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In nuclear physics research, effective range is a physical parameter in the dimension of length to characterize an effective scattering square well potential. It is related to the scattering phase shift by, k cot δ = − γ + 1 2 ( γ 2 + k 2 ) r 0 + O ( k 4 r o 3 ) {\displaystyle k\cot \delta =-\gamma +{\frac {1}{2}}\left(\gamma ^{2}+k^{2}\right)r_{0}+O\left(k^{4}r_{o}^{3}\right)} .where γ {\displaystyle \gamma } is defined by the relation of deuteron binding energy ϵ = ℏ 2 / M γ 2 {\displaystyle \epsilon =\hbar ^{2}/M\gamma ^{2}} . In the limit of zero energy ( k 2 / 2 m = 0 {\displaystyle k^{2}/2m=0} ), the scattering length can be related to effective length with α = 1 a = γ ( 1 − 1 2 γ r 0 ) {\displaystyle \alpha ={\frac {1}{a}}=\gamma \left(1-{\frac {1}{2}}\gamma r_{0}\right)} . == References == | https://en.wikipedia.org/wiki/Effective_range |
In nuclear physics these methods are used to study properties of the nucleus itself. Methods for studies of the nucleus: Gamma spectroscopy Hypernuclear spectroscopyMethods for condensed matter studies: Nuclear magnetic resonance (NMR) Mössbauer spectroscopy Perturbed angular correlation (PAC, TDPAC, PAC spectroscopy) Muon spin spectroscopy Nuclear orientation Channeling Nuclear reaction analysis Nuclear quadrupole resonance (NQR)Methods for trace element analysis: Neutron activation analysis (NAA) == References == | https://en.wikipedia.org/wiki/Nuclear_spectroscopy |
In nuclear physics, Ronen's golden rule for cluster radioactivity is that the most favorable parents for heavy ion emission (cluster radioactivity) are those that emit clusters which have atomic mass A z {\displaystyle A_{z}} which is given by A z = A z − 2 + 4 + B z / 2 {\displaystyle A_{z}=A_{z-2}+4+B_{z/2}} . The atomic number Z {\displaystyle Z} is even, A 0 = 0 {\displaystyle A_{0}=0} , B z / 2 = 0 {\displaystyle B_{z/2}=0} for Z / 2 {\displaystyle Z/2} - odd and B z / 2 = 2 {\displaystyle B_{z/2}=2} for Z / 2 {\displaystyle Z/2} - even. The daughter nuclei is preferably magic, close to the double magic 208Pb. | https://en.wikipedia.org/wiki/Ronen's_golden_rule_for_cluster_radioactivity |
In nuclear physics, a beta decay transition is the change in state of an atomic nucleus undergoing beta decay. (β-decay) When undergoing beta decay, a nucleus emits a beta particle and a corresponding neutrino, transforming the original nuclide into one with the same mass, but differing charge. (an isobar) There are several types of beta decay transition. | https://en.wikipedia.org/wiki/Gamow-Teller_transition |
In a Fermi transition, the spins of the two emitted particles are anti-parallel, for a combined spin S = 0 {\displaystyle S=0} . As a result, the total angular momentum of the nucleus is unchanged by the transition. By contrast, in a Gamow-Teller transition, the spins of the two emitted particles are parallel, with total spin S = 1 {\displaystyle S=1} , leading to a change in angular momentum between the initial and final states of the nucleus.The theoretical work in describing these transitions was done between 1934 and 1936 by George Gamow and Edward Teller at George Washington University. | https://en.wikipedia.org/wiki/Gamow-Teller_transition |
In nuclear physics, a decay product (also known as a daughter product, daughter isotope, radio-daughter, or daughter nuclide) is the remaining nuclide left over from radioactive decay. Radioactive decay often proceeds via a sequence of steps (decay chain). For example, 238U decays to 234Th which decays to 234mPa which decays, and so on, to 206Pb (which is stable): U 238 ⟶ Th 234 ⏟ daughter of 238 U ⟶ Pa 234 m ⏟ granddaughter of 238 U ⟶ ⋯ ⟶ Pb 206 ⏞ decay products of 238 U {\displaystyle {\ce {^{238}U->}}\overbrace {\underbrace {\ce {^{234}Th}} _{\ce {daughter~of~^{238}U}}{\ce {->}}\underbrace {\ce {^{234\!m}Pa}} _{\ce {granddaughter~of~^{238}U}}{\ce {->\cdots ->{^{206}Pb}}}} ^{\ce {decay~products~of~^{238}U}}} In this example: 234Th, 234mPa,...,206Pb are the decay products of 238U. 234Th is the daughter of the parent 238U. | https://en.wikipedia.org/wiki/Daughter_nucleus |
234mPa (234 metastable) is the granddaughter of 238U.These might also be referred to as the daughter products of 238U.Decay products are important in understanding radioactive decay and the management of radioactive waste. For elements above lead in atomic number, the decay chain typically ends with an isotope of lead or bismuth. Bismuth itself decays to thallium, but the decay is so slow as to be practically negligible. | https://en.wikipedia.org/wiki/Daughter_nucleus |
In many cases, individual members of the decay chain are as radioactive as the parent, but far smaller in volume/mass. Thus, although uranium is not dangerously radioactive when pure, some pieces of naturally occurring pitchblende are quite dangerous owing to their radium-226 content, which is soluble and not a ceramic like the parent. Similarly, thorium gas mantles are very slightly radioactive when new, but become more radioactive after only a few months of storage as the daughters of 232Th build up. | https://en.wikipedia.org/wiki/Daughter_nucleus |
Although it cannot be predicted whether any given atom of a radioactive substance will decay at any given time, the decay products of a radioactive substance are extremely predictable. Because of this, decay products are important to scientists in many fields who need to know the quantity or type of the parent product. Such studies are done to measure pollution levels (in and around nuclear facilities) and for other matters. | https://en.wikipedia.org/wiki/Daughter_nucleus |
In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. As a result, atomic nuclei with a 'magic' number of protons or neutrons are much more stable than other nuclei. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126 (sequence A018226 in the OEIS). For protons, this corresponds to the elements helium, oxygen, calcium, nickel, tin, lead, and the hypothetical unbihexium, although 126 is so far only known to be a magic number for neutrons. | https://en.wikipedia.org/wiki/Magic_number_(physics) |
Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the semi-empirical mass formula and are hence more stable against nuclear decay. The unusual stability of isotopes having magic numbers means that transuranium elements could theoretically be created with extremely large nuclei and yet not be subject to the extremely rapid radioactive decay normally associated with high atomic numbers. Large isotopes with magic numbers of nucleons are said to exist in an island of stability. | https://en.wikipedia.org/wiki/Magic_number_(physics) |
Unlike the magic numbers 2–126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed. Before this was realized, higher magic numbers, such as 184, 258, 350, and 462 (sequence A033547 in the OEIS), were predicted based on simple calculations that assumed spherical shapes: these are generated by the formula 2 ( ( n 1 ) + ( n 2 ) + ( n 3 ) ) {\displaystyle 2({\tbinom {n}{1}}+{\tbinom {n}{2}}+{\tbinom {n}{3}})} (see Binomial coefficient). It is now believed that the sequence of spherical magic numbers cannot be extended in this way. Further predicted magic numbers are 114, 122, 124, and 164 for protons as well as 184, 196, 236, and 318 for neutrons. However, more modern calculations predict 228 and 308 for neutrons, along with 184 and 196. | https://en.wikipedia.org/wiki/Magic_number_(physics) |
