Nick Connor, Author at Radiation Dosimetry

What is Interaction of Radiation with Matter – Definition

December 14, 2019 by Nick Connor

Knowledge of interactions of radiation with matter constitute key knowledge of modern physics and reactor physics. Each type particle interacts in a different way. Radiation Dosimetry

Knowledge of interactions of radiation with matter constitute key knowledge of modern physics. Modern physics is an experimental science and it is based on experiments, which provide key information for our understanding of nature. Most modern nuclear or particle experiments use a variety of sophisticated devices (detectors) for measuring and detection of sub-atomic particles. In order to be detected, a particle must leave some trace of its presence in a detector. Particles mostly deposit energy along its path. Knowledge of this interaction, how different particles deposit energy in the matter and how much energy particles deposit, is fundamental for our understanding of the problem.

Each type particle interacts in a different way, therefore we must describe interaction of particles (radiation as a flow of these particles) separately. For example charged particles with high energies can directly ionize atoms. On the other hand electrically neutral particles interacts only indirectly, but can also transfer some or all of their energies to the matter. This is the key feature of the categorization of radiation sources. They are usually categorized into two general types as follows:

Charged particles (directly ionizing)
- Beta particles. Beta particles are fast electrons or positrons emitted in nuclear beta decay, as well as energetic electrons produced by any other process.
- Heavy charged particles. Heavy charged particles are all energetic ions with mass of one atomic mass unit or greater, such as protons, alpha particles (helium nuclei) or fission fragments.
Neutral particles (indirectly ionizing)
- Photon radiation (electromagnetic radiation). Photons are particles/waves (Wave-Particle Duality) without rest mass or electrical charge. Also visible light is electromagnetic radiation, but with much lower energies. The electromagnetic radiation of interest includes X-rays emitted in the rearrangement of electron shells of atoms and gamma rays that are emitted from nucleus.
- Neutrons. Neutrons can be emitted by nuclear fission or by the decay of some radioactive atoms. Neutrons have zero electrical charge and cannot directly cause ionization.
- Neutrinos. Neutrinos are electrically neutral, weakly interacting elementary particles, which have very low cross sections for any interaction with matter and therefore low probabilities for colliding in matter.

The design of all nuclear reactors and other nuclear systems depends fundamentally on the way in which radiation interacts with matter. This knowledge is very important for understanding of:

Neutron Moderation. How neutrons slow down to thermal energies.
Power Distribution. Where is the energy generated?
Reactor Power Measurement. How can we measure the reactor power and how can we control the chain reaction.
Radiation Shielding. How can we shield all the various types of radiation produced in the reactor core.

In nuclear reactor we can typically encounter with one of following types of radiation:

Interaction of Heavy Charged Particles

Heavy charged particles are all energetic ions with mass of one atomic mass unit or greater, such as protons, alpha particles (helium nuclei) or fission fragments. Especially knowledge of the interaction of fission fragments and alpha particles must be well known in the engineering of nuclear reactors.

Description of Alpha Particles

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.

Fission fragment yields — Fission fragment yield for different nuclei. The most probable fragment masses are around mass 95 (Krypton) and 137 (Barium).

Description of Fission Fragments

Nuclear fission fragments are the fragments left after a nucleus fissions. Typically, when uranium 235 nucleus undergoes fission, the nucleus splits into two smaller nuclei, along with a few neutrons and release of energy in the form of heat (kinetic energy of the these fission fragments) and gamma rays. The average of the fragment mass is about 118, but very few fragments near that average are found. It is much more probable to break up into unequal fragments, and the most probable fragment masses are around mass 95 (Krypton) and 137 (Barium).

Most of these fission fragments are highly unstable (radioactive) and undergo further radioactive decays to stabilize itself. Fission fragments interact strongly with the surrounding atoms or molecules traveling at high speed, causing them to ionize.

Most of energy released by one fission (~160MeV of total ~200MeV) appears as kinetic energy of the fission fragments.

Nature of Interaction of Charged Particles with Matter

Since the electromagnetic interaction extends over some distance, it is not necessary for the light or heavy charged particle to make a direct collision with an atom. They can transfer energy simply by passing close by. Heavy charged particles, such as fission fragments or alpha particles interact with matter primarily through coulomb forces between their positive charge and the negative charge of the electrons from atomic orbitals. On the other hand, the internal energy of an atom is quantised, therefore only certain amount of energy can be transferred. In general, 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 charged particle causing it to decelerate. The positive ions and free electrons created by the passage of the charged particle will then reunite, releasing energy in the form of heat (e.g. vibrational energy or rotational energy of atoms). This is the principle how fission fragments heat up fuel in the reactor core. 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.

The distance required to bring the particle to rest is referred to as its range. The range of fission fragments in solids amounts to only a few microns, and thus most of the energy of fission is converted to heat very close to the point of fission. In case of gases the range increases to a few centimeters in dependence of gas parameters (density, type of gas etc.) The trajectory of heavy charged particles are not greatly affected, because they interacts with light atomic electrons. Other charged particles, such as the alpha particles behave similarly with one exception – for lighter charged particles the ranges are somewhat longer.

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, n_ion 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.

Bragg Curve

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.

Interaction of Beta Radiation

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.

beta decay — Beta decay of C-14 nucleus.

Spectrum of beta particles

Energy spectrum of beta decay — The shape of this energy curve depends on what fraction of the reaction energy (Q value-the amount of energy released by the reaction) is carried by the electron or neutrino.

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

Nature of Interaction of Beta Radiation with Matter

Summary of types of interactions:

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

Comparison of particles in a cloud chamber. Source: wikipedia.org

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. Its 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”).

Modified Bethe formula for beta particles.

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.

Bremsstrahlung vs. Ionization — Fractional energy loss per radiation length in lead as a
function of electron or positron energy. Source: http://pdg.lbl.gov/

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:

Cherenkov Radiation

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

Cherenkov Radiation in the reactor core.

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.

Beta Particle

Interaction of Gamma Radiation

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

Barium-137m is a product of a common fission product – Caesium – 137. The main gamma ray of Barium-137m is 661keV photon.

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.

Photoelectric Effect

Key Characteristics

Photoelectric effect with photons from visible spectrum on potassium plate – threshold energy – 2eV

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

Definition of Photoelectric Effect

Gamma absorption by an atom. Source: laradioactivite.com/ — Gamma absorption by an atom.
Source: laradioactivite.com/

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

E_e=hν-E_b

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

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

Compton Scattering

Key Characteristics

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

Definition of Compton Scattering

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

Pair Production

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

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

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

Pair production in nuclear field and electron field. — Cross section of pair production in nuclear field and electron field.

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

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

Neutron interactions

Neutrons are neutral particles, therefore they travel in straight lines, deviating from their path only when they actually collide with a nucleus to be scattered into a new direction or absorbed. Neither the electrons surrounding (atomic electron cloud) a nucleus nor the electric field caused by a positively charged nucleus affect a neutron’s flight. In short, neutrons collide with nuclei, not with atoms. A very descriptive feature of the transmission of neutrons through bulk matter is the mean free path length (λ – lambda), which is the mean distance a neutron travels between interactions. It can be calculated from following equation:

λ=1/Σ

Neutrons may interact with nuclei in one of following ways:

Neutron cross-section

The extent to which neutrons interact with nuclei is described in terms of quantities known as cross-sections. Cross-sections are used to express the likelihood of particular interaction between an incident neutron and a target nucleus. It must be noted this likelihood do not depend on real target dimensions. In conjunction with the neutron flux, it enables the calculation of the reaction rate, for example to derive the thermal power of a nuclear power plant. The standard unit for measuring the microscopic cross-section (σ-sigma) is the barn, which is equal to 10^-28 m². This unit is very small, therefore barns (abbreviated as “b”) are commonly used. The microscopic cross-section can be interpreted as the effective ‘target area’ that a nucleus interacts with an incident neutron.

A macroscopic cross-section is derived from microscopic and the material density:

Σ=σ.N

Here σ, which has units of m², is referred to as the microscopic cross-section. Since the units of N (nuclei density) are nuclei/m³, the macroscopic cross-section Σ have units of m^-1, thus in fact is an incorrect name, because it is not a correct unit of cross-sections.

