## What is Mass Attenuation Coefficient – Definition

The mass attenuation coefficient is defined as the ratio of the linear attenuation coefficient and absorber density (μ/ρ). Radiation Dosimetry

## 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.

Half Value Layer

Gamma Ray Attenuation

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## What is Neutrino – Definition

A neutrino is an elementary subatomic particle with infinitesimal mass and with no electric charge. Neutrinos are weakly interacting subatomic particles with ½ unit of spin. Radiation Dosimetry
A neutrino is an elementary subatomic particle with infinitesimal mass (less than 0.3 eV..?) and with no electric charge. Neutrinos belong to the family of leptons, which means they do not interact via strong nuclear force. Neutrinos are weakly interacting subatomic particles with ½ unit of spin. The term neutrino comes from Italian meaning “little neutral one” and neutrinos are denoted by the Greek letter ν (nu). There are three types of charged leptons, each associated with neutrino, forming three generations (between generations, particle differ by their quantum number and mass). The first generation consist of the electron (e) and electron-neutrino (νe). The second generation consist of the muon (μ) and muon neutrino (νμ) The third generation consist of the tau (τ) and the tau neutrino (ντ). Each type of neutrino is associated with an antimatter particle, called an antineutrino, which also has neutral electric charge and 1/2 spin. Currently (2015), it is not resolved, whether the neutrino and its antiparticle are not identical particles.

Carrying no electric charge they are not affected by electromagnetic forces that act on another charged leptons, such as electrons. Since neutrinos  belong to the family of leptons, they are not subject to the strong force. Neutrinos are subject to the weak force, which is of much shorter range than electromagnetic force and gravity force. Therefore, neutrinos are the most penetrating subatomic particles, capable of passing through Earth without any interaction. It is estimated neutrinos have interaction cross-sections about 20 orders of magnitude less than typical cross-sections of scattering of two nucleons (~10-47m2 = 10-19barn). It is estimated neutrino cross-section for interaction increases linearly with energy of incident neutrino.

Reference: Griffiths, David, Introduction to Elementary Particles, Wiley, 1987.

Source: wikipedia.org
The inside of a cylindrical antineutrino detector before being filled with clear liquid scintillator, which reveals antineutrino interactions by the very faint flashes of light they emit. Sensitive photomultiplier tubes line the detector walls, ready to amplify and record the telltale flashes.
Photo: Roy Kaltschmidt, LBNL
Source: Daya Bay Reactor Neutrino Experiment

Discovery of the Neutrino

## Discovery of the Neutrino

The study of beta decay provided the first physical evidence for the existence of the neutrino. The discovery of the neutrino is based on the law of conservation of energy during the process of beta decay.

In both alpha and gamma decay, the resulting particle (alpha particle or photon) has a narrow energy distribution, since the particle carries the energy from the difference between the initial and final nuclear states. For example, in case of alpha decay, when a parent nucleus breaks down spontaneously to yield a daughter nucleus and an alpha particle, the sum of the mass of the two products does not quite equal the mass of the original nucleus (see Mass Defect). As a result of the law of conservation of energy, this difference appears in the form of the kinetic energy of the alpha particle. Since the same particles appear as products at every breakdown of a particular parent nucleus, the mass-difference should always be the same, and the kinetic energy of the alpha particles should also always be the same. In other words, the beam of alpha particles should be monoenergetic.

It was expected that the same considerations would hold for a parent nucleus breaking down to a daughter nucleus and a beta particle. Because only the electron and the recoiling daughter nucleus were observed beta decay, the process was initially assumed to be a two body process, very much like alpha decay. It would seem reasonable to suppose that the beta particles would form also a monoenergetic beam.

To demonstrate energetics of two-body beta decay, consider the beta decay in which an electron is emitted and the parent nucleus is at rest, conservation of energy requires:

Since the electron is much lighter particle it was expected that it will carry away most of the released energy, which would have a unique value Te-.

But the reality was different. The spectrum of beta particles measured by Lise Meitner and Otto Hahn in 1911 and by Jean Danysz in 1913 showed multiple lines on a diffuse background, however. Moreover virtually all of the emitted beta particles have energies below that predicted by energy conservation in two-body decays. The electrons emitted in beta decay have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. When this was first observed, it appeared to threaten the survival of one of the most important conservation laws in physics!