In nuclear physics, 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 specific nuclear reaction may be the fission of heavy isotopes (e.g., uranium-235, 235U). A nuclear chain reaction releases several million times more energy per reaction than any chemical reaction. | https://en.wikipedia.org/wiki/Reactivity_(nuclear) |
In nuclear physics, a shake is 10 nanoseconds, the approximate time for a generation within a nuclear chain reaction. The term comes from the expression "two shakes of a lamb's tail", meaning quickly. | https://en.wikipedia.org/wiki/List_of_humorous_units_of_measurement |
In nuclear physics, a stripping reaction is a nuclear reaction in which part of the incident nucleus combines with the target nucleus, and the remainder proceeds with most of its original momentum in almost its original direction. This reaction was first described by Stuart Thomas Butler in 1950. Deuteron stripping reactions have been extensively used to study nuclear reactions and structure, this occurs where the incident nucleus is a deuteron and only a proton emerges from the target nucleus. A simple one-step stripping reaction can be represented as A+a →B+b A + (b+x)a→(A+x)b+b where A represents the target core, b represents the projectile core, and x is the transferred mass which may represent any number of particles. == References == | https://en.wikipedia.org/wiki/Stripping_reaction_(physics) |
In nuclear physics, ab initio methods seek to describe the atomic nucleus from the bottom up by solving the non-relativistic Schrödinger equation for all constituent nucleons and the forces between them. This is done either exactly for very light nuclei (up to four nucleons) or by employing certain well-controlled approximations for heavier nuclei. Ab initio methods constitute a more fundamental approach compared to e.g. the nuclear shell model. Recent progress has enabled ab initio treatment of heavier nuclei such as nickel.A significant challenge in the ab initio treatment stems from the complexities of the inter-nucleon interaction. | https://en.wikipedia.org/wiki/Ab_initio_methods_(nuclear_physics) |
The strong nuclear force is believed to emerge from the strong interaction described by quantum chromodynamics (QCD), but QCD is non-perturbative in the low-energy regime relevant to nuclear physics. This makes the direct use of QCD for the description of the inter-nucleon interactions very difficult (see lattice QCD), and a model must be used instead. The most sophisticated models available are based on chiral effective field theory. | https://en.wikipedia.org/wiki/Ab_initio_methods_(nuclear_physics) |
This effective field theory (EFT) includes all interactions compatible with the symmetries of QCD, ordered by the size of their contributions. The degrees of freedom in this theory are nucleons and pions, as opposed to quarks and gluons as in QCD. The effective theory contains parameters called low-energy constants, which can be determined from scattering data.Chiral EFT implies the existence of many-body forces, most notably the three-nucleon interaction which is known to be an essential ingredient in the nuclear many-body problem.After arriving at a Hamiltonian H {\displaystyle H} (based on chiral EFT or other models) one must solve the Schrödinger equation where | Ψ ⟩ {\displaystyle \vert {\Psi }\rangle } is the many-body wavefunction of the A nucleons in the nucleus. Various ab initio methods have been devised to numerically find solutions to this equation: Green's function Monte Carlo (GFMC) No-core shell model (NCSM) Coupled cluster (CC) Self-consistent Green's function (SCGF) In-medium similarity renormalization group (IM-SRG) | https://en.wikipedia.org/wiki/Ab_initio_methods_(nuclear_physics) |
In nuclear physics, an atomic nucleus is called a halo nucleus or is said to have a nuclear halo when it has a core nucleus surrounded by a "halo" of orbiting protons or neutrons, which makes the radius of the nucleus appreciably larger than that predicted by the liquid drop model. Halo nuclei form at the extreme edges of the table of nuclides — the neutron drip line and proton drip line — and have short half-lives, measured in milliseconds. These nuclei are studied shortly after their formation in an ion beam. Typically, an atomic nucleus is a tightly bound group of protons and neutrons. | https://en.wikipedia.org/wiki/Halo_nucleus |
However, in some nuclides, there is an overabundance of one species of nucleon. In some of these cases, a nuclear core and a halo will form. Often, this property may be detected in scattering experiments, which show the nucleus to be much larger than the otherwise expected value. | https://en.wikipedia.org/wiki/Halo_nucleus |
Normally, the cross-section (corresponding to the classical radius) of the nucleus is proportional to the cube root of its mass, as would be the case for a sphere of constant density. Specifically, for a nucleus of mass number A, the radius r is (approximately) r = r ∘ A 1 3 , {\displaystyle r=r_{\circ }A^{\frac {1}{3}},} where r ∘ {\displaystyle r_{\circ }} is 1.2 fm. One example of a halo nucleus is 11Li, which has a half-life of 8.6 ms. | https://en.wikipedia.org/wiki/Halo_nucleus |
It contains a core of 3 protons and 6 neutrons, and a halo of two independent and loosely bound neutrons. It decays into 11Be by the emission of an antineutrino and an electron. | https://en.wikipedia.org/wiki/Halo_nucleus |
Its mass radius of 3.16 fm is close to that of 32S or, even more impressively, of 208Pb, both much heavier nuclei.Experimental confirmation of nuclear halos is recent and ongoing. Additional candidates are suspected. Several nuclides including 9B, 13N, and 15N are calculated to have a halo in the excited state but not in the ground state. | https://en.wikipedia.org/wiki/Halo_nucleus |
In nuclear physics, an energy amplifier is a novel type of nuclear power reactor, a subcritical reactor, in which an energetic particle beam is used to stimulate a reaction, which in turn releases enough energy to power the particle accelerator and leave an energy profit for power generation. The concept has more recently been referred to as an accelerator-driven system (ADS) or accelerator-driven sub-critical reactor. None have ever been built. | https://en.wikipedia.org/wiki/Energy_amplifier |
In nuclear physics, atomic physics, and nuclear chemistry, the nuclear shell model is a model of the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels. The first shell model was proposed by Dmitri Ivanenko (together with E. Gapon) in 1932. The model was developed in 1949 following independent work by several physicists, most notably Maria Goeppert Mayer and J. Hans D. Jensen, who shared half of the 1963 Nobel Prize in Physics for their contributions.The nuclear shell model is partly analogous to the atomic shell model, which describes the arrangement of electrons in an atom, in that a filled shell results in better stability. When adding nucleons (protons or neutrons) to a nucleus, there are certain points where the binding energy of the next nucleon is significantly less than the last one. | https://en.wikipedia.org/wiki/Nuclear_shell_model |
This observation, that there are specific magic quantum numbers of nucleons (2, 8, 20, 28, 50, 82, 126) which are more tightly bound than the following higher number, is the origin of the shell model. The shells for protons and neutrons are independent of each other. Therefore, there can exist both "magic nuclei", in which one nucleon type or the other is at a magic number, and "doubly magic quantum nuclei", where both are. | https://en.wikipedia.org/wiki/Nuclear_shell_model |
Due to some variations in orbital filling, the upper magic numbers are 126 and, speculatively, 184 for neutrons, but only 114 for protons, playing a role in the search for the so-called island of stability. Some semi-magic numbers have been found, notably Z = 40, which gives the nuclear shell filling for the various elements; 16 may also be a magic number.In order to get these numbers, the nuclear shell model starts from an average potential with a shape somewhere between the square well and the harmonic oscillator. To this potential, a spin orbit term is added. | https://en.wikipedia.org/wiki/Nuclear_shell_model |
Even so, the total perturbation does not coincide with experiment, and an empirical spin orbit coupling must be added with at least two or three different values of its coupling constant, depending on the nuclei being studied. The magic numbers of nuclei, as well as other properties, can be arrived at by approximating the model with a three-dimensional harmonic oscillator plus a spin–orbit interaction. A more realistic but also complicated potential is known as the Woods–Saxon potential. | https://en.wikipedia.org/wiki/Nuclear_shell_model |
In nuclear physics, atomic recoil is the result of the interaction of an atom with an energetic elementary particle, when the momentum of the interacting particle is transferred to the atom as a whole without altering non-translational degrees of freedom of the atom. It is a purely quantum phenomenon. Atomic recoil was discovered by Harriet Brooks, Canada's first female nuclear physicist, in 1904, but interpreted wrongly. | https://en.wikipedia.org/wiki/Atomic_Recoil |
Otto Hahn reworked, explained and demonstrated it in 1908/09. The physicist Walther Gerlach described radioactive recoil as "a profoundly significant discovery in physics with far-reaching consequences".If the transferred momentum of atomic recoil is enough to disrupt the crystal lattice of the material, a vacancy defect is formed; therefore a phonon is generated. Closely related to atomic recoil are electron recoil (see photoexcitation and photoionization) and nuclear recoil, in which momentum transfers to the atomic nucleus as whole. Nuclear recoil can cause the nucleus to be displaced from its normal position in the crystal lattice, which can result in the daughter atom being more susceptible to dissolution. This leads for example to an increase in the ratio of 234U to 238U in certain cases, which can be exploited in dating (see Uranium–thorium dating).In some cases, quantum effects can forbid momentum transfer to an individual nucleus, and momentum is transferred to the crystal lattice as a whole (see Mössbauer effect). | https://en.wikipedia.org/wiki/Atomic_Recoil |
In nuclear physics, atoms decay or react where the atom's nucleus splits, producing several atoms. In nuclear computation, a computational thread splits into several processing threads. | https://en.wikipedia.org/wiki/Nuclear_computation |
In nuclear physics, atoms may react together to fuse where several atomic nuclei may fuse into one nucleus. In nuclear computation, several computational threads fuse into one processing thread. | https://en.wikipedia.org/wiki/Nuclear_computation |
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which an atomic nucleus emits a beta particle (fast energetic electron or positron), transforming into an isobar of that nuclide. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called positron emission. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. | https://en.wikipedia.org/wiki/Bound-state_β−_decay |
The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or valley of stability. For either electron or positron emission to be energetically possible, the energy release (see below) or Q value must be positive. | https://en.wikipedia.org/wiki/Bound-state_β−_decay |
Beta decay is a consequence of the weak force, which is characterized by relatively lengthy decay times. Nucleons are composed of up quarks and down quarks, and the weak force allows a quark to change its flavour by emission of a W boson leading to creation of an electron/antineutrino or positron/neutrino pair. For example, a neutron, composed of two down quarks and an up quark, decays to a proton composed of a down quark and two up quarks. Electron capture is sometimes included as a type of beta decay, because the basic nuclear process, mediated by the weak force, is the same. In electron capture, an inner atomic electron is captured by a proton in the nucleus, transforming it into a neutron, and an electron neutrino is released. | https://en.wikipedia.org/wiki/Bound-state_β−_decay |
In nuclear physics, coupled cluster saw significantly less use than in quantum chemistry during the 1980s and 1990s. More powerful computers, as well as advances in theory (such as the inclusion of three-nucleon interactions), have spawned renewed interest in the method since then, and it has been successfully applied to neutron-rich and medium-mass nuclei. Coupled cluster is one of several ab initio methods in nuclear physics and is specifically suitable for nuclei having closed or nearly closed shells. | https://en.wikipedia.org/wiki/Coupled_cluster |
In nuclear physics, double beta decay is a type of radioactive decay in which two neutrons are simultaneously transformed into two protons, or vice versa, inside an atomic nucleus. As in single beta decay, this process allows the atom to move closer to the optimal ratio of protons and neutrons. As a result of this transformation, the nucleus emits two detectable beta particles, which are electrons or positrons. | https://en.wikipedia.org/wiki/Double_positron_decay |
The literature distinguishes between two types of double beta decay: ordinary double beta decay and neutrinoless double beta decay. In ordinary double beta decay, which has been observed in several isotopes, two electrons and two electron antineutrinos are emitted from the decaying nucleus. In neutrinoless double beta decay, a hypothesized process that has never been observed, only electrons would be emitted. | https://en.wikipedia.org/wiki/Double_positron_decay |
In nuclear physics, hyperdeformation is theoretically predicted states of an atomic nucleus with extremely elongated shape and very high angular momentum. Less elongated states, superdeformation, have been well observed, but the experimental evidence for hyperdeformation is more limited. Hyperdeformed states correspond to an axis ratio of 3:1. | https://en.wikipedia.org/wiki/Hyperdeformation |
They would be caused by a third minimum in the potential energy surface, the second causing superdeformation and the first minimum being normal deformation. Hyperdeformation is predicted to be found in 107Cd. == References == | https://en.wikipedia.org/wiki/Hyperdeformation |
