the individual current bursts serves as the basic signal that is recorded. The average current is given by the product of the event rate and the average charge produced per event. E I0 = rQ = r q (4.3) W Where r is the event rate, Q is the charge produced for each event, E is the average charge deposited per each event and W average energy required to produce a unit charge pair. Pulse mode Current mode operation is used with many detectors when event rates are very high. Detectors that are applied to radiation dosimetry are also normally op- erated in current mode. Most applications, however, are better served by pre- serving information on the amplitude and timing of individual events that only pulse mode can provide. The nature of the signal pulse produced from a single event depends on the input characteristics of the circuit to which the detector is connected. The equivalent circuit can often be represented as a RC parallel. In most cases, the time-dependent voltage V(t) across the load resistance is the fundamental signal voltage on which pulse mode operation is based. Two separate extremes of operation can be identified that depend on the relative  4.2. GENERAL PROPERTIES 53 value of the time constant of the measuring circuit. From simple circuit analysis, this time constant is given by the product of R and C, or τ = RC. 1. τ ≪ tc : In this extreme the time constant of the external circuit is kept small com- pared with the charge collection time, so that the current flowing through the load resistance R is essentially equal to the instantaneous value of the current flowing in the detector. Radiation detectors are sometimes oper- ated under these conditions when high event rates or timing information is more important than accurate energy information. 2. τ ≫ tc : It is generally more common to operate detectors in the opposite extreme in which the time constant of the external circuit is much larger than the detector charge collection time. In this case, very little current will flow in the load resistance during the charge collection time and the detector current is momentarily integrated on the capacitance. If we assume that the time between pulses is sufficiently large, the capacitance will then discharge through the resistance, returning the voltage across the load resistance to zero. The time required for the signal pulse to reach its maximum value is determined by the charge collection time within the detector itself. No properties of the external or load circuit influence the rise time of the pulses. On the other hand, the decay time of the pulses, or the time required to restore the signal voltage to zero, is determined only by the time constant of the load circuit. The amplitude of a signal pulse Vmax is determined simply by the ratio of the total charge Q created within the detector during one radiation interaction divided by the capacitance C of the equivalent load circuit. Because this capacitance is normally fixed, the amplitude of the signal pulse is directly proportional to the corresponding charge generated within the detector and is given by the simple expression Q Vmax = (4.4) C Thus, the output of a detector operated in pulse mode normally consists of a sequence of individual signal pulses, each representing the results of the interaction of a single quantum of radiation within the detector. Furthermore, the amplitude of each individual pulse reflects the amount of charge generated due to each individual interaction. A very common analytical method is to record the distribution of these amplitudes from which some information can often be inferred about the incident radiation. Pulse mode operation is the more common choice for most radiation detector applications because of several inherent advantages over current mode. First, the sensitivity that is achievable is often many factors greater than when using current mode because each individual quantum of radiation can be detected as a distinct pulse. In current mode, the minimum detectable current may represent an average interaction rate in the detector that is many times greater. The second and more important advantage is that each pulse amplitude carries some information that is often a useful or even necessary part of a particular application. 54 CHAPTER 4. DETECTOR GENERALITIES 4.2.3 Pulse height spectra When operating a radiation detector in pulse mode, each individual pulse am- plitude carries important information regarding the charge generated by that particular radiation interaction in the detector. If we examine a large number of such pulses, their amplitudes will not all be the same. Variations may be due either to differences in the radiation energy or to fluctuations in the inher- ent response of the detector to mono-energetic radiation. The pulse amplitude distribution is a fundamental property of the detector output that is used to deduce information about the incident radiation or the operation of the detector itself. The most common way of displaying pulse amplitude information is through the differential pulse height distribution. Figure 4.3 (a) gives a hypothetical distribution for purposes of example. (a) The abscissa is a linear pulse am- (b) integral distribution for the same plitude scale that runs from zero to pulse source. The abscissa is the same a value larger than the amplitude of pulse height scale shown for the differ- any pulse observed from the source. ential distribution The horizontal scale then has units of pulse amplitude [V ], whereas the ver- tical scale has units of inverse ampli- tude [V −1 ]. Figure 