Radiation Dosimetry

In radiation protection, the committed dose is a dose quantity that measures the stochastic health risk due to an intake of radioactive material into the human body. Commited dose is given the symbol E(t), where t is the integration time in years following the intake. The SI unit of E(t) is the sievert (Sv) or but rem (roentgen equivalent man) is still commonly used (1 Sv = 100 rem). Unit of sievert was named after the Swedish scientist Rolf Sievert, who did a lot of the early work on dosimetry in radiation therapy.

Committed dose allows to determine the biological consequences of irradiation caused by radioactive material, that  is inside our body. A committed dose of 1 Sv from an internal source represents the same effective risk as the same amount of effective dose of 1 Sv applied uniformly to the whole body from an external source.

As an example, let assume an intake of radioactive tritium. For tritium, the annual limit intake (ALI) is 1 x 10⁹ Bq. If you take in 1 x 10⁹ Bq of tritium, you will receive a whole-body dose of 20 mSv. Note that, the biological half-life about 10 days, while the radioactive half-life is about 12 years. Instead of years, it takes a couple of months until the tritium has been pretty well eliminated. The committed effective dose, E(t), is therefore 20 mSv. It does not depend whether a person intakes this amount of activity in a short time or in a long time. In every case, this person gets the same whole-body dose of 20 mSv.

The ICRP defines two dose quantities for individual committed dose.

Committed Effective Dose

According to the ICRP, the committed effective dose, E(t) is defined as:

“The sum of the products of the committed organ or tissue equivalent doses and the appropriate tissue weighting factors (w_T), where t is the integration time in years following the intake. The commitment period is taken to be 50 years for adults, and to age 70 years for children.”

Committed Equivalent Dose

According to the ICRP, the committed equivalent dose, H_T(t) is defined as:

“The time integral of the equivalent dose rate in a particular tissue or organ that will be received by an individual following intake of radioactive material into the body by a Reference Person, where t is the integration time in years.”

Special Reference: ICRP, 2007. The 2007 Recommendations of the International Commission on Radiological Protection. ICRP Publication 103. Ann. ICRP 37 (2-4).

Internal Dose Uptake

If the source of radiation is inside our body, we say, it is internal exposure. The intake of radioactive material can occur through various pathways such as ingestion of radioactive contamination in food or liquids, inhalation of radioactive gases, or through intact or wounded skin. Most radionuclides will give you much more radiation dose if they can somehow enter your body, than they would if they remained outside.

But when a radioactive compound enters the body, the activity will decrease with time, due both to radioactive decay and to biological clearance. The decrease varies from one radioactive compound to another. For this purpose, the biological half-life is defined in radiation protection.

The biological half-life is the time taken for the amount of a particular element in the body to decrease to half of its initial value due to elimination by biological processes alone, when the rate of removal is roughly exponential. The biological half-life depends on the rate at which the body normally uses a particular compound of an element. Radioactive isotopes that were ingested or taken in through other pathways will gradually be removed from the body via bowels, kidneys, respiration and perspiration. This means that a radioactive substance can be expelled before it has had the chance to decay.

As a result, the biological half-life significantly influences the effective half-life and the overall dose from internal contamination. If a radioactive compound with radioactive half-life (t_1/2) is cleared from the body with a biological half-life t_b, the effective half-life (t_e) is given by the expression:

As can be seen, the biological mechanisms always decreases the overall dose from internal contamination.  Moreover, if t_1/2 is large in comparison to t_b, the effective half-life is approximately the same as t_b.

For example, tritium has the biological half-life about 10 days, while the radioactive half-life is about 12 years. On the other hand, radionuclides with very short radioactive half-lives have also very short effective half-lives. These radionuclides will deliver, for all practical purposes, the total radiation dose within the first few days or weeks after intake.

For tritium, the annual limit intake (ALI) is 1 x 10⁹ Bq. If you take in 1 x 10⁹ Bq of tritium, you will receive a whole-body dose of 20 mSv. The committed effective dose, E(t), is therefore 20 mSv. It does not depend whether a person intakes this amount of activity in a short time or in a long time. In every case, this person gets the same whole-body dose of 20 mSv.

See also:

Effective Dose

Nature of Interaction of Beta Radiation with Matter

Summary of types of interactions:

• Inelastic collisions with atomic electrons (Excitation and Ionization)
• Elastic scattering off nuclei
• Bremsstrahlung.
• Cherenkov radiation.
• Annihilation (only positrons)

Nature of an interaction of a beta radiation with matter is different from the alpha radiation, despite the fact that beta particles are also charged particles. In comparison with alpha particles, beta particles have much lower mass and they reach mostly relativistic energies.  Their mass is equal to the mass of the orbital electrons with which they are interacting and unlike the alpha particle a much larger fraction of its kinetic energy can be lost in a single interaction. Since the beta particles mostly reach relativistic energies, the nonrelativistic Bethe formula cannot be used. For high energy electrons an similar expression has also been derived by Bethe to describe the specific energy loss due to excitation and ionization (the “collisional losses”).

Moreover, beta particles can interact via electron-nuclear interaction (elastic scattering off nuclei), which can significantly change the direction of beta particle. Therefore their path is not so straightforward. The beta particles follow a very zig-zag path through absorbing material, this resulting path of particle is longer than the linear penetration (range) into the material.

Beta particles also differ from other heavy charged particles in the fraction of energy lost by radiative process known as the bremsstrahlung. From classical theory, when a charged particle is accelerated or decelerated, it must radiate energy and the deceleration radiation is known as the bremsstrahlung (“braking radiation”).

There is another mechanism by which beta particles loss energy via production of electromagnetic radiation. When the beta particle moves faster than the speed of light (phase velocity) in the material it generates a shock wave of electromagnetic radiation known as the Cherenkov radiation.

Positrons interact similarly with matter when they are energetic. But when the positron comes to rest, it interacts with a negatively charged electron, resulting in the annihilation of the electron-positron pair.

See also:

Beta Particle

See also:

Spectrum of Beta Radiation

Spectrum of beta particles

In the process of beta decay, either an electron or a positron is emitted. This emission is accompanied by the emission of antineutrino (β- decay) or neutrino (β+ decay), which shares energy and momentum of the decay. The beta emission has a characteristic spectrum. This characteristic spectrum is caused by the fact that either a neutrino or an antineutrino is emitted with emission of beta particle. The shape of this energy curve depends on what fraction of the reaction energy (Q value-the amount of energy released by the reaction) is carried by the massive particle. Beta particles can therefore be emitted with any kinetic energy ranging from 0 to Q. By 1934, Enrico Fermi had developed a Fermi theory of beta decay, which predicted the shape of this energy curve.

See also:

Nature of Interaction of Beta Particles

See also:

Beta Particle

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Bremsstrahlung

Bremsstrahlung

The bremsstrahlung  is electromagnetic radiation produced by the acceleration or deceleration of a charged particle when deflected by magnetic fields (an electron by magnetic field of particle accelerator) or another charged particle (an electron by an atomic nucleus). The name bremsstrahlung comes from the German. The literal translation is ‘braking radiation’. From classical theory, when a charged particle is accelerated or decelerated, it must radiate energy.

The bremsstrahlung is one of possible interactions of light charged particles with matter (especially with high atomic numbers).

The two commonest occurrences of bremsstrahlung are by:

• Deceleration of charged particle. When charged particles enter a material they are decelerated by the electric field of the atomic nuclei and atomic electrons.
• Acceleration of charged particle. When ultra-relativistic charged particles move through magnetic fields they are forced to move along a curved path. Since their direction of motion is continually changing, they are also accelerating and so emit bremsstrahlung, in this case it is referred to as synchrotron radiation.

Since the bremsstrahlung is much stronger for lighter particles, this effect is much more important for beta particles than for protons, alpha particles, and heavy charged nuclei (fission fragments). This effect can be neglected at particle energies below about 1 MeV, because the energy loss due to bremsstrahlung is very small. Radiation loss starts to become important only at particle energies well above the minimum ionization energy. At relativistic energies the ratio of loss rate by bremsstrahlung to loss rate by ionization is approximately proportional to the product of the particle’s kinetic energy and the atomic number of the absorber.

The cross section of bremsstrahlung depends on mostly these terms:

So the ratio of stopping powers of bremsstrahlung and ionization losses is:

,where E is the particle’s (electron’s) kinetic energy, Z is the mean atomic number of the material and E’ is a proportionality constant; E’ ≈ 800 MeV. The kinetic energy at which energy loss by bremsstrahlung is equal to the energy loss by ionization and excitation (collisional losses) is called the critical energy. Another paremeter is the radiation length, defined as the distance over which the incident electron’s energy is reduced by a factor 1/e (0.37) due to radiation losses alone. Following table give some typical values:

See also:

Spectrum of Beta Radiation

See also:

Beta Particle

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Cherenkov Radiation

Cherenkov Radiation

The cherenkov radiation is electromagnetic radiation emitted when a charged particle (such as an electron) moves through a dielectric medium faster than the phase velocity of light in that medium. It is similar to the bow wave produced by a boat travelling faster than the speed of water waves. Cherenkov radiation occurs only if the particle’s speed is higher than the phase velocity of light in the material. Even at high energies the energy lost by Cherenkov radiation is much less than that by the other mechanisms (collisions, bremsstrahlung). It is named after Soviet physicist Pavel Alekseyevich Cherenkov, who shared the Nobel Prize in physics in 1958 with Ilya Frank and Igor Tamm for the discovery of Cherenkov radiation, made in 1934.

Cherenkov radiation can be used to detect high-energy charged particles (especially beta particles). In nuclear reactors or in a spent nuclear fuel pool, beta particles (high-energy electrons) are released as the fission fragments decay. The glow is visible also after the chain reaction stops (in the reactor). The cherenkov radiation can characterize the remaining radioactivity of spent nuclear fuel, therefore it can be used for measuring of fuel burnup.

Cherenkov Radiation – Youtube

See also:

Bremsstrahlung

See also:

Beta Particle

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Positron Interactions

Positron Interactions

The coulomb forces that constitute the major mechanism of energy loss for electrons are present for either positive or negative charge on the particle and constitute the major mechanism of energy loss also for positrons. Whatever the interaction involves a repulsive or attractive force between the incident particle and orbital electron (or atomic nucleus), the impulse and energy transfer for particles of equal mass are about the same. Therefore positrons interact similarly with matter when they are energetic. The track of positrons in material is similar to the track of electrons. Even their specific energy loss and range are about the same for equal initial energies.

At the end of their path, positrons differ significantly from electrons. When a positron (antimatter particle) comes to rest, it interacts with an electron (matter particle), resulting in the annihilation of the both particles and the complete conversion of their rest mass to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

Positron Annihilation

Electron–positron annihilation occurs when a negatively charged electron and a positively charged positron collide.When a low-energy electron annihilates a low-energy positron (antiparticle of electron), they can only produce two or more photons (gamma rays). The production of only one photon is forbidden because of conservation of linear momentum and total energy. The production of another particle is also forbidden because of both particles (electron-positron) together do not carry enough mass-energy to produce heavier particles. When an electron and a positron collide, they annihilate resulting in the complete conversion of their rest mass to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

e⁻ + e⁺ → γ + γ (2x 0.511 MeV)

This process must satisfy a number of conservation laws, including:

• Conservation of electric charge. The net charge before and after is zero.
• Conservation of linear momentum and total energy. T
• Conservation of angular momentum.

See also:

Cherenkov Radiation

See also:

Beta Particle

See also:

Positron Annihilation

Positron Annihilation

Electron–positron annihilation occurs when a negatively charged electron and a positively charged positron collide.When a low-energy electron annihilates a low-energy positron (antiparticle of electron), they can only produce two or more photons (gamma rays). The production of only one photon is forbidden because of conservation of linear momentum and total energy. The production of another particle is also forbidden because of both particles (electron-positron) together do not carry enough mass-energy to produce heavier particles. When an electron and a positron collide, they annihilate resulting in the complete conversion of their rest mass to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

e⁻ + e⁺ → γ + γ (2x 0.511 MeV)

This process must satisfy a number of conservation laws, including:

• Conservation of electric charge. The net charge before and after is zero.
• Conservation of linear momentum and total energy. T
• Conservation of angular momentum.