In nuclear physics, properties of a nucleus depend on evenness or oddness of its atomic number (proton number) Z, neutron number N and, consequently, of their sum, the mass number A. Most importantly, oddness of both Z and N tends to lower the nuclear binding energy, making odd nuclei generally less stable. This effect is not only experimentally observed, but is included in the semi-empirical mass formula and explained by some other nuclear models, such as the nuclear shell model. This difference of nuclear binding energy between neighbouring nuclei, especially of odd-A isobars, has important consequences for beta decay. The nuclear spin is zero for even-Z, even N nuclei, integer for all even-A nuclei, and odd half-integer for all odd-A nuclei. | https://en.wikipedia.org/wiki/Odd–odd_nuclei |
The neutron–proton ratio is not the only factor affecting nuclear stability. Adding neutrons to isotopes can vary their nuclear spins and nuclear shapes, causing differences in neutron capture cross sections and gamma spectroscopy and nuclear magnetic resonance properties. If too many or too few neutrons are present with regard to the nuclear binding energy optimum, the nucleus becomes unstable and subject to certain types of nuclear decay. Unstable nuclides with a nonoptimal number of neutrons or protons decay by beta decay (including positron decay), electron capture, or other means, such as spontaneous fission and cluster decay. | https://en.wikipedia.org/wiki/Odd–odd_nuclei |
In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms. Wigner postulated that the spacings between the lines in the spectrum of a heavy atom nucleus should resemble the spacings between the eigenvalues of a random matrix, and should depend only on the symmetry class of the underlying evolution. In solid-state physics, random matrices model the behaviour of large disordered Hamiltonians in the mean-field approximation. In quantum chaos, the Bohigas–Giannoni–Schmit (BGS) conjecture asserts that the spectral statistics of quantum systems whose classical counterparts exhibit chaotic behaviour are described by random matrix theory.In quantum optics, transformations described by random unitary matrices are crucial for demonstrating the advantage of quantum over classical computation (see, e.g., the boson sampling model). Moreover, such random unitary transformations can be directly implemented in an optical circuit, by mapping their parameters to optical circuit components (that is beam splitters and phase shifters).Random matrix theory has also found applications to the chiral Dirac operator in quantum chromodynamics, quantum gravity in two dimensions, mesoscopic physics, spin-transfer torque, the fractional quantum Hall effect, Anderson localization, quantum dots, and superconductors | https://en.wikipedia.org/wiki/Empirical_singular_values_distribution |
In nuclear physics, resonance escape probability p {\displaystyle 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 ψ {\displaystyle \psi } , and the sum of the two factors is p + ψ = 1 {\displaystyle 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. | https://en.wikipedia.org/wiki/Resonance_escape_probability |
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 compute it, neutron transport theory is used. | https://en.wikipedia.org/wiki/Resonance_escape_probability |
In nuclear physics, secular equilibrium is a situation in which the quantity of a radioactive isotope remains constant because its production rate (e.g., due to decay of a parent isotope) is equal to its decay rate. | https://en.wikipedia.org/wiki/Secular_equilibrium |
In nuclear physics, separation energy is the energy needed to remove one nucleon (or other specified particle or particles) from an atomic nucleus. The separation energy is different for each nuclide and particle to be removed. Values are stated as "neutron separation energy", "two-neutron separation energy", "proton separation energy", "deuteron separation energy", "alpha separation energy", and so on. The lowest separation energy among stable nuclides is 1.67 MeV, to remove a neutron from beryllium-9. | https://en.wikipedia.org/wiki/Separation_energy |
The energy can be added to the nucleus by an incident high-energy gamma ray. If the energy of the incident photon exceeds the separation energy, a photodisintegration might occur. Energy in excess of the threshold value becomes kinetic energy of the ejected particle. By contrast, nuclear binding energy is the energy needed to completely disassemble a nucleus, or the energy released when a nucleus is assembled from nucleons. It is the sum of multiple separation energies, which should add to the same total regardless of the order of assembly or disassembly. | https://en.wikipedia.org/wiki/Separation_energy |
In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 and the analytical solution was provided by Harry Bateman in 1910.If, at time t, there are N i ( t ) {\displaystyle N_{i}(t)} atoms of isotope i {\displaystyle i} that decays into isotope i + 1 {\displaystyle i+1} at the rate λ i {\displaystyle \lambda _{i}} , the amounts of isotopes in the k-step decay chain evolves as: d N 1 ( t ) d t = − λ 1 N 1 ( t ) d N i ( t ) d t = − λ i N i ( t ) + λ i − 1 N i − 1 ( t ) d N k ( t ) d t = λ k − 1 N k − 1 ( t ) {\displaystyle {\begin{aligned}{\frac {dN_{1}(t)}{dt}}&=-\lambda _{1}N_{1}(t)\\{\frac {dN_{i}(t)}{dt}}&=-\lambda _{i}N_{i}(t)+\lambda _{i-1}N_{i-1}(t)\\{\frac {dN_{k}(t)}{dt}}&=\lambda _{k-1}N_{k-1}(t)\end{aligned}}} (this can be adapted to handle decay branches). While this can be solved explicitly for i = 2, the formulas quickly become cumbersome for longer chains. The Bateman equation is a classical master equation where the transition rates are only allowed from one species (i) to the next (i+1) but never in the reverse sense (i+1 to i is forbidden). | https://en.wikipedia.org/wiki/Bateman_equation |
In nuclear physics, the Geiger–Nuttall law or Geiger–Nuttall rule relates the decay constant of a radioactive isotope with the energy of the alpha particles emitted. Roughly speaking, it states that short-lived isotopes emit more energetic alpha particles than long-lived ones. The relationship also shows that half-lives are exponentially dependent on decay energy, so that very large changes in half-life make comparatively small differences in decay energy, and thus alpha particle energy. | https://en.wikipedia.org/wiki/Geiger–Nuttall_law |
In practice, this means that alpha particles from all alpha-emitting isotopes across many orders of magnitude of difference in half-life, all nevertheless have about the same decay energy. Formulated in 1911 by Hans Geiger and John Mitchell Nuttall as a relation between the decay constant and the range of alpha particles in air, in its modern form the Geiger–Nuttall law is log 10 T 1 / 2 = A ( Z ) E + B ( Z ) {\displaystyle \log _{10}T_{1/2}={\frac {A(Z)}{\sqrt {E}}}+B(Z)} where T 1 / 2 {\displaystyle T_{1/2}} is the half-life, E the total kinetic energy (of the alpha particle and the daughter nucleus), and A and B are coefficients that depend on the isotope's atomic number Z. The law works best for nuclei with even atomic number and even atomic mass. The trend is still there for even-odd, odd-even, and odd-odd nuclei but is not as pronounced. | https://en.wikipedia.org/wiki/Geiger–Nuttall_law |
In nuclear physics, the astrophysical S-factor S(E) is a rescaling of a nuclear reaction's total cross section σ(E) to account for the Coulomb repulsion between the charged reactants. It determines the rates of nuclear fusion reactions that occur in the cores of stars. | https://en.wikipedia.org/wiki/S-factor |
In nuclear physics, the chiral model, introduced by Feza Gürsey in 1960, is a phenomenological model describing effective interactions of mesons in the chiral limit (where the masses of the quarks go to zero), but without necessarily mentioning quarks at all. It is a nonlinear sigma model with the principal homogeneous space of a Lie group G {\displaystyle G} as its target manifold. When the model was originally introduced, this Lie group was the SU(N) , where N is the number of quark flavors. The Riemannian metric of the target manifold is given by a positive constant multiplied by the Killing form acting upon the Maurer–Cartan form of SU(N). | https://en.wikipedia.org/wiki/Chiral_model |
The internal global symmetry of this model is G L × G R {\displaystyle G_{L}\times G_{R}} , the left and right copies, respectively; where the left copy acts as the left action upon the target space, and the right copy acts as the right action. Phenomenologically, the left copy represents flavor rotations among the left-handed quarks, while the right copy describes rotations among the right-handed quarks, while these, L and R, are completely independent of each other. The axial pieces of these symmetries are spontaneously broken so that the corresponding scalar fields are the requisite Nambu−Goldstone bosons. | https://en.wikipedia.org/wiki/Chiral_model |
The model was later studied in the two-dimensional case as an integrable system, in particular an integrable field theory. Its integrability was shown by Faddeev and Reshetikhin in 1982 through the quantum inverse scattering method. The two-dimensional principal chiral model exhibits signatures of integrability such as a Lax pair/zero-curvature formulation, an infinite number of symmetries, and an underlying quantum group symmetry (in this case, Yangian symmetry). This model admits topological solitons called skyrmions. Departures from exact chiral symmetry are dealt with in chiral perturbation theory. | https://en.wikipedia.org/wiki/Chiral_model |
In nuclear physics, the concept of a neutron cross section is used to express the likelihood of interaction between an incident neutron and a target nucleus. The neutron cross section σ can be defined as the area in cm2 for which the number of neutron-nuclei reactions taking place is equal to the product of the number of incident neutrons that would pass through the area and the number of target nuclei. In conjunction with the neutron flux, it enables the calculation of the reaction rate, for example to derive the thermal power of a nuclear power plant. The standard unit for measuring the cross section is the barn, which is equal to 10−28 m2 or 10−24 cm2. | https://en.wikipedia.org/wiki/Neutron_cross-section |
The larger the neutron cross section, the more likely a neutron will react with the nucleus. An isotope (or nuclide) can be classified according to its neutron cross section and how it reacts to an incident neutron. Nuclides that tend to absorb a neutron and either decay or keep the neutron in its nucleus are neutron absorbers and will have a capture cross section for that reaction. | https://en.wikipedia.org/wiki/Neutron_cross-section |
Isotopes that undergo fission are fissionable fuels and have a corresponding fission cross section. The remaining isotopes will simply scatter the neutron, and have a scatter cross section. Some isotopes, like uranium-238, have nonzero cross sections of all three. | https://en.wikipedia.org/wiki/Neutron_cross-section |
Isotopes which have a large scatter cross section and a low mass are good neutron moderators (see chart below). Nuclides which have a large absorption cross section are neutron poisons if they are neither fissile nor undergo decay. A poison that is purposely inserted into a nuclear reactor for controlling its reactivity in the long term and improve its shutdown margin is called a burnable poison. | https://en.wikipedia.org/wiki/Neutron_cross-section |
In nuclear physics, the internal conversion coefficient describes the rate of internal conversion. The internal conversion coefficient may be empirically determined by the following formula: There is no valid formulation for an equivalent concept for E0 (electric monopole) nuclear transitions. There are theoretical calculations that can be used to derive internal conversion coefficients. | https://en.wikipedia.org/wiki/Internal_conversion_coefficient |
Their accuracy is not generally under dispute, but since the quantum mechanical models they depend on only take into account electromagnetic interactions between the nucleus and electrons, there may be unforeseen effects. Internal conversion coefficients can be looked up from tables, but this is time-consuming. Computer programs have been developed (see the BrIcc Program) which present internal conversion coefficients quickly and easily. | https://en.wikipedia.org/wiki/Internal_conversion_coefficient |
Theoretical calculations of interest are the Rösel, Hager-Seltzer, and the Band, superseded by the Band-Raman calculation called BrIcc. The Hager-Seltzer calculations omit the M and higher-energy shells on the grounds (usually valid) that those orbitals have little electron density at the nucleus and can be neglected. To first approximation this assumption is valid, upon comparing several internal conversion coefficients for different isotopes for transitions of about 100 keV. The Band and Band-Raman calculations assume that the M shell may contribute to internal conversion to a non-negligible extent, and incorporates a general term (called "N+") which takes into account the small effect of any higher shells there may be, while the Rösel calculation works like the Band, but does not assume that all shells contribute and so generally terminates at the N shell. Additionally, the Band-Raman calculation can now consider ("frozen orbitals") or neglect ("no hole") the effect of the electron vacancy; the frozen-orbitals approximation is considered generally superior. | https://en.wikipedia.org/wiki/Internal_conversion_coefficient |
In nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known isotopes of these elements. It is predicted to appear as an "island" in the chart of nuclides, separated from known stable and long-lived primordial radionuclides. Its theoretical existence is attributed to stabilizing effects of predicted "magic numbers" of protons and neutrons in the superheavy mass region.Several predictions have been made regarding the exact location of the island of stability, though it is generally thought to center near copernicium and flerovium isotopes in the vicinity of the predicted closed neutron shell at N = 184. These models strongly suggest that the closed shell will confer further stability towards fission and alpha decay. | https://en.wikipedia.org/wiki/Island_of_stability |
While these effects are expected to be greatest near atomic number Z = 114 and N = 184, the region of increased stability is expected to encompass several neighboring elements, and there may also be additional islands of stability around heavier nuclei that are doubly magic (having magic numbers of both protons and neutrons). Estimates of the stability of the nuclides within the island are usually around a half-life of minutes or days; some estimates predict half-lives of millions of years.Although the nuclear shell model predicting magic numbers has existed since the 1940s, the existence of long-lived superheavy nuclides has not been definitively demonstrated. Like the rest of the superheavy elements, the nuclides within the island of stability have never been found in nature; thus, they must be created artificially in a nuclear reaction to be studied. Scientists have not found a way to carry out such a reaction, for it is likely that new types of reactions will be needed to populate nuclei near the center of the island. Nevertheless, the successful synthesis of superheavy elements up to Z = 118 (oganesson) with up to 177 neutrons demonstrates a slight stabilizing effect around elements 110 to 114 that may continue in unknown isotopes, consistent with the existence of the island of stability. | https://en.wikipedia.org/wiki/Island_of_stability |
In nuclear physics, the second magic number. In particle physics, the eightfold way is used to classify sub-atomic particles. In statistical mechanics, the eight-vertex model has 8 possible configurations of arrows at each vertex. | https://en.wikipedia.org/wiki/8 |
In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons. As the name suggests, it is based partly on theory and partly on empirical measurements. The formula represents the liquid-drop model proposed by George Gamow, which can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. | https://en.wikipedia.org/wiki/Liquid_drop_model |
It was first formulated in 1935 by German physicist Carl Friedrich von Weizsäcker, and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today. The formula gives a good approximation for atomic masses and thereby other effects. However, it fails to explain the existence of lines of greater binding energy at certain numbers of protons and neutrons. These numbers, known as magic numbers, are the foundation of the nuclear shell model. | https://en.wikipedia.org/wiki/Liquid_drop_model |
In nuclear physics, the symmetry energy reflects the variation of the binding energy of the nucleons in the nuclear matter depending on its neutron to proton ratio as a function of baryon density. Symmetry energy is an important parameter in the equation of state describing the nuclear structure of heavy nuclei and neutron stars. == References == | https://en.wikipedia.org/wiki/Symmetry_energy |
In nuclear physics, the valley of stability (also called the belt of stability, nuclear valley, energy valley, or beta stability valley) is a characterization of the stability of nuclides to radioactivity based on their binding energy. Nuclides are composed of protons and neutrons. The shape of the valley refers to the profile of binding energy as a function of the numbers of neutrons and protons, with the lowest part of the valley corresponding to the region of most stable nuclei. The line of stable nuclides down the center of the valley of stability is known as the line of beta stability. | https://en.wikipedia.org/wiki/Valley_of_stability |
The sides of the valley correspond to increasing instability to beta decay (β− or β+). The decay of a nuclide becomes more energetically favorable the further it is from the line of beta stability. The boundaries of the valley correspond to the nuclear drip lines, where nuclides become so unstable they emit single protons or single neutrons. | https://en.wikipedia.org/wiki/Valley_of_stability |
Regions of instability within the valley at high atomic number also include radioactive decay by alpha radiation or spontaneous fission. The shape of the valley is roughly an elongated paraboloid corresponding to the nuclide binding energies as a function of neutron and atomic numbers.The nuclides within the valley of stability encompass the entire table of nuclides. The chart of those nuclides is also known as a Segrè chart, after the physicist Emilio Segrè. | https://en.wikipedia.org/wiki/Valley_of_stability |
The Segrè chart may be considered a map of the nuclear valley. The region of proton and neutron combinations outside of the valley of stability is referred to as the sea of instability.Scientists have long searched for long-lived heavy isotopes outside of the valley of stability, hypothesized by Glenn T. Seaborg in the late 1960s. These relatively stable nuclides are expected to have particular configurations of "magic" atomic and neutron numbers, and form a so-called island of stability. | https://en.wikipedia.org/wiki/Valley_of_stability |
In nuclear physics, transient equilibrium is a situation in which equilibrium is reached by a parent-daughter radioactive isotope pair where the half-life of the daughter is shorter than the half-life of the parent. Contrary to secular equilibrium, the half-life of the daughter is not negligible compared to parent's half-life. An example of this is a molybdenum-99 generator producing technetium-99 for nuclear medicine diagnostic procedures. Such a generator is sometimes called a cow because the daughter product, in this case technetium-99, is milked at regular intervals. Transient equilibrium occurs after four half-lives, on average. | https://en.wikipedia.org/wiki/Transient_equilibrium |
In nuclear polyadenylation, a poly(A) tail is added to an RNA at the end of transcription. On mRNAs, the poly(A) tail protects the mRNA molecule from enzymatic degradation in the cytoplasm and aids in transcription termination, export of the mRNA from the nucleus, and translation. Almost all eukaryotic mRNAs are polyadenylated, with the exception of animal replication-dependent histone mRNAs. | https://en.wikipedia.org/wiki/Polyadenylation |
These are the only mRNAs in eukaryotes that lack a poly(A) tail, ending instead in a stem-loop structure followed by a purine-rich sequence, termed histone downstream element, that directs where the RNA is cut so that the 3′ end of the histone mRNA is formed.Many eukaryotic non-coding RNAs are always polyadenylated at the end of transcription. There are small RNAs where the poly(A) tail is seen only in intermediary forms and not in the mature RNA as the ends are removed during processing, the notable ones being microRNAs. But, for many long noncoding RNAs – a seemingly large group of regulatory RNAs that, for example, includes the RNA Xist, which mediates X chromosome inactivation – a poly(A) tail is part of the mature RNA. | https://en.wikipedia.org/wiki/Polyadenylation |
In nuclear power technology, burnup (also known as fuel utilization) is a measure of how much energy is extracted from a primary nuclear fuel source. It is measured as the fraction of fuel atoms that underwent fission in %FIMA (fissions per initial metal atom) or %FIFA (fissions per initial fissile atom) as well as, preferably, the actual energy released per mass of initial fuel in gigawatt-days/metric ton of heavy metal (GWd/tHM), or similar units. | https://en.wikipedia.org/wiki/Burnup |
In nuclear power technology, online refuelling is a technique for changing the fuel of a nuclear reactor while the reactor is critical. This allows the reactor to continue to generate electricity during routine refuelling, and therefore improve the availability and profitability of the plant. | https://en.wikipedia.org/wiki/Online_refuelling |
In nuclear reactor engineering, a per cent mille is equal to one-thousandth of a percent of the reactivity, denoted by Greek lowercase letter rho. Reactivity is a dimensionless unit representing a departure from criticality, calculated by: ρ = ( k eff − 1 ) / k eff {\displaystyle \rho =(k_{\text{eff}}-1)/k_{\text{eff}}} where keff denotes the effective multiplication factor for the reaction. Therefore, one pcm is equal to: 1 pcm = ρ ⋅ 10 5 {\displaystyle 1~{\text{pcm}}=\rho \cdot 10^{5}} This unit is commonly used in the operation of light-water reactor sites because reactivity values tend to be small, so measuring in pcm allows reactivity to be expressed using whole numbers. | https://en.wikipedia.org/wiki/Per_cent_mille |
In nuclear safety and radioactive waste management, CS Group produces high-performance simulators and creates specialized scientific software. The firm participated in creating simulator platforms for nuclear plants (including specialized simulators of EDF, the French electric company). | https://en.wikipedia.org/wiki/CS_Communication_&_Systèmes |
In nuclear science and pharmacokinetics, the agent of interest might be situated in a decay chain, where the accumulation is governed by exponential decay of a source agent, while the agent of interest itself decays by means of an exponential process. These systems are solved using the Bateman equation. In the pharmacology setting, some ingested substances might be absorbed into the body by a process reasonably modeled as exponential decay, or might be deliberately formulated to have such a release profile. | https://en.wikipedia.org/wiki/Exponentially_decaying |
In nuclear science, the decay chain refers to a series of radioactive decays of different radioactive decay products as a sequential series of transformations. It is also known as a "radioactive cascade". The typical radioisotope does not decay directly to a stable state, but rather it decays to another radioisotope. | https://en.wikipedia.org/wiki/Actinium_series |
Thus there is usually a series of decays until the atom has become a stable isotope, meaning that the nucleus of the atom has reached a stable state. Decay stages are referred to by their relationship to previous or subsequent stages. A parent isotope is one that undergoes decay to form a daughter isotope. | https://en.wikipedia.org/wiki/Actinium_series |
One example of this is uranium (atomic number 92) decaying into thorium (atomic number 90). The daughter isotope may be stable or it may decay to form a daughter isotope of its own. The daughter of a daughter isotope is sometimes called a granddaughter isotope. | https://en.wikipedia.org/wiki/Actinium_series |
Note that the parent isotope becomes the daughter isotope, unlike in the case of a biological parent and daughter. The time it takes for a single parent atom to decay to an atom of its daughter isotope can vary widely, not only between different parent-daughter pairs, but also randomly between identical pairings of parent and daughter isotopes. The decay of each single atom occurs spontaneously, and the decay of an initial population of identical atoms over time t, follows a decaying exponential distribution, e−λt, where λ is called a decay constant. | https://en.wikipedia.org/wiki/Actinium_series |
One of the properties of an isotope is its half-life, the time by which half of an initial number of identical parent radioisotopes can be expected statistically to have decayed to their daughters, which is inversely related to λ. Half-lives have been determined in laboratories for many radioisotopes (or radionuclides). These can range from nearly instantaneous (less than 10−21 seconds) to more than 1019 years. The intermediate stages each emit the same amount of radioactivity as the original radioisotope (i.e. there is a one-to-one relationship between the numbers of decays in successive stages) but each stage releases a different quantity of energy. | https://en.wikipedia.org/wiki/Actinium_series |
If and when equilibrium is achieved, each successive daughter isotope is present in direct proportion to its half-life; but since its activity is inversely proportional to its half-life, each nuclide in the decay chain contributes as many individual transformations as the head of the chain, though not the same energy. For example, uranium-238 is weakly radioactive, but pitchblende, a uranium ore, is 13 times more radioactive than the pure uranium metal because of the radium and other daughter isotopes it contains. Not only are unstable radium isotopes significant radioactivity emitters, but as the next stage in the decay chain they also generate radon, a naturally-occurring radioactive noble gas that is very dense. Rock containing thorium and/or uranium (such as some types of granite) emits radon gas that due to its density tends accumulate in enclosed places such as basements or underground mines. The quantity of isotopes in the decay chains at a certain time are calculated with the Bateman equation. | https://en.wikipedia.org/wiki/Actinium_series |
In nuclear spectroscopy methods, the nucleus is used to probe the local structure in materials. The methods mainly base on hyperfine interactions with the surrounding atoms and ions. Important methods are nuclear magnetic resonance, Mössbauer spectroscopy, and perturbed angular correlation. | https://en.wikipedia.org/wiki/Hyperfine_coupling |
In nuclear strategy, a counterforce target is one that has a military value, such as a launch silo for intercontinental ballistic missiles, an airbase at which nuclear-armed bombers are stationed, a homeport for ballistic missile submarines, or a command and control installation.The intent of a counterforce strategy (attacking counterforce targets with nuclear weapons) is to conduct a preemptive nuclear strike which has as its aim to disarm an adversary by destroying its nuclear weapons before they can be launched. That would minimize the impact of a retaliatory second strike. However, counterforce attacks are possible in a second strike as well, especially with weapons like UGM-133 Trident II. | https://en.wikipedia.org/wiki/Counterforce |
A counterforce target is distinguished from a countervalue target, which includes an adversary's population, knowledge, economic, or political resources. In other words, a counterforce strike is against an adversary's military, and a countervalue strike is against an adversary's cities. A closely related tactic is the decapitation strike, which destroys an enemy's nuclear command and control facilities and similarly has a goal to eliminate or reduce the enemy's ability to launch a second strike. Counterforce targets are almost always near to civilian population centers, which would not be spared in the event of a counterforce strike. | https://en.wikipedia.org/wiki/Counterforce |
In nuclear strategy, a first strike or preemptive strike is a preemptive surprise attack employing overwhelming force. First strike capability is a country's ability to defeat another nuclear power by destroying its arsenal to the point where the attacking country can survive the weakened retaliation while the opposing side is left unable to continue war. The preferred methodology is to attack the opponent's strategic nuclear weapon facilities (missile silos, submarine bases, bomber airfields), command and control sites, and storage depots first. The strategy is called counterforce. | https://en.wikipedia.org/wiki/Preemptive_nuclear_strike |