To account for this energy release, Pauli proposed (in 1931) that there was emitted in the decay process another particle, later named by Fermi the neutrino. It was clear, this particle must be highly penetrating and that the conservation of electric charge requires the neutrino to be electrically neutral. This would explain why it was so hard to detect this particle. The term neutrino comes from Italian meaning “little neutral one” and neutrinos are denoted by the Greek letter ν (nu). In the process of beta decay the neutrino carries the missing energy and also in this process the law of conservation of energy remains valid.

## Production of Neutrinos

Neutrinos can be produced in several ways. The most powerful source of neutrinos in the solar system is doubtless the Sun itself. Billions of solar neutrinos per second pass (mostly without any interaction) through every square centimeter (~6 x 1010 cm-2s-1) on the Earth’s surface. In the Sun, neutrinos are produced after fusion reaction of two protons during positive beta decay of helium-2 nucleus.

Each nuclear reactor is also very powerful source of neutrinos. In fact, antineutrinos. 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.

Reference: Griffiths, David, Introduction to Elementary Particles, Wiley, 1987.

Fundamental Particles

Antineutrino

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## What is Antineutrino – Definition

Antineutrinos are the antiparticles of neutrinos. The antineutrino is an elementary subatomic particle with infinitesimal mass and with no electric charge. Radiation Dosimetry
Antineutrinos are the antiparticles of neutrinos. The antineutrino is an elementary subatomic particle with infinitesimal mass (less than 0.3eV..?) and with no electric charge. Neutrinos and antineutrinos belong to the family of leptons, which means they do not interact via strong nuclear force. Neutrinos are gravitational and weakly interacting subatomic particles with ½ unit of spin. Also antineutrinos (as neutrinos) are very penetrating subatomic particles, capable of passing through Earth without any interaction. Currently (2015), it is not resolved, whether the neutrino and its antiparticle are not identical particles.

Antineutrinos are produced in the negative beta 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. Therefore each nuclear reactor is very powerful source of antineutrinos and researchers around the world investigate the possibilities of using antineutrinos for reactor monitoring.

On the other hand the most powerful source of neutrinos in the solar system is doubtless the Sun itself. Billions of solar neutrinos per second pass (mostly without any interaction) through every square centimeter (~6 x 1010 cm-2s-1) on the Earth’s surface. In the Sun, neutrinos are produced after fusion reaction of two protons during positive beta decay of helium-2 nucleus.

## Detection of Antineutrinos

Since neutrinos do not ionize matter, they cannot be detected directly. The antineutrino detection (1995 Nobel Prize for Frederick Reines and Clyde Cowan) is  based on the reaction:

This interaction is symmetrical to the beta decay of free neutron, therefore it sometimes referred to as inverse beta decay. All detection methods require the neutrinos to carry a minimum threshold energy of 1.8 MeV. Only antineutrinos with an energy above the threshold of 1.8 MeV can cause interactions with the protons in the water, producing positrons and neutrons.

## Nuclear Reactor as the Antineutrino Source

Nuclear reactors are the major source of human-generated antineutrinos. This is due to the fact that antineutrinos are produced in a negative beta decay. In a nuclear reactor occurs especially the β decay, because the common feature of the fission fragments 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. The existence of emission of antineutrinos and their very low cross-section for any interaction leads to very interesting phenomenon. Roughly about 5% (or about 12 MeV of 207 MeV) of released energy per one fission is radiated away from reactor in the form of antineutrinos. For a typical nuclear reactor with a thermal power of 3000 MWth (~1000MWe of electrical power), the total power produced is in fact higher, approximately 3150 MW, of which 150 MW is radiated away into space as antineutrino radiation. This amount of energy is forever lost, since antineutrinos are able to penetrate all reactor materials without any interaction. In fact, a common statement in physics texts is that the mean free path of a neutrino is approximately a light-year of lead. Moreover, a neutrino of moderate energy can easily penetrate a thousand light-years of lead (according to the J. B. Griffiths).

Please note that billions of solar neutrinos per second pass (mostly without any interaction) through every square centimeter (~6×1010) on the Earth’s surface and antineutrino radiation is by no means dangerous.

