⚛️Intro to Applied Nuclear Physics Unit 7 – Radiation Detection & Measurement

Fundamentals of Radiation

• Radiation is the emission and propagation of energy through space or a medium in the form of waves or particles
• Includes electromagnetic radiation (gamma rays, X-rays, UV, visible light, infrared, microwaves, radio waves) and particle radiation (alpha particles, beta particles, neutrons)
• Characterized by its wavelength, frequency, and energy, which are related by the equation $E = hν = hc/λ$, where $E$ is energy, $h$ is Planck's constant, $ν$ is frequency, $c$ is the speed of light, and $λ$ is wavelength
• Ionizing radiation has sufficient energy to ionize atoms or molecules, while non-ionizing radiation does not
  • Ionizing radiation examples include X-rays, gamma rays, and high-energy particles (alpha, beta, neutrons)
  • Non-ionizing radiation examples include visible light, infrared, microwaves, and radio waves
• Radioactive decay is the spontaneous emission of radiation from an unstable atomic nucleus, resulting in the transformation of the nucleus into a more stable state
• Half-life is the time required for half of a given quantity of a radioactive substance to decay, and it is a characteristic property of each radioactive isotope
• Activity is the rate of radioactive decay, measured in becquerels (Bq) or curies (Ci), where 1 Bq = 1 decay per second and 1 Ci = 3.7 × 10^10 Bq

Types of Radiation and Their Properties

• Alpha radiation consists of helium nuclei (two protons and two neutrons) emitted from the nucleus of an atom during radioactive decay
  • Highly ionizing but has a short range in air (a few centimeters) and can be stopped by a sheet of paper or skin
  • Poses a significant health risk if inhaled or ingested due to its high linear energy transfer (LET)
• Beta radiation involves the emission of electrons (β⁻) or positrons (β⁺) from the nucleus during radioactive decay
  • Moderately ionizing with a longer range in air compared to alpha particles (several meters) and can be stopped by a few millimeters of aluminum or plastic
  • Can penetrate skin and cause damage to shallow tissues
• Gamma radiation is high-energy electromagnetic radiation emitted from the nucleus during radioactive decay or nuclear reactions
  • Highly penetrating and can travel long distances in air, requiring dense materials like lead or concrete for effective shielding
  • Interacts with matter through photoelectric absorption, Compton scattering, and pair production, depending on the photon energy
• X-rays are similar to gamma rays but originate from electron transitions in the atom's inner shells or from the deceleration of charged particles (bremsstrahlung)
  • Used extensively in medical imaging (radiography, CT scans) and industrial applications (non-destructive testing)
• Neutron radiation consists of free neutrons emitted during nuclear fission, fusion, or certain radioactive decays
  • Highly penetrating and can cause significant biological damage through indirect ionization (via secondary charged particles produced by neutron interactions)
  • Classified as fast (>0.1 MeV), epithermal (1 eV - 0.1 MeV), or thermal (<1 eV) neutrons based on their kinetic energy

Radiation Interaction with Matter

• Photoelectric absorption occurs when a photon transfers all its energy to an atomic electron, ejecting it from the atom
  • Dominant interaction for low-energy photons (typically below 100 keV) and high-Z materials
  • Results in the complete absorption of the photon and the emission of a photoelectron with energy equal to the photon energy minus the electron's binding energy
• Compton scattering is the inelastic scattering of a photon by a loosely bound atomic electron
  • Prevalent for intermediate photon energies (100 keV - 10 MeV) and low-Z materials
  • The photon transfers a portion of its energy to the electron, resulting in a scattered photon with lower energy and a recoil electron
• Pair production is the creation of an electron-positron pair from a photon in the presence of a nucleus or electron
  • Occurs for photon energies exceeding twice the electron rest mass energy (1.022 MeV)
  • The photon disappears, and its energy is converted into the mass and kinetic energy of the electron-positron pair
• Charged particles (electrons, protons, alpha particles) primarily interact with matter through Coulomb interactions with atomic electrons, leading to ionization and excitation
  • The stopping power $(-dE/dx)$ describes the average rate of energy loss per unit path length and depends on the particle's charge, velocity, and the material's properties (density, atomic number)
• Neutrons interact with matter through elastic scattering, inelastic scattering, and nuclear reactions (capture, fission)
  • Elastic scattering is the primary interaction mechanism for fast neutrons, resulting in the transfer of kinetic energy to the recoil nucleus
  • Thermal neutrons are more likely to undergo capture reactions, such as $(n,\gamma)$, $(n,p)$, or $(n,\alpha)$, depending on the target nucleus

