Periodic Table

Discovery of Gamma Rays

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

See also:

Description of Gamma Rays

See also:

Gamma Ray

See also:

Characteristics of Gamma Rays

See above:See also:

Gamma Ray  

See also:

Discovery of Gamma Rays

Characteristics of Gamma Rays / Radiation

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

See also:

Discovery of Gamma Rays

See also:

Gamma Ray

See also:

Photoelectric Effect

Description of Gamma Radiation

Gamma rays, also known as gamma radiation, refers to electromagnetic radiation (no rest mass, no charge) of a very high energies. Gamma rays are high-energy photons with very short wavelengths and thus very high frequency. Since the gamma rays are in substance only a very high-energy photons, they are very penetrating matter and are thus biologically hazardous. Gamma rays can travel thousands of feet in air and can easily pass through the human body.Gamma rays are emitted by unstable nuclei in their transition from a high energy state to a lower state known as gamma decay. In most practical laboratory sources, the excited nuclear states are created in the decay of a parent radionuclide, therefore a gamma decay typically accompanies other forms of decay, such as alpha or beta decay.Radiation and also gamma rays are all around us. In, around, and above the world we live in. It is a part of our natural world that has been here since the birth of our planet. Natural sources of gamma rays on Earth are inter alia gamma rays from naturally occurring radionuclides, particularly potassium-40.  Potassium-40 is a radioactive isotope of potassium which has a very long half-life of 1.251×10⁹ years (comparable to the age of Earth). This isotope can be found in soil, water also in meat and bananas. This is not the only example of natural source of gamma rays.

See also: Discovery of Gamma Rays

Characteristics of Gamma Rays / Radiation

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

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

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

 

Photoelectric Effect

• 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.

See also: Albert Einstein and the Photoelectric Effect

Definition of Photoelectric effect

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

E_e=hν-E_b

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

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

 

Cross-Sections of Photoelectric Effect

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

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

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

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

Compton Scattering

Key characteristics of Compton Scattering

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

Definition of Compton Scattering

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

Compton Scattering Formula

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

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

where

λ is the initial wavelength of photon

λ’ is the wavelength after scattering,

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

m_e is the electron rest mass (0.511 MeV)

c is the speed of light

Θ is the scattering angle.

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

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

Compton Scattering – Cross-Sections

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

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

 

Compton Edge

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

Inverse Compton Scattering

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

 

The atom consist of a small but massive nucleus surrounded by a cloud of rapidly moving electrons. The nucleus is composed of protons and neutrons. Total number of protons in the nucleus is called the atomic number of the atom and is given the symbol Z. The total electrical charge of the nucleus is therefore +Ze, where e (elementary charge) equals to 1,602 x 10^-19 coulombs. In a neutral atom there are as many electrons as protons moving about nucleus. It is the electrons that are responsible for the chemical bavavior of atoms, and which identify the various chemical elements.

Hydrogen (H), for example , consist of one electron and one proton. The number of neutrons in a nucleus is known as the neutron number and is given the symbol N. The total number of nucleons, that is, protons and neutrons in a nucleus, is equal to Z + N = A, where A is called the atomic mass number. The various species of atoms whose nuclei contain particular numbers of protons and neutrons are called nuclides. Each nuclide is denoted by chemical symbol of the element (this specifies Z) with tha atomic mass number as supescript.

Thus the symbol ¹H refers to the nuclide of hydrogen with a single proton as nucleus. ²H is the hydrogen nuclide with a neutron as well as a proton in the nucleus (2H is also called deuterium or heavy hydrogen). Atoms such as ¹H, ²H whose nuclei contain the same number of protons but different number of neutrons (different A) are known as isotopes. Uranium, for instance, has three isotopes occuring in nature – ²³⁸U, ²³⁵U and ²³⁴U. The stable isotopes (plus a few of the unstable isotopes) are the atoms that are found in the naturally occuring elements in nature. However, they are not found in equal amounts. Some isotopes of a given element are more abundant than others. For example 99,27% of naturally occuring uranium atoms are the isotope ²³⁸U, 0,72% are the isotope ²³⁵U and 0,0055% are the isotope ²³⁴U. Exact structure of atoms is described by Atomic Theory and Theory of Nuclear Structure.

Volume of an Atom and Nucleus

The atom consist of a small but massive nucleus surrounded by a cloud of rapidly moving electrons. The nucleus is composed of protons and neutrons. Typical nuclear radii are of the order 10⁻¹⁴ m. Assuming spherical shape, nuclear radii can be calculated according to following formula:

r = r₀ . A^1/3

where r₀ = 1.2 x 10^-15 m = 1.2 fm

If we use this approximation, we therefore expect the volume of the nucleus to be of the order of 4/3πr³ or 7,23 ×10⁻⁴⁵ m³ for hydrogen nuclei or 1721×10⁻⁴⁵ m³ for ²³⁸U nuclei. These are volumes of nuclei and atomic nuclei (protons and neutrons) contains of about 99.95% of mass of atom.

Is an atom an empty space?

The volume of an atom is about 15 orders of magnitude larger than the volume of a nucleus. For uranium atom, the Van der Waals radius is about 186 pm = 1.86 ×10⁻¹⁰ m. The Van der Waals radius, r_w, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom.  Assuming spherical shape, the uranium atom have volume of about  26.9 ×10⁻³⁰ m³. But this “huge” space is occupied primarily by electrons, because the nucleus occupies only about 1721×10⁻⁴⁵ m³ of space. These electrons together weigh only a fraction (let say 0.05%) of entire atom.