In nuclear strategy, a retaliatory strike or second-strike capability is a country's assured ability to respond to a nuclear attack with powerful nuclear retaliation against the attacker. To have such an ability (and to convince an opponent of its viability) is considered vital in nuclear deterrence, as otherwise the other side might attempt to try to win a nuclear war in one massive first strike against its opponent's own nuclear forces. | https://en.wikipedia.org/wiki/Second-strike_capability |
In nuclear strategy, minimal deterrence, also known as minimum deterrence and finite deterrence, is an application of deterrence theory in which a state possesses no more nuclear weapons than is necessary to deter an adversary from attacking. Pure minimal deterrence is a doctrine of no first use, holding that the only mission of nuclear weapons is to deter a nuclear adversary by making the cost of a first strike unacceptably high. To present a credible deterrent, there must be the assurance that any attack would trigger a retaliatory strike. In other words, minimal deterrence requires rejecting a counterforce strategy in favor of pursuing survivable force that can be used in a countervalue second strike. | https://en.wikipedia.org/wiki/Minimum_deterrence |
While the United States and the Soviet Union each developed robust first- and second-strike capabilities during the Cold War, the People's Republic of China pursued a doctrine of minimal nuclear deterrence. Assuming that decision-makers make cost-benefit analyses when deciding to use force, China's doctrine calls for acquiring a nuclear arsenal only large enough to destroy an adversary's "strategic points" in such a way that the expected costs of a first strike outweigh the anticipated benefits. India has also adopted this strategy, which they term Minimum Credible Deterrence.The "minimum credible deterrence" (also known as N-deterrence) policy of Pakistan is a defence and strategic principle on which the country's nuclear weapons program is based. | https://en.wikipedia.org/wiki/Minimum_deterrence |
This doctrine is not a part of the nuclear doctrine, which is designed for the use of the atomic weapons in a full-scale declared war if the conditions of the doctrine are surpassed. Instead, the policy of the Minimum Credible Deterrence falls under minimal deterrence as an inverse to the Mutually Assured Destruction (MAD), which is widely regarded as designed to dissuade India from taking any military actions against Pakistan, as it did during the Indo-Pakistani War of 1971. Pakistan refuses to adopt a no first use policy, while India and China have adopted no first use policies. | https://en.wikipedia.org/wiki/Minimum_deterrence |
Pakistan's foreign minister Shamshad Ahmad had warned that if Pakistan is ever invaded or attacked, it will use "any weapon in its arsenal" to defend itself. Minimal deterrence represents one way of solving the security dilemma and avoiding an arms race. | https://en.wikipedia.org/wiki/Minimum_deterrence |
Decision-makers often feel pressured to expand their arsenals when they perceive them to be vulnerable to an adversary's first strike, especially when both sides seek to achieve the advantage. Eliminating this perceived vulnerability reduces the incentive to produce more and advanced weapons. For example, the United States’ nuclear force exceeds the requirements of minimal deterrence, and is structured to strike numerous targets in multiple countries and to have the ability to conduct successful counterforce strikes with high confidence. | https://en.wikipedia.org/wiki/Minimum_deterrence |
In response to this, China continues to modernize its nuclear forces because its leaders are concerned about the survivability of their arsenal in the face of the United States’ advances in strategic reconnaissance, precision strike, and missile defense.One disadvantage of minimal deterrence is that it requires an accurate understanding of the level of damage an adversary finds unacceptable, especially if that understanding changes over time so that a previously credible deterrent is no longer credible. A minimal deterrence strategy must also account for the nuclear firepower that would be "lost" or "neutralized" during an adversary's counterforce strike. Additionally, a minimal deterrence capability may embolden a state when it confronts a superior nuclear power, as has been observed in the relationship between China and the United States. Finally, while pursuing minimal deterrence during arms negotiations allows states to make reductions without becoming vulnerable, further reductions may be undesirable once minimal deterrence is reached because they will increase a state's vulnerability and provide an incentive for an adversary to secretly expand its nuclear arsenal. | https://en.wikipedia.org/wiki/Minimum_deterrence |
In nuclear transitions governed by strong and electromagnetic interactions (which are invariant under parity), the physical laws would be the same if the interaction was reflected in a mirror. Hence the sum of a vector and a pseudovector is not meaningful. However, the weak force, which governs beta decay and the corresponding nuclear transitions, does depend on the chirality of the interaction, and in this case pseudovectors and vectors are added. The Gamow–Teller transition is a pseudovector transition, that is, the selection rules for beta decay caused by such a transition involve no parity change of the nuclear state. | https://en.wikipedia.org/wiki/Gamow-Teller_transition |
The spin of the parent nucleus can either remain unchanged or change by ±1. However, unlike the Fermi transition, transitions from spin 0 to spin 0 are excluded. In terms of total nuclear angular momentum, the Gamow–Teller transition ( I i → I f {\displaystyle I_{i}\rightarrow I_{f}} ) is Δ I = I f − I i = { 0 I i = I f = 0 1 I i = 0 and I f = 1 {\displaystyle \Delta I=I_{f}-I_{i}={\begin{cases}0&I_{i}=I_{f}=0\\1&I_{i}=0{\text{ and }}I_{f}=1\end{cases}}} Examples 2 6 He 4 → 3 6 Li 3 + β − + ν ¯ e {\displaystyle {}_{2}^{6}{\text{He}}_{4}\rightarrow {}_{3}^{6}{\text{Li}}_{3}+\beta ^{-}+{\bar {\nu }}_{\text{e}}} I i = 0 + → I f = 1 + ⇒ Δ I = 1 {\displaystyle I_{i}=0^{+}\rightarrow I_{f}=1^{+}\Rightarrow \Delta I=1} also Δ π = 0 ⇒ {\displaystyle \Delta \pi =0\Rightarrow } parity is conserved: π ( Y ℓ m ) = ( − 1 ) ℓ ⇒ {\displaystyle \pi (Y_{\ell \,m})=(-1)^{\ell }\Rightarrow } the final 6Li 1+ state has L = 1 {\displaystyle L=1} and the β + ν ¯ e {\displaystyle \beta +{\bar {\nu }}_{\text{e}}} state has S = 1 {\displaystyle S=1} states that couple to an even parity state. | https://en.wikipedia.org/wiki/Gamow-Teller_transition |
In nuclear war, after nuclear weapons accidents, and with the contemporary threat of "dirty bomb" radiological warfare, measuring the intensity of high-intensity ionizing radiation, and the cumulative dose received by personnel, is critical safety information. The survey function measures the type of active ionizing radiation present from: Alpha particles beta particles neutrons X-rays Gamma raysWhile alpha particle emitters such as those in depleted uranium (DU) (i.e., uranium 238) are not a hazard at a distance, alpha particle measurements are necessary for safe handling of projectile dust, or of damaged vehicles with DU armor. | https://en.wikipedia.org/wiki/Nuclear_MASINT |
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