4.3 The number of pulses whose amplitude lies between two specific values, H1 and H2, can be obtained by integrating the area under the distribution between those two limits, as shown by the cross hatched area in Fig. 4.2a: Z H2 dN dH (4.5) H1 dH Referring to Figure 4.3 (a) ,the maximum pulse height observed (H5 ) is simply the point along the abscissa at which the distribution goes to zero. Peaks in the distribution (H4 ), indicate pulse amplitudes about which a large number of pulses may be found. On the other hand, valleys or low points in the spectrum (H3 ), indicate values of the pulse amplitude around which relatively few pulses occur. The physical interpretation of differential pulse height spectra always involves areas under the spectrum between two given limits of pulse height. A less common way of displaying the same information about the distribution of pulse amplitudes is through the integral pulse height distribution (Figure 4.3 (b)). The ordinate N must always be a monotonically decreasing function of H. Because all pulses have some finite amplitude, the value of the integral spectrum 4.2. GENERAL PROPERTIES 55 at H = 0 must be the total number of pulses observed. The value of the integral distribution must decrease to zero at the maximum observed pulse height (H5 ). The differential and integral distributions convey exactly the same information and one can be derived from the other. 4.2.4 Counting curves and plateaus When radiation detectors are operated in pulse counting mode, the pulses from the detector are fed to a counting device with a fixed discrimination level. Signal pulses must exceed a given level Hd in order to be registered by the counting circuit. Sometimes it is possible to vary the level Hd during the course of the measurement to provide information about the amplitude distribution of the pulses. Assuming that Hd can be varied between 0 and H5 in Figure 4.3, a series of measurements can be carried out in which the number of pulses N per unit time is measured as Hd is changed. In setting up a pulse counting measurement, it is often desirable to establish an operating point that will provide maximum stability over long periods of time. For example, small drifts in the value of Hd could be expected in any real application, and one would like to establish conditions under which these drifts would have minimal influence on the measured counts. One such stable operating point can be achieved at a discrimination point set at the level H3 in Figure 4.3. Because the slope of the integral distribution is a minimum at that point, small changes in the discrimination level will have minimum impact on the total number of pulses recorded. In general, regions of minimum slope on the integral distribution are called counting plateaus and represent areas of operation in which minimum sensitivity to drifts in discrimination level are achieved. An experiment can be carried out in which the number of pulses recorded is measured as a function of the gain1 applied, sometimes called the counting curve. In the example shown in Figure 4.4, the minimum slope in the counting curve should correspond to a gain of about 3, in which case the discrimination point is near the minimum of the valley in the differential pulse height distribution. In some types of radiation detectors, such as Geiger-Mueller tubes or scin- tillation counters, the gain can conveniently be varied by changing the applied voltage to the detector. Although the gain may not change linearly with volt- age, the qualitative features of the counting curve can be traced by a simple measurement of the detector counting rate as a function of voltage. In order to select an operating point of maximum stability, plateaus are again sought in the counting curve that results, and the voltage is often selected to lie at a point of minimum slope on this counting curve. 4.2.5 Energy resolution In many applications of radiation detectors, the object is to measure the energy distribution of the incident radiation. These efforts are classified under the 1 Can be defined as the ratio of the voltage amplitude for a given event in the detector to the same amplitude before some parameter (such as amplification or detector voltage) was changed. The highest voltage gain will result in the largest maximum pulse height, but in all cases the area under the differential distribution will be a constant. 56 CHAPTER 4. DETECTOR GENERALITIES Figure 4.4: Example of counting curve generated by varying gain under constant source conditions. The three plots at the top give the corresponding differential pulse height spectra. general term radiation spectroscopy. At this point we discuss some general properties of detectors when applied to radiation spectroscopy. One important property of a detector in radiation spectroscopy can be exam- ined by noting its response to a monoenergetic source of that radiation. Figure 4.5 illustrates the differential pulse height distribution that might be produced by a detector under these conditions. This distribution is called the response function of the detector for the energy used in the determination. Provided the same number of pulses are recorded in both cases, the areas under each peak are equal. Although both distributions are centered at the same average value H0 , the width of the distribution in the poor resolution case is much greater. This width reflects the fact that a large amount of fluctuation was recorded from pulse to pulse even though the same energy was deposited in the detector for each event. If the amount of these fluctuations