## 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 Alpha Particle – Definition

Alpha particles are energetic nuclei of helium. The production of alpha particles is termed alpha decay. Alpha particles consist of two protons and two neutrons. Radiation Dosimetry
Alpha particles are energetic nuclei of helium. The production of alpha particles is termed alpha decay. Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus. Alpha particles are relatively large and carry a double positive charge. They are not very penetrating and a piece of paper can stop them. They travel only a few centimeters but deposit all their energies along their short paths. In nuclear reactors they are produced for example in the fuel (alpha decay of heavy nuclei). Alpha particles are commonly emitted by all of the heavy radioactive nuclei occuring in the nature (uranium, thorium or radium), as well as the transuranic elements (neptunium, plutonium or americium). Especially energetic alpha particles (except artificially accelerated helium nuclei) are produced in a nuclear process, which is known as a ternary fission. In this process, the nucleus of uranium is splitted into three charged particles (fission fragments) instead of the normal two. The smallest of the fission fragments most probably (90% probability) being an extra energetic alpha particle.

## Interaction of Alpha Particles with Matter

Since the electromagnetic interaction extends over some distance, it is not necessary for an alpha particles to make a direct collision with an atom. They can transfer energy simply by passing close by. Alpha particles interact with matter primarily through coulomb forces between their positive charge and the negative charge of the electrons from atomic orbitals. In general, the alpha particles (like other charged particles) transfer energy mostly by:

• Excitation. The charged particle can transfer energy to the atom, raising electrons to a higher energy levels.
• Ionization. Ionization can occur, when the charged particle have enough energy to remove an electron. This results in a creation of ion pairs in surrounding matter.

Creation of pairs requires energy, which is lost from the kinetic energy of the alpha particle causing it to decelerate. The positive ions and free electrons created by the passage of the alpha particle will then reunite, releasing energy in the form of heat (e.g. vibrational energy or rotational energy of atoms). There are considerable differences in the ways of energy loss and scattering between the passage of light charged particles such as positrons and electrons and heavy charged particles such as fission fragments, alpha particles, muons. Most of these differences are based on the different dynamics of the collision process. In general, when a heavy particle collides with a much lighter particle (electrons in the atomic orbitals), the laws of energy and momentum conservation predict that only a small fraction of the massive particle’s energy can be transferred to the less massive particle. The actual amount of transferred energy depends on how closely the charged particles passes through the atom and it depends also on restrictions from quantisation of energy levels.

## Stopping Power – Bethe Formula

A convenient variable that describes the ionization properties of surrounding medium is the stopping power. The linear stopping power of material is defined as the ratio of the differential energy loss for the particle within the material to the corresponding differential path length:

,where T is the kinetic energy of the charged particle, nion is the number of electron-ion pairs formed per unit path length, and I denotes the average energy needed to ionize an atom in the medium. For charged particles, S increases as the particle velocity decreases. The classical expression that describes the specific energy loss is known as the Bethe  formula. The non-relativistic formula was found by Hans Bethe in 1930. The relativistic version (see below) was found also by  Hans Bethe in 1932.

In this expression, m is the rest mass of the electron, β equals to v/c, what expresses the particle’s velocity relative to the speed of light, γ is the Lorentz factor of the particle, Q equals to its charge, Z is the atomic number of the medium and n is the atoms density in the volume. For nonrelativistic particles (heavy charged particles are mostly nonrelativistic), dT/dx is dependent on 1/v2. This is can be explained by the greater time the charged particle spends in the negative field of the electron, when the velocity is low.

The stopping power of most materials is very high for heavy charged particles and these particles have very short ranges. For example, the range of a 5 MeV alpha particle is approximately only 0,002 cm in aluminium alloy. Most alpha particles can be stopped by an ordinary sheet of paper or living tissue. Therefore the shielding of alpha particles does not pose a difficult problem, but on the other hand alpha radioactive nuclides can lead to serious health hazards when they are ingested or inhaled (internal contamination).

## Bragg Curve

The Bragg curve is typical for alpha particles and for other heavy charged particles and describes energy loss of ionizing radiation during travel through matter. For this curve is typical the Bragg peak, which is the result of 1/v2 dependency of the stopping power. This peak occurs because the cross section of interaction increases immediately before the particle come to rest. For most of the track, the charge remains unchanged and the specific energy loss increases according to the 1/v2. Near the end of the track, the charge can be reduced through electron pickup and the curve can fall off.