## Example – Amount of antineutrinos produced:

Stable nuclei with most likely mass number A from U-235 fission are  and . These nuclei have together 98 protons and 136 neutrons, while fission fragments (parent nuclei) have together 92 protons and 142 neutrons. This means after each U-235 fission the fission fragments must undergo on average 6 negative beta decays (6 neutrons must decay to 6 protons) and therefore 6 antineutrinos must be produced per each fission. The typical nuclear reactor therefore produces approximately 6 x 1020 antineutrinos per second (~200 MeV/fission; ~6 antineutrinos/fission; 3000 MWth; 9.375 x 1019 fissions/sec).

Reference: Griffiths, David, Introduction to Elementary Particles, Wiley, 1987.

Neutrino

Fundamental Particles

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## What is Detection of Antineutrinos / Neutrinos – Definition

Since neutrinos do not ionize matter, they cannot be detected directly. The antineutrino detection is based on the inverse beta decay. Detection of Antineutrinos. Radiation Dosimetry
Since neutrinos do not ionize matter, they cannot be detected directly. The antineutrino detection (1995 Nobel Prize for Frederick Reines and Clyde Cowan) is  based on the reaction:

This interaction is symmetrical to the beta decay of free neutron, therefore it sometimes referred to as inverse beta decay. All detection methods require the neutrinos to carry a minimum threshold energy of 1.8 MeV. Only antineutrinos with an energy above the threshold of 1.8 MeV can cause interactions with the protons in the water, producing positrons and neutrons.

Reference: Griffiths, David, Introduction to Elementary Particles, Wiley, 1987.

Antineutrino

Nuclear Reactor as the Antineutrino Source

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## What is Shielding of Ionizing Radiation – Definition

Shielding of ionizing radiation simply means having some material between the source of radiation and you (or some device) that will absorb the radiation. Radiation Dosimetry
Radiation protection is the science and practice of protecting people and the environment from the harmful effects of ionizing radiation. It is a serious topic not only in nuclear power plants, but also in industry or in medical centres. In radiation protection there are three ways how to protect people from identified radiation sources:
• Limiting Time. The amount of radiation exposure depends directly (linearly) on the time people spend near the source of radiation. The dose can be reduced by limiting exposure time.
• Distance. The amount of radiation exposure depends on the distance from the source of radiation. Similarly to a heat from a fire, if you are too close, the intensity of heat radiation is high and you can get burned. If you are at the right distance, you can withstand there without any problems and moreover it is comfortable. If you are too far from heat source, the insufficiency of heat can also hurt you. This analogy, in a certain sense, can be applied to radiation also from radiation sources.
• Shielding. Finally, if the source is too intensive and time or distance do not provide sufficient radiation protection, the shielding must be used. Radiation shielding usually consist of barriers of lead, concrete or water. There are many many materials, which can be used for radiation shielding, but there are many many situations in radiation protection. It highly depends on the type of radiation to be shielded, its energy and many other parametres. For example, even depleted uranium can be used as a good protection from gamma radiation, but on the other hand uranium is absolutely inappropriate shielding of neutron radiation.
Radiation shielding simply means having some material between the source of radiation and you (or some device) that will absorb the radiation. The amount of shielding required, the type or material of shielding strongly depends on several factors. We are not talking about any optimisation.

In fact in some cases an inappropriate shielding may even worsen the radiation situation instead of protecting people from the ionizing radiation.  Basic factors, which have to be considered during proposal of radiation shielding, are:

• Type of the ionizing radiation to be shielded
• Energy spectrum of the ionizing radiation
• Length of exposure
• Distance from the source of the ionizing radiation
• Requirements on the attenuation of the ionizing radiation – ALARA or ALARP principles
• Design degree of freedom
• Other physical requirements (e.g. transparence in case of leaded glass screens)

## Shielding of Radiation in Nuclear Power Plants

Generally in nuclear industry the radiation shielding has many purposes. In nuclear power plants the main purpose is to reduce the radiation exposure to persons and staff in the vicinity of radiation sources. In NPPs the main source of radiation is conclusively the nuclear reactor and its reactor core. Nuclear reactors are in generall powerful sources of entire spectrum of types of ionizing radiation. Shielding used for this purpose is called biological shielding.