Neutron cross-sections constitute a key parameters of nuclear fuel. Neutron cross-sections must be calculated for fresh fuel assemblies usually in two-Dimensional models of the fuel lattice.

The neutron cross-section is variable and depends on:

Target nucleus (hydrogen, boron, uranium, etc.) Each isotop has its own set of cross-sections.
Type of the reaction (capture, fission, etc.). Cross-sections are different for each nuclear reaction.
Neutron energy (thermal neutron, resonance neutron, fast neutron). For a given target and reaction type, the cross-section is strongly dependent on the neutron energy. In the common case, the cross section is usually much larger at low energies than at high energies. This is why most nuclear reactors use a neutron moderator to reduce the energy of the neutron and thus increase the probability of fission, essential to produce energy and sustain the chain reaction.
Target energy (temperature of target material – Doppler broadening) This dependency is not so significant, but the target energy strongly influences inherent safety of nuclear reactors due to a Doppler broadening of resonances.

Typical cross-sections of materials in the reactor

Following table shows neutron cross-sections of the most common isotopes of reactor core.

Reactor Antineutrinos

Antineutrino detector — 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

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 MW_th (~1000MW_e 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 $_{40}^{94}textrm{Zr}$ and $_{58}^{140}textrm{Ce}$ . 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 MW_th; 9.375 x 10¹⁹ fissions/sec).

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

References:

Knoll, Glenn F., RADIATION DETECTION AND MEASUREMENT, 4th edition

Lamarsh, John R., INTRODUCTION TO NUCLEAR ENGINEERING, 2nd edition

What is Shielding of Neutron Radiation – Definition

December 14, 2019 by Nick Connor

Shielding of neutron radiation is very complicated. There are three main features of neutrons, which are crucial in the shielding of neutrons. Water or concrete. Radiation Dosimetry

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 nuclear 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. 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. In short, it depends on type of radiation to be shielded, which shielding will be effective or not.

Radiation Protection Principles - Time, Distance, Shielding

radiation protection pronciples - time, distance, shielding — Principles of Radiation Protection – Time, Distance, Shielding

Shielding of Neutrons

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 (e.g. radiative capture or even fission), which is accompanied by a number of other types of radiation. In short, neutrons make matter radioactive, therefore with neutrons we have to shield also the other types of radiation.

Basic materials for shielding of neutrons.

14N(n,p)14C - the nuclear reaction of importance in the radiation protection

14N (n,p) 14C

This nuclear reaction (charged particle reaction) continually take place especially in the earth’s atmosphere, forming equilibrium amounts of the radionuclide ¹⁴C. In nuclear power plants, it is important especially from radiation protection point of view. The reaction is responsible for most of the radiation dose delivered to the human body by thermal neutrons. The nitrogen atoms are contained in proteins, therefore if the human body is exposed to thermal neutrons, then these thermal neutrons may be absorbed by ¹⁴N, causing a proton emission. Protons are directly ionizing particles and deposit their energy over a very short distance in the body tissue.

Principles of Neutron Shielding

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 atoms (e.g. 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.
Table of cross-sections

Absorb this slow 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.

What is Detection of Neutrons – Definition

December 14, 2019 by Nick Connor

Neutrons are not directly ionizing and they have usually to be converted into charged particles before they can be detected. Detection of neutrons. Radiation Dosimetry

neutron detection — Generally every type of neutron detector must be equipped with converter and one of the conventional radiation detectors.
Source: large.stanford.edu

Detection of neutrons is very specific, since the neutrons are electrically neutral particles, thus they are mainly subject to strong nuclear forces but not to electric forces. Therefore neutrons are not directly ionizing and they have usually to be converted into charged particles before they can be detected. Generally every type of neutron detector must be equipped with converter (to convert neutron radiation to common detectable radiation) and one of the conventional radiation detectors (scintillation detector, gaseous detector, semiconductor detector, etc.).

Neutron Converters

Two basic types of neutron interactions with matter are for this purpose available:

Elastic scattering. The free neutron can be scattered by a nucleus, transferring some of its kinetic energy to the nucleus. If the neutron has enough energy to scatter off nuclei the recoiling nucleus ionizes the material surrounding the converter. In fact, only hydrogen and helium nuclei are light enough for practical application. Charge produced in this way can be collected by the conventional detector to produce a detected signal. Neutrons can transfer more energy to light nuclei. This method is appropriate for detecting fast neutrons (fast neutrons do not have high cross-section for absorption) allowing detection of fast neutrons without a moderator.
Neutron absorption. This is a common method allowing detection of neutrons of entire energy spectrum. This method is is based on variety of absorption reactions (radiation capture, nuclear fission, rearrangement reactions, etc.). The neutron is here absorbed by target material (converter) emitting secondary particles such as protons, alpha particles, beta particles, photons (gamma rays) or fission fragments. Some reactions are threshold reactions (requiring a minimum energy of neutrons), but most of reactions occurs at epithermal and thermal energies. That means the moderation of fast neutrons is required leading in poor energy information of the neutrons. Most common nuclei for the neutron converter material are:
- ¹⁰B(n,α). Where the neutron capture cross-section for thermal neutrons is σ = 3820 barns and the natural boron has abundance of ¹⁰B 19,8%.
- ³He(n,p). Where the neutron capture cross-section for thermal neutrons is σ = 5350 barns and the natural helium has abundance of ³He 0.014%.
- ⁶Li(n,α). Where the neutron capture cross-section for thermal neutrons is σ = 925 barns and the natural lithium has abundance of ⁶Li 7,4%.
- ¹¹³Cd(n,ɣ). Where the neutron capture cross-section for thermal neutrons is σ = 20820 barns and the natural cadmium has abundance of ¹¹³Cd 12,2%.
- ²³⁵U(n,fission). Where the fission cross-section for thermal neutrons is σ = 585 barns and the natural uranium has abundance of ²³⁵U 0.711%. Uranium as a converter produces fission fragments which are heavy charged particles. This have significant advantage. The heavy charged particles (fission fragments) create a high output signal, because the fragments deposit a large amount of energy in a detector sensitive volume. This allows an easy discrimination of the background radiation (e.i. gamma radiation). This important feature can be used for example in a nuclear reactor power measurement, where the neutron field is accompanied by a significant gamma background.

Detection of Thermal Neutrons

Thermal neutrons are neutrons in thermal equilibrium with a surrounding medium of temperature 290K (17 °C or 62 °F). Most probable energy at 17°C (62°F) for Maxwellian distribution is 0.025 eV (~2 km/s). This part of neutron’s energy spectrum constitutes most important part of spectrum in thermal reactors.

Thermal neutrons have a different and often much larger effective neutron absorption cross-section (fission or radiative capture) for a given nuclide than fast neutrons.

In general, there are many detection principles and many types of detectors. In nuclear reactors, gaseous ionization detectors are the most common, since they are very efficient, reliable and cover a wide range of neutron flux. Various types of gaseous ionization detectors constitute so called the excore nuclear instrumentation system (NIS). The excore nuclear instrumentation system monitors the power level of the reactor by detecting neutron leakage from the reactor core.

Detection of Neutrons using Ionization Chamber

Ionization chambers are often used as the charged particle detection device. For example, if the inner surface of the ionization chamber is coated with a thin coat of boron, the (n,alpha) reaction can take place. Most of (n,alpha) reactions of thermal neutrons are 10B(n,alpha)7Li reactions accompanied by 0.48 MeV

Moreover, isotope boron-10 has high (n,alpha) reaction cross-section along the entire neutron energy spectrum. The alpha particle causes ionization within the chamber, and ejected electrons cause further secondary ionizations.

Another method for detecting neutrons using an ionization chamber is to use the gas boron trifluoride (BF₃) instead of air in the chamber. The incoming neutrons produce alpha particles when they react with the boron atoms in the detector gas. Either method may be used to detect neutrons in nuclear reactor. It must be noted, BF₃ counters are usually operated in the proportional region.

Fission Chamber – Wide Range Detectors

Fission chambers are ionization detectors used to detect neutrons. Fission chambers may be used as the intermediate range detectors to monitor neutron flux (reactor power) at the intermediate flux level. They also provide indication, alarms, and reactor trip signals. The design of this instrument is chosen to provide overlap between the source range channels and full span of the power range instruments.

