## What is Committed Dose – Committed Effective Dose – Definition

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). 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 (wT), 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, HT(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 (t1/2) is cleared from the body with a biological half-life tb, the effective half-life (te) is given by the expression: As can be seen, the biological mechanisms always decreases the overall dose from internal contamination.  Moreover, if t1/2 is large in comparison to tb, the effective half-life is approximately the same as tb.

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.

References:

1. Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8/2010. ISBN-13: 978-0470131480.
2. Stabin, Michael G., Radiation Protection and Dosimetry: An Introduction to Health Physics, Springer, 10/2010. ISBN-13: 978-1441923912.
3. Martin, James E., Physics for Radiation Protection 3rd Edition, Wiley-VCH, 4/2013. ISBN-13: 978-3527411764.
4. U.S.NRC, NUCLEAR REACTOR CONCEPTS
5. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Nuclear and Reactor Physics:

1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Effective Dose

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## What is Nature of Interaction of Beta Radiation with Matter – Definition

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. Radiation Dosimetry

## 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.
• 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.

Beta Particle

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## What is Spectrum of Beta Particles – Definition

This characteristic spectrum is caused by the fact that either a neutrino or an antineutrino is emitted with emission of beta particle. Radiation Dosimetry

## Spectrum of beta particles 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 electron or neutrino.

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.

Nature of Interaction of Beta Particles

Beta Particle

Bremsstrahlung

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## What is Bremsstrahlung – Definition

The bremsstrahlung is electromagnetic radiation produced by the acceleration or deceleration of a charged particle when deflected by magnetic fields or another charged particle. Radiation Dosimetry

## 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: Beta Particle

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## What is Cherenkov Radiation – Definition

The cherenkov radiation is electromagnetic radiation emitted when a charged particlemoves through a dielectric medium faster than the phase velocity of light. Radiation Dosimetry

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.

Bremsstrahlung

Beta Particle

Positron Interactions

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## What is Positron Interaction – Definition

Positrons interact similarly with matter when they are energetic. At the end of their path, positrons differ significantly from electrons. Radiation Dosimetry

## 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 When a positron (antimatter particle) comes to rest, it interacts with an electron, resulting in the annihilation of the both particles and the complete conversion of their rest mass to pure energy in the form of two oppositely directed 0.511 MeV photons.

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.

Beta Particle

Positron Annihilation

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## What is Positron Annihilation – Definition

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. Radiation Dosimetry

## Positron Annihilation When a positron (antimatter particle) comes to rest, it interacts with an electron, resulting in the annihilation of the both particles and the complete conversion of their rest mass to pure energy in the form of two oppositely directed 0.511 MeV photons.

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.

Positron Interactions

Beta Particle

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## What is Gamma Ray / Gamma Radiation – Definition

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. Radiation Dosimetry

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.

Photon
A photon, the quantum of electromagnetic radiation,  is an elementary particle, which is the force carrier of the electromagnetic force. The modern photon concept was developed (1905) by Albert Einstein to explain of the photoelectric effect, in which he proposed the existence of discrete energy packets during the transmission of light.

Before Albert Einstein, notably the German physicist Max Planck had prepared the way for the concept by explaining that objects that emit and absorb light do so only in amounts of energy that are quantized, that means every change of energy can occur only by certain particular discrete amounts and the object cannot change energy in any arbitrary way. The concept of modern photon came into general use after the physicist Arthur H. Compton demonstrated (1923) the corpuscular nature of X-rays. This was the validation that  Einstein’s hypothesis that light itself is quantized.

The term photon comes from Greek phōtos, “light” and a photon is usually denoted by the symbol γ (gamma). The photons are also symbolized by hν (in chemistry and optical engineering), where h is Planck’s constant and the Greek letter ν (nu) is the photon’s frequency. The radiation frequency is key parameter of all photons, because it determines the energy of a photon. Photons are categorized according to the energies from low-energy radio waves and infrared radiation, through visible light, to high-energy X-rays and gamma rays.

Photons are gauge bosons for electromagnetism, having no electric charge or rest mass and one unit of spin. Common to all photons is the speed of light, the universal constant of physics. In empty space, the photon moves at c (the speed of light – 299 792 458 metres per second).

## 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

Key features of gamma rays are summarized in following few points:
• 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

Albert Einstein and Photoelectric Effect / Discovery
The phenomenon, that a surface (typically alkali metals) when exposed to electromagnetic radiation (visible light) emits electrons, was discovered by Hertz and Hallwachs in 1887 during experiments with a spark-gap generator. Hertz found that the sensitivity of his spark-gap device can be increased by exposition to visible or ultraviolet light and that light obviously had some electrical effect. He did not further pursue investigation of this effect.
Shortly after Hertz’s discovery in 1899, English physicist J.J.Thomson showed that UV light, which fall onto metal surface, trigger the emission of electrons from the surface. In 1902, Hungarian physicist Philipp Lenard made the first quantitative measurements of the photoelectric effect. He observed that the energy of individual emitted electrons increased with the frequency of the light (which is related to the color). The luminiferous aether. It was hypothesised that the Earth moves through a “medium” of aether that carries light. It has been replaced in modern physics by the theory of relativity and quantum theory.Source: wikipedia.org

While this is interesting, it is hardly explainable by classical theory of electromagnetic radiation which assumed the existence of a stationary medium (the luminiferous aether) through which light propagated. Subsequent investigations into the photoelectric effect results in the fact that these explorations did not fit with the classical theory of electromagnetic radiation.