But this is not the only purpose of radiation shielding. Shields are also used in some reactors to reduce the intensity of gamma rays or neutrons incident on the reactor vessel. This radiation shielding protects the reactor vessel and its internals (e.g. the core support barrel) from the excessive heating due to gamma ray absorption fast neutron moderation. Such shields are usually referred to as thermal shields.

In nuclear power plants the central problem is to shield against gamma rays and neutrons, because the ranges of charged particles (such as beta particles and alpha particles) in matter are very short. On the other hand we must deal with shielding of all types of radiation, because each nuclear reactor is a significant source of all types of ionizing radiation.

The following features of alpha particles are crucial in their shielding.

• Alpha particles are energetic nuclei of helium and they are relatively heavy and carry a double positive charge.
• Alpha particles interact with matter primarily through coulomb forces (ionization and excitation of matter) between their positive charge and the negative charge of the electrons from atomic orbitals.
• Alpha particles heavily ionize matter and they quickly lose their kinetic energy. On the other hand they deposit all their energies along their short paths.
• The stopping power is well described by the Bethe formula.

The stopping power of most materials is very high for alpha particles and for heavy charged particles. Therefore alpha particles have very short ranges. For example, the ranges of a 5 MeV alpha particle (most have such initial energy) are approximately only 0,002 cm in aluminium alloy or approximately 3.5 cm in air. Most alpha particles can be stopped by a thin piece of paper. Even the dead cells in the outer layer of human skin provides adequate shielding because alpha particles can’t penetrate it.

Therefore the shielding of alpha radiation alone does not pose a difficult problem. On the other hand alpha radioactive nuclides can lead to serious health hazards when they are ingested or inhaled (internal contamination). When they are ingested or inhaled, the alpha particles from their decay significantly harm the internal living tissue. Moreover pure alpha radiation is very rare, alpha decay is frequently accompanied by gamma radiation which shielding is another issue.

The following features of beta particles (electrons) are crucial in their shielding.

• Beta particles are energetic electrons, they are relatively light and carry a single negative charge.
• 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.
• 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.
• Since they have very low mass, beta particles reach mostly relativistic energies.
• Beta particles also differ from other heavy charged particles in the fraction of energy lost by radiative process known as the bremsstrahlung. Therefore for high energy beta radiation shielding dense materials are inappropriate.
• 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.

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. Lead and plastic are commonly used to shield beta radiation. Radiation protection literature is ubiquitous in advising the placement of plastic first to absorb all the beta particles before any lead shielding is used. This advice is based on the well established theory that radiative losses (bremsstrahlung production) are more prevalent in higher atomic number (Z) materials than in low Z materials.

Shielding of Positrons

## Shielding of Positrons

See first: Shielding of Beta Radiation – Electrons

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.

## Characteristics of Gamma Rays

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.
• 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.

In short, effective shielding of gamma radiation is in most cases based on use of materials with two following material properties:

• high-density of material.
• high atomic number of material  (high Z materials)

However, low-density materials and low Z materials can be compensated with increased thickness, which is as significant as density and atomic number in shielding applications.

A lead is widely used as a gamma shield.  Major advantage of lead shield is in its compactness due to its higher density. On the other hand depleted uranium is much more effective due to its higher Z.  Depleted uranium is used for shielding in portable gamma ray sources.

In nuclear power plants shielding of a reactor core can be provided by materials of reactor pressure vessel, reactor internals (neutron reflector). Also heavy concrete is usually used to shield both neutrons and gamma radiation.

Although water is neither high density nor high Z material, it is commonly used as gamma shields. Water provides a radiation shielding of fuel assemblies in a spent fuel pool during storage or during transports from and into the reactor core.

In general, the gamma radiation shielding is more complex and difficult than the alpha or beta radiation shielding. In order to understand comprehensively the way how a gamma ray loses its initial energy, how can be attenuated and how can be shielded we must have detailed knowledge of the its interaction mechanisms.