In case of fission chambers, the chamber is coated with a thin layer of highly enriched uranium-235 to detect neutrons. Neutrons are not directly ionizing and they have usually to be converted into charged particles before they can be detected. A thermal neutron will cause an atom of uranium-235 to fission, with the two fission fragments produced having a high kinetic energy and causing ionization of the argon gas within the detector. One advantage of using uranium-235 coating rather than boron-10 is that the fission fragments have a much higher energy than the alpha particle from a boron reaction. Therefore fission chambers are very sensitive to neutron flux and this allows the fission chambers to operate in higher gamma fields than an uncompensated ion chamber with boron lining.

Activation Foils and Flux Wires

Neutrons may be detected using activation foils and flux wires. This method is based on neutron activation, where an analyzed sample is first irradiated with neutrons to produce specific radionuclides. The radioactive decay of these produced radionuclides is specific for each element (nuclide). Each nuclide emits the characteristic gamma rays which are measured using gamma spectroscopy, where gamma rays detected at a particular energy are indicative of a specific radionuclide and determine concentrations of the elements.

Selected materials for activation foils are for example:

indium,
gold,
rhodium,
iron
aluminum
niobium

These elements have large cross sections for the radiative capture of neutrons. Use of multiple absorber samples allows characterization of the neutron energy spectrum. Activation also allows recreation of an historic neutron exposure. Commercially available criticality accident dosimeters often utilize this method. By measuring the radioactivity of thin foils, we can determine the amount of neutrons to which the foils were exposed.

Flux wires may be used in nuclear reactors to measure reactor neutron flux profiles. Principles are the same. Wire or foil is inserted directly into the reactor core, remains in the core for the length of time required for activation to the desired level. After activation, the flux wire or foil is rapidly removed from the reactor core and the activity counted. Activated foils can also discriminate energy levels by placing a cover over the foil to filter out (absorb) certain energy level neutrons. For example, cadmium is widely used to absorb thermal neutrons in a thermal neutron filters.

Detection of Fast Neutrons

Fast neutrons are neutrons of kinetic energy greater than 1 MeV (~15 000 km/s). In nuclear reactors, these neutrons are usually named fission neutrons. The fission neutrons have a Maxwell-Boltzmann distribution of energy with a mean energy (for 235U fission) 2 MeV. Inside a nuclear reactor the fast neutrons are slowed down to the thermal energies via a process called neutron moderation. These neutrons are also produced by nuclear processes such as nuclear fission or (ɑ,n) reactions.

In general, there are many detection principles and many types of detectors. Bu it must be added, detection of fast neutrons is very sophisticated discipline, since fast neutrons cross section are much smaller than in the energy range for slow neutrons. Fast neutrons are often detected by first moderating (slowing) them to thermal energies. However, during that process the information on the original energy of the neutron, its direction of travel, and the time of emission is lost.

Proton Recoil – Recoil Detectors

The most important type of detectors for fast neutrons are those which directly detect recoil particles, in particular recoil protons resulting from elastic (n, p) scattering. In fact, only hydrogen and helium nuclei are light enough for practical application. In the latter case the recoil particles are detected in a detector. Neutrons can transfer more energy to light nuclei. This method is appropriate for detecting fast neutrons allowing detection of fast neutrons without a moderator. This methods allows the energy of the neutron to be measured together with the neutron fluence, i.e. the detector can be used as a spectrometer. Typical fast neutron detectors are liquid scintillators, helium-4 based noble gas detectors and plastic detectors (scintillators). For example, the plastic has a high hydrogen content, therefore, it is useful for fast neutron detectors, when used as a scintillator.

Bonner Spheres Spectrometer

There are several methods for detecting slow neutrons, and few methods for detecting fast neutrons. Therefore, one technique for measuring fast neutrons is to convert them to slow
neutrons, and then measure the slow neutrons. One of possible methods is based on Bonner spheres. The method was first described in 1960 by Ewing and Tom W. Bonner and employs thermal neutron detectors (usually inorganic scintillators such as ⁶LiI) embedded in moderating spheres of different sizes. Bonner spheres have been used widely for the measurement of neutron spectra with neutron energies ranged from thermal up to at least 20 MeV. A Bonner sphere neutron spectrometer (BSS) consists of a thermal-neutron detector, a set polyethylene spherical shells and two optional lead shells of various sizes. In order to detect thermal neutrons a ³He detector or inorganic scintillators such as ⁶LiI can be used. LiGlass scintillators are very popular for detection of thermal neutrons. The advantage of LiGlass scintillators is their stability and their large range of sizes.

Detection of Neutrons using Scintillation Counter

Scintillation counters are used to measure radiation in a variety of applications including hand held radiation survey meters, personnel and environmental monitoring for radioactive contamination, medical imaging, radiometric assay, nuclear security and nuclear plant safety. They are widely used because they can be made inexpensively yet with good efficiency, and can measure both the intensity and the energy of incident radiation.

Scintillation counters can be used to detect alpha, beta, gamma radiation. They can be used also for detection of neutrons. For these purposes, different scintillators are used.

Neutrons. Since the neutrons are electrically neutral particles, they are mainly subject to strong nuclear forces but not to electric forces. Therefore neutrons are not directly ionizing and they have usually to be converted into charged particles before they can be detected. Generally every type of neutron detector must be equipped with converter (to convert neutron radiation to common detectable radiation) and one of the conventional radiation detectors (scintillation detector, gaseous detector, semiconductor detector, etc.). Fast neutrons (>0.5 MeV) primarily rely on the recoil proton in (n,p) reactions. Materials rich in hydrogen, for example plastic scintillators, are therefore best suited for their detection. Thermal neutrons rely on nuclear reactions such as the (n,γ) or (n,α) reactions, to produce ionization. Materials such as LiI(Eu) or glass silicates are therefore particularly well-suited for the detection of thermal neutrons. The advantage of 6LiGlass scintillators is their stability and their large range of sizes.

What is Interaction of Neutrons with Matter – Definition

December 14, 2019 by Nick Connor

Neutrons may interact with matter in many ways. Neutrons are neutral particles,therefore they collide with nuclei, not with atoms. Interactions of Neutrons with Matter. Radiation Dosimetry

Interactions of Neutrons with Matter

λ=1/Σ

Neutrons may interact with nuclei in one of following ways:

Types of neutron-nuclear reactions

Elastic Scattering Reaction

Generally, a neutron scattering reaction occurs when a target nucleus emits a single neutron after a neutron-nucleus interaction. In an elastic scattering reaction between a neutron and a target nucleus, there is no energy transferred into nuclear excitation.

Inelastic Scattering Reaction

In an inelastic scattering reaction between a neutron and a target nucleus some energy of the incident neutron is absorbed to the recoiling nucleus and the nucleus remains in the excited state. Thus while momentum is conserved in an inelastic collision, kinetic energy of the “system” is not conserved.

Neutron Absorption

The neutron absorption reaction is the most important type of reactions that take place in a nuclear reactor. The absorption reactions are reactions, where the neutron is completely absorbed and compound nucleus is formed. This is the very important feature, because the mode of decay of such compound nucleus does not depend on the way the compound nucleus was formed. Therefore a variety of emissions or decays may follow. The most important absorption reactions are divided by the exit channel into two following reactions:

Radiative Capture. Most absorption reactions result in the loss of a neutron coupled with the production of one or more gamma rays. This is referred to as a capture reaction, and it is denoted by σ_γ.

Neutron-induced Fission Reaction. Some nuclei (fissionable nuclei) may undergo a fission event, leading to two or more fission fragments (nuclei of intermediate atomic weight) and a few neutrons. In a fissionable material, the neutron may simply be captured, or it may cause nuclear fission. For fissionable materials we thus divide the absorption cross section as σ_a = σ_γ + σ_f.

Radiative Capture

The neutron capture is one of the possible absorption reactions that may occur. In fact, for non-fissionable nuclei it is the only possible absorption reaction. Capture reactions result in the loss of a neutron coupled with the production of one or more gamma rays. This capture reaction is also referred to as a radiative capture or (n, γ) reaction, and its cross-section is denoted by σ_γ.

The radiative capture is a reaction, in which the incident neutron is completely absorbed and compound nucleus is formed. The compound nucleus then decays to its ground state by gamma emission. This process can occur at all incident neutron energies, but the probability of the interaction strongly depends on the incident neutron energy and also on the target energy (temperature). In fact the energy in the center-of-mass system determines this probability.