is made smaller, the width of the corresponding distribution will also become smaller and the peak will approach a sharp spike or a mathematical delta function. A formal definition of detector energy resolution is shown in Figure 4.6. The FWHM assumes that any background or continuum on which the peak may be superimposed is negligible or has been subtracted away. The energy resolution of the detector is conventionally defined as the FWHM divided by the location of the peak centroid H0. The energy resolution R is thus a dimensionless fraction conventionally expressed as a percentage. It should be clear that the smaller the figure for the energy resolution, the better the detector will be able to distinguish between two radiations whose energies lie near each other. An approximate rule 4.2. GENERAL PROPERTIES 57 Figure 4.5: Examples of response functions for detectors with relatively good resolu- tion and relatively poor resolution. Figure 4.6: Definition of detector resolution. For peaks whose shape is Gaussian with standard deviation a of thumb is that one should be able to resolve two energies that are separated by more than one value of the detector FWHM. In a wide category of detector applications, the statistical noise represents the dominant source of fluctuation in the signal and thus sets an important limit on detector performance. The statistical noise arises from the fact that the charge Q generated within the detector by a quantum of radiation is not a continuous variable but instead represents a discrete number of charge carriers. For example, in an ion chamber the charge carriers are the ion pairs produced by the passage of the charged particle through the chamber, whereas in a scintil- lation counter they are the number of electrons collected from the photocathode of the photomultiplier tube. In all cases the number of carriers is discrete and subject to random fluctuation from event to event even though exactly the same amount of energy is deposited in the detector. An estimate can be made of the amount of inherent fluctuation by assuming that the formation of each charge carrier is a Poisson process. Under this assumption, if a total number N of charge √carriers is generated on the average, one would expect a standard devia- tion of N. If this were the only source of fluctuation in the signal, the response 58 CHAPTER 4. DETECTOR GENERALITIES function, should have a Gaussian shape, because N is typically a large number. The response of many detectors is approximately linear, so that the average pulse amplitude H0 = KN , where K is a proportionality constant. The stan-√ dard deviation σ of the peak √ in the pulse height spectrum is then σ = K N and its FWHM is 2.35K N. We then would calculate a limiting resolution R due only to statistical fluctuations in the number of charge carriers as FWHM 2.35 RPoisson limit = = √ (4.6) H0 N The great popularity of semiconductor detectors stems from the fact that a very large number of charge carriers are generated in these devices per unit energy lost by the incident radiation. Careful measurements of the energy reso- lution of some types of radiation detectors have shown that the achievable values for R can be lower by a factor as large as 3 or 4 than the minimum predicted by the statistical arguments given above. These results would indicate that the processes that give rise to the formation of each individual charge carrier are not independent, and therefore the total number of charge carriers cannot be described by simple Poisson statistics. The Fano factor has been introduced in an attempt to quantify the departure of the observed statistical fluctuations in the number of charge carriers from pure Poisson statistics and is defined as observed variance in N F = (4.7) Poisson predicted variance and it is found r F Rstatistical limit = 2.35 (4.8) N Although the Fano factor is substantially less than unity for semiconductor diode detectors and proportional counters, other types such as many scintillation detectors appear to show a limiting resolution consistent with Poisson statistics and the Fano factor would, in these cases, be unity. 4.2.6 Detection efficiency All radiation detectors will, in principle, give rise to an output pulse for each quantum of radiation that interacts within its active volume. For primary charged radiation such as alpha or beta particles, interaction in the form of ionization or excitation will take place immediately upon entry of the particle into the active volume. After traveling a small fraction of its range, a typical particle will form enough ion pairs along its path to ensure that the resulting pulse is large enough to be recorded. Thus, it is often easy to arrange a situ- ation in which a detector will see every alpha or beta particle that enters its active volume. Under these conditions, the detector is said to have a counting efficiency of 100%. On the other hand, uncharged radiations such as gamma rays or neutrons must first undergo a significant interaction in the detector before detection is possible. Because these radiations can travel large distances between interac- tions, detectors are often less than 100% efficient. It then becomes necessary to have a precise figure for the detector efficiency in order to relate the number of 4.2. GENERAL PROPERTIES 59 pulses counted to the number of neutrons or photons incident on the detector. It is convenient to subdivide counting efficiencies into two classes: absolute and intrinsic. Absolute efficiencies are defined as number of pulses recorded ϵabs = (4.9) number of radiation