The Bragg curve also differs somewhat due to the effect of straggling. For a given material the range will be the nearly the same for all particles of the same kind with the same initial energy. Because the details of the microscopic interactions undergone by any specific particle vary randomly, a small variation in the range can be observed. This variation is called straggling and it is caused by the statistical nature of the energy loss process which consists of a large number of individual collisions.

This phenomenon, which is described by the Bragg curve, is exploited in particle therapy of cancer, because this allows to concentrate the stopping energy on the tumor while minimizing the effect on the surrounding healthy tissue.

Neutron

Fundamental Particles

Beta Particle

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## What is Stopping Power – Bethe Formula – Definition

The classical expression that describes the specific stopping power is known as the Bethe formula. The non-relativistic formula was found by Hans Bethe in 1930. Radiation Dosimetry
A convenient variable that describes the ionization properties of surrounding medium is the stopping power. The linear stopping power of material is defined as the ratio of the differential energy loss for the particle within the material to the corresponding differential path length:

,where T is the kinetic energy of the charged particle, nion is the number of electron-ion pairs formed per unit path length, and I denotes the average energy needed to ionize an atom in the medium. For charged particles, S increases as the particle velocity decreases. The classical expression that describes the specific energy loss is known as the Bethe  formula. The non-relativistic formula was found by Hans Bethe in 1930. The relativistic version (see below) was found also by  Hans Bethe in 1932.

In this expression, m is the rest mass of the electron, β equals to v/c, what expresses the particle’s velocity relative to the speed of light, γ is the Lorentz factor of the particle, Q equals to its charge, Z is the atomic number of the medium and n is the atoms density in the volume. For nonrelativistic particles (heavy charged particles are mostly nonrelativistic), dT/dx is dependent on 1/v2. This is can be explained by the greater time the charged particle spends in the negative field of the electron, when the velocity is low.

The stopping power of most materials is very high for heavy charged particles and these particles have very short ranges. For example, the range of a 5 MeV alpha particle is approximately only 0,002 cm in aluminium alloy. Most alpha particles can be stopped by an ordinary sheet of paper or living tissue. Therefore the shielding of alpha particles does not pose a difficult problem, but on the other hand alpha radioactive nuclides can lead to serious health hazards when they are ingested or inhaled (internal contamination).

Specifics of Fission Fragments

The fission fragments three two key features (somewhat different from alpha particles or protons), which influence their energy loss during its travel through matter.

• High initial energy. Results in a large effective charge.
• Large effective charge. The fission fragments start out with lack of many electrons, therefore their specific loss is greater than alpha’s specific loss, for example.
•  Immediate electron pickup. Results in changes of (-dE/dx) during the travel.

These features results  in the continuous decrease in the effective charge carried by the fission fragment as the fragment comes to rest and continuous decrease in -dE/dx. The resulting decrease in -dE/dx (from the electron pickup) is larger than the increase that accompanies a reduction in velocity. The range of typical fission fragment can be approximately half that of a 5 MeV alpha particle.

Interaction of Heavy Charged Particles with Matter

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## What is Bragg Curve and Bragg Peak – Definition

The Bragg curve is typical for heavy charged particles and describes energy loss of ionizing radiation during travel through matter. Radiation Dosimetry

The Bragg curve is typical for heavy charged particles and describes energy loss of ionizing radiation during travel through matter. For this curve is typical the Bragg peak, which is the result of 1/v2 dependency of the stopping power. This peak occurs because the cross section of interaction increases immediately before the particle come to rest. For most of the track, the charge remains unchanged and the specific energy loss increases according to the 1/v2. Near the end of the track, the charge can be reduced through electron pickup and the curve can fall off.

The Bragg curve also differs somewhat due to the effect of straggling. For a given material the range will be the nearly the same for all particles of the same kind with the same initial energy. Because the details of the microscopic interactions undergone by any specific particle vary randomly, a small variation in the range can be observed. This variation is called straggling and it is caused by the statistical nature of the energy loss process which consists of a large number of individual collisions.

This phenomenon, which is described by the Bragg curve, is exploited in particle therapy of cancer, because this allows to concentrate the stopping energy on the tumor while minimizing the effect on the surrounding healthy tissue.