Nuclear Fission

Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts (lighter nuclei). The fission process often produces free neutrons and photons (in the form of gamma rays), and releases a large amount of energy. In nuclear physics, nuclear fission is either a nuclear reaction or a radioactive decay process. The case of decay process is called spontaneous fission and it is very rare process.

Neutron Emission

Although the neutron emission is usually associated with nuclear decay, it must be also mentioned in connection with neutron nuclear reactions. Some neutrons interacts with a target nucleus via a compound nucleus. Among these compound nucleus reactions are also reactions, in which a neutron is ejected from nucleus and they may be referred to as neutron emission reactions. The point is that compound nuclei lose its excitation energy in a way, which is identical to the radioactive decay. Very important feature is the fact the mode of decay of compound nucleus does not depend on the way the compound nucleus was formed.

Charged Particle Ejection

Charged particle reactions are usually associated with formation of a compound nucleus, which is excited to a high energy level, that such compound nucleus can eject a new charged particle while the incident neutron remains in the nucleus. After the new particle is ejected, the remaining nucleus is completely changed, but may or may not exist in an excited state depending upon the mass-energy balance of the reaction. This type of reaction is more common for charged particles as incident particles (such as alpha particles, protons, and so on).

The case of neutron-induced charged particle reactions is not so common, but there are some neutron-induced charged particle reactions, that are of importance in the reactivity control and also in the detection of neutrons.

Neutron cross-section

A macroscopic cross-section is derived from microscopic and the material density:

Σ=σ.N

Neutron cross-sections constitute a key parameters of nuclear fuel. Neutron cross-sections must be calculated for fresh fuel assemblies usually in two-Dimensional models of the fuel lattice.

The neutron cross-section is variable and depends on:

Target nucleus (hydrogen, boron, uranium, etc.) Each isotop has its own set of cross-sections.
Type of the reaction (capture, fission, etc.). Cross-sections are different for each nuclear reaction.
Neutron energy (thermal neutron, resonance neutron, fast neutron). For a given target and reaction type, the cross-section is strongly dependent on the neutron energy. In the common case, the cross section is usually much larger at low energies than at high energies. This is why most nuclear reactors use a neutron moderator to reduce the energy of the neutron and thus increase the probability of fission, essential to produce energy and sustain the chain reaction.
Target energy (temperature of target material – Doppler broadening) This dependency is not so significant, but the target energy strongly influences inherent safety of nuclear reactors due to a Doppler broadening of resonances.

Law 1/v

1/v Law — For thermal neutrons (in 1/v region), absorption cross sections increases as the velocity (kinetic energy) of the neutron decreases.
Source: JANIS 4.0

For thermal neutrons (in 1/v region), absorption cross-sections increases as the velocity (kinetic energy) of the neutron decreases. Therefore the 1/v Law can be used to determine shift in absorbtion cross-section, if the neutron is in equilibrium with a surrounding medium. This phenomenon is due to the fact the nuclear force between the target nucleus and the neutron has a longer time to interact.

$sigma_a sim frac{1}{v}}} sim frac{1}{sqrt{E}}}}} sim frac{1}{sqrt{T}}}}}$

This law is aplicable only for absorbtion cross-section and only in the 1/v region.

Example of cross- sections in 1/v region:

The absorbtion cross-section for 238U at 20°C = 293K (~0.0253 eV) is:

$sigma_a(293K) = 2.68b$ .

The absorbtion cross-section for 238U at 1000°C = 1273K is equal to:

This cross-section reduction is caused only due to the shift of temperature of surrounding medium.

Resonance neutron capture

Resonance peaks for radiative capture of U238. At resonance energies the probability of capture can be more than 100x higher as the base value.
Source: JANIS program

Absorption cross section is often highly dependent on neutron energy. Note that the nuclear fission produces neutrons with a mean energy of 2 MeV (200 TJ/kg, i.e. 20,000 km/s). The neutron can be roughly divided into three energy ranges:

Fast neutron. (10MeV – 1keV)
Resonance neutron (1keV – 1eV)
Thermal neutron. (1eV – 0.025eV)

The resonance neutrons are called resonance for their special bahavior. At resonance energies the cross-section can reach peaks more than 100x higher as the base value of cross-section. At this energies the neutron capture significantly exceeds a probability of fission. Therefore it is very important (for thermal reactors) to quickly overcome this range of energy and operate the reactor with thermal neutrons resulting in increase of probability of fission.

Doppler broadening

Doppler effect improves reactor stability. Broadened resonance (heating of a fuel) results in a higher probability of absorbtion, thus causes negative reactivity insertion (reduction of reactor power).

A Doppler broadening of resonances is very important phanomenon, which improves reactor stability. The prompt temperature coefficient of most thermal reactors is negative, owing to an nuclear Doppler effect. Although the absorbtion cross-section depends significantly on incident neutron energy, the shape of the cross-section curve depends also on target temperature.

Nuclei are located in atoms which are themselves in continual motion owing to their thermal energy. As a result of these thermal motions neutrons impinging on a target appears to the nuclei in the target to have a continuous spread in energy. This, in turn, has an effect on the observed shape of resonance. The resonance becomes shorter and wider than when the nuclei are at rest.

Although the shape of a resonance changes with temperature, the total area under the resonance remains essentially constant. But this does not imply constant neutron absorbtion. Despite the constant area under resonance, a resonance integral, which determines the absorbtion, increases with increasing target temperature. This, of course, decreases coefficient k (negative reactivity is inserted).

Typical cross-sections of materials in the reactor

Following table shows neutron cross-sections of the most common isotopes of reactor core.

What is Radioactive Decay – Definition

December 14, 2019 by Nick Connor

Nuclear decay (Radioactive decay) occurs when an unstable atom loses energy by emitting ionizing radiation. Radioactive decay is a random process at the level of single atoms. Radiation Dosimetry

What is Radioactive Decay

Notation of nuclear reactions - radioactive decays — Notation of nuclear reactions – radioactive decays
Source: chemwiki.ucdavis.edu

Nuclear decay (Radioactive decay) occurs when an unstable atom loses energy by emitting ionizing radiation. Radioactive decay is a random process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay. In other words, a nucleus of a radionuclide has no “memory”. A nucleus does not “age” with the passage of time. Thus, the probability of its breaking down does not increase with time, but stays constant no matter how long the nucleus has existed. During its unpredictable decay this unstable nucleus spontaneosly and randomly decomposes to form a different nucleus (or a different energy state – gamma decay), giving off radiation in the form of atomic partices or high energy rays. This decay occurs at a constant, predictable rate that is referred to as half-life. A stable nucleus will not undergo this kind of decay and is thus non-radioactive.

There are three basic modes of radioactive decay:

Alpha decay. Alpha decay represents the disintegration of a parent nucleus to a daughter through the emission of the nucleus of a helium atom. Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus. Because of its very large mass (more than 7000 times the mass of the beta particle) and its charge, it heavy ionizes material and has a very short range.
Beta decay. Beta decay or β decay represents the disintegration of a parent nucleus to a daughter through the emission of the beta particle. Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei such as potassium-40. The beta particles have greater range of penetration than alpha particles, but still much less than gamma rays.The beta particles emitted are a form of ionizing radiation also known as beta rays. The production of beta particles is termed beta decay.
Gamma decay. Gamma decay or γ decay represents the disintegration of a parent nucleus to a daughter through the emission of gamma rays (high energy photons). Gamma rays are electromagnetic radiation (high energy photons) of an very high frequency and of a high energy. They are produced by the decay of nuclei as they transition from a high energy state to a lower state known as gamma decay. Most of nuclear reactions are accompanied by gamma emission.