quanta emitted by source and are dependent not only on detector properties but also on the details of the counting geometry (primarily the distance from the source to the detector). The intrinsic efficiency is defined as number of pulses recorded ϵint = (4.10) number of radiation quanta incident on the detector and no longer includes the solid angle subtended by the detector as an im- plicit factor. The two efficiencies are simply related for isotropic sources by ϵint = ϵabs (4π/Ω), where Ω is the solid angle of the detector seen from the actual source position and (4π/Ω) can be termed as geometric efficiency, so: Absolute efficiency = Geometric efficiency · Intrinsic efficiency It is much more convenient to tabulate values of intrinsic rather than absolute efficiencies because the geometric dependence is much milder for the former. The intrinsic efficiency of a detector usually depends primarily on the detector material, the radiation energy, and the physical thickness of the detector in the direction of the incident radiation. A slight dependence on distance between the source and the detector does remain, however, because the average path length of the radiation through the detector will change somewhat with this spacing. For a parallel beam of mono-energetic photons incident on a detector of uniform thickness: ϵint = 1 − e−µx (4.11) Counting efficiencies are also categorized by the nature of the event recorded. If we accept all pulses from the detector, then it is appropriate to use total efficiencies. In this case all interactions, no matter how low in energy, are assumed to be counted. 4.2.7 Dead time In nearly all detector systems, there will be a minimum amount of time that must separate two events in order that they be recorded as two separate pulses. In some cases the limiting time may be set by processes in the detector itself, and in other cases the limit may arise in the associated electronics. This minimum time separation is usually called the dead time of the counting system. Because of the random nature of radioactive decay, there is always some probability that a true event will be lost because it occurs too quickly following a preceding event. These ”dead time losses” can become rather severe when high counting rates are encountered, and any accurate counting measurements made under these conditions must include some correction for these losses. 60 CHAPTER 4. DETECTOR GENERALITIES Models for dead time behavior Two models of dead time behavior of counting systems have come into common usage: paralyzable and nonparalyzable response. These models represent idealized behavior, one or the other of which often adequately resembles the response of a real counting system. Figure 4.7: Illustration of two assumed models of dead time behavior for radiation detectors. At the bottom of the figure is the corresponding dead time behavior of a detector assumed to be nonparalyzable. A fixed time T is assumed to follow each true event that occurs during the ”live period” of the detector. True events that occur during the dead period are lost and assumed to have no effect whatsoever on the behavior of the detector. In the example shown, the nonparalyzable detector would record four counts from the six true interactions. The same dead time T is assumed to follow each true interaction that occurs during the live period of the paralyzable detector. True events that occur during the dead period, however, although still not recorded as counts, are assumed to extend the dead time by another period T following the lost event. In the example shown, only three counts are recorded for the six true events. Figure 4.8: Behavior of a paralyzable and nonparalyzable systems as a function of the recorded pulses (m) and the effective pulses (n). Chapter 5 Gas filled detectors 5.1 General properties of gas filled detectors Gas-filled detectors were among the first devices used for radiation de- tection. They may be used to de- tect either thermal neutrons via nu- clear reactions or fast neutrons via re- coil interactions. After the initial in- teraction with the neutron has taken place, the remaining detection equip- ment is similar, although there may be changes in high-voltage or ampli- fier gain setting to compensate for changes in the magnitude of the de- tected signal. The exterior appear- ance of a gas detector is that of a metal cylinder with an electrical con- nector at one end. Detector walls are about 0.5 mm thick and are manu- factured from either stainless steel or Figure 5.1: Schematic representation of aluminum. Aluminum tubes are usu- a gas filled detector. An electric field de- ally preferred because of their higher termines the charge collection on the elec- detection efficiency. trodes, then, when a pulse is collected, a The detection of neutrons requires drop occurs across the resistor. Alterna- the transfer of some or all of the tively, a current flows through R indicating the average interaction rate. neutrons’ energy to charged particles. The charged particle will then ionize and excite the atoms along its path until its energy is exhausted. In a gas filled detector, approximately 30 eV is required to create an ion pair. The maximum number of ion pairs produced is then E/30 eV , where E is the kinetic energy of the charged particle(s) in eV.For example, an energy transfer of 765 keV will release a total positive and negative charge of about 8 × 10−15. If little or no voltage is applied to the tube, most of the ions will recombine and no electrical output signal is produced. If a positive voltage is applied to 