See also:

Positron Interactions

See also:

Beta Particle

Gamma rays, also known as gamma radiation, refers to electromagnetic radiation (no rest mass, no charge) of a very high energies. Gamma rays are high-energy photons with very short wavelengths and thus very high frequency. Since the gamma rays are in substance only a very high-energy photons, they are very penetrating matter and are thus biologically hazardous. Gamma rays can travel thousands of feet in air and can easily pass through the human body.

Gamma rays are emitted by unstable nuclei in their transition from a high energy state to a lower state known as gamma decay. In most practical laboratory sources, the excited nuclear states are created in the decay of a parent radionuclide, therefore a gamma decay typically accompanies other forms of decay, such as alpha or beta decay.

Radiation and also gamma rays are all around us. In, around, and above the world we live in. It is a part of our natural world that has been here since the birth of our planet. Natural sources of gamma rays on Earth are inter alia gamma rays from naturally occurring radionuclides, particularly potassium-40.  Potasium-40 is a radioactive isotope of potassium which has a very long half-life of 1.251×10⁹ years (comparable to the age of Earth). This isotope can be found in soil, water also in meat and bananas. This is not the only example of natural source of gamma rays.

Discovery of Gamma Rays

Gamma rays were discovered shortly after discovery of X-rays. In 1896, French scientist Henri Becquerel discovered that uranium minerals could expose a photographic plate through another material. Becquerel presumed that uranium emitted some invisible light similar to X-rays, which were recently discovered by W.C.Roentgen. He called it “metallic phosphorescence”. In fact, Henri Becquerel had found gamma radiation being emitted by radioisotope ²²⁶Ra (radium), which is part of the Uranium series of uranium decay chain.
Gamma rays were first thought to be particles with mass, for example extremely energetic beta particles. This opinion failed, because this radiation cannot be deflected by a magnetic field, what indicated they had no charge. In 1914, gamma rays were observed to be reflected from crystal surfaces, proving they must be electromagnetic radiation, but with higher energy (higher frequency and shorter wavelengths).

Characteristics of Gamma Rays / Radiation

• Gamma rays are high-energy photons (about 10 000 times as much energy as the visible photons), the same photons as the photons forming the visible range of the electromagnetic spectrum – light.
• Photons (gamma rays and X-rays) can ionize atoms directly (despite they are electrically neutral) through the Photoelectric effect and the Compton effect, but secondary (indirect) ionization is much more significant.
• Gamma rays ionize matter primarily via indirect ionization.
• Although a large number of possible interactions are known, there are three key interaction mechanisms  with matter.
  • Photoelectric effect
  • Compton scattering
  • Pair production
• Gamma rays travel at the speed of light and they can travel thousands of meters in air before spending their energy.
• Since the gamma radiation is very penetrating matter, it must be shielded by very dense materials, such as lead or uranium.
• The distinction between X-rays and gamma rays is not so simple and has changed in recent decades.  According to the currently valid definition, X-rays are emitted by electrons outside the nucleus, while gamma rays are emitted by the nucleus.
• Gamma rays frequently accompany the emission of alpha and beta radiation.

Image: The relative importance of various processes of gamma radiation interactions with matter.

Photoelectric Effect

• The photoelectric effect dominates at low-energies of gamma rays.
• The photoelectric effect leads to the emission of photoelectrons from matter when light (photons) shines upon them.
• The maximum energy an electron can receive in any one interaction is hν.
• Electrons are only emitted by the photoelectric effect if photon reaches or exceeds a threshold energy.
• A free electron (e.g. from atomic cloud) cannot absorb entire energy of the incident photon. This is a result of the need to conserve both momentum and energy.
• The cross-section for the emission of n=1 (K-shell) photoelectrons is higher than that of n=2 (L-shell) photoelectrons. This is a result of the need to conserve momentum and energy.