Additional important decay modes:

Electron capture. Electron capture is a process, in which a parent nucleus captures one of its orbital electrons and emits a neutrino. Electron capture, known also as inverse beta decay is sometimes included as a type of beta decay, because the basic nuclear process, mediated by the weak interaction, is the same.
Internal conversion. Internal conversion is an electromagnetic process, by which a nuclear excited state decays by the direct emission of one of its atomic electrons. Internal conversion competes with gamma emission, but in this case the electromagnetic multipole fields of the nucleus do not result in the emission of a gamma ray, instead, the fields interact directly with atomic electrons. In contrast to beta decay, which is governed by a weak force, the electron is emitted from the radioactive atom, but not from the nucleus.
Neutron decay. Neutron decay is a type of radioactive decay of nuclei containing excess neutrons (especially fission products), in which a neutron is simply ejected from the nucleus. This type of radiation plays key role in nuclear reactor control, because these neutrons are delayed neutrons.
Proton decay. Proton decay is a rare type of radioactive decay of nuclei containing excess protons, in which a proton is simply ejected from the nucleus.
Spontaneous fission. Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements.

Nature of Decay

Barium-137m is a product of a common fission product - Caesium - 137. The main gamma ray of Barium-137m is 661keV photon. — Barium-137m is a product of a common fission product – Caesium – 137. The main gamma ray of Barium-137m is 661keV photon.

As was written, atomic nuclei consist of protons and neutrons, which attract each other through the nuclear force, while protons repel each other via the electromagnetic force due to their positive charge. These two forces compete, leading to various stability of nuclei. There are only certain combinations of neutrons and protons, which forms stable nuclei. Neutrons stabilize the nucleus, because they attract each other and protons , which helps offset the electrical repulsion between protons. As a result, as the number of protons increases, an increasing ratio of neutrons to protons is needed to form a stable nucleus. If there are too many (neutrons also obey the Pauli exclusion principle) or too few neutrons for a given number of protons, the resulting nucleus is not stable and it undergoes radioactive decay. Most atoms found in nature are stable and do not emit particles or energy that change form over time. Of the first 82 elements in the periodic table, 80 have isotopes considered to be stable. Technetium, promethium and all the elements with an atomic number over 82 are unstable and decompose through radioactive decay. Unstable isotopes decay spontaneously through various radioactive decay pathways, most commonly alpha decay, beta decay, gamma decay or electron capture. Many other rare types of decay, such as spontaneous fission or neutron emission are known.

Conservation Laws in Nuclear Decay

In analyzing nuclear reactions, we apply the many conservation laws. Nuclear reactions are subject to classical conservation laws for charge, momentum, angular momentum, and energy(including rest energies). Additional conservation laws, not anticipated by classical physics, are:

Certain of these laws are obeyed under all circumstances, others are not. We have accepted conservation of energy and momentum. In all the examples given we assume that the number of protons and the number of neutrons is separately conserved. We shall find circumstances and conditions in which this rule is not true. Where we are considering non-relativistic nuclear reactions, it is essentially true. However, where we are considering relativistic nuclear energies or those involving the weak interactions, we shall find that these principles must be extended.

Some conservation principles have arisen from theoretical considerations, others are just empirical relationships. Notwithstanding, any reaction not expressly forbidden by the conservation laws will generally occur, if perhaps at a slow rate. This expectation is based on quantum mechanics. Unless the barrier between the initial and final states is infinitely high, there is always a non-zero probability that a system will make the transition between them.

For purposes of analyzing non-relativistic reactions, it is sufficient to note four of the fundamental laws governing these reactions.

Conservation of nucleons. The total number of nucleons before and after a reaction are the same.
Conservation of charge. The sum of the charges on all the particles before and after a reaction are the same
Conservation of momentum. The total momentum of the interacting particles before and after a reaction are the same.
Conservation of energy. Energy, including rest mass energy, is conserved in nuclear reactions.

Reference: Lamarsh, John R. Introduction to Nuclear engineering 2nd Edition

Activity – Specific Activity

A measure of radioactivity (activity) is based on counting of disintegrations per second. The SI unit of activity is the becquerel (Bq), equal to one reciprocal second. The activity depends only on the number of decays per second, not on the type of decay, the energy of the decay products, or the biological effects of the radiation. It can be used to characterize the rate of emission of ionizing radiation. Specific activity is the activity per quantity of a radionuclide, thus specific activity is defined as the activity per quantity of atoms of a particular radionuclide. It is usually given in units of Bq/g, but another commonly used unit of activity is the curie (Ci) allowing the definition of specific activity in Ci/g.

Units of activity (the curie and the becquerel) can be also used to characterize an overall quantity of controlled or accidental releases of radioactive atoms.

Units of Activity

Becquerel. The becquerel is SI unit of radioactivity defined in 1974. It is named in honour of Henri Becquerel, a French physicist who discovered radioactivity in 1896. One becquerel (1Bq) is equal to 1 disintegration per second.
Curie. The curie is a non-SI unit of radioactivity defined in 1910. It was originally defined as equivalent to the number of disintegrations that one gram of radium-226 will undergo in one second. Currently, a curie is defined as 1Ci = 3.7 x 10¹⁰ disintegrations per second.
Rutherford. Rutherford (symbol Rd) is also a non-SI unit defined as the activity of a quantity of radioactive material in which one million nuclei decay per second.

Radioactive Decay Law

Calculations of the decay of radioactive nuclei are relatively straightforward, owing to the fact that there is only one fundamental law governing all decay process. This law states that the probability per unit time that a nucleus will decay is a constant, independent of time. This constant is called the decay constant and is denoted by λ, “lambda”. The radioactive decay of certain number of atoms (mass) is exponential in time.

Radioactive decay law: N = N.e^-λt

The rate of nuclear decay is also measured in terms of half-lives. The half-life is the amount of time it takes for a given isotope to lose half of its radioactivity. If a radioisotope has a half-life of 14 days, half of its atoms will have decayed within 14 days. In 14 more days, half of that remaining half will decay, and so on. Half lives range from millionths of a second for highly radioactive fission products to billions of years for long-lived materials (such as naturally occurring uranium). Notice that short half lives go with large decay constants. Radioactive material with a short half life is much more radioactive (at the time of production) but will obviously lose its radioactivity rapidly. No matter how long or short the half life is, after seven half lives have passed, there is less than 1 percent of the initial activity remaining.

The radioactive decay law can be derived also for activity calculations or mass of radioactive material calculations:

(Number of nuclei) N = N.e^-λt (Activity) A = A.e^-λt (Mass) m = m.e^-λt

, where N (number of particles) is the total number of particles in the sample, A (total activity) is the number of decays per unit time of a radioactive sample, m is the mass of remaining radioactive material.

Half-Life and Decay Constant

In calculations of radioactivity one of two parameters (decay constant or half-life), which characterize the rate of decay, must be known. There is a relation between the half-life (t_1/2) and the decay constant λ. The relationship can be derived from decay law by setting N = ½ N_o. This gives:

where ln 2 (the natural log of 2) equals 0.693. If the decay constant (λ) is given, it is easy to calculate the half-life, and vice-versa.

Half-Life and Radioactivity - Example

Half-Life and Radioactivity – Example

The relationship between half-life and the amount of a radionuclide required to give an activity of one curie is shown in the figure. This amount of material can be calculated using λ, which is the decay constant of certain nuclide:

The following figure illustrates the amount of material necessary for 1 curie of radioactivity. It is obvious, that the longer the half-life, the greater the quantity of radionuclide needed to produce the same activity. Of course, the longer lived substance will remain radioactive for a much longer time. As can be seen, the amount of material necessary for 1 curie of radioactivity can vary from an amount too small to be seen (0.00088 gram of cobalt-60), through 1 gram of radium-226, to almost three tons of uranium-238.

Example – Radioactive Decay Law

A sample of material contains 1 mikrogram of iodine-131. Note that, iodine-131 plays a major role as a radioactive isotope present in nuclear fission products, and it a major contributor to the health hazards when released into the atmosphere during an accident. Iodine-131 has a half-life of 8.02 days.

Calculate:

The number of iodine-131 atoms initially present.
The activity of the iodine-131 in curies.
The number of iodine-131 atoms that will remain in 50 days.
The time it will take for the activity to reach 0.1 mCi.

Solution:

The number of atoms of iodine-131 can be determined using isotopic mass as below.

N_I-131 = m_I-131 . N_A / M_I-131

N_I-131= (1 μg) x (6.02×10²³ nuclei/mol) / (130.91 g/mol)

N_I-131 = 4.6 x 10¹⁵ nuclei

The activity of the iodine-131 in curies can be determined using its decay constant:

where ln 2 (the natural log of 2) equals 0.693. If the decay constant (λ) is given, it is easy to calculate the half-life, and vice-versa.