61 62 CHAPTER 5. GAS FILLED DETECTORS the anode, the electrons will move toward it and the positively charged ions will move toward the cathode. An electrical output signal will be produced whose magnitude depends on the applied voltage, the geometry of the counter, and the fill gas. These parameters determine whether the detector operates in the ionization region, the proportional region, or the Geiger-Mueller region. Figure 5.2: Operation modalities of gas counter. The collected charge is shown for α and β particles. In the ionization region enough voltage has been applied to collect nearly all the electrons before they can recombine. At this point a plateau is reached and further small increases in voltage yield no more electrons. Detectors operate in this region are called ion chambers. The charge collected is proportional to the energy deposited in the gas and independent of the applied voltage. The region beyond the ionization region is called the proportional region. Here the electric field strength is large enough so that the primary electrons can gain sufficient energy to ionize the gas molecules and create secondary ionization. If the field strength is increased further, the secondary electrons can also ionize gas molecule. This process continues rapidly as the field strength increases, thus producing a large multiplication of the number of ions formed during the primary event. The cumulative amplification process is known as avalanche 5.1. GENERAL PROPERTIES OF GAS FILLED DETECTORS 63 ionization1. When a total of A ion pairs result from a single primary pair, the process has a gas amplification factor of A. It will be unity in an ionization chamber where no secondary ions are formed and as high as 103 to 105 in a well designed proportional counter. Note that in the proportional region the charge collected is also linearly proportional to the energy deposited in the gas. For the amplification process to proceed, an electron must acquire sufficient energy, in one or more mean free paths, to ionize a neutral molecule. The mean free path in proportional counter gas is equals approximately to 1-2 pm. For amplifications of 106 , fewer than 20 mean free paths are necessary, which indi- cates that only a small region around the wire is involved in the multiplication process. In the rest of the volume, the electrons drift toward the anode. Because the amplification process requires a very high electric field, an advantage of the cylindrical detector design is the high electric field near the inner wire. The total amplification will be proportional to the electric field traversed, not the distance traversed. As the applied voltage is increased further, the proportionality between the primary charge deposited and the output signal is gradually lost. This loss is primarily due to saturation effects at the anode wire. As the primary ions reach the high field regions near the anode wire, the avalanche process begins and quickly grows to a maximum value as secondary electrons create additional avalanches axially along the wire. Unlike operation in the proportional region where the avalanche is localized, the avalanche now extends the full length of the anode wire and the multiplication process terminates only when the electro- static field is sufficiently distorted to prevent further acceleration of secondary electrons. For weakly ionizing primary events, amplification factors of up to 1010 are possible. Detectors operated in this region are called Geiger-Mueller counters. They require very simple electronics and form the basis for rugged field inspection instruments. Because they are saturated by each event, Geiger counters cannot be used in high-count-rate applications, but this limitation does not interfere with their use as low-level survey meters. Neutron counters operated in either the ionization or proportional mode can provide an average output current or individual pulses, depending on the associated electronics. Measuring only the average output current is useful for radiation dosimetry and reactor power monitors. For assay of nuclear material it is customary to operate neutron counters in the pulse mode so that individual neutron events can be registered. Number of ion pairs formed At a minimum, the particle must transfer an amount of energy equal to the ionization energy of the gas molecule to permit the ionization process to occur. In most gases of interest for radiation detectors, the ionization energy for the least tightly bound electron shells is between 10 and 25 eV. However, there are other mechanisms by which the incident particle may lose energy within the gas that do not create ions. Examples are excitation processes in which an electron may be elevated to a higher bound state in the molecule without being 1 An electron avalanche is a process in which a number of free electrons in a transmission medium are subjected to strong acceleration by an electric field and subsequently collide with other atoms of the medium, thereby ionizing them (impact ionization). This releases additional electrons which accelerate and collide with further atoms, releasing more electrons. 64 CHAPTER 5. GAS FILLED DETECTORS Figure 5.3: Mean energy W to produce an ion pair in N2 completely removed. Therefore, the average energy lost by the incident particle per ion pair formed (defined as the W-value) is always substantially greater than the ionization energy. The W-value is in principle a function of the species of gas involved, the type of radiation and its energy. Empirical observations, however, show that, at sufficien