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Radiation Detection and Counting Statistics

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## Radiation Detection and Counting Statistics

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**Radiation Detection and Counting Statistics**Please Read: Chapters 3 (all 3 parts), 8, and 26 in Doyle**Types of Radiation**• Charged Particle Radiation • Electrons • b particles • Heavy Charged Particles • a particles • Fission Products • Particle Accelerators • Uncharged Radiation • Electromagnetic Radiation • g-rays • x-rays • Neutrons • Fission, Fusion reactions • Photoneutrons Can be easily stopped/shielded! More difficult to shield against!**Penetration Distances for Different Forms of Radiation**a’s b’s g’s n’s Paper Plastic (few cm) Lead (few in) Concrete (few feet)**Why is Radiation Detection Difficult?**• Can’t see it • Can’t smell it • Can’t hear it • Can’t feel it • Can’t taste it • We take advantage of the fact that radiation produces ionized pairs to try to create an electrical signal**How a Radiation Detector Works**• The radiation we are interested in detecting all interact with materials by ionizing atoms • While it is difficult (sometime impossible) to directly detect radiation, it is relatively easy to detect (measure) the ionization of atoms in the detector material. • Measure the amount of charge created in a detector • electron-ion pairs, electron-hole pairs • Use ionization products to cause a secondary reaction • use free, energized electrons to produce light photons • Scintillators • We can measure or detect these interactions in many different ways to get a multitude of information**General Detector Properties**• Characteristics of an “ideal” radiation detector • High probability that radiation will interact with the detector material • Large amount of charge created in the interaction process • average energy required for creation of ionization pair (W) • Charge must be separated an collected by electrodes • Opposite charges attract, “recombination” must be avoided • Initial Generated charge in detector (Q) is very small (e.g., 10-13C) • Signal in detector must be amplified • Internal Amplification (multiplication in detector) • External Amplification (electronics) • Want to maximize V**Types of Radiation Detectors**• Gas Detectors • Ionization Chambers • Proportional Counters • Geiger-Mueller Tubes (Geiger Counters) • Scintillation Detectors • Inorganic Scintillators • Organic Scintillators • Semiconductor Detectors • Silicon • High Purity Germanium**Gas Detectors**• Most common form of radiation detector • Relatively simple construction • Suspended wire or electrode plates in a container • Can be made in very large volumes (m3) • Mainly used to detect b-particles and neutrons • Ease of use • Mainly used for counting purposes only • High value for W (20-40 eV / ion pair) • Can give you some energy information • Inert fill gases (Ar, Xe, He) • Low efficiency of detection • Can increase pressure to increase efficiency • g-rays are virtually invisible**Ionization Chambers**• Two electric plates surrounded by a metal case • Electric Field (E=V/D) is applied across electrodes • Electric Field is low • only original ion pairs created by radiation are collected • Signal is very small • Can get some energy information • Resolution is poor due to statistics, electronic noise, and microphonics Good for detecting heavy charged particles, betas**Proportional Counters**• Wire suspended in a tube • Can obtain much higher electric field • E 1/r • Near wire, E is high • Electrons are energized to the point that they can ionize other atoms • Detector signal is much larger than ion chamber • Can still measure energy • Same resolution limits as ion chamber • Used to detect alphas, betas, and neutrons**Geiger Counters**• Apply a very large voltage across the detector • Generates a significantly higher electric field than proportional counters • Multiplication near the anode wire occurs • Geiger Discharge • Quench Gas • Generated Signal is independent of the energy deposited in the detector • Primarily Beta detection • Most common form of detector No energy information! Only used to count / measure the amount of radiation. Signal is independent of type of radiation as well!**Examples of Geiger Counters**Geiger counters generally come in compact, hand carried instruments. They can be easily operated with battery power and are usually calibrated to give you radiation dose measurements in rad/hr or rem/hr.