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Angular Correlation Of Electron Positron Annihilation Radiation
Angular Correlation of Electron Positron Annihilation Radiation (ACAR or ACPAR) is a technique of solid state physics to investigate the electronic structure of metals. It uses positrons which are implanted into a sample and annihilation, annihilate with the electrons. In the majority of annihilation events, two Gamma quantum, gamma quanta are created that are, in the Frame of reference, reference frame of the electron-positron pair, emitted in exactly opposite directions. In the laboratory frame, there is a small angular deviation from collinearity, which is caused by the momentum of the electron. Hence, measuring the angular correlation of the annihilation radiation yields information about the momentum distribution of the electrons in the solid. Investigation of the electronic structure All the macroscopic electronic and magnetic properties of a solid result from its microscopic electronic structure. In the simple free electron model, the electrons do not interact with each ...
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Electronic Structure
In quantum chemistry, electronic structure is the state of motion of electrons in an electrostatic field created by stationary nuclei. The term encompasses both the wave functions of the electrons and the energies associated with them. Electronic structure is obtained by solving quantum mechanical equations for the aforementioned clamped-nuclei problem. Electronic structure problems arise from the Born–Oppenheimer approximation. Along with nuclear dynamics, the electronic structure problem is one of the two steps in studying the quantum mechanical motion of a molecular system. Except for a small number of simple problems such as hydrogen-like atoms, the solution of electronic structure problems require modern computers. Electronic structure problem is routinely solved with quantum chemistry computer programs. Electronic structure calculations rank among the most computationally intensive tasks in all scientific calculations. For this reason, quantum chemistry calculatio ...
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ARPES
Angle-resolved photoemission spectroscopy (ARPES) is an experimental technique used in condensed matter physics to probe the allowed energies and momenta of the electrons in a material, usually a crystalline solid. It is based on the photoelectric effect, in which an incoming photon of sufficient energy ejects an electron from the surface of a material. By directly measuring the kinetic energy and emission angle distributions of the emitted photoelectrons, the technique can map the electronic band structure and Fermi surfaces. ARPES is best suited for the study of one- or two-dimensional materials. It has been used by physicists to investigate high-temperature superconductors, graphene, Topological insulator, topological materials, quantum well states, and materials exhibiting charge density waves. ARPES systems consist of a monochromatic light source to deliver a narrow beam of photons, a sample holder connected to a manipulator used to position the sample of a material, a ...
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Wire Chamber
A wire chamber or multi-wire proportional chamber is a type of proportional counter that detects charged particles and photons and can give positional information on their trajectory, by tracking the trails of gaseous ionization. was located via Dr. C.N. BootPHY304 Particle Physics Sheffield University/ref> Description The multi-wire chamber uses an array of wires at high voltage (anode), which run through a chamber with conductive walls held at ground potential (cathode). Alternatively, the wires may be at ground potential and the cathode held at a high negative voltage; the important thing is that a uniform electric field draws extra electrons or negative ions to the anode wires with little lateral motion. The chamber is filled with carefully chosen gas, such as an argon/methane mix, such that any ionizing particle that passes through the tube will ionize surrounding gaseous atoms. The resulting ions and electrons are accelerated by the electric field across the chamber, causi ...
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Gamma Camera
A gamma camera (γ-camera), also called a scintillation camera or Anger camera, is a device used to image gamma radiation emitting radioisotopes, a technique known as scintigraphy. The applications of scintigraphy include early drug development and nuclear medical imaging to view and analyse images of the human body or the distribution of medically injected, inhaled, or ingested radionuclides emitting gamma rays. Imaging techniques Scintigraphy ("scint") is the use of gamma cameras to capture emitted radiation from internal radioisotopes to create two-dimensional images. SPECT (single photon emission computed tomography) imaging, as used in nuclear cardiac stress testing, is performed using gamma cameras. Usually one, two or three detectors or heads, are slowly rotated around the patient's torso. Multi-headed gamma cameras can also be used for positron emission tomography (PET) scanning, provided that their hardware and software can be configured to detect "coincidences" (nea ...
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Semiconductor Detector
A semiconductor detector in ionizing radiation detection physics is a device that uses a semiconductor (usually silicon or germanium) to measure the effect of incident charged particles or photons. Semiconductor detectors find broad application for radiation protection, gamma and X-ray spectrometry, and as particle detectors. Detection mechanism In semiconductor detectors, ionizing radiation is measured by the number of charge carriers set free in the detector material which is arranged between two electrodes, by the radiation. Ionizing radiation produces free electrons and electron holes. The number of electron-hole pairs is proportional to the energy of the radiation to the semiconductor. As a result, a number of electrons are transferred from the valence band to the conduction band, and an equal number of holes are created in the valence band. Under the influence of an electric field, electrons and holes travel to the electrodes, where they result in a pulse that can b ...
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Doppler Broadening
In atomic physics, Doppler broadening is broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting (or absorbing) particles result in different Doppler shifts, the cumulative effect of which is the emission (absorption) line broadening. This resulting line profile is known as a Doppler profile. A particular case is the thermal Doppler broadening due to the thermal motion of the particles. Then, the broadening depends only on the frequency of the spectral line, the mass of the emitting particles, and their temperature, and therefore can be used for inferring the temperature of an emitting (or absorbing) body being spectroscopically investigated. Derivation When a particle moves (e.g., due to the thermal motion) towards the observer, the emitted radiation is shifted to a higher frequency. Likewise, when the emitter moves away, the frequency is lowered. For non-relativistic thermal ve ...
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Doppler Shift
The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842. A common example of Doppler shift is the change of pitch heard when a vehicle sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession. The reason for the Doppler effect is that when the source of the waves is moving towards the observer, each successive wave crest is emitted from a position closer to the observer than the crest of the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrivals of successive wave crests at the observer is reduced, causing an increa ...
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Momentum Wiki
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum is : \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum f ...
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Heaviside Step Function
The Heaviside step function, or the unit step function, usually denoted by or (but sometimes , or ), is a step function, named after Oliver Heaviside (1850–1925), the value of which is zero for negative arguments and one for positive arguments. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one. The function was originally developed in operational calculus for the solution of differential equations, where it represents a signal that switches on at a specified time and stays switched on indefinitely. Oliver Heaviside, who developed the operational calculus as a tool in the analysis of telegraphic communications, represented the function as . The Heaviside function may be defined as: * a piecewise function: H(x) := \begin 1, & x > 0 \\ 0, & x \le 0 \end * using the Iverson bracket notation: H(x) := 0.html" ;"title=">0">>0/math> * an indicator function: H(x) := \mathbf_=\mathbf 1_(x) * ...
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Wave Function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi, respectively). The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state. For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier tran ...
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Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ...
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Positron Lifetime Spectroscopy
Positron annihilation spectroscopy (PAS) or sometimes specifically referred to as Positron annihilation lifetime spectroscopy (PALS) is a non-destructive spectroscopy technique to study voids and defects in solids. Theory The technique operates on the principle that a positron or positronium will annihilate through interaction with electrons. This annihilation releases gamma rays that can be detected; the time between emission of positrons from a radioactive source and detection of gamma rays due to annihilation corresponds to the lifetime of positron or positronium. When positrons are injected into a solid body, they interact in some manner with the electrons in that species. For solids containing free electrons (such as metals or semiconductors), the implanted positrons annihilate rapidly unless voids such as vacancy defects are present. If voids are available, positrons will reside in them and annihilate less rapidly than in the bulk of the material, on time scales up to ~1 n ...
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