See also XCOM – photon cross-section DB: XCOM: Photon Cross Sections Database

There are three main features of neutrons, which are crucial in the shielding of neutrons.
• Neutrons have no net electric charge, therefore they cannot be affected or stopped by electric forces. Neutrons ionize matter only indirectly, which makes neutrons highly penetrating type of radiation.
• Neutrons scatter with heavy nuclei very elastically. Heavy nuclei very hard slow down a neutron let alone absorb a fast neutron.
• An absorption of neutron (one would say shielding) causes initiation of certain nuclear reaction (capture, rearrangement or even fission), which is accompanied by a number of other types of radiation. In short, only neutrons make matter radioactive, therefore with neutrons we have to shield also the other types of radiation.

The best materials for shielding neutrons must be able to:

• Slow down neutrons (the same principle as the neutron moderation). First point can be fulfilled only by material containing light hydrogen atoms, such as water, polyethylene, and concrete. The nucleus of a hydrogen nucleus contains only a proton. Since a proton and a neutron have almost identical masses, a neutron scattering on a hydrogen nucleus can give up a great amount of its energy (even entire kinetic energy of a neutron can be transferred to a proton after one collision). This is similar to a billiard. Since a cue ball and another billiard ball have identical masses, the cue ball hitting another ball can be made to stop and the other ball will start moving with the same velocity. On the other hand, if a ping pong ball is thrown against a bowling ball (neutron vs. heavy nucleus), the ping pong ball will bounce off with very little change in velocity, only a change in direction. Therefore lead is quite ineffective for blocking neutron radiation, as neutrons are uncharged and can simply pass through dense materials.
• Absorb this slowed neutron. Thermal neutrons can be easily absorbed by capture in materials with high neutron capture cross sections (thousands of barns) like boron, lithium or cadmium. Generally, only a thin layer of such absorbator is sufficient to shield thermal neutrons. Hydrogen (in the form of water), which can be used to slow down neutrons, have absorbtion cross-section 0.3 barns. This is not enough, but this insufficiency can be offset by sufficient thickness of water shield.

• Shield the accompanying radiation. In the case of cadmium shield the absorption of neutrons is accompanied by strong emission of gamma rays. Therefore additional shield is necessary to attenuate the gamma rays. This phenomenon practically does not exist for lithium and is much less important for boron as a neutron absorption material. For this reason, materials containing boron are used often in neutron shields. In addition, boron (in the form of boric acid) is well soluble in water making this combination very efective neutron shield.

## Water as a neutron shield

Water due to the high hydrogen content and the availability is efective and common neutron shielding. However, due to the low atomic number of hydrogen and oxygen, water is not acceptable shield against the gamma rays. On the other hand in some cases this disadvantage (low density) can be compensated by high thickness of the water shield.  In case of neutrons, water perfectly moderates neutrons, but with absorption of neutrons by hydrogen nucleus secondary gamma rays with the high energy are produced. These gamma rays highly penetrates matter and therefore it can increase requirements on the thickness of the water shield. Adding a boric acid can help with this problem (neutron absorbtion on boron nuclei without strong gamma emission), but results in another problems with corrosion of construction materials.

## Concrete as a neutron shield

Most commonly used neutron shielding in many sectors of the nuclear science and engineering is shield of concrete. Concrete is also hydrogen-containing material, but unlike water concrete have higher density (suitable for secondary gamma shielding) and does not need any maintenance. Because concrete is a mixture of several different materials its composition is not constant. So when referring to concrete as a neutron shielding material, the material used in its composition should be told correctly. Generally concrete are divided to “ordinary “ concrete and “heavy” concrete. Heavy concrete uses heavy natural aggregates such as barites  (barium sulfate) or magnetite or manufactured aggregates such as iron, steel balls, steel punch or other additives. As a result of these additives, heavy concrete have higher density than ordinary concrete (~2300 kg/m3). Very heavy concrete can achieve density up to 5,900 kg/m3 with iron additives or up to 8900 kg/m3 with lead additives. Heavy concrete provide very effective protection against neutrons.

## Calculation of Shielded Dose Rate in Sieverts from Contaminated Surface

Assume a surface, which is contamined by 1.0 Ci of 137Cs. Assume that this contaminant can be aproximated by the point isotropic source which contains 1.0 Ci of 137Cs, which has a half-life of 30.2 years. Note that the relationship between half-life and the amount of a radionuclide required to give an activity of one curie is shown below. This amount of material can be calculated using λ, which is the decay constant of certain nuclide:

About 94.6 percent decays by beta emission to a metastable nuclear isomer of barium: barium-137m. The main photon peak of Ba-137m is 662 keV. For this calculation, assume that all decays go through this channel.