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_50d) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

As can be seen, after 50 days the number of iodine-131 atoms and thus the activity will be about 75 times lower. After 82 days the activity will be approximately 1200 times lower. Therefore, the time of ten half-lives (factor 2¹⁰ = 1024) is widely used to define residual activity.

Decay Chain

In physics, a radioactive decay chain is a sequence of unstable atomic nuclei and their modes of decays, which leads to a stable nucleus. Sources of these unstable nuclei are different, but mostly engineers deal with naturally occurringradioactive decay chains known as radioactive series. Note that, in nuclear reactors, there are many types of decay chains of fission fragments. Fission fragments are highly unstable (radioactive) and undergo further radioactive decays to stabilize itself.

Decay Heat in Reactor

Decay Heat

When a reactor is shut down, fission essentially ceases, but decay energy is still being produced. The energy produced after shutdown is referred to as decay heat. The amount of decay heat production after shutdown is directly influenced by the power history (fission products accumulation) of the reactor prior to shutdown and by the level of fuel burnup (actinidies accumulation – especially in case of spent fuel handling). A reactor operated at full power for 10 days prior to shutdown has much higher decay heat generation than a reactor operated at low power for the same period. On the other hand, when the reactor changes its power from 50% to 100% of full power, the ratio of decay heat to neutron power drops to roughly half its previous level, and then builds up slowly as the fission product inventory adjusts to the new power.

The decay heat produced after a reactor shutdown from full power is initially equivalent to about 6 to 7% of the rated thermal power. Since radioactive decay is a random process at the level of single atoms, it is governed by the radioactive decay law. Note that, irradiated nuclear fuel contains a large number of different isotopes that contribute to decay heat, which are all subject to the radioactive decay law. Therefore a model describing decay heat must consider decay heat to be a sum of exponential functions with different decay constants and initial contribution to the heat rate. Fission fragments with a short half-life are much more radioactive (at the time of production) and contribute significantly to decay heat, but will obviously lose its share rapidly. On the other hand, fission fragments and transuranic elements with a long half-life are less radioactive (at the time of production) and produces less decay heat, but will obviously lose its share more slowly. This decay heat generation rate diminishes to about 1% approximately one hour after shutdown.

What is Radioactive Decay Law – Definition

December 14, 2019 by Nick Connor

Radioactive decay law states that the probability per unit time that a nucleus will decay is a constant, independent of time. This law describes the rate of nuclear decay. Radiation Dosimetry

The radioactive decay law is an universal law that describes the statistical behaviour of a large number of nuclides.

As was written, radioactive decay is a random process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay. In other words, a nucleus of a radionuclide has no “memory”. A nucleus does not “age” with the passage of time. Thus, the probability of its breaking down does not increase with time, but stays constant no matter how long the nucleus has existed. During its unpredictable decay this unstable nucleus spontaneosly and randomly decomposes to form a different nucleus (or a different energy state – gamma decay), giving off radiation in the form of atomic partices or high energy rays.

Calculations of the decay of radioactive nuclei are relatively straightforward, owing to the fact that there is only one fundamental law governing all decay process.

The radioactive decay law states that the probability per unit time that a nucleus will decay is a constant, independent of time. This constant is called the decay constant and is denoted by λ, “lambda”. This constant probability may vary greatly between different types of nuclei, leading to the many different observed decay rates. The radioactive decay of certain number of atoms (mass) is exponential in time.

Radioactive decay law: N = N.e^-λt

The radioactive decay law can be derived also for activity calculations or mass of radioactive material calculations:

(Number of nuclei) N = N.e^-λt (Activity) A = A.e^-λt (Mass) m = m.e^-λt

Table of examples of half lives and decay constants. Notice that short half lives go with large decay constants. Radioactive material with a short half life is much more radioactive but will obviously lose its radioactivity rapidly.

Activity – Specific Activity

Units of activity (the curie and the becquerel) can be also used to characterize an overall quantity of controlled or accidental releases of radioactive atoms.

Units of Activity

Becquerel. The becquerel is SI unit of radioactivity defined in 1974. It is named in honour of Henri Becquerel, a French physicist who discovered radioactivity in 1896. One becquerel (1Bq) is equal to 1 disintegration per second.
Curie. The curie is a non-SI unit of radioactivity defined in 1910. It was originally defined as equivalent to the number of disintegrations that one gram of radium-226 will undergo in one second. Currently, a curie is defined as 1Ci = 3.7 x 10¹⁰ disintegrations per second.
Rutherford. Rutherford (symbol Rd) is also a non-SI unit defined as the activity of a quantity of radioactive material in which one million nuclei decay per second.

Decay Constant and Half-Life

where ln 2 (the natural log of 2) equals 0.693. If the decay constant (λ) is given, it is easy to calculate the half-life, and vice-versa.

Bateman Equations

In physics, the Bateman equations are a set of first-order differential equations, which describe the time evolution of nuclide concentrations undergoing serial or linear decay chain. The model was formulated by Ernest Rutherford in 1905 and the analytical solution for the case of radioactive decay in a linear chain was provided by Harry Bateman in 1910. This model can be also used in nuclear depletion codes to solve nuclear transmutation and decay problems.

For example, ORIGEN is a computer code system for calculating the buildup, decay, and processing of radioactive materials. ORIGEN uses a matrix exponential method to solve a large system of coupled, linear, first-order ordinary differential equations (similar to the Bateman equations) with constant coefficients.

The Bateman equations for radioactive decay case of n – nuclide series in linear chain describing nuclide concentrations are as follows shown in the figure.

Example – Radioactive Decay Law

Calculate:

The number of iodine-131 atoms initially present.
The activity of the iodine-131 in curies.
The number of iodine-131 atoms that will remain in 50 days.
The time it will take for the activity to reach 0.1 mCi.

Solution:

The number of atoms of iodine-131 can be determined using isotopic mass as below.

N_I-131 = m_I-131 . N_A / M_I-131

N_I-131= (1 μg) x (6.02×10²³ nuclei/mol) / (130.91 g/mol)

N_I-131 = 4.6 x 10¹⁵ nuclei

The activity of the iodine-131 in curies can be determined using its decay constant:

The iodine-131 has half-live of 8.02 days (692928 sec) and therefore its decay constant is:

Using this value for the decay constant we can determine the activity of the sample:

3) and 4) The number of iodine-131 atoms that will remain in 50 days (N_50d) and the time it will take for the activity to reach 0.1 mCi can be calculated using the decay law:

References:

Radiation Protection:

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

Nuclear and Reactor Physics:

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

What is Form of Ionizing Radiation – Definition

December 14, 2019 by Nick Connor

There are several forms and types of ionizing radiation. Ionizing radiation is categorized by the nature of the particles or electromagnetic waves that create the ionizing effect. Radiation Dosimetry

There are several forms and types of ionizing radiation. Ionizing radiation is categorized by the nature of the particles or electromagnetic waves that create the ionizing effect. These particles/waves have different ionization mechanisms, and may be grouped as:

Directly ionizing. Charged particles (atomic nuclei, electrons, positrons, protons, muons, etc.) can ionize atoms directly by fundamental interaction through the Coulomb force if it carries sufficient kinetic energy. These particles must be moving at relativistic speeds to reach the required kinetic energy. Even 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.
- Alpha radiation. Alpha radiation consist of alpha particles at high energy/speed. 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.
- Beta radiation. Beta radiation consist of free electrons or positrons at relativistic speeds. Beta particles (electrons) are much smaller than alpha particles. They carry a single negative charge. They are more penetrating than alpha particles, but thin aluminum metal can stop them. They can travel several meters but deposit less energy at any one point along their paths than alpha particles.
Indirectly ionizing. Indirect ionizing radiation is electrically neutral particles and therefore does not interact strongly with matter. The bulk of the ionization effects are due to secondary ionizations.
- Photon radiation (Gamma or X-rays). Photon radiation consist of high energy photons. These photons are particles/waves (Wave-Particle Duality) without rest mass or electrical charge. They can travel 10 meters or more in air. This is a long distance compared to alpha or beta particles. However, gamma rays deposit less energy along their paths. Lead, water, and concrete stop gamma radiation. Photons (gamma rays and X-rays) can ionize atoms directly through the Photoelectric effect and the Compton effect, where the relatively energetic electron is produced. The secondary electron will go on to produce multiple ionization events, therefore the secondary (indirect) ionization is much more significant.
- Neutron radiation. Neutron radiation consist of free neutrons at any energies/speeds. Neutrons can be emitted by nuclear fission or by the decay of some radioactive atoms. Neutrons have zero electrical charge and cannot directly cause ionization. Neutrons ionize matter only indirectly. For example, when neutrons strike the hydrogen nuclei, proton radiation (fast protons) results. Neutrons can range from high speed, high energy particles to low speed, low energy particles (called thermal neutrons). Neutrons can travel hundreds of feet in air without any interaction.

