Forbidden Transition
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Forbidden Transition
In spectroscopy, a forbidden mechanism (forbidden transition or forbidden line) is a spectral line associated with absorption or emission of photons by atomic nuclei, atoms, or molecules which undergo a transition that is not allowed by a particular selection rule but is allowed if the approximation associated with that rule is not made. For example, in a situation where, according to usual approximations (such as the electric dipole approximation for the interaction with light), the process cannot happen, but at a higher level of approximation (e.g. magnetic dipole, or electric quadrupole) the process is allowed but at a low rate. An example is phosphorescent glow-in-the-dark materials, which absorb light and form an excited state whose decay involves a spin flip, and is therefore forbidden by electric dipole transitions. The result is emission of light slowly over minutes or hours. Should an atomic nucleus, atom or molecule be raised to an excited state and should the transitio ...
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Spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter waves and acoustic waves can also be considered forms of radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO) In simpler terms, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum. Historically, spectroscopy originated as the study of the wavelength dependence of the absorption by gas phase matter of visible light dispersed by a prism. Spectroscopy, primarily in the electromagnetic spectrum, is a fundamental exploratory tool in the fields of astronomy, chemistry, materials science, and physics, allowing the composition, physical structure and e ...
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Beta Decay
In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which a beta particle (fast energetic electron or positron) is emitted from an atomic nucleus, transforming the original nuclide to 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. 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 em ...
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Tauc Plot
A Tauc plot is used to determine the optical bandgap, or Tauc bandgap, of either disordered or amorphous semiconductors. In his original work Jan Tauc () showed that the optical absorption spectrum of amorphous germanium resembles the spectrum of the indirect transitions in crystalline germanium (plus a tail due to localized states at lower energies), and proposed an extrapolation to find the optical bandgap of these crystalline-like states. Typically, a Tauc plot shows the quantity hν (the photon energy) on the abscissa (x-coordinate) and the quantity (αhν)1/2 on the ordinate (y-coordinate), where α is the absorption coefficient of the material. Thus, extrapolating this linear region to the abscissa yields the energy of the optical bandgap of the amorphous material. A similar procedure is adopted to determine the optical bandgap of crystalline semiconductors. In this case, however, the ordinate is given by (α)1/r, in which the exponent 1/r denotes the nature of the transit ...
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Semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glass. Its electrical resistivity and conductivity, resistivity falls as its temperature rises; metals behave in the opposite way. Its conducting properties may be altered in useful ways by introducing impurities ("doping (semiconductor), doping") into the crystal structure. When two differently doped regions exist in the same crystal, a semiconductor junction is created. The behavior of charge carriers, which include electrons, ions, and electron holes, at these junctions is the basis of diodes, transistors, and most modern electronics. Some examples of semiconductors are silicon, germanium, gallium arsenide, and elements near the so-called "metalloid staircase" on the periodic table. After silicon, gallium arsenide is the second-most common s ...
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Solid State Laser
A solid-state laser is a laser that uses a gain medium that is a solid, rather than a liquid as in dye lasers or a gas as in gas lasers. Semiconductor-based lasers are also in the solid state, but are generally considered as a separate class from solid-state lasers, called laser diodes. Solid-state media Generally, the active medium of a solid-state laser consists of a glass or crystalline "host" material, to which is added a "dopant" such as neodymium, chromium, erbium, thulium or ytterbium.Z. Su, J. D. Bradley, N. Li, E. S. Magden, Purnawirman, D. Coleman, N. Fahrenkopf, C. Baiocco, T. Adam, G. Leake, D. Coolbaugh, D. Vermeulen, and M. R. Watts (2016"Ultra-Compact CMOS-Compatible Ytterbium Microlaser" ''Integrated Photonics Research, Silicon and Nanophotonics 2016'', IW1A.3. Many of the common dopants are rare-earth elements, because the excited states of such ions are not strongly coupled with the thermal vibrations of their crystal lattices (phonons), and their operational t ...
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Dopants
A dopant, also called a doping agent, is a trace of impurity element that is introduced into a chemical material to alter its original electrical or optical properties. The amount of dopant necessary to cause changes is typically very low. When doped into crystalline substances, the dopant's atoms get incorporated into its crystal lattice. The crystalline materials are frequently either crystals of a semiconductor such as silicon and germanium for use in solid-state electronics, or transparent crystals for use in the production of various laser types; however, in some cases of the latter, noncrystalline substances such as glass can also be doped with impurities. In solid-state electronics using the proper types and amounts of dopants in semiconductors is what produces the p-type semiconductors and n-type semiconductors that are essential for making transistors and diodes. Transparent crystals Lasing media The procedure of doping tiny amounts of the metals chromium (Cr), neod ...
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Neodymium
Neodymium is a chemical element with the symbol Nd and atomic number 60. It is the fourth member of the lanthanide series and is considered to be one of the rare-earth metals. It is a hard, slightly malleable, silvery metal that quickly tarnishes in air and moisture. When oxidized, neodymium reacts quickly producing pink, purple/blue and yellow compounds in the +2, +3 and +4 oxidation states. It is generally regarded as having one of the most complex spectra of the elements. Neodymium was discovered in 1885 by the Austrian chemist Carl Auer von Welsbach, who also discovered praseodymium. It is present in significant quantities in the minerals monazite and bastnäsite. Neodymium is not found naturally in metallic form or unmixed with other lanthanides, and it is usually refined for general use. Neodymium is fairly common—about as common as cobalt, nickel, or copper—and is widely distributed in the Earth's crust. Most of the world's commercial neodymium is mined in China, as is ...
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Erbium
Erbium is a chemical element with the symbol Er and atomic number 68. A silvery-white solid metal when artificially isolated, natural erbium is always found in chemical combination with other elements. It is a lanthanide, a rare-earth element The rare-earth elements (REE), also called the rare-earth metals or (in context) rare-earth oxides or sometimes the lanthanides (yttrium and scandium are usually included as rare earths), are a set of 17 nearly-indistinguishable lustrous silve ..., originally found in the gadolinite mine in Ytterby, Sweden, which is the source of the element's name. Erbium's principal uses involve its pink-colored Er3+ ions, which have optical fluorescent properties particularly useful in certain laser applications. Erbium-doped glasses or crystals can be used as optical amplification media, where Er3+ ions are optically pumped at around 980 or and then radiate light at in stimulated emission. This process results in an unusually mechanically simple la ...
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Double Beta Decay
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. 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. History The idea of double beta decay was first proposed by M. Goeppert-Mayer in 1935. In 1937, E. Majorana demonstrated that all results of beta decay ...
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Parity (physics)
In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point reflection): :\mathbf: \beginx\\y\\z\end \mapsto \begin-x\\-y\\-z\end. It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity. The weak interaction is chiral and thus provides a means for probing chirality in physics. In interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions. A matrix representation of P (in any number of dimensions) has determinant equal to −1, and hence is distinct from a rotat ...
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Nuclear Spin
In atomic physics, the spin quantum number is a quantum number (designated ) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. The phrase was originally used to describe the fourth of a set of quantum numbers (the principal quantum number , the azimuthal quantum number , the magnetic quantum number , and the spin quantum number ), which completely describe the quantum state of an electron in an atom. The name comes from a physical spinning of the electron about an axis, as proposed by Uhlenbeck and Goudsmit. The value of is the component of spin angular momentum parallel to a given direction (the –axis), which can be either +1/2 or –1/2 (in units of the reduced Planck constant). However this simplistic picture was quickly realized to be physically impossible because it would require the electrons to rotate faster than the speed of light. It was therefore replaced by a more abstract quantum-mechanical ...
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Selection Rules
In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in atomic nuclei, and so on. The selection rules may differ according to the technique used to observe the transition. The selection rule also plays a role in chemical reactions, where some are formally spin-forbidden reactions, that is, reactions where the spin state changes at least once from reactants to products. In the following, mainly atomic and molecular transitions are considered. Overview In quantum mechanics the basis for a spectroscopic selection rule is the value of the ''transition moment integral''  :\int \psi_1^* \, \mu \, \psi_2 \, \mathrm\tau\,, where \psi_1 and \psi_2 are the wave functions of the two states, "state 1" and "state 2", involved in the transition, and is the transition moment operator. This ...
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