Compton Scattering from the Deuteron at Low Energies
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7. Gamma and X-Ray Interactions in Matter
Photon interactions in matter Gamma- and X-Ray • Compton effect • Photoelectric effect Interactions in Matter • Pair production • Rayleigh (coherent) scattering Chapter 7 • Photonuclear interactions F.A. Attix, Introduction to Radiological Kinematics Physics and Radiation Dosimetry Interaction cross sections Energy-transfer cross sections Mass attenuation coefficients 1 2 Compton interaction A.H. Compton • Inelastic photon scattering by an electron • Arthur Holly Compton (September 10, 1892 – March 15, 1962) • Main assumption: the electron struck by the • Received Nobel prize in physics 1927 for incoming photon is unbound and stationary his discovery of the Compton effect – The largest contribution from binding is under • Was a key figure in the Manhattan Project, condition of high Z, low energy and creation of first nuclear reactor, which went critical in December 1942 – Under these conditions photoelectric effect is dominant Born and buried in • Consider two aspects: kinematics and cross Wooster, OH http://en.wikipedia.org/wiki/Arthur_Compton sections http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=22551 3 4 Compton interaction: Kinematics Compton interaction: Kinematics • An earlier theory of -ray scattering by Thomson, based on observations only at low energies, predicted that the scattered photon should always have the same energy as the incident one, regardless of h or • The failure of the Thomson theory to describe high-energy photon scattering necessitated the • Inelastic collision • After the collision the electron departs -
Compton Effect
Module 5 : MODERN PHYSICS Lecture 25 : Compton Effect Objectives In this course you will learn the following Scattering of radiation from an electron (Compton effect). Compton effect provides a direct confirmation of particle nature of radiation. Why photoelectric effect cannot be exhited by a free electron. Compton Effect Photoelectric effect provides evidence that energy is quantized. In order to establish the particle nature of radiation, it is necessary that photons must carry momentum. In 1922, Arthur Compton studied the scattering of x-rays of known frequency from graphite and looked at the recoil electrons and the scattered x-rays. According to wave theory, when an electromagnetic wave of frequency is incident on an atom, it would cause electrons to oscillate. The electrons would absorb energy from the wave and re-radiate electromagnetic wave of a frequency . The frequency of scattered radiation would depend on the amount of energy absorbed from the wave, i.e. on the intensity of incident radiation and the duration of the exposure of electrons to the radiation and not on the frequency of the incident radiation. Compton found that the wavelength of the scattered radiation does not depend on the intensity of incident radiation but it depends on the angle of scattering and the wavelength of the incident beam. The wavelength of the radiation scattered at an angle is given by .where is the rest mass of the electron. The constant is known as the Compton wavelength of the electron and it has a value 0.0024 nm. The spectrum of radiation at an angle consists of two peaks, one at and the other at . -
Compton Scattering from Low to High Energies
Compton Scattering from Low to High Energies Marc Vanderhaeghen College of William & Mary / JLab HUGS 2004 @ JLab, June 1-18 2004 Outline Lecture 1 : Real Compton scattering on the nucleon and sum rules Lecture 2 : Forward virtual Compton scattering & nucleon structure functions Lecture 3 : Deeply virtual Compton scattering & generalized parton distributions Lecture 4 : Two-photon exchange physics in elastic electron-nucleon scattering …if you want to read more details in preparing these lectures, I have primarily used some review papers : Lecture 1, 2 : Drechsel, Pasquini, Vdh : Physics Reports 378 (2003) 99 - 205 Lecture 3 : Guichon, Vdh : Prog. Part. Nucl. Phys. 41 (1998) 125 – 190 Goeke, Polyakov, Vdh : Prog. Part. Nucl. Phys. 47 (2001) 401 - 515 Lecture 4 : research papers , field in rapid development since 2002 1st lecture : Real Compton scattering on the nucleon & sum rules IntroductionIntroduction :: thethe realreal ComptonCompton scatteringscattering (RCS)(RCS) processprocess ε, ε’ : photon polarization vectors σ, σ’ : nucleon spin projections Kinematics in LAB system : shift in wavelength of scattered photon Compton (1923) ComptonCompton scatteringscattering onon pointpoint particlesparticles Compton scattering on spin 1/2 point particle (Dirac) e.g. e- Klein-Nishina (1929) : Thomson term ΘL = 0 Compton scattering on spin 1/2 particle with anomalous magnetic moment Stern (1933) Powell (1949) LowLow energyenergy expansionexpansion ofof RCSRCS processprocess Spin-independent RCS amplitude note : transverse photons : Low -
The Equation of Radiative Transfer How Does the Intensity of Radiation Change in the Presence of Emission and / Or Absorption?
