4.4 Calibration and efficiency of detectors

Calibrating radiation detectors is crucial for accurate measurements. Energy calibration links channel numbers to radiation energies, while efficiency calibration determines how well the detector records events. These processes use standard sources and account for factors like geometry and detector type.

Dead time correction is vital for precise radioactivity measurements. It compensates for periods when the detector can't record events, especially important at high radiation intensities. Geometric and intrinsic efficiencies, along with peak-to-total ratio and self-absorption, also impact detector performance and measurement accuracy.

Calibration Techniques

Energy and Efficiency Calibration

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• Energy calibration establishes the relationship between the channel number and the corresponding energy of the detected radiation
  • Involves using standard radioactive sources with known energies
  • Allows for accurate identification of unknown radionuclides based on their characteristic gamma-ray energies
• Efficiency calibration determines the detector's ability to detect and record radiation events
  • Measures the ratio of the number of counts recorded by the detector to the number of radiation events emitted by the source
  • Depends on factors such as the geometry of the source-detector arrangement, the type of detector, and the energy of the radiation
• Standard sources with well-known activities and emission probabilities are used for both energy and efficiency calibrations
  • Examples of standard sources include $^{137}$Cs, $^{60}$Co, and $^{152}$Eu
  • These sources cover a wide range of energies and allow for the creation of calibration curves

Dead Time Correction

• Dead time is the period after each detected event during which the detector is unable to record another event
  • Occurs due to the finite processing time required by the detector and associated electronics
  • Can lead to an underestimation of the true count rate, especially at high radiation intensities
• Dead time correction is necessary to obtain accurate measurements of radioactivity
  • Involves measuring the dead time of the detector system using techniques such as the two-source method or the pulser method
  • The measured count rates are then corrected using mathematical algorithms that account for the dead time losses
  • Dead time correction is particularly important when measuring high-activity samples or when comparing measurements made with different detectors or at different times

Efficiency Factors

Geometric and Intrinsic Efficiency

• Geometric efficiency is the fraction of radiation emitted by the source that reaches the detector
  • Depends on the solid angle subtended by the detector at the source position
  • Can be improved by placing the source closer to the detector or by using a larger detector
• Intrinsic efficiency is the fraction of radiation that reaches the detector and is actually detected and recorded
  • Depends on the detector material, thickness, and energy of the radiation
  • For example, NaI(Tl) scintillation detectors have high intrinsic efficiency for gamma-rays, while HPGe detectors have lower intrinsic efficiency but better energy resolution
• The total efficiency of a detector system is the product of the geometric efficiency and the intrinsic efficiency
  • Maximizing both factors is essential for achieving high sensitivity and accurate quantification of radioactivity

Peak-to-Total Ratio and Self-Absorption

• Peak-to-total ratio (P/T) is the ratio of the counts in the full-energy peak to the total counts in the spectrum
  • Provides a measure of the detector's ability to resolve the full-energy peak from the background and other interfering peaks
  • A high P/T ratio indicates good energy resolution and is desirable for accurate radionuclide identification and quantification
• Self-absorption occurs when radiation emitted by the sample is absorbed within the sample itself before reaching the detector
  • Particularly significant for low-energy radiation and dense or thick samples
  • Can lead to an underestimation of the true activity if not properly corrected
• Self-absorption correction factors can be determined using mathematical models or by measuring the sample with different geometries or at different energies
  • For example, the transmission method involves measuring the attenuation of a collimated beam of radiation passing through the sample
  • The measured attenuation factors are then used to correct the observed count rates for self-absorption effects