Calculate the primary photon dose rate, in sieverts per hour (Sv.h-1), at the outer surface of a 5 cm thick lead shield. Then calculate the equivalent and effective dose rates for two cases.

1. Assume that this external radiation field penetrates uniformly through the whole body. That means: Calculate the effective whole-body dose rate.
2. Assume that this external radiation field penetrates only lungs and the other organs are completely shielded. That means: Calculate the effective dose rate.

Note that, primary photon dose rate neglects all secondary particles. Assume that the effective distance of the source from the dose point is 10 cm. We shall also assume that the dose point is soft tissue and it can reasonably be simulated by water and we use the mass energy absorption coefficient for water.

Solution:

The primary photon dose rate is attenuated exponentially, and the dose rate from primary photons, taking account of the shield, is given by:

As can be seen, we do not account for the buildup of secondary radiation. If secondary particles are produced or if the primary radiation changes its energy or direction, then the effective attenuation will be much less.  This assumption generally underestimates the true dose rate, especially for thick shields and when the dose point is close to the shield surface, but this assumption simplifies all calculations. For this case the true dose rate (with the buildup of secondary radiation) will be more than two times higher.

To calculate the absorbed dose rate, we have to use in the formula:

• k = 5.76 x 10-7
• S = 3.7 x 1010 s-1
• E = 0.662 MeV
• μt/ρ =  0.0326 cm2/g (values are available at NIST)
• μ =  1.289 cm-1 (values are available at NIST)
• D = 5 cm
• r = 10 cm

Result:

The resulting absorbed dose rate in grays per hour is then:

Since the radiation weighting factor for gamma rays is equal to one and we have assumed the uniform radiation field (the tissue weighting factor is also equal to unity), we can directly calculate the equivalent dose rate and the effective dose rate (E = HT) from the absorbed dose rate as:

In this case we assume a partial irradiation of lungs only. Thus, we have to use the tissue weighting factor, which is equal to wT = 0.12. The radiation weighting factor for gamma rays is equal to one. As a result, we can calculate the effective dose rate as:

Note that, if one part of the body (e.g.,the lungs) receives a radiation dose, it represents a risk for a particularly damaging effect (e.g., lung cancer). If the same dose is given to another organ it represents a different risk factor.

If we want to account for the buildup of secondary radiation, then we have to include the buildup factor. The extended formula for the dose rate is then:

## Buildup Factors for Gamma Rays Shielding

The buildup factor is a correction factor that considers the influence of the scattered radiation plus any secondary particles in the medium during shielding calculations. If we want to account for the buildup of secondary radiation, then we have to include the buildup factor. The buildup factor is then a multiplicative factor which accounts for the response to the uncollided photons so as to include the contribution of the scattered photons. Thus, the buildup factor can be obtained as a ratio of the total dose to the response for uncollided dose.

The extended formula for the dose rate calculation is:

The ANSI/ANS-6.4.3-1991 Gamma-Ray Attenuation Coefficients and Buildup Factors for Engineering Materials Standard, contains derived gamma-ray attenuation coefficients and buildup factors for selected engineering materials and elements for use in shielding calculations (ANSI/ANS-6.1.1, 1991).

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## What is Shielding of Alpha Radiation – Definition

Shielding of alpha radiation alone does not pose a difficult problem. Most alpha particles can be easily stopped by a thin piece of paper. Radiation Dosimetry

Radiation Protection Principles - Time, Distance, Shielding
In radiation protection there are three ways how to protect people from identified radiation sources:
• Limiting Time. The amount of radiation exposure depends directly (linearly) on the time people spend near the source of radiation. The dose can be reduced by limiting exposure time.
• Distance. The amount of radiation exposure depends on the distance from the source of radiation. Similarly to a heat from a fire, if you are too close, the intensity of heat radiation is high and you can get burned. If you are at the right distance, you can withstand there without any problems and moreover it is comfortable. If you are too far from heat source, the insufficiency of heat can also hurt you. This analogy, in a certain sense, can be applied to radiation also from radiation sources.
• Shielding. Finally, if the source is too intensive and time or distance do not provide sufficient radiation protection, the shielding must be used. Radiation shielding usually consist of barriers of lead, concrete or water. There are many many materials, which can be used for radiation shielding, but there are many many situations in radiation protection. It highly depends on the type of radiation to be shielded, its energy and many other parametres. For example, even depleted uranium can be used as a good protection from gamma radiation, but on the other hand uranium is absolutely inappropriate shielding of neutron radiation.