The equation of radiative transfer How does the intensity of radiation change in the presence of emission and / or absorption? Definition of solid angle and steradian Sphere radius r - area of a patch dS on the surface is: dS = rdq ¥ rsinqdf ≡ r2dW q dS dW is the solid angle subtended by the area dS at the center of the † sphere. Unit of solid angle is the steradian. 4p steradians cover whole sphere. ASTR 3730: Fall 2003 Definition of the specific intensity Construct an area dA normal to a light ray, and consider all the rays that pass through dA whose directions lie within a small solid angle dW. Solid angle dW dA The amount of energy passing through dA and into dW in time dt in frequency range dn is: dE = In dAdtdndW Specific intensity of the radiation. † ASTR 3730: Fall 2003 Compare with definition of the flux: specific intensity is very similar except it depends upon direction and frequency as well as location. Units of specific intensity are: erg s-1 cm-2 Hz-1 steradian-1 Same as Fn Another, more intuitive name for the specific intensity is brightness. ASTR 3730: Fall 2003 Simple relation between the flux and the specific intensity: Consider a small area dA, with light rays passing through it at all angles to the normal to the surface n: n o In If q = 90 , then light rays in that direction contribute zero net flux through area dA. q For rays at angle q, foreshortening reduces the effective area by a factor of cos(q). -
The Basic Interactions Between Photons and Charged Particles With
Outline Chapter 6 The Basic Interactions between • Photon interactions Photons and Charged Particles – Photoelectric effect – Compton scattering with Matter – Pair productions Radiation Dosimetry I – Coherent scattering • Charged particle interactions – Stopping power and range Text: H.E Johns and J.R. Cunningham, The – Bremsstrahlung interaction th physics of radiology, 4 ed. – Bragg peak http://www.utoledo.edu/med/depts/radther Photon interactions Photoelectric effect • Collision between a photon and an • With energy deposition atom results in ejection of a bound – Photoelectric effect electron – Compton scattering • The photon disappears and is replaced by an electron ejected from the atom • No energy deposition in classical Thomson treatment with kinetic energy KE = hν − Eb – Pair production (above the threshold of 1.02 MeV) • Highest probability if the photon – Photo-nuclear interactions for higher energies energy is just above the binding energy (above 10 MeV) of the electron (absorption edge) • Additional energy may be deposited • Without energy deposition locally by Auger electrons and/or – Coherent scattering Photoelectric mass attenuation coefficients fluorescence photons of lead and soft tissue as a function of photon energy. K and L-absorption edges are shown for lead Thomson scattering Photoelectric effect (classical treatment) • Electron tends to be ejected • Elastic scattering of photon (EM wave) on free electron o at 90 for low energy • Electron is accelerated by EM wave and radiates a wave photons, and approaching • No -
Slides for Statistics, Precision, and Solid Angle
Slides for Statistics, Precision, and Solid Angle 22.01 – Intro to Radiation October 14, 2015 22.01 – Intro to Ionizing Radiation Precision etc., Slide 1 Solid Angles, Dose vs. Distance • Dose decreases with the inverse square of distance from the source: 1 퐷표푠푒 ∝ 푟2 • This is due to the decrease in solid angle subtended by the detector, shielding, person, etc. absorbing the radiation 22.01 – Intro to Ionizing Radiation Precision etc., Slide 2 Solid Angles, Dose vs. Distance • The solid angle is defined in steradians, and given the symbol Ω. • For a rectangle with width w and length l, at a distance r from a point source: 푤푙 Ω = 4푎푟푐푡푎푛 2푟 4푟2 + w2 + 푙2 • A full sphere has 4π steradians (Sr) 22.01 – Intro to Ionizing Radiation Precision etc., Slide 3 Solid Angles, Dose vs. Distance http://www.powerfromthesun.net/Book/chapter02/chapter02.html • Total luminance (activity) of a source is constant, but the flux through a surface decreases with distance Courtesy of William B. Stine. Used with permission. 22.01 – Intro to Ionizing Radiation Precision etc., Slide 4 Exponential Gamma Attenuation • Gamma sources are attenuated exponentially according to this formula: Initial intensity Mass attenuation coefficient 흁 Distance through − 흆 흆풙 푰 = 푰ퟎ풆 material Transmitted intensity Material density • Attenuation means removal from a narrowly collimated beam by any means 22.01 – Intro to Ionizing Radiation Precision etc., Slide 5 Exponential Gamma Attenuation Look up values in NIST x-ray attenuation tables: http://www.nist.gov/pml/data/xraycoef/ Initial -
General Method of Solid Angle Calculation Using Attitude Kinematics
