Attenuation coefficient

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The attenuation coefficient, is a basic quantity used in calculations of the penetration of materials by quantum particles or other energy beams. It is a measure of attenuation.

Contents

[edit] Linear Attenuation Coefficient

The linear attenuation coefficient, also called the narrow beam attenuation coefficient, is a quantity which describes the extent to which the intensity of energy beam is reduced as it passes through a specific material. This might be electromagnetic radiation beam or sound beam.

  • It is used in the context of X-rays or Gamma rays, where it is represented using the symbol μ, and measured in cm-1.
  • It is also used for modeling solar and infrared radiative transfer in the atmosphere, albeit usually denoted with another symbol (given the standard use of μ = cos(θ) for slant paths).
  • In the case of ultrasound attenuation it is usually denoted as α and measured in dB/cm/MHz.[1] [2]

A small linear attenuation coefficient indicates that the material in question is relatively transparent, while a larger values indicate greater degrees of opacity. The linear attenuation coefficient is dependent upon the type of material and the energy of the radiation. Generally, the higher the energy of the incident photons and the less dense the material in question, the lower the corresponding linear attenuation coefficient will be.

The measured intensity I of transmitted through a layer of material with thickness x and density ρ is related to the incident intensity I0 according to the inverse exponential power law that is usually referred to as Beer-Lambert law:

I = I_{0} \, e^{-\alpha \, x},

where x denotes the path length. The Half Value Layer (HVL) signifies the thickness of a material required to reduce the intensity of the emergent radiation to half its incident magnitude. It is from these equations that engineers decide how much protection is needed for "safety" from potentially harmful radiation. The attenuation factor of a material is obtained by the ratio of the emergent and incident radiation intensities I / I0.

The linear attenuation coefficient and mass attenuation coefficient are related such that the mass attenuation coefficient is simply α/ρ, where ρ is the density in g/cm3.

The linear attenuation coefficient is also inversely related to mean free path.

[edit] Mass Attenuation Coefficients

Mass Attenuation Coefficient of Iron with contributing sources of attenuation: Coherent scattering, Incoherent scattering, Photoelectric Absorption, and two types of Pair Production. The discontinuity of Photoelectric Absorption values are due to compton edge. Graph's data came from NIST's XCOM database.
Mass Attenuation Coefficient of Iron with contributing sources of attenuation: Coherent scattering, Incoherent scattering, Photoelectric Absorption, and two types of Pair Production. The discontinuity of Photoelectric Absorption values are due to compton edge. Graph's data came from NIST's XCOM database.
Mass Attenuation Coefficient values shown for all elements with atomic number Z smaller than 100 collected for photons with energies from 1 keV to 20 MeV. The discontinuities in the values are due to compton edges which were also shown.
Mass Attenuation Coefficient values shown for all elements with atomic number Z smaller than 100 collected for photons with energies from 1 keV to 20 MeV. The discontinuities in the values are due to compton edges which were also shown.

If the mass attenuation coefficient α / ρ is used to calculate the attenuation factor I / I0, then the Beer-Lambert's exponential attenuation law must be modified such that the mass thickness \rho\,x of the material is used:

I = I_{0} \, e^{-(\alpha/\rho)\, x \rho},

Tables of photon mass attenuation coefficients are essential in radiological physics, radiography (for medical and security purposes), dosimetry, diffraction, interferometry, crystallography and other branches of physics. The photons can be in form of x-ray, gamma-ray, and bremsstrahlung radiation.

The values of mass attenuation coefficients are dependent upon the absorption and scattering of the incident radiation caused by several different mechanisms such as:

The actual values have been thoroughly examined and are available to the general public through three databases run by National Institute of Standards and Technology (NIST):

  1. XAAMDI database[3]
  2. XCOM database[4]
  3. FFAST database[5]

[edit] See also

[edit] References

  1. ^ ISO 20998-1:2006 "Measurement and characterization of particles by acoustic methods"
  2. ^ Dukhin, A.S. and Goetz, P.J. "Ultrasound for characterizing colloids", Elsevier, 2002
  3. ^ Hubbell, J. H.; Seltzer, S. M.. Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients. National Institute of Standards and Technology (NIST). Retrieved on Sep. 2007.
  4. ^ Berger, M.J.; J.H. Hubbell, S.M. Seltzer, J. Chang, J.S. Coursey, R. Sukumar, and D.S. Zucker. XCOM: Photon Cross Sections Database. National Institute of Standards and Technology (NIST). Retrieved on Sep. 2007.
  5. ^ Chantler, C.T.; Olsen, K., Dragoset, R.A., Chang, J., Kishore, A.R., Kotochigova, S.A., and Zucker, D.S.. X-Ray Form Factor, Attenuation and Scattering Tables (version 2.1).. National Institute of Standards and Technology (NIST). Retrieved on Sep. 2007.