Stopping Power – Bethe Formula

Interaction of Heavy Charged Particles with Matter

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

Interactions of beta radiation (beta particles) are based mainly on two mechanisms. An excitation and ionization of atoms, and production of bremsstrahlung. Radiation Dosimetry

## Description Beta Particles

Beta particles are high-energy, high-speed electrons or positrons emitted by certain fission fragments or by certain primordial radioactive nuclei such as potassium-40. The beta particles are a form of ionizing radiation also known as beta rays. The production of beta particles is termed beta decay. There are two forms of beta decay, the electron decay (β− decay) and the positron decay (β+ decay). In a nuclear reactor occurs especially the β− decay, because the common feature of the fission products is an excess of neutrons (see Nuclear Stability). An unstable fission fragment with the excess of neutrons undergoes β− decay, where the neutron is converted into a proton, an electron, and an electron antineutrino.

β- particles
β- particles (electrons) are energetic electrons. The electrons are negatively charged, almost massless particles that nevertheless account for most of the size of the atom. Electrons were discovered by Sir John Joseph Thomson in 1897. Electrons are located in an electron cloud, which is the area surrounding the nucleus of the atom. The electron is only one member of a class of elementary particles, which forms an atom.
β+ particles
β+ particles (positrons) are antiparticles of negative electrons. Positrons, also called positive electrons,  have a positive electric charge and have the same mass and magnitude of charge as the electrons. An annihilation occurs, when a low-energy positron collides with a low-energy electron.

## 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.

## Nature of Interaction of Beta Radiation with Matter

Summary of types of interactions:

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.

## 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:

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.

## 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.

Interaction of Heavy Charged Particles with Matter

Interaction of Gamma Radiation with Matter

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## What is Beta Particle – Definition

Beta particles / radiation are high-energy, high-speed electrons or positrons. The beta particles are a form of ionizing radiation also known as beta rays. Radiation Dosimetry

## Description Beta Particles

Beta particles are high-energy, high-speed electrons or positrons emitted by certain fission fragments or by certain primordial radioactive nuclei such as potassium-40. The beta particles are a form of ionizing radiation also known as beta rays. The production of beta particles is termed beta decay. There are two forms of beta decay, the electron decay (β− decay) and the positron decay (β+ decay). In a nuclear reactor occurs especially the β− decay, because the common feature of the fission products is an excess of neutrons (see Nuclear Stability). An unstable fission fragment with the excess of neutrons undergoes β− decay, where the neutron is converted into a proton, an electron, and an electron antineutrino.

β- particles
β- particles (electrons) are energetic electrons. The electrons are negatively charged, almost massless particles that nevertheless account for most of the size of the atom. Electrons were discovered by Sir John Joseph Thomson in 1897. Electrons are located in an electron cloud, which is the area surrounding the nucleus of the atom. The electron is only one member of a class of elementary particles, which forms an atom.
β+ particles
β+ particles (positrons) are antiparticles of negative electrons. Positrons, also called positive electrons,  have a positive electric charge and have the same mass and magnitude of charge as the electrons. An annihilation occurs, when a low-energy positron collides with a low-energy electron.

## 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.

## Nature of Interaction of Beta Radiation with Matter

Summary of types of interactions:

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.

## 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:

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.

## 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.

## Shielding of Beta Particles – Electrons

Beta radiation ionizes matter weaker than alpha radiation. On the other hand the ranges of beta particles are longer and depends strongly on initial kinetic energy of particle. Some have enough energy to be of concern regarding external exposure. A 1 MeV beta particle can travel approximately 3.5 meters in air. Such beta particles can penetrate into the body and deposit dose to internal structures near the surface. Therefore greater shielding than in case of alpha radiation is required.

Materials with low atomic number Z are appropriate as beta particle shields. With high Z materials the bremsstrahlung (secondary radiation – X-rays) is associated. This radiation is created during slowing down of beta particles while they travel in a very dense medium. Heavy clothing, thick cardboard or thin aluminium plate will provide protection from beta radiation and prevents of production of the bremsstrahlung.

## Shielding of Beta Particles – Positrons

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).

Therefore any positron shield have to include also a gamma ray shield. In order to minimize the bremsstrahlung a multi-layered radiation shield is appropriate. Material for the first layer must fulfill the requirements for negative beta radiation shielding. First layer of such shield may be for example a thin aluminium plate (to shield positrons), while the second layer of such shield may be a dense material such as lead or depleted uranium.

Alpha Particle

Fundamental Particles

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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

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.