Definition of Photoelectric effect

In the photoelectric effect, a photon undergoes an interaction with an electron which is bound in an atom. In this interaction the incident photon completely disappears and an energetic photoelectron is ejected by the atom from one of its bound shells. The kinetic energy of the ejected photoelectron (E_e) is equal to the incident photon energy (hν) minus the binding energy of the photoelectron in its original shell (E_b).

E_e=hν-E_b

Therefore photoelectrons are only emitted by the photoelectric effect if photon reaches or exceeds a threshold energy – the binding energy of the electron – the work function of the material. For gamma rays with energies of more than hundreds keV, the photoelectron carries off the majority of the incident photon energy – hν.

Following a photoelectric interaction, an ionized absorber atom is created with a vacancy in one of its bound shells. This vacancy is will be quickly filled by an electron from a shell with a lower binding energy (other shells) or through capture of a free electron from the material. The rearrangement of electrons from other shells creates another vacancy, which, in turn, is filled by an electron from an even lower binding energy shell. Therefore a cascade of more characteristic X-rays can be also generated. The probability of characteristic x-ray emission decreases as the atomic number of the absorber decreases. Sometimes , the emission of an Auger electron occurs.

Cross-Sections of Photoelectric Effect

At small values of gamma ray energy the photoelectric effect dominates. The mechanism is also enhaced for materials of high atomic number Z. It is not simple to derive analytic expression for the probability of photoelectric absorption of gamma ray per atom over all ranges of gamma ray energies. The probability of photoelectric absorption per unit mass is approximately proportional to:

τ_{(photoelectric)} = constant x Z^N/E^3.5

where Z is the atomic number, the exponent n varies between 4 and 5. E is the energy of the incident photon. The proportionality to higher powers of the atomic number Z is the main reason for using of high Z materials, such as lead or depleted uranium in gamma ray shields.

Although the probability of the photoelectric absorption of gamma photon decreases, in general, with increasing photon energy, there are sharp discontinuities in the cross-section curve. These are called “absoption edges” and they correspond to the binding energies of electrons from atom’s bound shells. For photons with the energy just above the edge, the photon energy is just sufficient to undergo the photoelectric interaction with electron from  bound shell, let say K-shell. The probability of such interaction is just above this edge much greater than that of photons of energy slightly below this edge. For gamma photons below this edge the interaction with electron from K-shell in energetically impossible and therefore the probability drops abruptly. These edges occur also at binding energies of electrons from other shells (L, M, N …..).

Compton Scattering

Key characteristics of Compton Scattering

• Compton scattering dominates at intermediate energies.
• It is the scattering of photons by atomic electrons  
• Photons undergo a wavelength shift called the Compton shift.
• The energy transferred to the recoil electron can vary from zero to a large fraction of the incident gamma ray energy

Definition of Compton Scattering

Compton scattering is the inelastic or nonclassical scattering of a photon (which may be an X-ray or gamma ray photon) by a charged particle, usually an electron. In Compton scattering, the incident gamma ray photon is deflected through an angle Θ with respect to its original direction. This deflection results in a decrease in energy (decrease in photon’s frequency) of the photon and is called the Compton effect. The photon transfers a portion of its energy to the recoil electron. The energy transferred to the recoil electron can vary from zero to a large fraction of the incident gamma ray energy, because all angles of scattering are possible. The Compton scattering was observed by A. H.Compton in 1923 at Washington University in St. Louis. Compton earned the Nobel Prize in Physics in 1927 for this new understanding about the particle-nature of photons.

