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Radiation Detection and Counting Statistics

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  1. Radiation Detection and Counting Statistics Please Read: Chapters 3 (all 3 parts), 8, and 26 in Doyle

  2. 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!

  3. 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)

  4. 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

  5. Ideal Properties for Detection of Radioactivity

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. Examples of Proportional Counters

  13. 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!

  14. 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.

  15. 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

  16. 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)

  17. Organic Scintillators Come in Many Forms

  18. 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)

  19. Inorganic Scintillators

  20. 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

  21. NaI Scintillator Ge Detector

  22. Ideal Detector for Detection of Radiation Excellent table on Page 61 shows numerous different technologies used in safeguards

  23. Counting Statistics

  24. 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

  25. 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”

  26. Example of the Binomial Distribution “Winners”: 3,4,5, or 6 P = 4/6 or 2/3 10 rolls of the die: n=10

  27. Results of the Binomial Distribution p = 2/3 n =10

  28. Some Properties of the Binomial Distribution It is normalized: Mean (average) value

  29. Standard Deviation “Predicted variance” “Standard Deviation” s is a “typical” value for

  30. For the Binomial Distribution: where n = number of trials and p = success probability Predicted Variance: Standard Deviation:

  31. For our Previous Example p = 2/3 n = 10

  32. The Poisson Distribution Provided p << 1

  33. For the Poisson Distribution Predicted Mean: Predicted Variance: Standard Deviation:

  34. 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?

  35. Discrete Poisson Distribution

  36. Gaussian (Normal) Distribution p << 1 Binomial Poisson Poisson Gaussian

  37. Example of Gaussian Statistics What is the predicted distribution in the number of people with birthdays today out of a group of 10,000?

  38. Distribution Gaussian Distribution

  39. The Universal Gaussian Curve

  40. Summary of Statistical Models For the Poisson and Gaussian Distributions: Predicted Variance: Standard Deviation:

  41. CAUTION!! Does not apply directly to: • Counting Rates • Sums or Differences of counts • Averages of independent counts • Any Derived Quantity

  42. 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, …)

  43. Sums or Differences of Counts u = x + y or u = x - y Recall:

  44. Example of Difference of Counts total = x = 2612 background = y = 1295 net = u = 1317 Therefore, net counts = 1317 ± 62.5

  45. Multiplication or Division by a Constant

  46. 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

  47. Multiplication or Division of Counts

  48. 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

  49. Average Value of Independent Counts Sum: S = x1 + x2 + x3 + … + xN Average: Single measurement: “Improvement Factor”: