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What is Neutron Source – Definition

A neutron source is any device that emits neutrons. Neutron sources have many applications, they can be used in research, engineering, medicine, chemistry and nuclear power. Material Properties
A neutron source is any device that emits neutrons. Neutron sources have many applications, they can be used in research, engineering, medicine, petroleum exploration, biology, chemistry and nuclear power. A neutron source is characterized by a number of factors:
  • Significance of the source
  • Intensity. The rate of neutrons emitted by the source.
  • Energy distribution of emitted neutrons.
  • Angular distribution of emitted neutrons.
  • Mode of emission. Continuous or pulsed operation.

Classification by significance of the source

  • Large (Significant) neutron sources
    • Nuclear Reactors. There are nuclei that can undergo fission on their own spontaneously, but only certain nuclei, like uranium-235, uranium-233 and plutonium-239, can sustain a fission chain reaction. This is because these nuclei release neutrons when they break apart, and these neutrons can induce fission of other nuclei. Uranium-235 which exists as 0.7% of naturally occurring uranium undergoes nuclear fission with thermal neutrons with the production of, on average, 2.4 fast neutrons and the release of ~ 180 MeV of energy per fission. Free neutrons released by each fission play very important role as a trigger of the reaction, but they can be also used fo another purpose. For example: One neutron is required to trigger a further fission. Part of free neutrons (let say 0.5 neutrons/fission) is absorbed in other material, but an excess of neutrons (0.9 neutrons/fission) is able to leave the surface of the reactor core and can be used as a neutron source.
    • Fusion Systems. Nuclear fusion is a nuclear reaction in which two or more atomic nuclei (e.g. D+T) collide at a very high energy and fuse together. Thy byproduct of DT fusion is a free neutron (see picture), therefore also nuclear fusion reaction has the potential to produces large quantities of neutrons.
    • Spallation Sources. A spallation source is a high-flux neutron source in which protons that have been accelerated to high energies hit a heavy target material, causing the emission of neutrons. The reaction occurs above a certain energy threshold for the incident particle, which is typically 5 – 15 MeV.
  • Medium neutron sources
    • Bremssstrahlung from Electron Accelerators / Photofission. Energetic electrons when slowed down rapidly in a heavy target emit intense gamma radiation during the deceleration process. This is known as Bremsstrahlung or braking radiation. The interaction of the gamma radiation with the target produces neutrons via the (γ,n) reaction, or the (γ,fission) reaction when a fissile target is used. e-→Pb → γ→ Pb →(γ,n) and (γ,fission). The Bremsstrahlung γ energy exceeds the binding energy of the “last” neutron in the target. A source strength of 1013 neutrons/second produced in short (i.e. < 5 μs) pulses can be readily realised.
    • Dense plasme focus. The dense plasma focus (DPF) is a device that is known as an efficient source of neutrons from fusion reactions. Mechanism of dense plasma focus (DPF) is based on nuclear fusion of short-lived plasma of deuterium and/or tritium. This device produces a short-lived plasma by electromagnetic compression and acceleration that is called a pinch. This plasma is during the pinch hot and dense enough to cause nuclear fusion and the emission of neutrons.
    • Light ion accelerators. Neutrons can be also produced by particle accelerators using targets of deuterium, tritium, lithium, beryllium, and other low-Z materials. In this case the target must be bombarded with accelerated hydrogen (H), deuterium (D), or tritium (T) nuclei.
  • Small neutron sources
    • Neutron Generators. Neutrons are produced in the fusion of deuterium and tritium in the following exothermic reaction. 2D + 3T → 4He + n + 17.6 MeV.  The neutron is produced with a kinetic energy of 14.1 MeV. This can be achieved on a small scale in the laboratory with a modest 100 kV accelerator for deuterium atoms bombarding a tritium target. Continuous neutron sources of ~1011 neutrons/second can be achieved relatively simply.
    • Radioisotope source – (α,n) reactions. In certain light isotopes the ‘last’ neutron in the nucleus is weakly bound and is released when the compound nucleus formed following α-particle bombardment decays. The bombardment of beryllium by α-particles leads to the production of neutrons by the following exothermic reaction: 4He + 9Be→12C + n + 5.7 MeV. This reaction yields a weak source of neutrons with an energy spectrum resembling that from a fission source and is used nowadays in portable neutron sources. Radium, plutonium or americium can be used as an α-emitter.
    • Radioisotope source – (γ,n) reactions. (γ,n) reactions can also be used for the same purpose. In this type of source, because of the greater range of the γ-ray, the two physical  components of the source can be separated making it possible to ‘switch off’ the reaction if so required by removing the radioactive source from the beryllium. (γ,n) sources produce a monoenergetic neutrons unlike (α,n) sources.  The (γ,n) source uses antimony-124 as the gamma emitter in the following endothermic reaction.

124Sb→124Te + β− + γ

γ + 9Be→8Be + n – 1.66 MeV

    • Radioisotope source – spontaneous fission. Certain isotopes undergo spontaneous fission with emission of neutrons. The most commonly used spontaneous fission source is the radioactive isotope californium-252. Cf-252 and all other spontaneous fission neutron sources are produced by irradiating uranium or another transuranic element in a nuclear reactor, where neutrons are absorbed in the starting material and its subsequent reaction products, transmuting the starting material into the SF isotope.
Nuclear chain reaction as a neutron source
A nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions.

Nuclear fusion reaction as a neutron source


Neutron Source Example Neutron Yield Released Energy

MeV / neutron

(α,n) reactions Radium-Beryllium source 8 x 10-5 / α 6,600,000
(D,T) fusion 400 keV deuterons in neutron generator 4 x 10-5 / deuteron 10,000
Electron Bremsstrahlung

/ Photofission

100 MeV electrons on uranium 5 x 10-2 / electron 2,000
Fission Induced fission of U-235  in thermal reactor 1 / fission 180
Spallation 800 MeV protons on uranium 30 / proton 55
(D,T) fusion Inertial confinement fusion 1 / fusion 18

See also:

Shielding of Neutrons

See also:

Neutron

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What is Nuclear Energy – Definition

What is nuclear energy? How is nuclear energy defined? Nuclear energy comes either from spontaneous nuclei conversions or induced nuclei conversions. Material Properties

What is Nuclear Energy

Nuclear energy comes either from spontaneous nuclei conversions or induced nuclei conversions. Among these conversions (nuclear reactions) belong for example nuclear fission, nuclear decay and nuclear fusion. Conversions are associated with mass and energy changes. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible, one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula:

E=MC2 - Nuclear energy
This formule describes equivalence of mass and energy.

, where M is the small amount of mass and C is the speed of light.

What that means? If the nuclear energy is generated (splitting atoms, nuclear fussion), a small amount of mass (saved in the nuclear binding energy) transforms into the pure energy (such as kinetic energy, thermal energy, or radiant energy).

Example:

The energy equivalent of one gram (1/1000 of a kilogram) of mass is equivalent to:

  • 89.9 terajoules
  • 25.0 million kilowatt-hours (≈ 25 GW·h)
  • 21.5 billion kilocalories (≈ 21 Tcal)
  • 85.2 billion BTUs

or to the energy released by combustion of the following:

  • 21.5 kilotons of TNT-equivalent energy (≈ 21 kt)
  • 568,000 US gallons of automotive gasoline

Any time energy is generated, the process can be evaluated from an E = mc2 perspective.

Nuclear Binding Energy – Mass Defect

 
Conservation of Mass-Energy
At the beginning of the 20th century, the notion of mass underwent a radical revision. Mass lost its absoluteness. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc2. In words, energy equals mass multiplied by the speed of light squared. Because the speed of light is a very large number, the formula implies that any small amount of matter contains a very large amount of energy. The mass of an object was seen to be equivalent to energy, to be interconvertible with energy, and to increase significantly at exceedingly high speeds near that of light. The total energy of an object was understood to comprise its rest mass as well as its increase of mass caused by increase in kinetic energy.

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. It was found the rest mass an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E = mc2) this binding energy is proportional to this mass difference and it is known as the mass defect.

E=mc2 represents the new conservation principle – the conservation of mass-energy.

Nuclear Binding Curve
Nuclear binding energy curve.
Nuclear binding energy curve.
Source: hyperphysics.phy-astr.gsu.edu

If the splitting releases energy and the fusion releases the energy, so where is the breaking point? For understanding this issue it is better to relate the binding energy to one nucleon, to obtain nuclear binding curve. The binding energy per one nucleon is not linear. There is a peak in the binding energy curve in the region of stability near iron and this means that either the breakup of heavier nuclei than iron or the combining of lighter nuclei than iron will yield energy.

The reason the trend reverses after iron peak is the growing positive charge of the nuclei. The electric force has greater range than strong nuclear force. While the strong nuclear force binds only close neighbors the electric force of each proton repels the other protons.

Example: Mass defect of a 63Cu
Calculate the mass defect of a 63Cu nucleus if the actual mass of 63Cu in its nuclear ground state is 62.91367 u.

63Cu nucleus has 29 protons and also has (63 – 29) 34 neutrons.

The mass of a proton is 1.00728 u and a neutron is 1.00867 u.

The combined mass is: 29 protons x (1.00728 u/proton) + 34 neutrons x (1.00867 u/neutron) = 63.50590 u

The mass defect is Δm = 63.50590 u – 62.91367 u =  0.59223 u

Convert the mass defect into energy (nuclear binding energy).

(0.59223 u/nucleus) x (1.6606 x 10-27 kg/u) = 9.8346 x 10-28 kg/nucleus

ΔE = Δmc2

ΔE = (9.8346 x 10-28 kg/nucleus) x (2.9979 x 108 m/s)2 = 8.8387 x 10-11 J/nucleus

The energy calculated in the previous example is the nuclear binding energy.  However, the nuclear binding energy may be expressed as kJ/mol (for better understanding).

Calculate the nuclear binding energy of 1 mole of 63Cu:

(8.8387 x 10-11 J/nucleus) x (1 kJ/1000 J) x (6.022 x 1023 nuclei/mol) = 5.3227 x 1010 kJ/mol of nuclei.

One mole of 63Cu (~63 grams) is bound by the nuclear binding energy (5.3227 x 1010 kJ/mol) which is equivalent to:

  • 14.8 million kilowatt-hours (≈ 15 GW·h)
  • 336,100 US gallons of automotive gasoline
Example: Mass defect of the reactor core
Calculate the mass defect of the 3000MWth reactor core after one year of operation.

It is known the average recoverable energy per fission is about 200 MeV, being the total energy minus the energy of the energy of antineutrinos that are radiated away.

The reaction rate per entire 3000MWth reactor core is about  9.33×1019 fissions / second.

The overall energy release in the units of joules is:

200×106 (eV) x 1.602×10-19 (J/eV) x 9.33×1019 (s-1) x 31.5×106 (seconds in year) = 9.4×1016 J/year

The mass defect is calculated as:

Δm = ΔE/c2

Δm = 9.4×1016 / (2.9979 x 108)2 = 1.046 kg

That means in a typical 3000MWth reactor core about 1 kilogram of matter is converted into pure energy.

Note that, a typical annual uranium load for a 3000MWth reactor core is about 20 tonnes of enriched uranium (i.e. about 22.7 tonnes of UO2). Entire reactor core may contain about 80 tonnes of enriched uranium.

Mass defect directly from E=mc2

The mass defect can be calculated directly from the Einstein relationship (E = mc2) as:

Δm = ΔE/c2

Δm = 3000×106 (W = J/s) x 31.5×106 (seconds in year) / (2.9979 x 108)= 1.051 kg

Nuclear Energy and Electricity Production

Today we use the nuclear energy to generate useful heat and electricity. This electricity is generated in nuclear power plants. The heat source in the nuclear power plant is a nuclear reactor. As is typical in all conventional thermal power stations the heat is used to generate steam which drives a steam turbine connected to a generator which produces electricity. In 2011 nuclear power provided 10% of the world’s electricity. In 2007, the IAEA reported there were 439 nuclear power reactors in operation in the world, operating in 31 countries. They produce base-load electricity 24/7 without emitting any pollutants into the atmosphere (this includes CO2).

Energy consumption
Source: https://www.llnl.gov/news/americans-using-more-energy-according-lawrence-livermore-analysis

Nuclear Energy Consumption – Summary

Nuclear Reactor
Pressure vessel of PWR.

Consumption of a 3000MWth (~1000MWe) reactor (12-months fuel cycle)

It is an illustrative example, following data do not correspond to any reactor design.

  • Typical reactor may contain about 165 tonnes of fuel (including structural material)
  • Typical reactor may contain about 100 tonnes of enriched uranium (i.e. about 113 tonnes of uranium dioxide).
  • This fuel is loaded within, for example, 157 fuel assemblies composed of over 45,000 fuel rods.
  • A common fuel assembly contain energy for approximately 4 years of operation at full power.
  • Therefore about one quarter of the core is yearly removed to spent fuel pool (i.e. about 40 fuel assemblies), while the remainder is rearranged to a location in the core better suited to its remaining level of enrichment (see Power Distribution).
  • The removed fuel (spent nuclear fuel) still contains about 96% of reusable material (it must be removed due to decreasing kinf of an assembly).
  • Annual natural uranium consumption of this reactor is about 250 tonnes of natural uranium (to produce of about 25 tonnes of enriched uranium).
  • Annual enriched uranium consumption of this reactor is about 25 tonnes of enriched uranium.
  • Annual fissile material consumption of this reactor is about 1 005 kg.
  • Annual matter consumption of this reactor is about 1.051 kg.
  • But it corresponds to about 3 200 000 tons of coal burned in coal-fired power plant per year.

See also: Fuel Consumption

See also:

Atomic and Nuclear Structure

See also:

Atomic and Nuclear Physics

See also:

Radiation

We hope, this article, Nuclear Energy, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Nuclear Fission – Definition

Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts (lighter nuclei). Neutron-induced Fission Reaction
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. In this section, the neutron-induced nuclear fission, the process of the greatest practical importance in reactor physics, will be discussed.
A Brief History of Nuclear Fission

Nuclear fission of heavy elements was discovered on December 17, 1938 by Otto Hahn and his assistant Fritz Strassmann. They attempted to create transuranic elements by bombarding uranium with neutrons. Rather than the heavy elements they expected, they got several unidentified products. When they finally identified one of the products as Barium-141, they were circumspective to publish the finding because it was so unexpected.

When they finally published the results in 1939, they came to the attention of Lise Meitner, an Austrian-born physicist who had worked with Hahn on his nuclear experiments. She was the first to realize that Hahn’s barium and other lighter products from the neutron bombardment experiments were coming from the fission of U-235. Meitner and Frisch carried out further experiments which showed that the U-235 fission can release large amounts of energy both as electromagnetic radiation and as kinetic energy of the fragments (heating the bulk material where fission takes place). They realized that this made possible a chain reaction with an unprecedented energy yield.

neutron nuclear reactions

Basics of Nuclear Fission

Basics of Nuclear Fission
There are nuclei that can undergo fission on their own spontaneously, but only certain nuclei, like uranium-235, uranium-233 and plutonium-239, can sustain a fission chain reaction. This is because these nuclei release neutrons when they break apart, and these neutrons can induce fission of other nuclei. Free neutrons released by each fission play very important role as a trigger of the reaction.
Nuclear fission
Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts (lighter nuclei). This nuclear reaction is triggered by the neutron. Source: chemwiki.ucdavis.edu
Chain Reaction

Chain reaction

A nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series of these reactions. The “one or more” is the key parameter of reactor physics. To raise or lower the power, the amount of reactions must be changed (using the control rods) so that the number of neutrons present (and hence the rate of power generation) is either reduced or increased.

Nuclear chain reaction
A nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions.
Key Features of Nuclear Fission
  • Nuclear fission is the main process generating nuclear energy.
  • Most of the energy (~85%) is released in the form of kinetic energy of the splitted parts.
  • Neutrons trigger the nuclear fission.
  • The fission process produces free neutrons (2 or 3).
  • The chain reaction means if the reaction induces one or more reactions.
  • The probability that fission will occur depends on incident neutron energy.
  • Therefore the moderator is used to slow down neutrons (to increase the probability of fission)
  • For reactors using light water as moderator, enriched uranium fuel is required.
  • Control rods contains material which absorb neutrons (boron, cadmium, …)
  • Withdrawal of the rods increases the parameter one or more (multiplication factor), thus increase the power.
  • Insertion of the rods decreases the parameter one or more (multiplication factor), thus decrease the power.
  • The multiplication factor is influenced also by other parameters such as temperature, fuel burnup and reactor poisoning.

Youtube animation

Principles of Nuclear Fission

In general, the neutron-induced fission reaction is the reaction, in which the incident neutron enters the heavy target nucleus (fissionable nucleus), forming a compound nucleus that is excited to such a high energy level (Eexcitation > Ecritical) that the nucleus splits into two large fission fragments. A large amount of energy is released in the form of radiation and fragment kinetic energy. Moreover and what is crucial, the fission process may produce 2, 3 or more free neutrons and these neutrons can trigger further fission and a chain reaction can take place. In order to understand the process of fission, we must understand processes, that occur inside the nucleus to be fissioned. At first, the nuclear binding energy must be defined.

 
Uranium - 235 Fission
Fissile / Fertile Material Cross-sections
Source: JANIS (Java-based nuclear information software)
http://www.oecd-nea.org/janis/

Uranium 235 is a fissile isotope and its fission cross-section for thermal neutrons is about 585 barns (for 0.0253 eV neutron). For fast neutrons its fission cross-section is on the order of barns. Most of absorption reactions result in fission reaction, but a minority results in radiative capture forming 236U. The cross-section for radiative capture for thermal neutrons is about 99 barns (for 0.0253 eV neutron). Therefore about 15% of all absorption reactions result in radiative capture of neutron. About 85% of all absorption reactions result in fission.

Uranium absorption reaction

Uranium - 233 Fission
Fissile / Fertile Material Cross-sections
Source: JANIS (Java-based nuclear information software)
http://www.oecd-nea.org/janis/

Uranium 233 is a very good fissile isotope and its fission cross-sectionfor thermal neutrons is about 531 barns (for 0.0253 eV neutron). For fast neutrons its fission cross-section is on the order of barns. Most of absorption reactions result in fission reaction, but a minority results in radiative capture forming 234U. The cross-section for radiative capture for thermal neutrons is about 45 barns (for 0.0253 eV neutron). Therefore about 6% of all absorption reactions result in radiative capture of neutron. About 94% of all absorption reactions result in fission. The capture-to-fission ratio is much smaller than the other two major fissile fuels 235U and 239U.

Uranium 233 absorption reaction

Plutonium - 239 Fission
Fissile / Fertile Material Cross-sections
Source: JANIS (Java-based nuclear information software)
http://www.oecd-nea.org/janis/

Plutonium 239 is a fissile isotope and its fission cross-section forthermal neutrons is about 750 barns (for 0.025 eV neutron). For fast neutrons its fission cross-section is on the order of barns. Most of absorption reactions result in fission reaction, but a part of reactions result in radiative capture forming 240Pu. The cross-section for radiative capture for thermal neutrons is about 270 barns (for 0.025 eV neutron). Therefore about 27% of all absorption reactions result in radiative capture of incident neutron. About 73% of all absorption reactions result in fission.

Plutonium fission vs. radiative capture

Nuclear Binding Energy

 
Binding Energy
A binding energy is generally the energy required to disassemble a whole system into separate parts. It is known the sum of separate parts has typically a higher potential energy than a bound system, therefore the bound system is more stable. A creation of bound system is often accompanied by subsequent energy release. We usually distinguish the binding energy according to these levels:
  • Atomic level
  • Molecular level
  • Nuclear level
At nuclear level the nuclear binding energy is the energy required to disassemble (to overcome the strong nuclear force) a nucleus of an atom into its component parts (protons and neutrons). The protons and neutrons in an atomic nucleus are held together by the nuclear forces (strong force). The mass of a nucleus is always less than the sum of masses of the constituent protons and neutrons when separated. The difference is a measure of the nuclear binding energy (Eb) which holds the nucleus together. According to the Einstein relationship (E=m.c2) this binding energy is proportional to this mass difference and it is known as the mass defect.
Nuclear binding energy curve.
Nuclear binding energy curve.
Source: hyperphysics.phy-astr.gsu.edu

During the nuclear splitting or nuclear fusion, some of the mass of the nucleus gets converted into huge amounts of energy and thus this mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. The nuclear binding energies are enormous, they are on the order of a million times greater than the electron binding energies of atoms.

For a nucleus with A (mass number) nucleons, the binding energy per nucleon Eb/A can be calculated. This calculated fraction is shown in the chart as a function of them mass number A. As can be seen, for low mass numbers Eb/A increases rapidly and reaches a maximum of 8.8 MeV at approximately A=60. The nuclei with the highest binding energies, that are most tightly bound belong to the “iron group” of isotopes (56Fe, 58Fe, 62Ni). After that, the binding energy per nucleon decreases. In the heavy nuclei (A>60) region, a more stable configuration is obtained, when a heavy nucleus splits into two lighter nuclei. This is the origin of the fission process. It may seem that all the heavy nuclei may undergo fission or even spontaneous fission. In fact, for all nuclei with atomic number greater than about 60, fission occurs very rarely. In order to fission process to take place, a sufficient amount of energy must be added to the nucleus and no matter how. The energetics and binding energies of certain nucleus are well described by the Liquid Drop Model, which examines the global properties of nuclei.

 
Example: Mass defect of a reactor core
Calculate the mass defect of the 3000MWth reactor core after one year of operation.

It is known the average recoverable energy per fission is about 200 MeV, being the total energy minus the energy of the energy of antineutrinos that are radiated away.

The reaction rate per entire 3000MWth reactor core is about  9.33×1019 fissions / second.

The overall energy release in the units of joules is:

200×106 (eV) x 1.602×10-19 (J/eV) x 9.33×1019 (s-1) x 31.5×106 (seconds in year) = 9.4×1016 J/year

The mass defect is calculated as:

Δm = ΔE/c2

Δm = 9.4×1016 / (2.9979 x 108)2 = 1.046 kg

That means in a typical 3000MWth reactor core about 1 kilogram of matter is converted into pure energy.

Note that, a typical annual uranium load for a 3000MWth reactor core is about 20 tonnes of enriched uranium (i.e. about22.7 tonnes of UO2). Entire reactor core may contain about 80 tonnes of enriched uranium.

Mass defect directly from E=mc2

The mass defect can be calculated directly from the Einstein relationship (E = mc2) as:

Δm = ΔE/c2

Δm = 3000×106 (W = J/s) x 31.5×106 (seconds in year) / (2.9979 x 108)= 1,051 kg

Liquid Drop Model

Liquid Drop ModelOne of the first models which could describe very well the behavior of the nuclear binding energies and therefore of nuclear masses was the mass formula of von Weizsaecker (also called the semi-empirical mass formula – SEMF), that was published in 1935 by German physicist Carl Friedrich von Weizsäcker. This theory is based on the liquid drop model proposed by George Gamow.

According to this model, the atomic nucleus behaves like the molecules in a drop of liquid. But in this nuclear scale, the fluid is made of nucleons (protons and neutrons), which are held together by the strong nuclear force. The liquid drop model of the nucleus takes into account the fact that the nuclear forces on the nucleons on the surface are different from those on nucleons in the interior of the nucleus. The interior nucleons are completely surrounded by other attracting nucleons. Here is the analogy with the forces that form a drop of liquid.

In the ground state the nucleus is spherical. If the sufficient kinetic or binding energy is added, this spherical nucleus may be distorted into a dumbbell shape and then may be splitted into two fragments. Since these fragments are a more stable configuration, the splitting of such heavy nuclei must be accompanied by energy release. This model does not explain all the properties of the atomic nucleus, but does explain the predicted nuclear binding energies.

The nuclear binding energy as a function of the mass number A and the number of
protons Z based on the liquid drop model can be written as:

Weizsaecker formula - semi-empirical mass formula

This formula is called the Weizsaecker Formula (or the semi-empirical mass formula). The physical meaning of this equation can be discussed term by term.

 
Volume term
Volume term – aV.A. The first two terms describe a spherical liquid drop of an incompressible fluid with a contribution from the volume scaling with A and from the surface, scaling with A2/3. The first positive term aV.A is known as the volume term and it is caused by the attracting strong forces between the nucleons. The strong force has a very limited range and a given nucleon may only interact with its direct neighbours. Therefore this term is proportional to A, instead of A2. The coefficient aV is usually about ~ 16 MeV.
Surface term
Surface term – asf.A2/3. The surface term is also based on the strong force, it is, in fact, a correction to the volume term. The point is that particles at the surface of the nucleus are not completely surrounded by other particles. In the volume term, it is suggested that each nucleon interacts with a constant number of nucleons, independent of A. This assumption is very nearly true for nucleons deep within the nucleus, but causes an overestimation of the binding energy on the surface. By analogy with a liquid drop this effect is indicated as the surface tension effect. If the volume of the nucleus is proportional to A, then the geometrical radius should be proportional to A1/3 and therefore the surface term must be proportional to the surface area i.e. proportional to A2/3.
Coulomb term
Coulomb term – aC.Z2.A-⅓. This term describes the Coulomb repulsion between the uniformly distributed protons and is proportional to the number of proton pairs Z2/R, whereby R is proportional to A1/3. This effect lowers the binding energy because of the repulsion between charges of equal sign.
Asymmetry term
Asymmetry term – aA.(A-2Z)2/A. This term cannot be described as ‘classically’ as the first three. This effect is not based on any of the fundamental forces, this effect is based only on the Pauli exclusion principle (no two fermions can occupy exactly the same quantum state in an atom). The heavier nuclei contain more neutrons than protons. These extra neutrons are necessary for stability of the heavier nuclei. They provide (via the attractive forces between the neutrons and protons) some compensation for the repulsion between the protons. On the other hand, if there are significantly more neutrons than protons in a nucleus, some of the neutrons will be higher in energy level in the nucleus. This is the basis for a correction factor, the so-called symmetry term.
Pairing term
Pairing term – δ(A,Z). The last term is the pairing term δ(A,Z). This term captures the effect of spin-coupling. 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.
Table of Calculated Binding Energies
the semi-empirical mass formula - weizsaecker formula
Table of binding energies fo some nuclides. Calculated according to the semi-empirical mass formula.
With the aid of the Weizsaecker formula the binding energy can be calculated very well for nearly all isotopes. This formula provides a good fit for heavier nuclei. For light nuclei, especially for 4He, it provides a poor fit. The main reason is the formula does not consider the internal shell structure of the nucleus.

In order to calculate the binding energy, the coefficients aV, aS, aC, aA and aP must be known. The coefficients have units of megaelectronvolts (MeV) and are calculated by fitting to experimentally measured masses of nuclei. They usually vary depending on the fitting methodology. According to ROHLF, J. W., Modern Physics from α to Z0 , Wiley, 1994., the coefficients in the equation are following:

Weizsaecker formula - semi-empirical mass formula

Using the Weizsaecker formula, also the mass of an atomic nucleus can be derived and is given by:

m = Z.mp +N.mn -Eb/c2

where mp and mn are the rest mass of a proton and a neutron, respectively, and Eb is the nuclear binding energy of the nucleus.

From the nuclear binding energy curve and from the table it can be seen that, in the case of splitting a 235U nucleus into two parts, the binding energy of the fragments (A ≈ 120) together is larger than that of the original 235U nucleus.
According to the Weizsaecker formula, the total energy released for such reaction will be approximately 235 x (8.5 – 7.6) ≈ 200 MeV.

See also: Liquid Drop Model

Critical Energy – Threshold Energy for Fission

In principle, any nucleus, if brought into sufficiently high excited state, can be splitted. For fission to occur, the excitation energy must be above a particular value for certain nuclide. The minimum excitation energy required for fission to occur is known as the critical energy (Ecrit) or threshold energy.

The critical energy depends on the nuclear structure and is quite large for light nuclei with Z < 90. For heavier nuclei with Z > 90, the critical energy is about 4 to 6 MeV for A-even nuclei, and generally is much lower for A-odd nuclei. It must be noted, some heavy nuclei (eg. 240Pu or 252Cf) exhibit fission even in the ground state (without externally added excitation energy). This phenomena is known as the spontaneous fission. This process occur without the addition of the critical energy by the quantum-mechanical process of quantum tunneling through the Coulomb barrier (similarly like alpha particles in the alpha decay). The spontaneous fission contributes to ensure sufficient neutron flux on source range detectors when reactor is subcritical in long term shutdown.

See also: Critical Energy – Threshold Energy for Fission

Critical Energy - Threshold Energy
The minimum excitation energy required for fission to occur is known as the critical energy (Ecrit) or threshold energy.
Critical Energy to Binding Energy
This table shows critical energies compared to binding energies of the last neutron of a number of nuclei.

Energy Release from Fission

In general, the nuclear fission results in the release of enormous quantities of energy. The amount of energy depends strongly on the nucleus to be fissioned and also depends strongly on the kinetic energy of an incident neutron. In order to calculate the power of a reactor, it is necessary to be able precisely identify the individual components of this energy. At first, it is important to distinguish between the total energy released and the energy that can be recovered in a reactor.

The total energy released in fission can be calculated from binding energies of initial target nucleus to be fissioned and binding energies of fission products. But not all the total energy can be recovered in a reactor. For example, about 10 MeV is released in the form of neutrinos (in fact antineutrinos). Since the neutrinos are weakly interacting (with extremely low cross-section of any interaction), they do not contribute to the energy that can be recovered in a reactor.

In order to understand this issue, we have to first investigate a typical fission reaction such as the one listed below.

Uranium absorption reaction

Using this picture, we can identify and also describe almost all the individual components of the total energy energy released during the fission reaction.

 
Kinetic energy of fission fragments
As can be seen when the compound nucleus splits, it breaks into two fission fragments. In most cases, the resultant fission fragments have masses that vary widely, but the most probable pair of fission fragments for the thermal neutron-induced fission of the 235U have masses of about 94 and 139.

The largest part of the energy produced during fission (about 80 % or about 170 MeV or about 27 picojoules) appears as kinetic energy of the fission fragments. The fission fragments interact strongly (intensely) with the surrounding atoms or molecules traveling at high speed, causing them to ionize. Creation of ion pairs requires energy, which is lost from the kinetic energy of the charged fission fragment causing it to decelerate. The positive ions and free electrons created by the passage of the charged fission fragment will then reunite, releasing energy in the form of heat (e.g. vibrational energy or rotational energy of atoms).

The range of these massive, highly charged particles in the fuel is of the order of micrometers, so that the recoil energy is effectively deposited as heat at the point of fission. This is the principle how fission fragments heat up fuel in the reactor core.

See also: Interaction of Heavy Charged Particles with Matter

Kinetic energy of prompt neutrons.
Prompt neutrons are emitted directly from fission and they are emitted within very short time of about 10-14 second. Usually more than 99 percent of the fission neutrons are the prompt neutrons, but the exact fraction is dependent on the nuclide to be fissioned and is also dependent on an incident neutron energy (usually increases with energy).

For example a fission of 235U by thermal neutron yields 2.43 neutrons, of which 2.42 neutrons are the prompt neutrons and 0.01585 neutrons (0.01585/2.43=0.0065=ß) are the delayed neutrons. Almost all prompt fission neutrons have energies between 0.1 MeV and 10 MeV. The mean neutron energy is about 2 MeV. The most probable neutron energy is about 0.7 MeV.

Most of this energy is deposited in the coolant (moderator), because the water have the highest macroscopic slowing down power (MSDP) of the materials that are in a reactor core (PWR). The range of neutrons in a reactor depends strongly on certain reactor type, in the case of PWRs it is usually of the order of centimeters.

Energy carried by prompt γ-rays.
With the prompt neutrons prompt gamma rays are associated. Most of prompt gamma rays are emitted after prompt neutrons. The fission reaction releases approximately ~7 MeV in prompt gamma rays.

The gamma rays are well attenuated by high-density and high Z materials. In a reactor core the largest share of the energy will be deposited in the fuel containing uranium dioxide, but a significant share of the energy will be deposited also in the fuel cladding and in the coolant (moderator).

The range of gamma rays in a reactor vary according to the initial energy of the gamma ray. It can be stated the most of gammas in a reactor have range from 10cm-1m.

Energy of β− decay.
About 6 MeV of fission energy is in the form of kinetic energy of electrons (beta particles). The fission fragments are neutron-rich nuclei and therefore they usually undergo beta decay in order to stabilize itself. Beta particles deposit their energy essentially in the fuel element, within about 1 mm of the fission fragment.
Energy of antineutrinos
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. The existence of emission of antineutrinos and their extremely low cross-section for any interaction leads to very interesting phenomenon. Roughly about 5% of released energy per one fission is radiated away from reactor in the form of antineutrinos.

For a typical nuclear reactor with a thermal power of 3000 MWth (~1000MWe of electrical power), the total power produced is in fact higher, approximately 3150 MW, of which 150 MW is radiated away into space as antineutrino radiation. This amount of energy is forever lost, because 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).

Energy of delayed γ-rays.
The fission fragments are neutron-rich and very unstable nuclei. These nuclei undergo many beta decays in order to stabilize itself. Gamma rays usually accompany the beta decay. Their energy is transferred as heat to the surrounding material similarly as the energy carried by prompt γ-rays.
Energy of γ-rays from radiative capture
A fraction of the neutron absorption reactions result in radiative capture followed by gamma ray emission, producing on average about 7 MeV per fission in the form of energetic gamma rays. Their energy is transferred as heat to the surrounding material similarly as the energy carried by prompt γ-rays.
Energy release per fission
The total energy released in a reactor is about 210 MeV per 235U fission, distributed as shown in the table. In a reactor, the average recoverable energy per fission is about 200 MeV, being the total energy minus the energy of the energy of antineutrinos that are radiated away. This means that about 3.1⋅1010 fissions per second are required to produce a power of 1 W. Since 1 gram of any fissile material contains about 2.5 x 1021 nuclei, the fissioning of 1 gram of fissile material yields about 1 megawatt-day (MWd) of heat energy.

As can be seen from the description of the individual components of the total energy energy released during the fission reaction, there is significant amount of energy generated outside the nuclear fuel (outside fuel rods). Especially the kinetic energy of prompt neutrons is largely generated in the coolant (moderator). This phenomena needs to be included in the nuclear calculations.

For LWR, it is generally accepted that about 2.5% of total energy is recovered in the moderator. This fraction of energy depends on the materials, their arrangement within the reactor, and thus on the reactor type.

Fission Fragments – Products of Nuclear Fission

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

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.

See also: Interaction of Heavy Charged Particles with Matter

Prompt and Delayed Neutrons

It is known the fission neutrons are of importance in any chain-reacting system. Neutrons trigger the nuclear fission of some nuclei (235U, 238U or even 232Th). What is crucial the fission of such nuclei produces 2, 3 or more free neutrons.

But not all neutrons are released at the same time following fission. Even the nature of creation of these neutrons is different. From this point of view we usually divide the fission neutrons into two following groups:

  • Prompt Neutrons. Prompt neutrons are emitted directly from fission and they are emitted within very short time of about 10-14 second.
  • Delayed Neutrons. Delayed neutrons are emitted by neutron rich fission fragments that are called the delayed neutron precursors. These precursors usually undergo beta decay but a small fraction of them are excited enough to undergo neutron emission. The fact the neutron is produced via this type of decay and this happens orders of magnitude later compared to the emission of the prompt neutrons, plays an extremely important role in the control of the reactor.

See also: Prompt Neutrons

See also: Delayed Neutrons

See also: Reactor control with and without delayed neutrons – Interactive chart

Neutron Production - Prompt Neutrons
Most of the neutrons produced in fission are prompt neutrons. Usually more than 99 percent of the fission neutrons are the prompt neutrons, but the exact fraction is dependent on certain nuclide to be fissioned and is also dependent on an incident neutron energy (usually increases with energy).

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Table of key prompt and delayed neutrons characteristics
Table of key prompt and delayed neutrons characteristics. Thermal vs. Fast Fission

Key Characteristics of Prompt Neutrons

  • Prompt neutrons are emitted directly from fission and they are emitted within very short time of about 10-14 second.
  • Most of the neutrons produced in fission are prompt neutrons – about 99.9%.
  • For example a fission of 235U by thermal neutron yields 2.43 neutrons, of which 2.42 neutrons are prompt neutrons and 0.01585 neutrons are the delayed neutrons.
  • The production of prompt neutrons slightly increase with incident neutron energy.
  • Almost all prompt fission neutrons have energies between 0.1 MeV and 10 MeV.
  • The mean neutron energy is about 2 MeV. The most probable neutron energy is about 0.7 MeV.
  • In reactor design the prompt neutron lifetime (PNL) belongs to key neutron-physical characteristics of reactor core.
  • Its value depends especially on the type of the moderator and on the energy of the neutrons causing fission.
  • In an infinite reactor (without escape) prompt neutron lifetime is the sum of the slowing down time and the diffusion time.
  • In LWRs the PNL increases with the fuel burnup.
  • The typical prompt neutron lifetime in thermal reactors is on the order of 10-4 second.
  • The typical prompt neutron lifetime in fast reactors is on the order of 10-7 second.

Key Characteristics of Delayed Neutrons

  • The presence of delayed neutrons is perhaps most important aspect of the fission process from the viewpoint of reactor control.
  • Delayed neutrons are emitted by neutron rich fission fragments that are called the delayed neutron precursors.
  • These precursors usually undergo beta decay but a small fraction of them are excited enough to undergo neutron emission.
  • The emission of neutron happens orders of magnitude later compared to the emission of the prompt neutrons.
  • About 240 n-emitters are known between 8He and 210Tl, about 75 of them are in the non-fission region.
  • In order to simplify reactor kinetic calculations it is suggested to group together the precursors based on their half-lives.
  • Therefore delayed neutrons are traditionally represented by six delayed neutron groups.
  • Neutrons can be produced also in (γ, n) reactions (especially in reactors with heavy water moderator) and therefore they are usually referred to as photoneutrons. Photoneutrons are usually treated no differently than regular delayed neutrons in the kinetic calculations.
  • The total yield of delayed neutrons per fission, vd, depends on:
    • Isotope, that is fissioned.
    • Energy of a neutron that induces fission.
  • Variation among individual group yields is much greater than variation among group periods.
  • In reactor kinetic calculations it is convenient to use relative units usually referred to as delayed neutron fraction (DNF).
  • At the steady state condition of criticality, with keff = 1, the delayed neutron fraction is equal to the precursor yield fraction β.
  • In LWRs the β decreases with fuel burnup. This is due to isotopic changes in the fuel.
  • Delayed neutrons have initial energy between 0.3 and 0.9 MeV with an average energy of 0.4 MeV.
  • Depending on the type of the reactor, and their spectrum, the delayed neutrons may be more (in thermal reactors) or less effective than prompt neutrons (in fast reactors). In order to include this effect into the reactor kinetic calculations the effective delayed neutron fraction – βeff must be defined.
  • The effective delayed neutron fraction is the product of the average delayed neutron fraction and the importance factor βeff = β . I.
  • The weighted delayed generation time is given by τ = ∑iτi . βi / β = 13.05 s, therefore the weighted decay constant λ = 1 / τ ≈ 0.08 s-1.
  • The mean generation time with delayed neutrons is about ~0.1 s, rather than ~10-5 as in section Prompt Neutron Lifetime, where the delayed neutrons were omitted.
  • Their presence completely changes the dynamic time response of a reactor to some reactivity change, making it controllable by control systems such as the control rods.

Capture-to-Fission Ratio

The probability that a neutron that is absorbed in a fissile nuclide causes a
fission is very important parameter of each fissile isotope. In terms of cross-sections, this probability is defined as:

σf / (σf + σγ) = 1 / (1 + σγf) = 1 / (1 + α),

where α = σγf is referred to as the capture-to-fission ratio. The capture-to-fission ratio may be used as an indicator of “quality” of fissile isotopes. The lower C/F ratio simply means that an absorption reaction will result in the fission rather than in the radiative capture. The ratio depends strongly on the incident neutron energy. In the fast neutron region, C/F ratio decreases. It is determined by the steeper decrease in radiative capture cross-section (see chart).

For 235U and 233U the thermal neutron capture-to-fission ratios are typically lower than those for fast neutrons (for mean energy of about 100 keV). It must be noted, the neutron flux of most fast reactors tends to peak around 200 keV, but the mean energy is between 100-200 keV depending on certain reactor design.

Further increase in neutron energy causes conversely a decrease in C/F ratio. This is not the case of 239Pu, for 100 keV neutrons, the C/F ratio is lower than for thermal neutrons. For the fissile isotopes (233U, 235U and 239Pu), a small capture-to-fission ratio is an advantage, because neutrons captured onto them are lost.

The capture-to-fission ratio
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library
capture-to-fission ratio

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Nuclear Fission Chain Reaction

Six Factor Formula - Four Factor FormulaThe chain reaction can take place only in the proper multiplication environment and only under proper conditions. It is obvious, if one neutron causes two further fissions, the number of neutrons in the multiplication system will increase in time and the reactor power (reaction rate) will also increase in time. In order to stabilize such multiplication environment, it is necessary to increase the non-fission neutron absorption in the system (e.g. to insert control rods). Moreover, this multiplication environment (nuclear reactor) behaves like the exponential system, that means the power increase is not linear, but it is exponential.

On the other hand, if one neutron causes less than one further fission, the number of neutrons in the multiplication system will decrease in time and the reactor power (reaction rate) will also decrease in time. In order to sustain the chain reaction, it is necessary to decrease the non-fission neutron absorption in the system (e.g. to withdraw control rods).

In fact, there is always a competition for the fission neutrons in the multiplication environment, some neutrons will cause further fission reaction, some will be captured by fuel materials or non-fuel materials and some will leak out of the system.

In order to describe the multiplication system, it is necessary to define the infinite and finite multiplication factor of a reactor. The method of calculations of multiplication factors has been developed in the early years of nuclear energy and is only applicable to thermal reactors, where the bulk of fission reactions occurs at thermal energies. This method well puts into the context all the processes, that are associated with the thermal reactors (e.g. the neutron thermalisation, the neutron diffusion or the fast fission), because the most important neutron-physical processes occur in energy regions that can be clearly separated from each other. In short, the calculation of multiplication factor gives a good insight in the processes that occur in each thermal multiplying system.

Distinction between Fissionable, Fissile and Fertile

In nuclear engineering, fissionable material (nuclide) is material  that is capable of undergoing fission reaction after absorbing either thermal (slow or low energy) neutron or fast (high energy) neutron. Fissionable materials are a superset of fissile materials. Fissionable materials also include an isotope 238U that can be fissioned only with high energy (>1MeV) neutron. These materials are used to fuel thermal nuclear reactors, because they are capable of sustaining a nuclear fission chain reaction.

Fissile materials undergoes fission reaction after absorption of the binding energy of thermal neutron. They do not require additional kinetic energy for fission. If the neutron has higher kinetic energy, this energy will be transformed into additional excitation energy of the compound nucleus. On the other hand, the binding energy released by compound nucleus of (238U + n) after absorption of thermal neutron is less than the critical energy, so the fission reaction cannot occur. The distinction is described in the following points.

  • Fissile materials are a subset of fissionable materials.
  • Fissionable material consist of isotopes that are capable of undergoing nuclear fission after capturing either fast neutron (high energy neutron – let say >1 MeV) or thermal neutron (low energy neutron – let say 0.025 eV).   Typical fissionable materials: 238U, 240Pu, but also 235U, 233U, 239Pu, 241Pu
  • Fissile material consist of fissionable isotopes that are capable of undergoing nuclear fission only after capturing a thermal neutron. 238is not fissile isotope, because 238U cannot be fissioned by thermal neutron. 238does not meet also alternative requirement to fissile materials. 238U is not capable of sustaining a nuclear fission chain reaction, because neutrons produced by fission of 238U have lower energies than original neutron (usually below the threshold energy of 1 MeV). Typical fissile materials: 235U, 233U, 239Pu, 241Pu.
  • Fertile material consist of isotopes that are not fissionable by thermal neutrons, but can be converted into fissile isotopes (after neutron absorption and subsequent nuclear decay). Typical fertile materials: 238U, 232Th.

Fissile materials undergoes fission reaction after absorption of the binding energy of thermal neutron. They do not require additional kinetic energy for fission. If the neutron has higher kinetic energy, this energy will be transformed into additional excitation energy of the compound nucleus. On the other hand, the binding energy released by compound nucleus of (238U + n) after absorption of thermal neutron is less than the critical energy, so the fission reaction cannot occur. The distinction is described in the following points.

  • Fissile materials are a subset of fissionable materials.
  • Fissionable material consist of isotopes that are capable of undergoing nuclear fission after capturing either fast neutron (high energy neutron – let say >1 MeV) or thermal neutron (low energy neutron – let say 0.025 eV).   Typical fissionable materials: 238U, 240Pu, but also 235U, 233U, 239Pu, 241Pu
  • Fissile material consist of fissionable isotopes that are capable of undergoing nuclear fission only after capturing a thermal neutron. 238is not fissile isotope, because 238U cannot be fissioned by thermal neutron. 238does not meet also alternative requirement to fissile materials. 238U is not capable of sustaining a nuclear fission chain reaction, because neutrons produced by fission of 238U have lower energies than original neutron (usually below the threshold energy of 1 MeV). Typical fissile materials: 235U, 233U, 239Pu, 241Pu.
  • Fertile material consist of isotopes that are not fissionable by thermal neutrons, but can be converted into fissile isotopes (after neutron absorption and subsequent nuclear decay). Typical fertile materials: 238U, 232Th.

See also: Neutron cross-section

Comparison of cross-sections

Source: JANIS (Java-based nuclear information software)  http://www.oecd-nea.org/janis/

Fissile / Fertile Material Cross-sections
Source: JANIS (Java-based Nuclear Data Information Software)
http://www.oecd-nea.org/janis/

Fissile / Fertile Material Cross-sections. Comparison of total fission cross-sections.

Fissile / Fertile Material Cross-sectionsUranium 235. Comparison of total fission cross-section and cross-section for radiative capture.
Fissile / Fertile Material Cross-sections
Source: JANIS (Java-based nuclear information software)
http://www.oecd-nea.org/janis/

Uranium 238. Comparison of total fission cross-section and cross-section for radiative capture.

See also:

See also:

Neutron Nuclear Reactions

See also:

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What is Nuclear Reaction – Definition

A nuclear reaction is considered to be the process in which two nuclear particles interact to produce two or more nuclear particles or ˠ-rays. Nuclear Reaction

A nuclear reaction is considered to be the process in which two nuclear particles (two nuclei or a nucleus and a nucleon) interact to produce two or more nuclear particles or ˠ-rays (gamma rays). Thus, a nuclear reaction must cause a transformation of at least one nuclide to another. Sometimes if a nucleus interacts with another nucleus or particle without changing the nature of any nuclide, the process is referred to a nuclear scattering, rather than a nuclear reaction. Perhaps the most notable nuclear reactions are the nuclear fusion reactions of light elements that power the energy production of stars and the Sun. Natural nuclear reactions occur also in the interaction between cosmic rays and matter.

The most notable man-controlled nuclear reaction is the fission reaction which occurs in nuclear reactorsNuclear reactors are devices to initiate and control a nuclear chain reaction, but there are not only manmade devices. The world’s first nuclear reactor operated about two billion years ago. The natural nuclear reactor formed at Oklo in Gabon, Africa, when a uranium-rich mineral deposit became flooded with groundwater that acted as a neutron moderator, and a nuclear chain reaction started.  These fission reactions were sustained for hundreds of thousands of years, until a chain reaction could no longer be supported. This was confirmed by existence of isotopes of the fission-product gas xenon and by different ratio of U-235/U-238 (enrichment of natural uranium).

See also: TALYS – a software for the simulation of nuclear reactions.

See also: JANIS – Java-based Nuclear Data Information System

Notation of Nuclear Reactions

Standard nuclear notation shows (see picture) the chemical symbol, the mass number and the atomic number of the isotope.

If the initial nuclei are denoted by a and b, and the product nuclei are denoted by c and d, the reaction can be represented by the equation:

 a + b → c + d

boron-neutron reaction
This equation describes neutron capture in the boron, which is diluted in the coolant. Boric acid is used in nuclear power plants as a long-term compensator of nuclear fuel reactivity.
Notation of nuclei
Notation of nuclei
Source: chemwiki.ucdavis.edu

Instead of using the full equations in the style above, in many situations a compact notation is used to describe nuclear reactions. This style of the form a(b,c)d is equivalent to a + b producing c + d. Light particles are often abbreviated in this shorthand, typically p means proton, n means neutron, d means deuteron, α means an alpha particle or helium-4, β means beta particle or electron, γ means gamma photon, etc. The reaction above would be written as 10B(n,α)7Li.

Basic Classification of Nuclear Reactions

In order to understand the nature of neutron nuclear reactions, the classification according to the time scale of of these reactions has to be introduced. Interaction time is critical for defining the reaction mechanism.

There are two extreme scenarios for nuclear reactions (not only neutron reactions):

  • A projectile and a target nucleus are within the range of nuclear forces for the very short time allowing for an interaction of a single nucleon only. These type of reactions are called the direct reactions.
  • A projectile and a target nucleus are within the range of nuclear forces for the time allowing for a large number of interactions between nucleons. These type of reactions are called the compound nucleus reactions.

In fact, there is always some non-direct (multiple internuclear interaction) component in all reactions, but the direct reactions have this component limited.

 
Basic Characteristics of Direct Reactions
  • The direct reactions are fast and involve a single-nucleon interaction.
  • The interaction time must be very short (~10-22 s).
  • The direct reactions require incident particle energy larger than ∼ 5 MeV/Ap. (Ap is the atomic mass number of a projectile)
  • Incident particles interact on the surface of a target nucleus rather than in the volume of a target nucleus.
  • Products of the direct reactions are not distributed isotropically in angle, but they are forward focused.
  • Direct reactions are of importance in measurements of nuclear structure.
Basic Characteristics of Compound Nucleus Reactions
  • The compound nucleus is a relatively long-lived intermediate state of particle-target composite system.
  • The compound nucleus reactions involve many nucleon-nucleon interactions.
  • The large number of collisions between the nucleons leads to a thermal equilibrium inside the compound nucleus.
  • The time scale of compound nucleus reactions is of the order of 10-18 s – 10-16 s.
  • The compound nucleus reactions is usually created if the projectile has low energy.
  • Incident particles interact in the volume of a target nucleus.
  • Products of the compound nucleus reactions are distributed near isotropically in angle (the nucleus loses memory of how it was created – the Bohr’s hypothesis of independence).
  • The mode of decay of compound nucleus do not depend on the way the compound nucleus is formed.
  • Resonances in the cross-section are typical for the compound nucleus reaction.

Types of Nuclear Reactions

Although the number of possible nuclear reactions is enormous, nuclear reactions can be sorted by types. Most of nuclear reactions are accompanied by gamma emission. Some examples are:

  • Elastic scattering. Occurs, when no energy is transferred between the target nucleus and the incident particle.

 208Pb (n, n) 208Pb

  •  Inelastic scattering. Occurs, when energy is transferred. The difference of kinetic energies is saved in excited nuclide.

 40Ca (α, α’) 40mCa

  • Capture reactions. Both charged and neutral particles can be captured by nuclei. This is accompanied by the emission of ˠ-rays. Neutron capture reaction produces radioactive nuclides (induced radioactivity).

 238U (n, ˠ) 239U

  • Transfer Reactions. The absorption of a particle accompanied by the emission of one or more particles is called the transfer reaction.

4He (α, p) 7Li

  • Fission reactions. 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.

235U (n, 3 n) fission products

  • Fusion reactions.  Occur when, two or more atomic nuclei collide at a very high speed and join to form a new type of atomic nucleus.The fusion reaction of deuterium and tritium is particularly interesting because of its potential of providing energy for the future.

3T (d, n) 4He

  • Spallation reactions. Occur, when a nucleus is hit by a particle with sufficient energy and momentum to knock out several small fragments or, smash it into many fragments.
  • 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. There are many types of radioactive decay:
    • Alpha radioactivity. Alha 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 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 rays are electromagnetic radiation of an very high frequency and are therefore high energy photons. 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 emissionNeutron 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.
Notation of nuclear reactions - radioactive decays
Radioactive decays
Source: chemwiki.ucdavis.edu

Conservation Laws in Nuclear Reactions

In analyzing nuclear reactions, we apply the many conservation lawsNuclear 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:

 
Law of Conservation of Lepton Number
Lepton Number. Conservation of Lepton NumberIn particle physics, the lepton number is used to denote which particles are leptons and which particles are not. Each lepton has a lepton number of and each antilepton has a lepton number of -1. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.

The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.

Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:

lepton-number-neutron-decay

Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum),  the third particle must be an electron antineutrino.

Law of Conservation of Baryon Number
In particle physics, the baryon number is used to denote which particles are baryons and which particles are not. Each baryon has a baryon number of 1 and each antibaryonhas a baryon number of -1. Other non-baryonic particles have a baryon number of 0. Since there are exotic hadrons like pentaquarks and tetraquarks, there is a general definition of baryon number as:

baryon-number-equation

where nq is the number of quarks, and nq is the number of antiquarks.

The baryon number is a conserved quantum number in all particle reactions.

The law of conservation of baryon number states that:

The sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction.

For example, the following reaction has never been observed:

baryon-number-example-violation

even if the incoming proton has sufficient energy and charge, energy, and so on, are conserved. This reaction does not conserve baryon number since the left side has B =+2, and the right has B =+1.

On the other hand, the following reaction (proton-antiproton pair production) does conserve B and does occur if the incoming proton has sufficient energy (the threshold energy = 5.6 GeV):

baryon-number-pair-production

As indicated, B = +2 on both sides of this equation.

From these and other reactions, the conservation of baryon number has been established as a basic principle of physics.

This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons. Thus, the decay would violate the conservation of baryon number. It must be added some theories have suggested that protons are in fact unstable with very long half-life (~1030 years) and that they decay into leptons. There is currently no experimental evidence that proton decay occurs.

Law of Conservation of Electric Charge
The law of conservation of electric charge can be demonstrated also on positron-electron pair production. Since a gamma ray is electrically neutral and sum of the electric charges of electron and positron is also zero, the electric charge in this reaction is also conserved.

Ɣ → e + e+

It must be added, in order for electron-positron pair production to occur, the electromagnetic energy of the photon must be above a threshold energy, which is equivalent to the rest mass of two electrons. The threshold energy (the total rest mass of produced particles) for electron-positron pair production is equal to 1.02MeV (2 x 0.511MeV) because the rest mass of a single electron is equivalent to 0.511MeV of energy. If the original photon’s energy is greater than 1.02MeV, any energy above 1.02MeV is according to the conservation law split between the kinetic energy of motion of the two particles. The presence of an electric field of a heavy atom such as lead or uranium is essential in order to satisfy conservation of momentum and energy. In order to satisfy both conservation of momentum and energy, the atomic nucleus must receive some momentum. Therefore a photon pair production in free space cannot occur.

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.

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

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

 
Example: Elastic Nuclear Collision
A neutron (n) of mass 1.01 u traveling with a speed of 3.60 x 104m/s interacts with a carbon (C) nucleus (mC = 12.00 u) initially at rest in an elastic head-on collision.

What are the velocities of the neutron and carbon nucleus after the collision?

Solution:

This is an elastic head-on collision of two objects with unequal masses. We have to use the conservation laws of momentum and of kinetic energy, and apply them to our system of two particles.

conservation-laws-elastic-collisions

We can solve this system of equation or we can use the equation derived in previous section. This equation stated that the relative speed of the two objects after the collision has the same magnitude (but opposite direction) as before the collision, no matter what the masses are.

solution-elastic-collision

The minus sign for v’ tells us that the neutron scatters back of the carbon nucleus, because the carbon nucleus is significantly heavier. On the other hand its speed is less than its initial speed. This process is known as the neutron moderation and it significantly depends on the mass of moderator nuclei.

Energetics of Nuclear Reactions – Q-value

Q-value of DT fusion reaction
Q-value of DT fusion reaction

In nuclear and particle physics the energetics of nuclear reactions is determined by the Q-value of that reaction. The Q-value of the reaction is defined as the difference between the sum of the masses of the initial reactants and the sum of the masses of the final products, in energy units (usually in MeV).

Consider a typical reaction, in which the projectile a and the target A gives place to two products, B and b. This can also be expressed in the notation that we used so far, a + A → B + b, or even in a more compact notation, A(a,b)B.

See also: E=mc2

The Q-value of this reaction is given by:

Q = [ma + mA – (mb + mB)]c2

which is the same as the excess kinetic energy of the final products:

Q = Tfinal – Tinitial

   = Tb + TB – (Ta + TA)

For reactions in which there is an increase in the kinetic energy of the products Q is positive. The positive Q reactions are said to be exothermic (or exergic). There is a net release of energy, since the kinetic energy of the final state is greater than the kinetic energy of the initial state.

For reactions in which there is a decrease in the kinetic energy of the products Q is negative. The negative Q reactions are said to be endothermic (or endoergic) and they require a net energy input.

The energy released in a nuclear reaction can appear mainly in one of three ways:

  • Kinetic energy of the products
  • Emission of gamma rays. Gamma rays are emitted by unstable nuclei in their transition from a high energy state to a lower state known as gamma decay.
  • Metastable state. Some energy may remain in the nucleus, as a metastable energy level.

A small amount of energy may also emerge in the form of X-rays. Generally, products of nuclear reactions may have different atomic numbers, and thus the configuration of their electron shells is different in comparison with reactants. As the electrons rearrange themselves and drop to lower energy levels, internal transition X-rays (X-rays with precisely defined emission lines) may be emitted.

See also: Q-value Calculator

Exothermic Reactions

 
Example: Exothermic Reaction - DT fusion
Q-value of DT fusion reaction
Q-value of DT fusion reaction

The DT fusion reaction of deuterium and tritium is particularly interesting because of its potential of providing energy for the future. Calculate the reaction Q-value.

3T (d, n) 4He

The atom masses of the reactants and products are:

m(3T) = 3.0160 amu

m(2D) = 2.0141 amu

m(1n) = 1.0087 amu

m(4He) = 4.0026 amu

Using the mass-energy equivalence, we get the Q-value of this reaction as:

Q = {(3.0160+2.0141) [amu] – (1.0087+4.0026) [amu]} x 931.481 [MeV/amu]

= 0.0188 x 931.481 = 17.5 MeV

Example: Exothermic Reaction - Tritium in Reactors
Cross-section of 10B(n,2alpha)T reaction.
Cross-section of 10B(n,2alpha)T reaction.

Tritium is a byproduct in nuclear reactors. Most of the tritium produced in nuclear power plants stems from the boric acid, which is commonly used as a chemical shim to compensate an excess of initial reactivity. Main reaction, in which the tritium is generated from boron is below:

10B(n,2*alpha)T

This reaction of a neutron with an isotope 10B is the main way, how radioactive tritium in primary circuit of all PWRs is generated. Note that, this reaction is a threshold reaction due to its cross-section.

Calculate the reaction Q-value.

The atom masses of the reactants and products are:

m(10B) = 10.01294 amu

m(1n) = 1.00866 amu

m(3T) = 3.01604 amu

m(4He) = 4.0026 amu

Using the mass-energy equivalence, we get the Q-value of this reaction as:

Q = {(10.0129+1.00866) [amu] – (3.01604+2 x 4.0026) [amu]} x 931.481 [MeV/amu]

= 0.00036 x 931.481 = 0.335 MeV

Endothermic Reactions

 
Example: Endothermic Reaction - Photoneutrons
In nuclear reactors the gamma radiation plays a significant role also in reactor kinetics and in a subcriticality control. Especially in nuclear reactors with D2O moderator (CANDU reactors) or with Be reflectors (some experimental reactors). Neutrons can be produced also in (γ, n) reactions and therefore they are usually referred to as photoneutrons.

A high energy photon (gamma ray) can under certain conditions eject a neutron from a nucleus. It occurs when its energy exceeds the binding energy of the neutron in the nucleus. Most nuclei have binding energies in excess of 6 MeV, which is above the energy of most gamma rays from fission. On the other hand there are few nuclei with sufficiently low binding energy to be of practical interest. These are: 2D, 9Be, 6Li, 7Li and 13C. As can be seen from the table the lowest threshold have 9Be with 1.666 MeV and 2D with 2.226 MeV.

Photoneutron sources
Nuclides with low photodisintegration
threshold energies.

In case of deuterium, neutrons can be produced by the interaction of gamma rays (with a minimum energy of 2.22 MeV) with deuterium:

Photoneutron - deuterium

The reaction Q-value is calculated below:

The atom masses of the reactant and products are:

m(2D) = 2.01363 amu

m(1n) = 1.00866 amu

m(1H) = 1.00728 amu

Using the mass-energy equivalence, we get the Q-value of this reaction as:

Q = {2.01363 [amu] – (1.00866+1.00728) [amu]} x 931.481 [MeV/amu]

= -0.00231 x 931.481 = -2.15 MeV

Example: Endothermic Reaction - (α,n) reaction
Calculate the reaction Q-value of the following reaction:

7Li (α, n) 10B

The atom masses of the reactants and products are:

m(4He) = 4.0026 amu

m(7Li) = 7.0160 amu

m(1n) = 1.0087 amu

m(10B) = 10.01294 amu

Using the mass-energy equivalence, we get the Q-value of this reaction as:

Q = {(7.0160+4.0026) [amu] – (1.0087+10.01294) [amu]} x 931.481 [MeV/amu]

= 0.00304 x 931.481 = -2.83 MeV

Test your Knowledge – Nuclear Reactions

quiz - nuclear reactions

With our simple quizzes, you can test your knowledge.

It is intuitive: start quiz and answer questions.

 
References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN: 978-0471805533
  7. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  8. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  9. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

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

See also:

Radioactive Decay

See also:

Atomic and Nuclear Physics

See also:

Binding Energy

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What is Nuclear Fusion – Definition

In nuclear physics, nuclear fusion is a nuclear reaction in which two or more atomic nuclei collide at a very high energy and fuse together into a new nucleus. Material Properties
“We say that we will put the sun into a box. The idea is pretty. The problem is, we don’t know how to make the box“.Pierre-Gilles de Gennes
Nuclear fusion reaction
Nuclear fusion is a nuclear reaction in which two or more atomic nuclei (e.g. D+T) collide at a very high energy and fuse together.
Source: chemwiki.ucdavis.edu

In nuclear physics, nuclear fusion is a nuclear reaction in which two or more atomic nuclei collide at a very high energy and fuse together into a new nucleus, e.g. helium. If light nuclei are forced together, they will fuse with a yield of energy because the mass of the combination will be less than the sum of the masses of the individual nuclei. If the combined nuclear mass is less than that of iron at the peak of the binding energy curve, then the nuclear particles will be more tightly bound than they were in the lighter nuclei, and that decrease in mass comes off in the form of energy according to the Albert Einstein relationship. For elements like the uranium and thorium, fission will yield energy. Fusion reactions have an energy density many times greater than nuclear fission and fusion reactions are themselves millions of times more energetic than chemical reactions.

The fusion power offers the opportunity of an almost inexhaustible source of energy for future, but it the fusion technology presents a real scientific and

Nuclear binding energy curve.
Nuclear binding energy curve.
Source: hyperphysics.phy-astr.gsu.edu

engineering challenges. For potential nuclear energy sources for humankind, the deuterium-tritium fusion reaction controlled by a magnetic confinement seems the most likely way. But nowadays also this way contains several insurmountable engineering challenges.

Fusion powers the Sun

The Sun is a hot star. Really hot star. But all of the heat and light coming from the Sun comes from the fusion reactions happening inside the core of the Sun. Inside the Sun, the pressure is million of times more than the surface of the Earth, and the temperature reaches more than 15 million Kelvin. Massive gravitational forces create the these conditions for nuclear fusion. On Earth, it is impossible to achieve such conditions.

The Sun
The Sun generates its energy by nuclear fusion of hydrogen nuclei into helium. In its core, the Sun fuses 620 million metric tons of hydrogen each second.
Source: hyperphysics.phy-astr.gsu.edu

The Sun burns hydrogen atoms, which fuse together to form helium nuclei, and a small amount of matter is converted into energy. In its core, the Sun consumes approximately 620 million metric tons of hydrogen each second. Hydrogen, heated to very high temperatures changes its state from a gaseous state to a plasma state. Normally, fusion is not possible because the strongly repulsive electrostatic forces between the positively charged nuclei prevent them from getting close enough together to collide and for fusion to occur. The mechanism, how to overcome the coulomb barrier is by the temperature and by the pressure. At close distances the attractive nuclear force allows the nuclei to fuse together.

Deuterium-Tritium Fusion

The fusion reaction of deuterium and tritium is particularly interesting because of its potential of providing energy for the future.
3T (d, n) 4He
The reaction yields ~17 MeV of energy per reaction but requires a enormous temperature of approximately 40 million Kelvins to overcome the coulomb barrier by the attractive nuclear force, which is stronger at close distances. The deuterium fuel is abundant, but tritium must be either bred from lithium or gotten in the operation of the deuterium cycle.

We hope, this article, Nuclear Fusion, helps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about materials and their properties.

What is Atomic and Nuclear Physics – Definition

A knowledge of atomic and nuclear physics is essential to nuclear engineers, who deal with nuclear reactors and another nuclear installations. Material Properties
A knowledge of atomic and nuclear physics is essential to nuclear engineers, who deal with nuclear reactors. It should be noted that atomic and nuclear physics is very extensive branch of science. Nuclear reactor physics belongs to an applied physics. Reactor physics, particle physics or other branches of modern physics have common fundamentals. Atomic and nuclear physics describes fundamental particles (i.e. electrons, protons, neutrons), their structure, properties and behavior.

Atomic and nuclear physics are not the same. The term atomic physics is often associated with nuclear power, due to the synonymous use of atomic and nuclear in standard English. However, physicists distinguish between atomic and nuclear physics. The atomic physics deals with the atom as a system consisting of a nucleus and electrons. The nuclear physics deals with the nucleus as a system consisting of a nucleons (protons and neutrons). Main difference is in the scale. While the term atomic deals with 1Å = 10-10m, where Å is an ångström (according to Anders Jonas Ångström), the  term nuclear deals with  1femtometre = 1fermi = 10-15m.

Atomic Physics

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. This includes ions as well as neutral atoms and, unless otherwise stated, for the purposes of this discussion it should be assumed that the term atom includes ions. Atomic physics also help to understand the physics of molecules, but there is also molecular physics, which describes physical properties of molecules.

 
Volume of an Atom and Nucleus
Structure of Matter.
Structure of Matter.

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 . A1/3

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?
atomic-nucleus-volume-min
A figurative depiction of the helium-4 atom with the electron cloud in shades of gray. Protons and neutrons are most likely found in exactly the same space, at the central point. Source wikipedia.org License CC BY-SA 3.0

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, rw, 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“).

Nuclear Physics

Nuclear physics is the field of physics that studies the constituents (protons and neutrons) and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation, but the modern nuclear physics contains also particle physics, which is taught in close association with nuclear physics. The nuclear physics  has provided application in many fields, including those in nuclear medicine (Positron Emission Tomography, isotopes production, etc.) and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.

These physical fundamentals consist of following topics:

 
Fundamental Particles
Three generations of matter.
Three generations of matter.

See also: Fundamental Particles

The physical world is composed of combinations of various subatomic or fundamental particles. These are the smallest building blocks of matter. All matter except dark matter is made of molecules, which are themselves made of atoms. The atoms consist of two parts. An atomic nucleus and an electron cloud. The electrons are spinning around the atomic nucleus. The nucleus itself is generally made of protons and neutrons but even these are composite objects. Inside the protons and neutrons, we find the quarks.

Quarks and electrons are some of the elementary particles. A number of fundamental particles have been discovered in various experiments. So many, that researchers had to organize them, just like Mendeleev did with his periodic table. This is summarized in a theoretical model (concerning the electromagnetic, weak, and strong nuclear interactions) called the Standard Model. In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles. Known elementary particles include the fundamental fermions and the fundamental bosons. The fermions are generally “matter particles” and “antimatter particles”.

  • Quarks. The quarks combine to form composite particles called hadrons, the best known and most stable are protons and neutrons
  • Antiquarks. For every quark there is a corresponding type of antiparticle. The antiquarks have the same mass, mean lifetime, and spin as their respective quarks, but the electric charge and other charges have the opposite sign.
  • Leptons. The best known of all leptons are the electrons and the neutrinos.
  • Antileptons. For every lepton there is a corresponding type of antiparticle. The best known of all antileptons are the positrons and the antineutrinos.

The bosons are generally “force particles” that mediate interactions among fermions.

  • Gauge bosons. The gauge boson is a force carrier of the fundamental interactions of nature.
  • Higgs boson.  The Higgs bosons give other particles mass via the Higgs mechanism. Their existence was confirmed by CERN on 14 March 2013.

Atom StructureHowever, only a few of these fundamental particles (in fact, some of these are not fundamental particles) are very important in nuclear engineering. Nuclear engineering or theory of nuclear reactors operates with much better known subatomic particles such as:

  • Electrons. The electrons are negatively charged, almost massless particles that nevertheless account for most of the size of the atom. Electrons were discovered by Sir John Joseph Thomson in 1897. Electrons are located in an electron cloud, which is the area surrounding the nucleus of the atom. The electron is only one member of a class of elementary particles, which forms an atom.
  • Protons. The protons are positively charged, massive particles that are located inside the atomic nucleus. Protons were discovered by Ernest Rutherford in the year 1919, when he performed his gold foil experiment.
  • Neutron. Neutrons are located in the nucleus with the protons. Along with protons, they make up almost all of the mass of the atom. Neutrons were discovered by James Chadwick in 1932, when he demonstrated that penetrating radiation incorporated beams of neutral particles.
  • Photon. A photon is an elementary particle, the force carrier for the electromagnetic force. The photon is the quantum of light (discrete bundle of electromagnetic energy). Photons are always in motion and, in a vacuum, have a constant speed of light to all observers (c = 2.998 x 108 m/s).
  • Neutrino. A neutrino is an elementary particle, one of particles which make up the universe. Neutrinos are electrically neutral, weakly interacting and therefore able to pass through great distances in matter without being affected by it.
  • Positron. Positron is an antiparticle of a negative electron. Positrons, also called positive electron,  have a positive electric charge and have the same mass and magnitude of charge as the electron. An annihilation occurs, when a low-energy positron collides with a low-energy electron.

See also: Fundamental Particles

Atomic and Nuclear Structure
Notation of nuclei
Notation of nuclei
Source: chemwiki.ucdavis.edu

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.

  • 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: Atomic and Nuclear Structure

Structure of Matter.
Structure of Matter.
Mass and Energy
Nuclear energy comes either from spontaneous nuclei conversions or induced nuclei conversions. Among these conversions (nuclear reactions) belong for example nuclear fission, nuclear decay and nuclear fusion. Conversions are associated with mass and energy changes. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible, one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula:
E=MC2 - Nuclear energy
This formule describes equivalence of mass and energy.

, where M is the small amount of mass and C is the speed of light.

What that means? If the nuclear energy is generated (splitting atoms, nuclear fussion), a small amount of mass transforms into the pure energy (such as kinetic energy, thermal energy, or radiant energy).

Example:

The energy equivalent of one gram (1/1000 of a kilogram) of mass is equivalent to:

89.9 terajoules
25.0 million kilowatt-hours (≈ 25 GW·h)
21.5 billion kilocalories (≈ 21 Tcal)
85.2 billion BTUs

or to the energy released by combustion of the following:

21.5 kilotons of TNT-equivalent energy (≈ 21 kt)
568,000 US gallons of automotive gasoline
Any time energy is generated, the process can be evaluated from an E = mc2 perspective.

Today we use the nuclear energy to generate useful heat and electricity. In 2011 nuclear power provided 10% of the world’s electricity. In 2007, the IAEA reported there were 439 nuclear power reactors in operation in the world, operating in 31 countries. They produce base-load electricity 24/7 without emitting any pollutants into the atmosphere (this includes CO2).

See also: Mass and Energy

Radiation

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.

Spectrum of Radiation

Forms of ionizing radiation

Interaction of Radiation with Matter
Interaction of Radiation with Matter

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 radiations. 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.

See also: Radiation

Nuclear Stability
Nuclide chart - Nuclear StabilityNuclear 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.

See also: Livechart – iaea.org

Detail of Nuclide Chart.
Detail of Nuclide Chart.
Source: 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.

Example:

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.

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.

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: Nuclear Stability

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. There are many types of radioactive decay:

  • Alpha radioactivity. 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. Consist 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.

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.

Table of examples of half lives and decay constants.
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.

See also: Radioactive Decay

Nuclear Reactions
A nuclear reaction is considered to be the process in which two nuclear particles (two nuclei or a nucleus and a nucleon) interact to produce two or more nuclear particles or ˠ-rays (gamma rays). Thus, a nuclear reaction must cause a transformation of at least one nuclide to another. Sometimes if a nucleus interacts with another nucleus or particle without changing the nature of any nuclide, the process is referred to a nuclear scattering, rather than a nuclear reaction. Perhaps the most notable nuclear reactions are the nuclear fusion reactions of light elements that power the energy production of stars and the Sun. Natural nuclear reactions occur also in the interaction between cosmic rays and matter.

Nuclear reactors are devices to initiate and control a chain nuclear reaction, but there are not only manmade devices. The world’s first nuclear reactor operated about two billion years ago. The natural nuclear reactor formed at Oklo in Gabon, Africa, when a uranium-rich mineral deposit became flooded with groundwater that acted as a neutron moderator, and a nuclear chain reaction started.  These fission reactions were sustained for hundreds of thousands of years, until a chain reaction could no longer be supported. This was confirmed by existence of isotopes of the fission-product gas xenon and by different ratio of U-235/U238 (enrichment of natural uranium).

 

Notation of nuclear reactions

Standard nuclear notation shows (see picture) the chemical symbol, the mass number and the atomic number of the isotope.

If the initial nuclei are denoted by a and b, and the product nuclei are denoted by c and d, the reaction can be represented by the equation:

 a + b → c + d

boron-neutron reaction
This equation describes neutron capture in the boron, which is diluted in the coolant. Boric acid is used in nuclear power plants as a long-term compensator of nuclear fuel reactivity.
Notation of nuclei
Notation of nuclei
Source: chemwiki.ucdavis.edu

Instead of using the full equations in the style above, in many situations a compact notation is used to describe nuclear reactions. This style of the form a(b,c)d is equivalent to a + b producing c + d. Light particles are often abbreviated in this shorthand, typically p means proton, n means neutron, d means deuteron, α means an alpha particle or helium-4, β means beta particle or electron, γ means gamma photon, etc. The reaction above would be written as 10B(n,α)7Li.

 

Nuclear reactions

 Although the number of possible nuclear reactions is enormous, nuclear reactions can be sorted by types. Most of nuclear reactions are accompanied by gamma emission. Some examples are:

  • Elastic scattering. Occurs, when no energy is transferred between the target nucleus and the incident particle.

 208Pb (n, n) 208Pb

  •  Inelastic scattering. Occurs, when energy is transferred. The difference of kinetic energies is saved in excited nuclide.

 40Ca (α, α’) 40mCa

  • Capture reactions. Both charged and neutral particles can be captured by nuclei. This is accompanied by the emission of ˠ-rays. Neutron capture reaction produces radioactive nuclides (induced radioactivity).

 238U (n, ˠ) 239U

  • Rearrangement Reactions. The absorption of a particle accompanied by the emission of one or more particles is called a rearrangement reaction.

4He (α, p) 7Li

  • Fission reactions. 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.

235U (n, 3 n) fission products

  • Fusion reactions.  Occur when, two or more atomic nuclei collide at a very high speed and join to form a new type of atomic nucleus.The fusion reaction of deuterium and tritium is particularly interesting because of its potential of providing energy for the future.

3T (d, n) 4He

  • Spallation reactions. Occur, when a nucleus is hit by a particle with sufficient energy and momentum to knock out several small fragments or, smash it into many fragments.
  • 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. There are many types of radioactive decay:
    • Alpha radioactivity. Alha 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 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 rays are electromagnetic radiation of an very high frequency and are therefore high energy photons. 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.
Notation of nuclear reactions - radioactive decays
Radioactive decays
Source: chemwiki.ucdavis.edu

Fundamental laws

For purposes of this article it is sufficient to note four of the fundamental laws governing these reactions.

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

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

See also: Nuclear Reactions

Binding Energy
Nuclear binding energy curve.
Nuclear binding energy curve.
Source: hyperphysics.phy-astr.gsu.edu

A binding energy is generally the energy required to disassemble a whole system into separate parts. It is known the sum of separate parts has typically a higher potential energy than a bound system, therefore the bound system is more stable. A creation of bound system is often accompanied by subsequent energy release. We usually distinguish the binding energy according to these levels:

At atomic level the atomic binding energy of the atom derives from electromagnetic interaction of electrons in the atomic cloud and nucleons (protons) in the nucleus. The atomic binding energy is the energy required to disassemble an atom into free electrons and a nucleus. This is more commonly known as ionization energy.

At molecular level the molecular binding energy of the molecule derives from bond-dissociation energy of atoms in a chemical bond.

At nuclear level the nuclear binding energy is the energy required to disassemble (to overcome the strong nuclear force) a nucleus of an atom into its component parts (protons and neutrons).

Nuclear binding energy

The component parts of nuclei are neutrons and protons, which are collectively called nucleons. The mass of a nucleus is always less than the sum masses of the constituent protons and neutrons when separated. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E=m.c2) this binding energy is proportional to this mass difference and it is known as the mass defect.

During the nuclear splitting or nuclear fusion, some of the mass of the nucleus gets converted into huge amounts of energy and thus this mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. The nuclear binding energies are enormous, they are on the order of a million times greater than the electron binding energies of atoms.

Nuclear Binding Curve

If the splitting releases energy and the fusion releases the energy, so where is the breaking point? For understanding this issue it is better to relate the binding energy to one nucleon, to obtain nuclear binding curve. The binding energy per one nucleon is not linear. There is a peak in the binding energy curve in the region of stability near iron and this means that either the breakup of heavier nuclei than iron or the combining of lighter nuclei than iron will yield energy.

The reason the trend reverses after iron peak is the growing positive charge of the nuclei. The electric force has greater range than strong nuclear force. While the strong nuclear force binds only close neighbors the electric force of each proton repels the other protons.

See also: Binding Energy

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What is Fundamental Particle – Definition

The physical world is composed of combinations of various subatomic or fundamental particles. These are the smallest building blocks of matter. Material Properties
The physical world is composed of combinations of various subatomic or fundamental particles. These are the smallest building blocks of matter. All matter except dark matter is made of molecules, which are themselves made of atoms. The atoms consist of two parts. An atomic nucleus and an electron cloud. The electrons are spinning around the atomic nucleus. The nucleus itself is generally made of protons and neutrons but even these are composite objects. Inside the protons and neutrons, we find the quarks.

Quarks and electrons are some of the elementary particles. A number of fundamental particles have been discovered in various experiments. So many, that researchers had to organize them, just like Mendeleev did with his periodic table. This is summarized in a theoretical model (concerning the electromagnetic, weak, and strong nuclear interactions) called the Standard Model. In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus it is unknown whether it is composed of other particles. Known elementary particles include the fundamental fermions and the fundamental bosons.

See also: Baryons

See also: Leptons

Fermions

The fermions are generally “matter particles” and “antimatter particles”:

Quarks
The quarks combine to form composite particles called hadrons, the best known and most stable are protons and neutrons.
Antiquarks
For every quark there is a corresponding type of antiparticle. The antiquarks have the same mass, mean lifetime, and spin as their respective quarks, but the electric charge and other charges have the opposite sign.
Leptons
The best known of all leptons are the electrons and the neutrinos.

See also: Leptons

Antileptons
For every lepton there is a corresponding type of antiparticle. The best known of all antileptons are the positrons and the antineutrinos.

Bosons

The bosons are generally “force particles” that mediate interactions among fermions: 

Gauge bosons
The gauge boson is a force carrier of the fundamental interactions of nature.
Higgs boson
The Higgs bosons give other particles mass via the Higgs mechanism. Their existence was confirmed by CERN on 14 March 2013.

Subatomic particles

However, only a few of these fundamental particles (in fact, some of these are not fundamental particles – e.i. neutron consist of three quarks) are very important in nuclear engineering. Nuclear engineering or theory of nuclear reactors operates with much better known subatomic particles such as: 

Electron
The electrons are negatively charged, almost massless particles that nevertheless account for most of the size of the atom. Electrons were discovered by Sir John Joseph Thomson in 1897. Electrons are located in an electron cloud, which is the area surrounding the nucleus of the atom. The electron is only one member of a class of elementary particles, which forms an atom.
Proton
The protons are positively charged, massive particles that are located inside the atomic nucleus. Protons were discovered by Ernest Rutherford in the year 1919, when he performed his gold foil experiment.
Neutron
Neutrons are located in the nucleus with the protons. Along with protons, they make up almost all of the mass of the atom. Neutrons were discovered by James Chadwick in 1932, when he demonstrated that penetrating radiation incorporated beams of neutral particles.
Photon
A photon is an elementary particle, the force carrier for the electromagnetic force. The photon is the quantum of light (discrete bundle of electromagnetic energy). Photons are always in motion and, in a vacuum, have a constant speed of light to all observers (c = 2.998 x 108 m/s).
Neutrino
A neutrino is an elementary particle, one of particles which make up the universe. Neutrinos are electrically neutral, weakly interacting and therefore able to pass through great distances in matter without being affected by it.
Positron
Positron is an antiparticle of a negative electron. Positrons, also called positive electron,  have a positive electric charge and have the same mass and magnitude of charge as the electron. An annihilation occurs, when a low-energy positron collides with a low-energy electron.

Three generations of matter. Fundamental Particles.
Three generations of matter.

Atom Structure

Fundametal Particles by The Science Channel

See also:

Atomic and Nuclear Physics

See also:

Atomic and Nuclear Structure

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