Radiation Detectors: Principles and Types

• Gas-filled detectors (ionization chambers, proportional counters, Geiger-Müller tubes) rely on the ionization of gas molecules by incident radiation
  • Ionization chambers collect the primary ionization charge, providing a signal proportional to the energy deposited in the gas
  • Proportional counters amplify the primary ionization through gas multiplication, enabling energy discrimination and higher sensitivity
  • Geiger-Müller tubes operate at high voltages, resulting in a strong avalanche effect and a large output pulse for each detected event
• Scintillation detectors use materials that emit light when exposed to ionizing radiation (organic crystals, plastics, inorganic crystals like NaI(Tl), CsI(Tl))
  • The light is collected by a photomultiplier tube (PMT) or photodiode, converting it into an electrical signal proportional to the energy deposited in the scintillator
  • Commonly used for gamma-ray spectroscopy and fast neutron detection (with pulse shape discrimination)
• Semiconductor detectors (silicon, germanium) are solid-state devices that rely on the creation of electron-hole pairs in the semiconductor material by incident radiation
  • The charge carriers are collected by an applied electric field, generating a signal proportional to the energy deposited
  • Offer excellent energy resolution and efficiency, making them suitable for high-resolution gamma-ray spectroscopy (HPGe detectors)
• Neutron detectors often rely on nuclear reactions that produce charged particles, which can then be detected by conventional means
  • Helium-3 proportional counters detect thermal neutrons through the $^3\text{He}(n,p)^3\text{H}$ reaction
  • Boron-lined or BF₃ proportional counters detect thermal neutrons via the $^{10}\text{B}(n,\alpha)^7\text{Li}$ reaction
  • Fission chambers use a thin layer of fissile material (e.g., $^{235}\text{U}$) to detect neutrons through induced fission events
• Thermoluminescent dosimeters (TLDs) and optically stimulated luminescence (OSL) dosimeters measure accumulated radiation dose in materials that trap charge carriers when exposed to ionizing radiation
  • The trapped charge is released through heating (TLDs) or optical stimulation (OSL), producing a luminescence signal proportional to the absorbed dose

Counting Statistics and Error Analysis

• Radioactive decay is a random process governed by Poisson statistics, where the standard deviation $\sigma$ of a count $N$ is given by $\sigma = \sqrt{N}$
• The relative uncertainty (or relative standard deviation) of a count is $\sigma/N = 1/\sqrt{N}$, which decreases with increasing count number
• Background radiation contributes to the total count and must be subtracted from the gross count to obtain the net count of the sample
  • The uncertainty in the net count is the quadrature sum of the uncertainties in the gross and background counts: $\sigma_\text{net} = \sqrt{\sigma_\text{gross}^2 + \sigma_\text{background}^2}$
• Counting time affects the precision of the measurement, with longer counting times resulting in better statistics and lower relative uncertainties
• Dead time is the time interval after each detected event during which the detector is insensitive to further events, leading to count losses at high count rates
  • The true count rate $n$ can be estimated from the measured count rate $m$ and the dead time $\tau$ using the formula: $n = m/(1 - m\tau)$
• Systematic errors, such as detector efficiency, geometry, and sample self-absorption, also contribute to the overall uncertainty and must be accounted for in the analysis
• Error propagation techniques are used to combine uncertainties from multiple sources and determine the uncertainty in the final result
  • For uncorrelated variables, the general formula for error propagation is: $\sigma_f^2 = \sum_i (\partial f/\partial x_i)^2 \sigma_i^2$, where $f$ is a function of variables $x_i$ with uncertainties $\sigma_i$

Spectroscopy and Energy Measurements

• Gamma-ray spectroscopy involves measuring the energy distribution of gamma photons emitted by a radioactive source or induced by nuclear reactions
  • High-resolution semiconductor detectors (HPGe) are commonly used for gamma-ray spectroscopy due to their excellent energy resolution
  • The resulting spectrum consists of characteristic peaks corresponding to the discrete energies of the gamma photons, as well as a continuous background due to Compton scattering and other interactions
• Energy calibration is the process of establishing a relationship between the detector's channel number and the corresponding energy, typically using known reference sources
  • Common calibration sources include $^{137}\text{Cs}$ (662 keV), $^{60}\text{Co}$ (1173 and 1332 keV), and $^{241}\text{Am}$ (59.5 keV)
  • A linear fit of the peak positions (channel numbers) versus the known energies is used to determine the calibration coefficients
• Energy resolution is a measure of a detector's ability to distinguish between gamma rays of similar energies, quantified by the full width at half maximum (FWHM) of a peak
  • The energy resolution depends on the detector material, size, and operating conditions, as well as the electronic noise and statistical fluctuations in the charge collection process
• Efficiency calibration determines the detector's intrinsic efficiency (the fraction of incident photons that are detected) as a function of energy
  • Absolute efficiency is measured using calibrated reference sources with known activities, while relative efficiency can be determined using sources with known relative intensities
• Coincidence and anti-coincidence techniques are used to reduce background and improve the signal-to-noise ratio in gamma-ray spectroscopy
  • Coincidence measurements require the simultaneous detection of two or more photons (e.g., cascading gamma rays) within a specified time window
  • Anti-coincidence techniques reject events that are detected simultaneously in the primary detector and a surrounding guard detector, effectively suppressing background from cosmic rays and other sources

