Resonance Escape Probability
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Resonance Escape Probability
In nuclear physics, resonance escape probability p is the probability that a neutron will slow down from fission energy to thermal energies without being captured by a nuclear resonance. A resonance absorption of a neutron in a nucleus does not produce nuclear fission. The probability of resonance absorption is called the ''resonance factor'' \psi, and the sum of the two factors is p + \psi = 1. Generally, the higher the neutron energy, the lower the probability of absorption, but for some energies, called ''resonance energies'', the resonance factor is very high. These energies depend on the properties of heavy nuclei. Resonance escape probability is highly determined by the heterogeneous geometry of a reactor, because fast neutrons resulting from fission can leave the fuel and slow to thermal energies in a moderator, skipping over resonance energies before reentering the fuel. Resonance escape probability appears in the four factor formula and the six factor formula. To comput ...
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Nuclear Physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons. Discoveries in nuclear physics have led to applications in many fields. This includes nuclear power, nuclear weapons, nuclear medicine and magnetic resonance imaging, industrial and agricultural isotopes, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology. Such applications are studied in the field of nuclear engineering. Particle physics evolved out of nuclear physics and the two fields are typically taught in close association. Nuclear astrophysics, the application of nuclear physics to astrophysics, is crucial in explaining the inner workings of stars and the origin of the chemical elements. History The history of nuclear physics as a discipl ...
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Thermal Energy
The term "thermal energy" is used loosely in various contexts in physics and engineering. It can refer to several different well-defined physical concepts. These include the internal energy or enthalpy of a body of matter and radiation; heat, defined as a type of energy transfer (as is thermodynamic work); and the characteristic energy of a degree of freedom, k_T, in a system that is described in terms of its microscopic particulate constituents (where T denotes temperature and k_ denotes the Boltzmann constant). Relation to heat and internal energy In thermodynamics, heat is energy transferred to or from a thermodynamic system by mechanisms other than thermodynamic work or transfer of matter, such as conduction, radiation, and friction. Heat refers to a quantity transferred between systems, not to a property of any one system, or "contained" within it. On the other hand, internal energy and enthalpy are properties of a single system. Heat and work depend on the way in which ...
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Resonance Absorption
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies. Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system. Small periodic forces that are near a resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy. Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, orbital resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance ( ...
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Nuclear Fission
Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay. Nuclear fission of heavy elements was discovered on Monday 19 December 1938, by German chemist Otto Hahn and his assistant Fritz Strassmann in cooperation with Austrian-Swedish physicist Lise Meitner. Hahn understood that a "burst" of the atomic nuclei had occurred. Meitner explained it theoretically in January 1939 along with her nephew Otto Robert Frisch. Frisch named the process by analogy with biological fission of living cells. For heavy nuclides, it is an exothermic reaction which 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). Like nuclear fusion, for fission to produce energy, the total binding energy ...
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Four Factor Formula
The four-factor formula, also known as Fermi's four factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in an infinite medium. The symbols are defined as: *\nu, \nu_f and \nu_t are the average number of neutrons produced per fission in the medium (2.43 for uranium-235). *\sigma_f^F and \sigma_a^F are the microscopic fission and absorption cross sections for fuel, respectively. *\Sigma_a^F and \Sigma_a are the macroscopic absorption cross sections in fuel and in total, respectively. *N_i is the number density of atoms of a specific nuclide. *I_ is the resonance integral for absorption of a specific nuclide. **I_ = \int_^ dE' \frac \frac. *\overline is the average lethargy gain per scattering event. **Lethargy is defined as decrease in neutron energy. *u_f (fast utilization) is the probability that a fast neutron is absorbed in fuel. *P_ is the probability that a fast neutron absorption in fuel causes fission. *P_ is the probabil ...
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Six Factor Formula
The six-factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in a non-infinite medium. The symbols are defined as: *\nu, \nu_f and \nu_t are the average number of neutrons produced per fission in the medium (2.43 for uranium-235). *\sigma_f^F and \sigma_a^F are the microscopic fission and absorption cross sections for fuel, respectively. *\Sigma_a^F and \Sigma_a are the macroscopic absorption cross sections in fuel and in total, respectively. *N_i is the number density of atoms of a specific nuclide. *I_ is the resonance integral for absorption of a specific nuclide. **I_ = \int_^ dE' \frac \frac. *\overline is the average lethargy gain per scattering event. **Lethargy is defined as decrease in neutron energy. *u_f (fast utilization) is the probability that a fast neutron is absorbed in fuel. *P_ is the probability that a fast neutron absorption in fuel causes fission. *P_ is the probability that a thermal neutron absorption in ...
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Neutron Transport
Neutron transport (also known as neutronics) is the study of the motions and interactions of neutrons with materials. Nuclear scientists and engineers often need to know where neutrons are in an apparatus, what direction they are going, and how quickly they are moving. It is commonly used to determine the behavior of nuclear reactor cores and experimental or industrial neutron beams. Neutron transport is a type of radiative transport. Background Neutron transport has roots in the Boltzmann equation, which was used in the 1800s to study the kinetic theory of gases. It did not receive large-scale development until the invention of chain-reacting nuclear reactors in the 1940s. As neutron distributions came under detailed scrutiny, elegant approximations and analytic solutions were found in simple geometries. However, as computational power has increased, numerical approaches to neutron transport have become prevalent. Today, with massively parallel computers, neutron transport is ...
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Nuclear Technology
Nuclear technology is technology that involves the nuclear reactions of atomic nuclei. Among the notable nuclear technologies are nuclear reactors, nuclear medicine and nuclear weapons. It is also used, among other things, in smoke detectors and gun sights. History and scientific background Discovery The vast majority of common, natural phenomena on Earth only involve gravity and electromagnetism, and not nuclear reactions. This is because atomic nuclei are generally kept apart because they contain positive electrical charges and therefore repel each other. In 1896, Henri Becquerel was investigating phosphorescence in uranium salts when he discovered a new phenomenon which came to be called radioactivity. He, Pierre Curie and Marie Curie began investigating the phenomenon. In the process, they isolated the element radium, which is highly radioactive. They discovered that radioactive materials produce intense, penetrating rays of three distinct sorts, which they labeled al ...
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