Sources of Radiation

Radiation is all around us. In, around, and above the world we live in. It is a natural energy force that surrounds us. It is a part of our natural world that has been here since the birth of our planet. All living creatures, from the beginning of time, have been, and are still being, exposed to ionizing radiation. Ionizing radiation is generated through nuclear reactions, nuclear decay, by very high temperature, or via acceleration of charged particles in electromagnetic fields. But in general, there are two broad categories of radiation sources:

Natural Background Radiation. Natural background radiation includes radiation produced by the Sun, lightnings, primordial radioisotopes or supernova explosions etc.
Man-Made Sources of Radiation. Man-made sources include medical uses of radiation, residues from nuclear tests, industrial uses of radiation etc.

Special Reference: Sources and effects of ionizing radiation, Annex B. UNSCEAR. New York, 2010. ISBN: 978-92-1-142274-0.

What is Nuclear Stability – Definition

December 14, 2019 by Nick Connor

Nuclear Stability is a concept that helps to identify the stability of an isotope. To identify the stability of an isotope it is needed to find the ratio of neutrons to protons. Radiation Dosimetry

Nuclear Stability is a concept that helps to identify the stability of an isotope. To identify the stability of an isotope it is needed to find the ratio of neutrons to protons. To determine the stability of an isotope you can use the ratio neutron/proton (N/Z). Also to help understand this concept there is a chart of the nuclides, known as a Segre chart. This chart shows a plot of the known nuclides as a function of their atomic and neutron numbers. It can be observed from the chart that there are more neutrons than protons in nuclides with Z greater than about 20 (Calcium). These extra neutrons are necessary for stability of the heavier nuclei. The excess neutrons act somewhat like nuclear glue.

Examples:

Positive beta decay

Nuclei, such as ¹⁵O, which are lacking in neutrons (consist of 8 protons and 7 neutrons) undergo positron decay (positive beta decay). In this process, one of the protons in the nucleus is transformed into a neutron, positron and neutrino.The positron and the neutrino are emitted. The number of protons is thus reduced from 8 to 7 (number of neutrons is increased from 7 to 8), so that the resulting nucleus is an isotope of nitrogen, ¹⁵N, which is stable.

Negative beta decay

On the other hand nuclei, such as ¹⁹O, which have excess of neutrons, decay by negative beta decay, emitting a negative electron and an antineutrino. In this process, one of the neutrons in the nucleus is transformed into a proton. The number of protons is thus increased from 8 to 9 (number of neutrons is reduced from 11 to 10), so that the resulting nucleus is an isotope of fluor, ¹⁹F, which is stable. It should be noted that in both positive or negative beta decays the atomic mass number remains the same.

Nuclear Stability – Periodic Table

Periodic Table - Nuclear Stability — Periodic table with elements colored according to the half-life of their most stable isotope.

Of the first 82 elements in the periodic table, 80 have isotopes considered to be stable. Technetium, promethium and all the elements with an atomic number over 82 are unstable and decompose through radioactive decay. No undiscovered heavy elements (with atomic number over 110) are expected to be stable, therefore lead is considered the heaviest stable element. For each of the 80 stable elements, the number of the stable isotopes is given. For example, tin has 10 such stable isotopes.

There are 80 elements with at least one stable isotope, but 114 to 118 chemical elements are known. All elements to element 98 are found in nature, and the remainder of the discovered elements are artificially produced, with isotopes all known to be highly radioactive with relatively short half-lives.

Bismuth, thorium, uranium and plutonium are primordial nuclides because they have half-lives long enough to still be found on the Earth, while all the others are produced either by radioactive decay or are synthesized in laboratories and nuclear reactors. Primordial nuclides are nuclides found on the Earth that have existed in their current form since before Earth was formed. Primordial nuclides are residues from the Big Bang, from cosmogenic sources, and from ancient supernova explosions which occurred before the formation of the solar system. Only 288 such nuclides are known.

Connection between Nuclear Stability and Radioactive Decay

The nuclei of radioisotopes are unstable. In an attempt to reach a more stable arrangement of its neutrons and protons, the unstable nucleus will spontaneously decay to form a different nucleus. If the number of neutrons changes in the process (number of protons remains), a different isotopes is formed and an element remains (e.g. neutron emission). If the number of protons changes (different atomic number) in the process, then an atom of a different element is formed. This decomposition of the nucleus is referred to as radioactive decay. During radioactive decay an unstable nucleus spontaneosly and randomly decomposes to form a different nucleus (or a different energy state – gamma decay), giving off radiation in the form of atomic partices or high energy rays. This decay occurs at a constant, predictable rate that is referred to as half-life. A stable nucleus will not undergo this kind of decay and is thus non-radioactive.

What is Radiation – Definition

December 14, 2019 by Nick Connor

What is radiation? How is radiation defined? Radiation is energy that comes from a source and travels through some material or through space. Light, heat and sound are types of radiation. Radiation Dosimetry

What is Radiation

Most general definition is that radiation is energy that comes from a source and travels through some material or through space. Light, heat and sound are types of radiation. This is very general definition, the kind of radiation discussed in this article is called ionizing radiation. Most people connect the term radiation only with ionizing radiation, but it is not correct. Radiation is all around us. In, around, and above the world we live in. It is a natural energy force that surrounds us. It is a part of our natural world that has been here since the birth of our planet. We should distinguish between:

Non-ionizing radiation. The kinetic energy of particles (photons, electrons, etc.) of non-ionizing radiation is too small to produce charged ions when passing through matter. The particles (photons) have only sufficient energy to change the rotational, vibrational or electronic valence configurations of target molecules and atoms. Sunlight, radio waves, and cell phone signals are examples of non-ionizing (photon) radiation. However, it can still cause harm, like when you get a sunburn.

Ionizing radiation. The kinetic energy of particles (photons, electrons, etc.) of ionizing radiation is sufficient and the particle can ionize (to form ion by losing electrons) target atoms to form ions. Simply ionizing radiation can knock electrons from an atom.

The boundary is not sharply defined, since different molecules and atoms ionize at different energies. This is typical for electromagnetic waves. Among electromagnetic waves belong, in order of increasing frequency (energy) and decreasing wavelength: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. Gamma rays, X-rays, and the higher ultraviolet part of the spectrum are ionizing, whereas the lower ultraviolet, visible light (including laser light), infrared, microwaves, and radio waves are considered non-ionizing radiation.

Forms of ionizing radiation

Ionizing radiation is categorized by the nature of the particles or electromagnetic waves that create the ionizing effect. These particles/waves have different ionization mechanisms, and may be grouped as:

Directly ionizing. Charged particles (atomic nuclei, electrons, positrons, protons, muons, etc.) can ionize atoms directly by fundamental interaction through the Coulomb force if it carries sufficient kinetic energy. These particles must be moving at relativistic speeds to reach the required kinetic energy. Even 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.
- Alpha radiation. Alpha radiation consist of alpha particles at high energy/speed. 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.
- Beta radiation. Beta radiation consist of free electrons or positrons at relativistic speeds. Beta particles (electrons) are much smaller than alpha particles. They carry a single negative charge. They are more penetrating than alpha particles, but thin aluminum metal can stop them. They can travel several meters but deposit less energy at any one point along their paths than alpha particles.
Indirectly ionizing. Indirect ionizing radiation is electrically neutral particles and therefore does not interact strongly with matter. The bulk of the ionization effects are due to secondary ionizations.
- Photon radiation (Gamma rays or X-rays). Photon radiation consist of high energy photons. These photons are particles/waves (Wave-Particle Duality) without rest mass or electrical charge. They can travel 10 meters or more in air. This is a long distance compared to alpha or beta particles. However, gamma rays deposit less energy along their paths. Lead, water, and concrete stop gamma radiation. Photons (gamma rays and X-rays) can ionize atoms directly through the Photoelectric effect and the Compton effect, where the relatively energetic electron is produced. The secondary electron will go on to produce multiple ionization events, therefore the secondary (indirect) ionization is much more significant.
- Neutron radiation. Neutron radiation consist of free neutrons at any energies/speeds. Neutrons can be emitted by nuclear fission or by the decay of some radioactive atoms. Neutrons have zero electrical charge and cannot directly cause ionization. Neutrons ionize matter only indirectly. For example, when neutrons strike the hydrogen nuclei, proton radiation (fast protons) results. Neutrons can range from high speed, high energy particles to low speed, low energy particles (called thermal neutrons). Neutrons can travel hundreds of feet in air without any interaction.