Radiation Dosimetry

• Absorbed dose is the energy deposited by ionizing radiation per unit mass of the absorbing material, measured in grays (Gy), where 1 Gy = 1 J/kg
  • The absorbed dose depends on the type and energy of the radiation, as well as the properties of the absorbing material
  • Can be measured using dosimeters such as ionization chambers, thermoluminescent dosimeters (TLDs), optically stimulated luminescence (OSL) dosimeters, and radiochromic films
• Equivalent dose is a measure of the biological effects of ionizing radiation, taking into account the varying effectiveness of different types of radiation in causing damage
  • Measured in sieverts (Sv), where 1 Sv = 1 J/kg multiplied by a radiation weighting factor $w_R$ that depends on the type and energy of the radiation
  • For photons and electrons, $w_R = 1$, while for alpha particles and heavy ions, $w_R = 20$
• Effective dose is a whole-body dose quantity that accounts for the varying sensitivity of different organs and tissues to radiation-induced health effects
  • Calculated as the sum of the equivalent doses to individual organs multiplied by their respective tissue weighting factors $w_T$, which represent the relative contribution of each organ to the total health risk
• Linear energy transfer (LET) is a measure of the density of ionization along the track of a charged particle, expressed in keV/μm
  • High-LET radiation (alpha particles, heavy ions) causes more localized damage and is generally more biologically effective than low-LET radiation (photons, electrons) for the same absorbed dose
• Dose rate is the absorbed dose delivered per unit time, typically expressed in Gy/h or Sv/h
  • The biological effects of radiation exposure depend not only on the total dose but also on the dose rate, with lower dose rates generally associated with lower risks due to cellular repair mechanisms
• Radiation protection principles aim to minimize the harmful effects of ionizing radiation on individuals and populations
  • The ALARA principle (As Low As Reasonably Achievable) emphasizes the importance of keeping radiation doses as low as practicable, considering social and economic factors
  • Dose limits are set by regulatory authorities to ensure that radiation exposures are kept below levels that could lead to unacceptable risks

Practical Applications and Safety Measures

• Radiation detection and measurement techniques are essential in various fields, including nuclear power, medical imaging and therapy, industrial non-destructive testing, and environmental monitoring
• In nuclear power plants, radiation detectors are used to monitor the reactor core, coolant systems, and environmental releases to ensure safe operation and compliance with regulations
  • Area monitors and personal dosimeters are employed to protect workers from excessive radiation exposure
  • Effluent monitoring systems continuously measure the radioactivity in gaseous and liquid discharges to the environment
• Medical applications of radiation include diagnostic imaging (X-rays, CT scans, nuclear medicine) and radiation therapy for cancer treatment
  • Strict protocols and quality assurance measures are in place to optimize image quality, minimize patient dose, and prevent accidental exposures
  • Radiopharmaceuticals are used in nuclear medicine for functional imaging and targeted therapy, requiring careful handling and patient management
• Industrial radiography uses high-energy X-rays or gamma rays to inspect materials and components for defects without damaging them
  • Proper shielding, collimation, and access control are essential to protect workers and the public from inadvertent exposures
• Environmental radiation monitoring involves the measurement of natural and anthropogenic radioactivity in air, water, soil, and biota
  • Helps assess the impact of nuclear facilities, fallout from nuclear accidents or weapons tests, and the distribution of naturally occurring radioactive materials (NORM)
  • Provides data for risk assessment, regulatory compliance, and public information
• Radiation safety programs are designed to protect workers, the public, and the environment from the harmful effects of ionizing radiation
  • Key elements include hazard identification, risk assessment, dose monitoring, engineering controls (shielding, ventilation), administrative controls (procedures, training), and personal protective equipment (PPE)
  • Regular audits and reviews ensure the effectiveness of the radiation safety program and identify areas for improvement
• Emergency preparedness and response plans are crucial for managing radiological incidents, such as accidents at nuclear facilities or the malicious use of radioactive materials
  • Involve the coordination of multiple agencies, including first responders, medical professionals, and radiation protection experts
  • Include provisions for sheltering, evacuation, decontamination, and medical treatment of affected individuals, as well as timely and accurate communication with the public