1 1 General method of solid angle calculation using attitude kinematics 2 3 Russell P. Patera1 4 351 Meredith Way, Titusville, FL 32780, United States 5 6 Abstract 7 A general method to compute solid angle is developed that is based on Ishlinskii’s theorem, which specifies the 8 relationship between the attitude transformation of an axis that completely slews about a conical region and the 9 solid angle of the enclosed region. After an axis slews about a conical region and returns to its initial orientation, it 10 will have rotated by an angle precisely equal to the enclosed solid angle. The rotation is the magnitude of the 11 Euler rotation vector of the attitude transformation produced by the slewing motion. Therefore, the solid angle 12 can be computed by first computing the attitude transformation of an axis that slews about the solid angle region 13 and then computing the solid angle from the attitude transformation. This general method to compute the solid 14 angle involves approximating the solid angle region’s perimeter as seen from the source, with a discrete set of 15 points on the unit sphere, which join a set of great circle arcs that approximate the perimeter of the region. Pivot 16 Parameter methodology uses the defining set of points to compute the attitude transformation of the axis due to 17 its slewing motion about the enclosed solid angle region. The solid angle is the magnitude of the resulting Euler 18 rotation vector representing the transformation. The method was demonstrated by comparing results to 19 published results involving the solid angles of a circular disk radiation detector with respect to point, line and disk 20 shaped radiation sources. -
From the Geometry of Foucault Pendulum to the Topology of Planetary Waves
From the geometry of Foucault pendulum to the topology of planetary waves Pierre Delplace and Antoine Venaille Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France Abstract The physics of topological insulators makes it possible to understand and predict the existence of unidirectional waves trapped along an edge or an interface. In this review, we describe how these ideas can be adapted to geophysical and astrophysical waves. We deal in particular with the case of planetary equatorial waves, which highlights the key interplay between rotation and sphericity of the planet, to explain the emergence of waves which propagate their energy only towards the East. These minimal in- gredients are precisely those put forward in the geometric interpretation of the Foucault pendulum. We discuss this classic example of mechanics to introduce the concepts of holonomy and vector bundle which we then use to calculate the topological properties of equatorial shallow water waves. Résumé La physique des isolants topologiques permet de comprendre et prédire l’existence d’ondes unidirectionnelles piégées le long d’un bord ou d’une interface. Nous décrivons dans cette revue comment ces idées peuvent être adaptées aux ondes géophysiques et astrophysiques. Nous traitons en parti- culier le cas des ondes équatoriales planétaires, qui met en lumière les rôles clés combinés de la rotation et de la sphéricité de la planète pour expliquer l’émergence d’ondes qui ne propagent leur énergie que vers l’est. Ces ingré- dients minimaux sont précisément ceux mis en avant dans l’interprétation géométrique du pendule de Foucault. -
Interactions of Photons with Matter
22.55 “Principles of Radiation Interactions” Interactions of Photons with Matter • Photons are electromagnetic radiation with zero mass, zero charge, and a velocity that is always c, the speed of light. • Because they are electrically neutral, they do not steadily lose energy via coulombic interactions with atomic electrons, as do charged particles. • Photons travel some considerable distance before undergoing a more “catastrophic” interaction leading to partial or total transfer of the photon energy to electron energy. • These electrons will ultimately deposit their energy in the medium. • Photons are far more penetrating than charged particles of similar energy. Energy Loss Mechanisms • photoelectric effect • Compton scattering • pair production Interaction probability • linear attenuation coefficient, µ, The probability of an interaction per unit distance traveled Dimensions of inverse length (eg. cm-1). −µ x N = N0 e • The coefficient µ depends on photon energy and on the material being traversed. µ • mass attenuation coefficient, ρ The probability of an interaction per g cm-2 of material traversed. Units of cm2 g-1 ⎛ µ ⎞ −⎜ ⎟()ρ x ⎝ ρ ⎠ N = N0 e Radiation Interactions: photons Page 1 of 13 22.55 “Principles of Radiation Interactions” Mechanisms of Energy Loss: Photoelectric Effect • In the photoelectric absorption process, a photon undergoes an interaction with an absorber atom in which the photon completely disappears. • In its place, an energetic photoelectron is ejected from one of the bound shells of the atom. • For gamma rays of sufficient energy, the most probable origin of the photoelectron is the most tightly bound or K shell of the atom. • The photoelectron appears with an energy given by Ee- = hv – Eb (Eb represents the binding energy of the photoelectron in its original shell) Thus for gamma-ray energies of more than a few hundred keV, the photoelectron carries off the majority of the original photon energy. -
Radiometry and Photometry
Radiometry and Photometry Wei-Chih Wang Department of Power Mechanical Engineering National TsingHua University W. Wang Materials Covered • Radiometry - Radiant Flux - Radiant Intensity - Irradiance - Radiance • Photometry - luminous Flux - luminous Intensity - Illuminance - luminance Conversion from radiometric and photometric W. Wang Radiometry Radiometry is the detection and measurement of light waves in the optical portion of the electromagnetic spectrum which is further divided into ultraviolet, visible, and infrared light. Example of a typical radiometer 3 W. Wang Photometry All light measurement is considered radiometry with photometry being a special subset of radiometry weighted for a typical human eye response. Example of a typical photometer 4 W. Wang Human Eyes Figure shows a schematic illustration of the human eye (Encyclopedia Britannica, 1994). The inside of the eyeball is clad by the retina, which is the light-sensitive part of the eye. The illustration also shows the fovea, a cone-rich central region of the retina which affords the high acuteness of central vision. Figure also shows the cell structure of the retina including the light-sensitive rod cells and cone cells. Also shown are the ganglion cells and nerve fibers that transmit the visual information to the brain. Rod cells are more abundant and more light sensitive than cone cells. Rods are 5 sensitive over the entire visible spectrum. W. Wang There are three types of cone cells, namely cone cells sensitive in the red, green, and blue spectral range. The approximate spectral sensitivity functions of the rods and three types or cones are shown in the figure above 6 W. Wang Eye sensitivity function The conversion between radiometric and photometric units is provided by the luminous efficiency function or eye sensitivity function, V(λ). -
Invariance Properties of the Dirac Monopole
fcs.- 0; /A }Ю-ц-^. KFKI-75-82 A. FRENKEL P. HRASKÓ INVARIANCE PROPERTIES OF THE DIRAC MONOPOLE Hungarian academy of Sciences CENTRAL RESEARCH INSTITUTE FOR PHYSICS BUDAPEST L KFKI-75-S2 INVARIÄHCE PROPERTIES OF THE DIRAC MONOPOLE A. Frenkel and P. Hraskó High Energy Physics Department Central Research Institute for Physics, Budapest, Hungary ISBN 963 371 094 4 ABSTRACT The quantum mechanical motion of a spinless electron in the external field of a magnetic monopolé of magnetic charge v is investigated. Xt is shown that Dirac's quantum condition 2 ue(hc)'1 • n for the string being unobservable ensures rotation invarlance and correct space reflection proper ties for any integer value of n. /he rotation and space reflection operators are found and their group theoretical properties are discussed, A method for constructing conserved quantities In the case when the potential ie not explicitly invariant under the symmetry operation is also presented and applied to the discussion of the angular momentum of the electron-monopole system. АННОТАЦИЯ Рассматривается кваитоаомеханическое движение бесспинового элект рона во внешнем поле монополя с Магнитки« зарядом и. Доказывается» что кван товое условие Дирака 2ув(пс)-1 •> п обеспечивает не только немаолтваемость стру ны »но и инвариантность при вращении и правильные свойства при пространственных отражениях для любого целого п. Даются операторы времени* я отражения, и об суждаются их групповые свойства. Указан также метод построения интегралов движения в случае, когда потенциал не является язно инвариантным по отношению операции симметрии, и этот метод применяется при изучении углового момента сис темы электрон-монопопь. KIVONAT A spin nélküli elektron kvantummechanikai viselkedését vizsgáljuk u mágneses töltésű monopolus kttlsö terében. -
International System of Units (Si)
[TECHNICAL DATA] INTERNATIONAL SYSTEM OF UNITS( SI) Excerpts from JIS Z 8203( 1985) 1. The International System of Units( SI) and its usage 1-3. Integer exponents of SI units 1-1. Scope of application This standard specifies the International System of Units( SI) and how to use units under the SI system, as well as (1) Prefixes The multiples, prefix names, and prefix symbols that compose the integer exponents of 10 for SI units are shown in Table 4. the units which are or may be used in conjunction with SI system units. Table 4. Prefixes 1 2. Terms and definitions The terminology used in this standard and the definitions thereof are as follows. - Multiple of Prefix Multiple of Prefix Multiple of Prefix (1) International System of Units( SI) A consistent system of units adopted and recommended by the International Committee on Weights and Measures. It contains base units and supplementary units, units unit Name Symbol unit Name Symbol unit Name Symbol derived from them, and their integer exponents to the 10th power. SI is the abbreviation of System International d'Unites( International System of Units). 1018 Exa E 102 Hecto h 10−9 Nano n (2) SI units A general term used to describe base units, supplementary units, and derived units under the International System of Units( SI). 1015 Peta P 10 Deca da 10−12 Pico p (3) Base units The units shown in Table 1 are considered the base units. 1012 Tera T 10−1 Deci d 10−15 Femto f (4) Supplementary units The units shown in Table 2 below are considered the supplementary units.