Shielding of Ionizing 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 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.

What is Stable Nuclei – Unstable Nuclei – Definition

December 14, 2019 by Nick Connor

There are only certain combinations of neutrons and protons, which forms stable nuclei. If there are too many or too few neutrons for a given number of protons, the resulting nucleus is not stable and it undergoes radioactive decay. Unstable isotopes decay through various radioactive decay pathways. Radiation Dosimetry

Stable Nuclei – Unstable Nuclei

A nuclear stability is determined by the competition between two fundamental interactions. Atomic nuclei consist of protons and neutrons, which attract each other through the nuclear force, while protons repel each other via the electromagnetic force due to their positive charge. These two forces compete, leading to various stability of nuclei. There are only certain combinations of neutrons and protons, which forms stable nuclei. Neutrons stabilize the nucleus, because they attract each other and protons , which helps offset the electrical repulsion between protons. As a result, as the number of protons increases, an increasing ratio of neutrons to protons is needed to form a stable nucleus. If there are too many (neutrons also obey the Pauli exclusion principle) or too few neutrons for a given number of protons, the resulting nucleus is not stable and it undergoes radioactive decay. Unstable isotopes decay through various radioactive decay pathways, most commonly alpha decay, beta decay, or electron capture. Many other rare types of decay, such as spontaneous fission or neutron emission are known.

The Pauli exclusion principle also influences the critical energy of fissile and fissionable nuclei. For example, actinides with odd neutron number are usually fissile (fissionable with slow neutrons) while actinides with even neutron number are usually not fissile (but are fissionable with fast neutrons). Heavy nuclei with an even number of protons and an even number of neutrons are (due to Pauli exclusion principle) very stable thanks to the occurrence of ‘paired spin’. On the other hand, nuclei with an odd number of protons and neutrons are mostly unstable.

Magic Numbers of Protons and Neutrons

A magic number is a number of nucleons in a nucleus, which corresponds to complete shells within the atomic nucleus. Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the mass formula of von Weizsaecker (also called the semi-empirical mass formula – SEMF) and are hence more stable against nuclear decay. Magic numbers are predicted by the nuclear shell model and are proved by observations that have shown that there are sudden discontinuities in the proton and neutron separation energies at specific values of Z and N. These correspond to the closing of shells (or sub-shells). Nuclei with closed shells are more tightly bound than the next higher number. The closing of shells occurs at Z or N = 2, 8, 20, 28, (40), 50, 82, 126. It is found that nuclei with even numbers of protons and neutrons are more stable than those with odd numbers. Nuclei which have both neutron number and proton number equal to one of the magic numbers can be called “doubly magic“, and are found to be particularly stable.There are further special propertis of nuclei, which have a magic number of nucleons:

Higher abundance in nature. For example, helium-4 is among the most abundant (and stable) nuclei in the universe.
The stable elements at the end of the decay series all have a “magic number” of neutrons or protons. The nuclei He-4, O-16, and Pb-208 (82 protons and 126 neutrons) that contain magic numbers of both neutrons and protons are particularly stable. The relative stability of these nuclei is reminiscent of that of inert gas atoms (closed electron shells).
Nuclei with N = magic number have much lower neutron absorption cross-sections than surrounding isotopes.
These nuclei appear to be perfectly spherical in shape; they have zero quadrupole electric moments.
Magic number nuclei have higher first excitation energy.

Unstable Nuclei – Decay Modes

Nuclear decay (Radioactive decay) occurs when an unstable atom loses energy by emitting ionizing radiation. Radioactive decay is a random process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a particular atom will decay. During radioactive decay an unstable nucleus spontaneosly and randomly decomposes to form a different nucleus (or a different energy state – gamma decay), giving off radiation in the form of atomic partices or high energy rays. This decay occurs at a constant, predictable rate that is referred to as half-life. A stable nucleus will not undergo this kind of decay and is thus non-radioactive. There are many modes of radioactive decay:

Alpha radioactivity. Alpha decay is the emission of alpha particles (helium nuclei). Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus. Because of its very large mass (more than 7000 times the mass of the beta particle) and its charge, it heavy ionizes material and has a very short range.
Beta radioactivity. Beta decay is the emission of beta particles. Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei such as potassium-40. The beta particles have greater range of penetration than alpha particles, but still much less than gamma rays.The beta particles emitted are a form of ionizing radiation also known as beta rays. The production of beta particles is termed beta decay.
Gamma radioactivity. Gamma radioactivity consist of gamma rays. Gamma rays are electromagnetic radiation (high energy photons) of an very high frequency and of a high energy. They are produced by the decay of nuclei as they transition from a high energy state to a lower state known as gamma decay. Most of nuclear reactions are accompanied by gamma emission.
Neutron emission. Neutron emission is a type of radioactive decay of nuclei containing excess neutrons (especially fission products), in which a neutron is simply ejected from the nucleus. This type of radiation plays key role in nuclear reactor control, because these neutrons are delayed neutrons.

The rate of nuclear decay is also measured in terms of half-lives. The half-life is the amount of time it takes for a given isotope to lose half of its radioactivity. Half lives range from millionths of a second for highly radioactive fission products to billions of years for long-lived materials (such as naturally occurring uranium). Notice that short half lives go with large decay constants. Radioactive material with a short half life is much more radioactive (at the time of production) but will obviously lose its radioactivity rapidly. No matter how long or short the half life is, after seven half lives have passed, there is less than 1 percent of the initial activity remaining.

References:

Nuclear and Reactor Physics:

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

Advanced Reactor Physics:

K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

Description of Alpha Particles

Description of Fission Fragments

Nature of Interaction of Charged Particles with Matter

Stopping Power – Bethe Formula

Bragg Curve

Description Beta Particles

Spectrum of beta particles

Nature of Interaction of Beta Radiation with Matter

Bremsstrahlung

Cherenkov Radiation

Positron Interactions

Positron Annihilation

Photoelectric Effect

Key Characteristics

Definition of Photoelectric Effect

Compton Scattering

Key Characteristics

Definition of Compton Scattering

Pair Production

Neutron interactions

Neutron cross-section

Typical cross-sections of materials in the reactor

Example – Amount of antineutrinos produced:

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Shielding of Neutrons

Principles of Neutron Shielding

Water as a neutron shield

Concrete as a neutron shield

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Neutron Converters

Detection of Thermal Neutrons

Detection of Neutrons using Ionization Chamber

Fission Chamber – Wide Range Detectors

Activation Foils and Flux Wires

Detection of Fast Neutrons

Proton Recoil – Recoil Detectors

Bonner Spheres Spectrometer

Detection of Neutrons using Scintillation Counter

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Interactions of Neutrons with Matter

Types of neutron-nuclear reactions

Neutron cross-section

Law 1/v

Resonance neutron capture

Doppler broadening

Typical cross-sections of materials in the reactor

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What is Radioactive Decay

Nature of Decay

Conservation Laws in Nuclear Decay

Activity – Specific Activity

Radioactive Decay Law

Half-Life and Decay Constant

Half-Life and Radioactivity – Example

Example – Radioactive Decay Law

Decay Chain

Decay Heat in Reactor

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Activity – Specific Activity

Decay Constant and Half-Life

Bateman Equations

Example – Radioactive Decay Law

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Examples:

Nuclear Stability – Periodic Table

Connection between Nuclear Stability and Radioactive Decay

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