Compton Scattering Formula

The Compton formula was published in 1923 in the Physical Review. Compton explained that the X-ray shift is caused by particle-like momentum of photons. Compton scattering formula is the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays. In the case of Compton scattering the photon of frequency f collides with an electron at rest. Upon collision, the photon bounces off electron, giving up some of its initial energy (given by Planck’s formula E=hf), While the electron gains momentum (mass x velocity), the photon cannot lower its velocity. As a result of momentum conservetion law, the photon must lower its momentum given by:

So the decrease in photon’s momentum must be translated into decrease in frequency (increase in wavelength Δλ = λ’ – λ). The shift of the wavelength increased with scattering angle according to the Compton formula:

where

λ is the initial wavelength of photon

λ’ is the wavelength after scattering,

h is the Planck constant = 6.626 x 10^-34 J.s

m_e is the electron rest mass (0.511 MeV)

c is the speed of light

Θ is the scattering angle.

The minimum change in wavelength (λ′ − λ) for the photon occurs when Θ = 0° (cos(Θ)=1) and is at least zero. The maximum change in wavelength (λ′ − λ) for the photon occurs when Θ = 180° (cos(Θ)=-1). In this case the photon transfers to the electron as much momentum as possible.The maximum change in wavelength can be derived from Compton formula:

The quantity h/m_ec is known as the Compton wavelength of the electron and is equal to 2.43×10⁻¹² m.

Compton Scattering – Cross-Sections

The probability of Compton scattering per one interaction with an atom increases linearly with atomic number Z, because it depends on the number of electrons, which are available for scattering in the target atom. The angular distribution of photons scattered from a single free electron is described by the Klein-Nishina formula:

where ε = E₀/m_ec² and r₀ is the “classical radius of the electron” equal to about 2.8 x 10^-13 cm. The formula gives the probability of scattering a photon into the solid angle element dΩ = 2π sin Θ dΘ when the incident energy is E₀.

Compton Edge

In spectrophotometry, the Compton edge is a feature of the spectrograph that results from the Compton scattering in the scintillator or detector. This feature is due to photons that undergo Compton scattering with a scattering angle of 180° and then escape the detector. When a gamma ray scatters off the detector and escapes, only a fraction of its initial energy can be deposited in the sensitive layer of the detector. It depends on the scattering angle of the photon, how much energy will be deposited in the detector. This leads to a spectrum of energies. The Compton edge energy corresponds to full backscattered photon.

Inverse Compton Scattering

Inverse Compton scattering is the scattering of low energy photons to high energies by relativistic electrons. Relativistic electrons can boost energy of low energy photons by a potentially enormous amount (even gamma rays can be produced). This phenomenon is very important in astrophysics.

Positron-Electron Pair Production

In order for electron-positron pair production to occur, the electromagnetic energy of the photon must be above a threshold energy, which is equivalent to the rest mass of two electrons. The threshold energy (the total rest mass of produced particles) for electron-positron pair production is equal to 1.02MeV (2 x 0.511MeV) because the rest mass of a single electron is equivalent to 0.511MeV of energy.

If the original photon’s energy is greater than 1.02MeV, any energy above 1.02MeV is according to the conservation law split between the kinetic energy of motion of the two particles.

The presence of an electric field of a heavy atom such as lead or uranium is essential in order to satisfy conservation of momentum and energy. In order to satisfy both conservation of momentum and energy, the atomic nucleus must receive some momentum. Therefore a photon pair production in free space cannot occur.

Moreover, the positron is the anti-particle of the electron, so when a positron comes to rest, it interacts with another electron, resulting in the annihilation of the both particles and the complete conversion of their rest mass back to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons). The pair production phenomenon is therefore connected with creation and destruction of matter in one reaction.

Positron-Electron Pair Production – Cross-Section

The probability of pair production, characterized by cross section, is a very complicated function based on quantum mechanics. In general the cross section increases approximately with the square of atomic number (σ_p ~ Z²) and increases with photon energy, but this dependence is much more complex.

Gamma Rays Attenuation

The total cross-section of interaction of a gamma rays with an atom is equal to the sum of all three mentioned partial cross-sections:

σ = σ_f + σ_C + σ_p 

• σ_f – Photoelectric effect

• σ_C – Compton scattering

• σ_p – Pair production

Depending on the gamma ray energy and the absorber material, one of the three partial cross-sections may become much larger than the other two. At small values of gamma ray energy the photoelectric effect dominates. Compton scattering dominates at intermediate energies. The compton scattering also increases with decreasing atomic number of matter, therefore the interval of domination is wider for light nuclei. Finally, electron-positron pair production dominates at high energies.