**Scintillator Detectors**• Voltage is not applied to these types of detectors • Radiation interactions result in the creation of light photons • Goal is to measure the amount of light created • Light created is proportion to radiation energy • To measure energy, need to convert light to electrical signal • Photomultiplier tube • Photodiode • Two general types • Organic • Inorganic } light electrons**Organic Scintillators**• Light is generated by fluorescence of molecules • Organic - low atomic numbers, relatively low density • Low detection efficiency for gamma-rays • Low light yield (1000 photons/MeV) - poor signal • Light response different for different types of radiation • Light is created quickly • Can be used in situations where speed (ns) is necessary • Can be used in both solid and liquid form • Liquid form for low energy, low activity beta monitoring, neutrino detection • Very large volumes (m3)**Inorganic Scintillators**• Generally, high atomic number and high density materials • NaI, CsI, BiGeO, Lithium glasses, ZnS • Light generated by electron transitions within the crystalline structure of the detector • Cannot be used in liquid form! • High light yield (~60,000 photons / MeV) • light yield in inorganics is slow (ms) • Commonly used for gamma-ray spectroscopy • W ~ 20 eV (resolution 5% for 1 MeV g-ray) • Neutron detection possible with some • Can be made in very large volumes (100s of cm3)**Solid State (Semiconductor) Detectors**• Radiation interactions yield electron-hole pairs • analogous to ion pairs in gas detectors • Very low W-value (1-5 eV) • High resolution gamma-ray spectroscopy • Energy resolution << 1% for 1 MeV gamma-rays • Some types must be cooled using cryogenics • Band structure is such that electrons can be excited at thermal temperatures • Variety of materials • Si, Ge, CdZnTe, HgI2, TlBr • Sizes < 100 cm3 [some even less than 1 cm3] • Efficiency issues for lower Z materials**NaI Scintillator**Ge Detector**Ideal Detector for Detection of Radiation**Excellent table on Page 61 shows numerous different technologies used in safeguards**Three Specific Models:**• Binomial Distribution – generally applicable to all constant-p processes. Cumbersome for large samples • Poisson Distribution – simplification to the Binomial Distribution if the success probability “p” is small. • Gaussian (Normal) Distribution – a further simplification permitted if the expected mean number of successes is large**The Binomial Distribution**n = number of trials p = probability of success for each trial We can then predict the probability of counting exactly “x” successes: P(x) is the predicted “Probability Distribution Function”**Example of the Binomial Distribution**“Winners”: 3,4,5, or 6 P = 4/6 or 2/3 10 rolls of the die: n=10**Results of the Binomial Distribution**p = 2/3 n =10**Some Properties of the Binomial Distribution**It is normalized: Mean (average) value**Standard Deviation**“Predicted variance” “Standard Deviation” s is a “typical” value for**For the Binomial Distribution:**where n = number of trials and p = success probability Predicted Variance: Standard Deviation:**For our Previous Example**p = 2/3 n = 10**The Poisson Distribution**Provided p << 1**For the Poisson Distribution**Predicted Mean: Predicted Variance: Standard Deviation:**Example of the Application of Poisson Statistics**“Is your birthday today?” Example: what is the probability that 4 people out of 1000 have a birthday today?**Gaussian (Normal) Distribution**p << 1 Binomial Poisson Poisson Gaussian**Example of Gaussian Statistics**What is the predicted distribution in the number of people with birthdays today out of a group of 10,000?**Summary of Statistical Models**For the Poisson and Gaussian Distributions: Predicted Variance: Standard Deviation:**CAUTION!!**Does not apply directly to: • Counting Rates • Sums or Differences of counts • Averages of independent counts • Any Derived Quantity**The “Error Propagation Formula”**Given: directly measured counts (or other independent variables) x, y, z, … for which the associated standard deviations are known to be sx, sy, sz, … Derive: the standard deviation of any calculated quantity u(x, y, z, …)**Sums or Differences of Counts**u = x + y or u = x - y Recall:**Example of Difference of Counts**total = x = 2612 background = y = 1295 net = u = 1317 Therefore, net counts = 1317 ± 62.5**Example of Division by a Constant**Calculation of a counting rate x = 11,367 counts t = 300 s rate r = 37.89 ± 0.36 s-1**Example of Division of Counts**Source 1: N1 = 36,102 (no BG) Source 2: N2 = 21,977 (no BG) R = N1/N2 = 36102/21977 = 1.643 R = 1.643 ± 0.014**Average Value of Independent Counts**Sum: S = x1 + x2 + x3 + … + xN Average: Single measurement: “Improvement Factor”: