Compton Effect

Example problems on photoelectric effect, and Compton effect. Content typical of Modern Physics textbook. Introduction to the basic physics involved in PV cells for power generation. UG level.

Solved example problems from Mahesh C. Jain textbook 'QMs A Textbook for UGs'. Users of this file may get the theory from any UG Modern Physics textbook.

Any errors and omissions apologies in advance.

We perform Monte Carlo simulations of cosmic ray-induced hard X-ray radiation from the Earth's atmosphere. We find that the shape of the spectrum emergent from the atmosphere in the energy range 25-300 keV is mainly determined by Compton scatterings and photoabsorption, and is almost insensitive to the incident cosmic-ray spectrum. We provide a fitting formula for the hard X-ray surface brightness of the atmosphere as would be measured by a satellite-born instrument, as a function of energy, solar modulation level, geomagnetic cutoff rigidity and zenith angle. A recent measurement by the INTEGRAL observatory of the atmospheric hard X-ray flux during the occultation of the cosmic X-ray background by the Earth agrees with our prediction within 10%. This suggests that Earth observations could be used for in-orbit calibration of future hard X-ray telescopes. We also demonstrate that the hard X-ray spectra generated by cosmic rays in the crusts of the Moon, Mars and Mercury should be significantly different from that emitted by the Earth's atmosphere.

A Maximum Likelihood (ML) image reconstruction technique using list-mode data has been applied to Compton scattering camera imaging. List-mode methods are appealing in Compton camera image reconstruction because the total number of data elements in the list (the number of detected photons) is significantly smaller than the number of possible combinations of position and energy measurements, leading to a much smaller problem than that faced by traditional iterative reconstruction techniques. For a realistic size device, the number of possible detector bins can be as large as 10 billion per pixel of the image, 3 or 4 orders of magnitude more than the number of counted photons. One difficulty in applying the list-mode technique is in determining the parameters which describe the response of the imaging system. In this work, a simple method for determining the required system matrix coefficients is employed, in which a back-projection is performed in list-mode, and response coefficients...

A fast algorithm is presented for back-projection of Compton camera projection data in a list mode fashion, in which the number of operations per photon per image slice scales at less than the dimension N of the reconstructed image. The method focuses on the mesh of grid lines which delineate the pixels in the image, rather than on the pixels themselves, and involves computation of the intersection of back-projected Compton cones with just the outermost edges in the image and those grid lines near these image boundary intersection points, for each plane (or slice) of the image. Depending on the orientation of the back projected cone and the image space grid lines, between 4 and N + 4 determinations (by quadratic solution) of conelmesh intersections are required per image slice per photon. Thus the total number of floating point operations per image slice scales as 4 to N+4 times the number of detected photons. Three dimensional back-projections can be obtained simply by stepping through the sequence of planes in the image space parallel to the Compton aperture. Back-projected images are presented, using data generated by Monte Carlo simulations of a practical detector configuration and various source distributions.

The Primary Electromagnetic Radiation (P-EM-R) is suggested to interact with inter-atomic electron during Compton Effect phenomena, producing Radiation Magnetic Force (F_mR) moving electron to higher binding Energy, where an increased in Total Circular Magnetic Field (B_CMFT) automatically formed electron Forced Binding Energy (E_bFE) and Secondary Radiation Energy (E_S); the E_bFE is added to the related Orbit Binding Energy (E_b-n) constituting Electron’s Kinetic Energy (E_k), while E_s is transformed into Secondary Electromagnetic Radiation (S-EM-R) through the Flip-Flop (F-F) mechanism, characterized by relativistic mass/velocity frequency and angle Ø_1 controlled, ended with increased S-EM-R wavelength releases at angle ϕ; a recoil force resulted from S-EM-R releases, ejecting electron at an angle θ, the force is added to E_bFE¸to form electron's energy (E_e); the E_s is also related to x-ray process of production from energetic electron impinging anode in an x-rays tube; the paper accommodates Compton formulas except the momentum photon; the paper is aimed at improving our understanding to the physical reality.

This research reviews the fundamentals of physics from 1785 to 1923, and shows that light can’t be “one electromagnetic wave (Maxwell’s Theory)” or “one quantized electromagnetic wave (Einstein’s Theory)”. Scientists have thought that the formula E=∫P(t)dt which defines energy of a wave can’t anticipate the result of photoelectric experiment. Moreover, Compton stated that the collision between light-ray and electron is like a collision between two particles. But this study explains that Light is composed of “numerous nonquantized electromagnetic waves” and this theory can satisfy all observations of scientists without any duality in nature or any contradiction between the classical and new physics. It also expresses that light just has a wave nature.

{{{{{ Keywords: Light, Wave-Particle Duality, Cathode Ray, Photoelectric Effect, Compton Effect, Charge, Electron, Coulomb’s Law, Conservation of Energy, Conservation of Charge, Electromagnetic Fields, Waves, Optics, Quantum, Coherent and Incoherent Light, Maxwell, Einstein, Compton, Physics, Shahab Shahrabadi }}}}}

See:
http://dx.doi.org/10.13140/RG.2.2.11869.67044

The huge potential drop between the footpoints of the closed field lines in the twisted magnetospheres of magnetars may accelerate electrons up to very high energies, c ) 10 6 . On the other hand, the comparison between the observed spectra of magnetars and spectra obtained by accurate theoretical models seems to favor of a picture in which the magnetosphere is filled by "slow" electrons (v [ 0.8c), rather than by ultra-relativistic particles.

The alleged existence of quantum with momentum in electromagnetic radiation is disputed, this is within the supposed balance of both Einstein's mass-energy equivalent with Planck's radiation energy, we realize this is untrue, except at one energy state represented by a single frequency, from the whole frequency spectrum; this formula is also analyzed and compared with the balance between kinetic energy and the Planck's radiation energy, the energy as well as the momentum for each is derived and showed to relate to an equivalent radiation energy and momentum equivalent to momentums given by mV and mc, which was coined for particle's mass; a momentum derived from the multiplication of Radiation Magnetic Force (F_mR) and change in time (Δt), designated as Magnetic Momentum (ρ_M), is related to the Electron Momentum (ρ_E) and both are in odd with the Compton Momentum (ρ_C), which showed great discrepancies with momentum of both the ρ_M€ and ρ_E, when plotted graphically; the paper established the condition for radiation momentum to remove electron from atom, which is only fulfilled by the Magnetic Momentum (ρ_M), rather than Compton Momentum (ρ_C); thus a conclusion is reached that, the use of the formula by Compton was not justified, it was misleading, and doesn't uphold scientific merit, while the Radiation Magnetic Force (F_mR) embedded in the electromagnetic radiation, is the force gives the proper and logical momentum that ejected photoelectrons and carried different mechanism in Compton Effect and others; this attempt aimed at restoring the common sense to the physical world.

Momentum distributions and mean kinetic energies of helium atoms, in pure fluid 3 He and 3 He-4 He mixtures, at T = 2 K and 3 He concentrations of x = 0.20 and x = 1.00, are presented. The experimental technique employed is deep inelastic neutron scattering measurements in the eV energy range, with wavevector transfer of typically 100Å −1 < q < 250Å −1 . Single-particle dynamical properties of 3 He-4 He mixtures are discussed in the context of previous results on mixtures at different concentrations and pure 3 He and 4 He.

This paper reviews the basic aspects, problems, and applications of Compton imaging including those related to nonmedical applications. The physics and technology at the base of this specific methodology are analyzed and the relative differences and merits with respect to other imaging techniques, using ionizing radiations, are reviewed. The basic Compton imaging approaches, i.e., point-by-point, line-by-line, and plane-by-plane, are analyzed. Specifically, physical design and technological aspects are reviewed and discussed. Furthermore, the most important clinical applications of the different methods are presented and discussed. Finally, possibilities and applications of the Compton imaging method to other nonmedical fields, as in the case of the important area of object defects recognition, are analyzed and reviewed.

We give a complete representation of virtual Compton scattering γ * p → γp at large initial photon virtuality Q 2 and small momentum transfer squared t in terms of the light-cone wavefunctions of the target proton. We verify the identities between the skewed parton distributions H(x, ζ, t) and E(x, ζ, t) which appear in deeply virtual Compton scattering and the corresponding integrands of the Dirac and Pauli form factors F 1 (t) and F 2 (t) and the gravitational form factors A q (t) and B q (t) for each quark and anti-quark constituent. We illustrate the general formalism for the case of deeply virtual Compton scattering on the quantum fluctuations of a fermion in quantum electrodynamics at one loop.

Virtual Compton Scattering off the proton: γ * p → γp is a new field of investigation of nucleon structure. Several dedicated experiments have been performed at low c.m. energy and various momentum transfers, yielding specific information on the proton. This talk reviews the concept of nucleon Generalized Polarizabilities and the present experimental status.

The Radon transform (RT) on straight lines deals as mathematical foundation for many tomographic modalities (e.g. Xray scanner, Positron Emission Tomography), using only primary radiation. In this paper, we consider a new RT defined on a pair of half-lines forming a letter V, arising from the modeling a two-dimensional emission imaging process by Compton scattered gamma rays. We establish its

We investigate the effects of dynamical Comptonization on the emergent radiation spectrum produced by near critical accretion onto a neutron star. The flow dynamics and the transfer of radiation are self-consistently solved in the case of a spherically symmetric, "cold", pure scattering flow, including general relativity. A sequence of models, each characterized by the value of the total observed luminosity, was obtained assuming that the spectrum at the star surface is black body in shape. It is found that when the luminosity approaches the Eddington limit dynamical effects become important shifting the spectrum to the blue and producing a power-law, high-energy tail. The relevance of these results in connection with the observed spectral properties of LMXBs, and of Cyg X-2 in particular, are discussed.

The thermal evolution of an inter-cluster gas of relativistic electrons heated by quasars with redshifts up to z = 3 and 4 is studied in the framework of a Friedmann-Robertson-Walker universe. The gas cools by Compton scattering with the microwave background radiation and by adiabatic cooling due to the universe expansion. Power and exponential laws of cosmological evolution of the comoving density of sources are considered. The obtained temperatures are sensitive to the form of these laws and to the heating epochs. Compared to the nonrelativistic models, the results obtained in the case of the power law present strong differences. These differences decrease when the exponential law is considered. Thermalization times are compared to the characteristic time of variation of the universe energy density and to the timescales of energy loss by bremsstrahlung radiation and by Compton scattering. It is shown that, in some cases, nonequilibrium effects may be important. The time delay effects in the propagation of electromagnetic waves in cosmic plasma are shown to be very important for the analysis of theoretical models.

ABSTRACT The concept of a two-plane planar Compton camera, consisting of scintillation detector elements, is presented. Several materials as C9H10, CaF2, YAlO3, NaI, and LaBr3 are considered for operation in the scatter and/or absorption plane. The performance of the Compton camera is optimized by means of Monte Carlo simulations to meet the requirements for Homeland Security applications. For a low-threshold detector system we propose to utilize C9H10 or CaF2 for the scatter plane and NaI or LaBr3 for the absorption plane. Particular effort must be focused to achieve low energy thresholds in particular for the detectors of the scatter plane if photons of incident energies below 200 keV are to be detected with reasonable efficiencies.

Compton reconstruction requires the computationally intensive, yet highly parallelizable, task of Cone of Response (CoR) back-projection. The acceleration of CoR back-projection is of significant importance as a faster algorithm allows the user to increase either the size or resolution of the imaging volume. Such acceleration also lends itself to the realization of real-time reconstruction. The image estimate is formed by calculating and histogramming voxel-cone intersections in the imaging volume. As the level of computation increases with the cube of the length or resolution of the volume, the bottleneck in processing the dataset is at the imaging-voxel level, as opposed to the event level. The reconstruction algorithm developed for the Pixelated Emission Detector for RadiOisotopes (PEDRO) system was optimized for threading at the voxel level and implemented in the C++ programming language. The benchmark C++ code was then extended with OpenCL to assess the acceleration that could be obtained by running the algorithm on a selection of commercially available Graphical Processing Units (GPUs). Increases of up to 102 times the benchmark speed were achieved

In the present investigation, low-energy x-rays (< 15 keV) scattered from powder, polymer, crystals and hydrogenous liquids (with preference for materials of low binding energy) at different scattering angles have been analysed. The scattered x-rays show unambiguous existence of a new modified line along with unmodified and Compton line. Since, the experimental observation of the inverse Doppler effect, i.e. increase of frequencies of reflecting waves from a receding boundary, has already been reported [Seddon and Bearpark (2003) Science, 302, 1537-1540]. Hence, it is quite logical to think that x-rays may also gain energy in contrast to Compton effect (where they lose energy) in material medium. Such type of new modified xray scattering (angle dependent) was observed. Expressions for photon of enhanced energy, ω3 , initial momentum of plasmon q and the total scattering cross section σN of this new phenomenon have been derived. The σN is found out to be proportional to √ ∈ and is about 100 times less than the Compton cross section using high-energy x-ray photon (100's of keV), usually used for Compton scattering studies. Both theoretically calculated and experimentally observed data match well with one another. The new modified line is to be clearly expected from materials of low atomic number with high dielectric constant using low-energy x-rays.

ABSTRACT Tomographic reconstruction based on origin ensembles (OE) is a new procedure for estimation of emission intensity distributions from projection measurements. The advantages of this method over standard iterative approaches are shorter computation time and easier implementation of complex system models in emission tomography (ET) inverse problems. The approach is not based on data likelihood, as are the standard iterative methods, but uses 3N-dimensional probability density functions (PDFs) of origin locations, where N is the number of detected events. In this work, the theory of OE was extended by introducing a parameter, β, which can be viewed as an image regularization parameter. With this extension, the system is called the canonical origin ensemble (COE), because of the resemblance to the canonical ensemble in statistical mechanics. The acquired dataset is considered a macroscopic state of the system, and locations of emissions (event origins) are viewed as unknown microscopic states described by the PDF. Monte Carlo simulations of the realistic geometry of 3D Positron Emission Tomography (PET) were generated using Simset. Photon attenuation was simulated, but randoms and Compton scatter were ignored. By measuring the image entropy, we found that the statistical system described by the COE undergoes a phase transition at β=1. Notably, the bias of the reconstructed values undergoes a similar transition at β=1. This indicates that, for realistic noise levels, COE reconstruction with β close to, but less than, 1 should be used for optimal image quality. A remarkable similarity between COE reconstructed image for β=1 and the image obtained using 10,000 iterations of list-mode 3D maximum likelihood-expectation maximization (ML-EM) was discovered. This work provides guidelines for improving the accuracy of the OE reconstruction method and demonstrates the use of attenuation correction for OE 3D list-mode PET.

Energy information is used to generate emission (99mTc, Eγ=140 keV) and transmission (57Co, Eγ=122 keV) images from a combined projection data set. These components are separated from each other and from Compton scatter by fitting the spectra at each pixel with a simple model. The method is tested using a cylindrical phantom containing inserts with differing attention. Emission and transmission position and energy (xyE) data were acquired in list mode and later summed to simulate simultaneous acquisition. Therefore, the true emission and transmission images are known. The quality and quantitative accuracy of the technique are evaluated by comparing images extracted from the combined data set to the “true” scatter-corrected transmission and emission images, respectively. Compared to using two energy windows, the spectrum fitting technique substantially reduced crosstalk. Although the resulting bias in the emission images was typically less than a few percent, the bias in the transmission images varied from -11% to +16% as the emission activity was increased with constant transmission source activity. Also, the variance added to the emission images obtained by the fitting procedure was found to be less than the variance caused by the stochastic nature of the emission and detection processes

Kylafis and Lamb (1979, hereafter KL) have recently completed a comprehensive study of X-ray emission from accreting nonmagnetic degenerate dwarfs. Their calculations assumed a common temperature for the electrons and the ions, and neglected electron conduction. However, when Compton cooling of the X-ray emission region becomes important at high masses, electron conduction begins to play a role (Kylafis 1978).

In this paper, we discuss the feasibility of measuring deeply virtual Compton scattering (DVCS) on nuclei in a collider setting, as for example, the planned high-luminosity Electron-Ion-Collider (EIC). We demonstrate that employing our recent model for nuclear generalized parton distributions (nGPDs), the one-photon unpolarized DVCS cross section as well as the azimuthal-and spin asymmetry are of the same size as in the proton case. This will allow for an experimental extraction of nuclear GPDs with high precision shedding new light not only on nuclear shadowing at small x bj but also on the interplay of shadowing and nuclear enhancement at x bj ∼ 0.1.

Single-photon emission computed tomography (SPECT) is based on the measurement of radiation emitted by a radiotracer injected into the patient. Because of photoelectric absorption and Compton scatter, the γ photons are attenuated inside the body before arriving at the detector. A quantitative reconstruction must consider the attenuation, which is usually non-uniform. Novikov and Natterer had derived an explicit formula for nonuniformly attenuated SPECT reconstruction of parallel-hole collimators. In this paper, we extend their researches to fan-beam collimators. Because any ray in fan-beam geometry can be treated as a ray in parallel-beam geometry, we derived a ray-driven analytical fan-beam reconstruction formula with non-uniform attenuation. Its accuracy is demonstrated computer simulation experiments * .

Measurements are reported of the mass attenuation coefficient of carbon taken by laboratories participating in the International Union of Crystallography 0108-7673/90/050402-07503.00 X-ray Attenuation Project. Data resulting from a similar study using silicon were published earlier [Creagh & Hubbell (1987). Acta Cryst. A43, 102-112].

Frequency upconversion of laser-generated photons by inverse Compton scattering for applications such as nuclear spectroscopy and gamma-gamma collider concepts on the future ILC would benefit from an increase of average source brightness. The primary obstacle to higher average brightness is the relatively small Thomson scattering cross section. It has been proposed that this limitation can be partially overcome by use of laser pulse recirculation. The traditional approach to laser recirculation entails resonant coupling of low-energy pulse train to a cavity through a partially reflective mirror [1]. Here we present an alternative, passive approach that is akin to "burst-mode" operation and does not require interferometeric alignment accuracy. Injection of a short and energetic laser pulse is achieved by placing a thin frequency converter, such as a nonlinear optical crystal, into the cavity in the path of the incident laser pulse. This method leads to the increase of x-ray/gamma-ray energy proportional to the increase in photon energy in frequency conversion. Furthermore, frequency tunability can be achieved by utilizing parametric amplifier in place of the frequency converter.

The mechanism of neutrino oscillations, which are the result of the Compton effect, that is, the scattering of CMB photons by neutrinos, is investigated. The scattering of highenergy photons by neutrinos leads to the formation of neutrons, which opens the way to the synthesis of baryonic matter in the Universe and restores the dynamic model of the stationary Universe. Confirmation of the stationary model of the Universe is the fact of the scattering of galaxies, which in fact is a consequence of the chaotic motion of galaxies in a limited volume. On an unlimited Universe scale, galaxies move randomly and therefore there are no Universe extensions.