Based on the definition of interaction cross-section, the dependence of gamma rays intensity on thickness of absorber material can be derive. If monoenergetic gamma rays are collimated into a narrow beam and if the detector behind the material only detects the gamma rays that passed through that material without any kind of interaction with this material, then the dependence should be simple exponential attenuation of gamma rays. Each of these interactions removes the photon from the beam either by absorbtion or by scattering away from the detector direction. Therefore the interactions can be characterized by a fixed probability of occurance per unit path length in the absorber. The sum of these probabilities is called the linear attenuation coefficient:

μ = τ_{(photoelectric)} +  σ_(Compton) + κ_(pair)

Linear Attenuation Coefficient

The attenuation of gamma radiation can be then described by the following equation.

I=I₀.e^-μx

, where I is intensity after attenuation,  I_o is incident intensity,  μ is the linear attenuation coefficient (cm^-1), and physical thickness of absorber (cm).

The materials listed in the table beside are air, water and a different elements from carbon (Z=6) through to lead (Z=82) and their linear attenuation coefficients are given for three gamma ray energies. There are two main features of the linear attenuation coefficient:

• The linear attenuation coefficient increases as the atomic number of the absorber increases.
• The linear attenuation coefficient for all materials decreases with the energy of the gamma rays.

Half Value Layer

The half value layer expresses the thickness of absorbing material needed for reduction of the incident radiation intensity by a factor of two. There are two main features of the half value layer:

• The half value layer decreases as the atomic number of the absorber increases. For example 35 m of air is needed to reduce the intensity of a 100 keV gamma ray beam by a factor of two whereas just 0.12 mm of lead can do the same thing.
• The half value layer for all materials increases with the energy of the gamma rays. For example from 0.26 cm for iron at 100 keV to about 1.06 cm at 500 keV.

Mass Attenuation Coefficient

When characterizing an absorbing material, we can use sometimes the mass attenuation coefficient.  The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). The attenuation of gamma radiation can be then described by the following equation:

I=I₀.e^-(μ/ρ).ρl

, where ρ is the material density, (μ/ρ) is the mass attenuation coefficient and ρ.l is the mass thickness. The measurement unit used for the mass attenuation coefficient cm²g^-1.

For intermediate energies the Compton scattering dominates and different absorbers have approximately equal mass attenuation coefficients. This is due to the fact that cross section of Compton scattering is proportional to the Z (atomic number) and therefore the coefficient is proportional to the material density ρ. At small values of gamma ray energy or at high values of gamma ray energy, where the coefficient is proportional to higher powers of the atomic number Z (for photoelectric effect σ_f ~ Z⁵; for pair production σ_p ~ Z²), the attenuation coefficient μ is not a constant.

Discovery of Gamma Rays

Gamma rays were discovered shortly after discovery of X-rays. In 1896, French scientist Henri Becquerel discovered that uranium minerals could expose a photographic plate through another material. Becquerel presumed that uranium emitted some invisible light similar to X-rays, which were recently discovered by W.C.Roentgen. He called it “metallic phosphorescence”. In fact, Henri Becquerel had found gamma radiation being emitted by radioisotope ²²⁶Ra (radium), which is part of the Uranium series of uranium decay chain.Gamma rays were first thought to be particles with mass, for example extremely energetic beta particles. This opinion failed, because this radiation cannot be deflected by a magnetic field, what indicated they had no charge. In 1914, gamma rays were observed to be reflected from crystal surfaces, proving they must be electromagnetic radiation, but with higher energy (higher frequency and shorter wavelengths).

See also:

Description of Gamma Rays

See also:

Gamma Ray

See also:

Characteristics of Gamma Rays

See above:See also:

Gamma Ray  

See also:

Discovery of Gamma Rays