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In gamma-ray spectrometry, the Compton edge is a feature of the measured gamma-ray energy spectrum that results from Compton scattering in the detector material. It corresponds to the highest energy that can be transferred to a weakly bound electron of a detector's atom by an incident photon in a single scattering process, and manifests itself as a ridge in the measured gamma-ray energy spectrum.
An example of a Tauc plot for a transparent conducting oxide. A Tauc plot [1] is used to determine the optical bandgap, or Tauc bandgap, of either disordered [2] or amorphous [3] semiconductors.
In a semiconductor or band insulator, the Fermi level is surrounded by a band gap, referred to as the band gap (to distinguish it from the other band gaps in the band structure). The closest band above the band gap is called the conduction band, and the closest band beneath the band gap is called the valence band.
The band gap is called "direct" if the crystal momentum of electrons and holes is the same in both the conduction band and the valence band; an electron can directly emit a photon. In an "indirect" gap, a photon cannot be emitted because the electron must pass through an intermediate state and transfer momentum to the crystal lattice.
Unit cell definition using parallelepiped with lengths a, b, c and angles between the sides given by α, β, γ [1]. A lattice constant or lattice parameter is one of the physical dimensions and angles that determine the geometry of the unit cells in a crystal lattice, and is proportional to the distance between atoms in the crystal.
A gamma ray cross section is a measure of the probability that a gamma ray interacts with matter. The total cross section of gamma ray interactions is composed of several independent processes: photoelectric effect, Compton (incoherent) scattering, electron-positron pair production in the nucleus field and electron-positron pair production in the electron field (triplet production).
In mathematics, Spouge's approximation is a formula for computing an approximation of the gamma function. It was named after John L. Spouge, who defined the formula in a 1994 paper. [ 1 ] The formula is a modification of Stirling's approximation , and has the form
Thus computing the gamma function becomes a matter of evaluating only a small number of elementary functions and multiplying by stored constants. The Lanczos approximation was popularized by Numerical Recipes , according to which computing the gamma function becomes "not much more difficult than other built-in functions that we take for granted ...