It may seem, that the space and in fact the matter is empty, but it is not. Due to the quantum nature of electrons, the electrons are not point particles, they are smeared out over the whole atom. The classical description cannot be used to describe things on the atomic scale. On the atomic scale, physicists have found that quantum mechanics describes things very well on that scale. Particle locations in quantum mechanics are not at an exact position, they are described by a probability density function. Therefore the space in an atom (between electrons and an atomic nucleus) is not empty, but it is filled by a probability density function of electrons (usually known as  “electron cloud“).

• Atomic Theory. Atomic theory is a scientific theory of the nature of matter, which states that matter is composed of discrete units called atoms. The word atom comes from the Ancient Greek adjective atomos, meaning “uncuttable”. Today it is known that also atoms are divisible. Atomic Theory consist of many models and discoveries, which gradually formed this theory.
• Theory of Nuclear Structure. Understanding the structure of the atomic nucleus is one of the central challenges in modern nuclear physics.

See also:

Fundamental Particles

See also:

Atomic and Nuclear Physics

See also:

Mass and Energy

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)

See also: Shielding of Ionizing Radiation

• Shielding of Alpha Radiation
• Shielding of Beta Radiation
• Shielding of Positrons
• Shielding of Gamma Radiation
• Shielding of Neutrons

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.

See also: Neutron Reflector

A little strange radiation shielding is usually used to protect material of reactor pressure vessel (especially in PWR power plants). Structural materials of pressure vessel and reactor internals are damaged especially by fast neutrons. Fast neutrons create structural defects, which in result lead to embrittlement of material of pressure vessel. In order to minimize the neutron flux at the vessel wall, also core loading strategy can be modified. In “out-in” fuel loading strategy fresh fuel assemblies are placed at the periphery of the core.  This configuration causes high neutron fluence at the vessel wall. Therefore the “in-out” fuel loading strategy (with low leakage loading patterns – L3P) has been adopted at many nuclear power plants. In contrast to “out-in” strategy, low leakage cores have fresh fuel assemblies in the second row, not at the periphery of the core. The periphery contains fuel with higher fuel burnup and lower relative power and serves as the very sophisticated radiation shield.

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

See also:

Mass and Energy

See also:

Atomic and Nuclear Physics

See also:

Nuclear Stability

See also: Livechart – iaea.org

Atomic nuclei consist of protons and neutrons, which attract each other through the nuclear force, while protons repel each other via the electric 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 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. It should be noted that all of these decay pathways may be accompanied by the subsequent emission of gamma radiation. Pure alpha or beta decays are very rare.

Examples:

Nuclear Stability – Periodic Table

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.

See also:

Radiation

See also:

Atomic and Nuclear Physics

See also:

Radioactive Decay

An experimental breakthrough came in 1930 with the observation by Bothe and Becker. They found that if the very energetic alpha particles emitted from polonium fell on certain light elements, specifically beryllium, boron, or lithium, an unusually penetrating radiation was produced. Since this radiation was not influenced by an electric field (neutrons have no charge), they presumed it was gamma rays (but much more penetrating). It was shown (Curie and Joliot) that when a paraffin target with this radiation is bombarded, it ejected protons with energy about 5.3 MeV. Paraffin is high in hydrogen content, hence offers a target dense with protons (since neutrons and protons have almost equal mass, protons scatter energetically from neutrons).These experimental results were difficult to interpret. James Chadwick was able to prove that the neutral particle could not be a photon by bombarding targets other than hydrogen, including nitrogen, oxygen, helium and argon. Not only were these inconsistent with photon emission on energy grounds, the cross-section for the interactions was orders of magnitude greater than that for Compton scattering by photons. In Rome, the young physicist Ettore Majorana suggested that the manner in which the new radiation interacted with protons required a new neutral particle.

The task was that of determining the mass of this neutral particle. James Chadwick chose to bombard boron with alpha particles and analyze the interaction of the neutral particles with nitrogen. These particlular targets were chosen partly because the masses of boron and nitrogen were well known. Using kinematics, Chadwick was able to determine the velocity of the protons. Then through conservation of momentum techniques, he was able to determine that the mass of the neutral radiation was almost exactly the same as that of a proton. In 1932, Chadwick proposed that the neutral particle was Rutherford’s neutron. In 1935, he was awarded the Nobel Prize for his discovery.

See also:

Neutron

See also:

Structure of the Neutron

Neutrons and protons are classified as hadrons, subatomic particles that are subject to the strong force and as baryons since they are composed of three quarks. The neutron is a composite particle made of two down quarks with charge −⅓  e and one up quark with charge +⅔ e. Since the neutron has no net electric charge, it is not affected by eletric forces, but the neutron does have a slight distribution of electric charge within it. This results in non-zero magnetic moment (dipole moment) of the neutron. Therefore the neutron interacts also via electromagnetic interaction, but much weaker than the proton.

The mass of the neutron is 939.565 MeV/c², whereas the mass of the three quarks is only about 12 MeV/c² (only about 1% of the mass-energy of the neutron). Like the proton, most of mass (energy) of the neutron is in the form of the strong nuclear force energy (gluons). The quarks of the neutron are held together by gluons, the exchange particles for the strong nuclear force. Gluons carry the color charge of the strong nuclear force.

See also:

Discovery of the Neutron

See also:

Neutron

See also:

Properties of the Neutron

Interactions of Neutrons with Matter

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:

Types of neutron-nuclear reactions

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.

See also: JANIS (Java-based nuclear information software) 

See also: Neutron cross-section

Law 1/v

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.

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:

.

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

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

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.

See also:

Neutron Energy

See also:

Neutron

See also:

Free Neutron