The following features of alpha particles are crucial in their shielding.

• Alpha particles are energetic nuclei of helium and they are relatively heavy and carry a double positive charge.
• Alpha particles interact with matter primarily through coulomb forces (ionization and excitation of matter) between their positive charge and the negative charge of the electrons from atomic orbitals.
• Alpha particles heavily ionize matter and they quickly lose their kinetic energy. On the other hand they deposit all their energies along their short paths.
• The stopping power is well described by the Bethe formula.

The stopping power of most materials is very high for alpha particles and for heavy charged particles. Therefore alpha particles have very short ranges. For example, the ranges of a 5 MeV alpha particle (most have such initial energy) are approximately only 0,002 cm in aluminium alloy or approximately 3.5 cm in air. Most alpha particles can be stopped by a thin piece of paper. Even the dead cells in the outer layer of human skin provides adequate shielding because alpha particles can’t penetrate it.

Therefore the shielding of alpha radiation alone does not pose a difficult problem. On the other hand alpha radioactive nuclides can lead to serious health hazards when they are ingested or inhaled (internal contamination). When they are ingested or inhaled, the alpha particles from their decay significantly harm the internal living tissue. Moreover pure alpha radiation is very rare, alpha decay is frequently accompanied by gamma radiation which shielding is another issue.

Basic materials for alpha particles shielding.

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## What is Shielding of Beta Radiation – Electrons – Definition

Shielding of beta radiation must use materials with low atomic number Z. Ranges of beta particles are longer and depends strongly on initial kinetic energy of particle. Radiation Dosimetry

Radiation Protection Principles - Time, Distance, Shielding
In radiation protection there are three ways how to protect people from identified radiation sources:
• Limiting Time. The amount of radiation exposure depends directly (linearly) on the time people spend near the source of radiation. The dose can be reduced by limiting exposure time.
• Distance. The amount of radiation exposure depends on the distance from the source of radiation. Similarly to a heat from a fire, if you are too close, the intensity of heat radiation is high and you can get burned. If you are at the right distance, you can withstand there without any problems and moreover it is comfortable. If you are too far from heat source, the insufficiency of heat can also hurt you. This analogy, in a certain sense, can be applied to radiation also from radiation sources.
• Shielding. Finally, if the source is too intensive and time or distance do not provide sufficient radiation protection, the shielding must be used. Radiation shielding usually consist of barriers of lead, concrete or water. There are many many materials, which can be used for radiation shielding, but there are many many situations in radiation protection. It highly depends on the type of radiation to be shielded, its energy and many other parametres. For example, even depleted uranium can be used as a good protection from gamma radiation, but on the other hand uranium is absolutely inappropriate shielding of neutron radiation.

## Description of 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.

## Shielding of Beta Radiation – Electrons

The following features of beta particles (electrons) are crucial in their shielding.

• Beta particles are energetic electrons, they are relatively light and carry a single negative charge.
• 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.
• 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.
• Since they have very low mass, beta particles reach mostly relativistic energies.
• Beta particles also differ from other heavy charged particles in the fraction of energy lost by radiative process known as the bremsstrahlung. Therefore for high energy beta radiation shielding dense materials are inappropriate.
• 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.

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. Lead and plastic are commonly used to shield beta radiation. Radiation protection literature is ubiquitous in advising the placement of plastic first to absorb all the beta particles before any lead shielding is used. This advice is based on the well established theory that radiative losses (bremsstrahlung production) are more prevalent in higher atomic number (Z) materials than in low Z materials.

function of electron or positron energy.

Source: http://pdg.lbl.gov/

Basic materials for alpha and beta particles shielding.