In 1905, Albert Einstein published four groundbreaking papers on the photoelectric effect, Brownian motion, special relativity, and the equivalence of mass and energy. These papers were published in the Annalen der Physik journal and contributed significantly to the foundation of modern physics. In the paper on the photoelectric effect (“On a Heuristic Viewpoint Concerning the Production and Transformation of Light”) he solved the paradox by describing light as composed of discrete quanta (German: das Lichtquant), rather than continuous waves.
This theory was builded on Max Planck’s blackbody radiation theory, which assumes that luminous energy can be absorbed or emitted only in discrete amounts, called quanta. The photon’s energy in each quantum of light is equal to its frequency (ν) multiplied by a constant known as Planck’s constant (h), or alternately, using the wavelength (λ) and the speed of light (c):

E=hc/λ=hν

Each photon above a threshold frequency (specific for each material) has the needed energy to eject a single electron, creating the observed effect. Einstein’s theory predicts that the maximum kinetic energy of emitted electron is dependent only on the frequency of the incident light and not on its intensity. Shining twice as much light (high-intensity) results in twice as many photons, and more electrons releasing, but the maximum kinetic energy of those individual electrons remains the same. Experimentation in the photoelectric effect was carried out extensively by Robert Millikan in 1915, Robert Millikan showed that Einstein’s prediction was correct. This discovery contributed to the quantum revolution in physics and earned Einstein the Nobel Prize in Physics in 1921.

• 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 .
• 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 (Ee) is equal to the incident photon energy (hν) minus the binding energy of the photoelectron in its original shell (Eb).

Ee=hν-Eb

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 ZN/E3.5

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 …..).

## 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: 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.Source: hyperphysics.phy-astr.gsu.edu

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

me 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/mec 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/mec2 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 general, pair production is a phenomenon of nature where energy is direct converted to matter. The phenomenon of pair production can be view two different ways. One way is as a particle and antiparticle and the other is as a particle and a hole. The first way can be represented by formation of electron and positron, from a packet of electromagnetic energy (high energy photon – gamma ray) traveling through matter.  It is one of the possible ways in which gamma rays interact with matter. At high energies this interaction dominates.

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 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 = σf + σC + σ

• σf – Photoelectric effect
• σC – Compton scattering
• σp – 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,  Io 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 σf ~ Z5; for pair production σp ~ Z2), the attenuation coefficient μ is not a constant.

## Example:

How much water schielding do you require, if you want to reduce the intensity of a 500 keV monoenergetic gamma ray beam (narrow beam) to 1% of its incident intensity? The half value layer for 500 keV gamma rays in water is 7.15 cm and the linear attenuation coefficient for 500 keV gamma rays in water is 0.097 cm-1.

The question is quite simple and can be described by following equation: If the half value layer for water is 7.15 cm, the linear attenuation coefficient is: Now we can use the exponential attenuation equation:  therefore   So the required thickness of water is about 47.5 cm.  This is relatively large thickness and it is caused by small atomic numbers of hydrogen and oxygen. If we calculate the same problem for lead (Pb), we obtain the thickness x=2.8cm.

Linear Attenuation Coefficients

Table of Linear Attenuation Coefficients (in cm-1) for a different materials at gamma ray energies of 100, 200 and 500 keV.

 Absorber 100 keV 200 keV 500 keV Air 0.000195/cm 0.000159/cm 0.000112/cm Water 0.167/cm 0.136/cm 0.097/cm Carbon 0.335/cm 0.274/cm 0.196/cm Aluminium 0.435/cm 0.324/cm 0.227/cm Iron 2.72/cm 1.09/cm 0.655/cm Copper 3.8/cm 1.309/cm 0.73/cm Lead 59.7/cm 10.15/cm 1.64/cm

## What is Discovery of Gamma Rays / Radiation – Definition

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. Radiation Dosimetry

## 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).

Description of Gamma Rays

Gamma Ray

Characteristics of Gamma Rays

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## What is Description of Gamma Ray – Definition

Gamma rays, also known as gamma radiation, refers to electromagnetic radiation (no rest mass, no charge) of a very high energies. Definition of Gamma rays. Radiation Dosimetry
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.
Photon
A photon, the quantum of electromagnetic radiation,  is an elementary particle, which is the force carrier of the electromagnetic force. The modern photon concept was developed (1905) by Albert Einstein to explain of the photoelectric effect, in which he proposed the existence of discrete energy packets during the transmission of light.Before Albert Einstein, notably the German physicist Max Planck had prepared the way for the concept by explaining that objects that emit and absorb light do so only in amounts of energy that are quantized, that means every change of energy can occur only by certain particular discrete amounts and the object cannot change energy in any arbitrary way. The concept of modern photon came into general use after the physicist Arthur H. Compton demonstrated (1923) the corpuscular nature of X-rays. This was the validation that  Einstein’s hypothesis that light itself is quantized.The term photon comes from Greek phōtos, “light” and a photon is usually denoted by the symbol γ (gamma). The photons are also symbolized by hν (in chemistry and optical engineering), where h is Planck’s constant and the Greek letter ν (nu) is the photon’s frequency. The radiation frequency is key parameter of all photons, because it determines the energy of a photon. Photons are categorized according to the energies from low-energy radio waves and infrared radiation, through visible light, to high-energy X-rays and gamma rays.Photons are gauge bosons for electromagnetism, having no electric charge or rest mass and one unit of spin. Common to all photons is the speed of light, the universal constant of physics. In empty space, the photon moves at c (the speed of light – 299 792 458 metres per second).
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