DOCSLIB.ORG

Relativistic Kinematics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Relativistic Kinematics General Appendix A-1 4/29/2015 Appendix A: Relativistic Kinematics In this appendix we review some of the calculations required to solve various high-energy collision problems using Special Relativity.1 Contents Some conventions regarding notation ........................................................................................................... A-2 CONSERVED QUANTITIES AND LORENTZ INVARIANTS; REST-MASS A-2 Lorentz transformation ................................................................................................................................. A-3 4-momentum and rest-mass .......................................................................................................................... A-3 Kinetic energy .............................................................................................................................................. A-4 SOME EFFECTS OF REFERENCE FRAME CHANGES A-5 Doppler shift ................................................................................................................................................. A-5 Relativistic beaming ..................................................................................................................................... A-5 Motion of the center of momentum frame .................................................................................................... A-6 COLLISIONS INVOLVING PHOTONS A-7 Photoelectric absorption and emission ......................................................................................................... A-7 Pair production ............................................................................................................................................. A-9 Compton scattering ..................................................................................................................................... A-10 INELASTIC COLLISIONS OF IDENTICAL PARTICLES A-11 1 Although several prominent theoretical physicists had developed the equations used by Einstein to describe the coordinate transformations of special relativity in the decades just preceding his seminal paper of 1905, it was his brilliant contribution to recognize that the theory must provide a fundamental, kinematical description of the behaviors of space and time themselves, independent of electromagnetism or any other dynamical (force- related) processes between material objects. General Appendix A-2 4/29/2015 Some conventions regarding notation Rest-mass, momentum, and energy will all be expressed in energy units, so that mc2 → m and pc → p . In other words, we use the speed of light as our unit of velocity: c ≡1. Thus velocities will expressed as vc→=v β (the symbols v and β will be used interchange- ably). Spatial positions will be expressed in units of time by dividing by c, so xc→ x . If we need to express a quantity such as velocity, position, momentum, or mass in its actual units, then we use a symbol without italics: x, v, p, m, etc., as shown in the above expressions. As illustrated by the examples above, spatial vectors will be denoted using an overscored arrow: x . The 3 components of a spatial vector are labeled as: a=++↔ axxˆˆ ay y az zˆ (, a xyz a , a ) = (, a123 a , a ) Any 4-vectors we use, such as the coordinates of a space-time event or a particle’s 4- momentum, will be denoted using an italic symbol (usually uppercase) with an underscore: X or P , for example, or as an ordered pair of a time-coordinate followed by a spatial vector, or as an ordered list of the time component followed by the 3 spatial components: x=(,) tx = (,) xx0 = (,, xxxx 0123 ,) Inertial observers’ reference frames (space-time coordinate systems) will be denoted as and ′ ; 4-vector coordinates in these systems are (,tx ) and (,tx′′ ), respectively. The two systems’ spatial axes are parallel and their origins coincide, so that (tx= 0, = 0) and (tx′′= 0, = 0) correspond to the same event. The relative velocity of ′ with respect to = − ′ ′ will normally be taken to be vv′ xˆ ; obviously, moves with velocity v xˆ in the coordinate system. CONSERVED QUANTITIES AND LORENTZ INVARIANTS; REST-MASS A dynamical quantity is conserved in a particular observer’s reference frame if it doesn’t vary with time. As in Newtonian mechanics, an isolated system’s total energy E and linear momentum p are conserved quantities; thus so is the system’s 4-momentum P= (,) Ep. These quantities are also additive, so that the total energy and total momentum of a collection of particles is simply the sum of those of the individual particles: P=Σ Pi =ΣΣ( Epii, ) (A-1) A quantity is a Lorentz invariant (or, simply, an invariant)2 if it has the same value in all inertial observers’ reference frames (i.e. it is independent of the state of motion of an inertial 2 The Lorentz transformation and Lorentz invariance were named by Henri Poincaré for the Dutch theoretical physicist Hendrik Antoon Lorentz, a towering figure in the development of the modern theories of classical electromagnetism and special relativity. Lorentz, along with George FitzGerald, Woldemar Voigt, and Joseph Larmor, developed the Lorentz contraction and time dilation equations during the period 1887-1900. Lorentz General Appendix A-3 4/29/2015 observer). For example, the archetypal invariant is the interval between two space-time events: 222 ()∆s ≡ ()( ∆ t − ∆ xx ⋅∆ )()( = ∆ t′ − ∆ x ′′ ⋅∆ x ) (A-2) In (A-2) the 4-vectors (,∆∆tx ) and (,∆∆tx′′ ) denote the separation of the two events as observed in any two reference frames and ′ . This property generalizes to the invariance of the scalar product of any two 4-vectors: (aa0 , )(⋅ bb 0 , ) ≡ ab 00 −⋅ ab =( aa0′′ , )( ⋅ bb0 ′′ , ) (A-3) The norm of a 4-vector A is AA⋅ and is a Lorentz invariant. If AA⋅>0, then A is called time-like; AA⋅<0 means A is space-like; a light-like 4-vector A has AA⋅=0. The interval 2 ()∆s is the norm of the space-time coordinate 4-vector (,∆∆tx ). A particle’s proper time (the interval ∆s between two events on its world-line) will be denoted as τ . Lorentz transformation Assume that some arbitrary 4-vector A has components (aa ,), with a=++ axˆˆ ay azˆ , in 0 xyz ′ = ˆ the reference frame . In the frame ()v ′ vx the components of A are related to those Λ ′′=Λ⋅ in by the Lorentz transformation (v′ ): (,)aa00 ( v′ )(,), aa defined so that: aaa00′ =γ − γβ x Lorentz aaa′ =γ − γβ (A-4) Transformation xx0 a′′y= aa yz; = a z 1 The boost γ ≡≥1. This transformation ensures that (A-3) is valid; it is analogous to 1− β 2 a coordinate-system rotation in 3-dimensional Euclidean space which preserves the value of the scalar product ab⋅ of two vectors in that space. 4-momentum and rest-mass A particle or system’s 4-momentum P= (,) Ep is a 4-vector, and its norm PP⋅ is a Lorentz invariant. This norm defines the system’s rest-mass (or, more simply, mass), m: m2≡⋅= PP E22 − p (A-5) Our systems will always have real m ≥ 0 ( P is never space-like). If m > 0, then a reference frame can be found in which the system’s spatial momentum vanishes (p = 0) . This was awarded the Nobel Prize in 1902 jointly with Pieter Zeeman for the original theory and later experimental observation of the Zeeman Effect. General Appendix A-4 4/29/2015 reference frame is called the system’s center of momentum frame or rest frame; in this frame mE= , or, using physical units, we get Einstein’s famous E= mc2 . Because an isolated system’s E and p are conserved, so is the system’s rest-mass m , which is also a Lorentz invariant. A massless particle, such as a photon, has m = 0, and Ep= . Its 4-momentum is light-like, and its speed is c in all reference frames. Consider a particle (or system) with m > 0. In its rest frame, the particle’s 4-momentum is Pm= ( ,0) . In another frame in which the particle has velocity v ()= β , its 4-momentum components undergo the Lorentz transformation (A-4) and are given by: PvEpmmvm()(,)(= =γ , γ ) = (,) γγ vmU = (A-6) The 4-vector Uv= (,γγ ) is called the particle’s 4-velocity. Since a time interval dτ in its rest frame (an interval of the particle’s proper time) is similarly boosted to the longer time interval dt= γ dτ in the frame within which it is moving (time dilation), we see that the 4- velocity is simply the rate of change of the particle’s coordinate 4-vector (,tx ) with respect 2 to its proper time: U= (, dt dττ dx d ). Since PP⋅= m, it must be the case that UU⋅=1 (which you should confirm). From (A-6) we also get the useful result (remember, v = β ): pE= β (A-7) which is also correct for massless particles such as photons (for which v =1). Since β ≤1, then pE≤ . Kinetic energy The kinetic energy T of a free particle (no externally-imposed potentials) is simply the difference between the particle’s energy E and its mass m: T= Em − . Using equation (A-6) we see that Tm=(γ − 1) (A-8) A relation between p and T analogous to the Newtonian Tp= 2 2 m may be derived using (A-5), realizing that E22−=− m( E m )( E += m ) TT ( + 2 m ) : p2 T = (A-9) 2mT+ In the nonrelativistic limit Tm , and the expression (A-9) approaches the Newtonian one. General Appendix A-5 4/29/2015 SOME EFFECTS OF REFERENCE FRAME CHANGES Doppler shift A free particle with well-defined 4-momentum P may be represented quantum-mechanically as a plane-wave with frequency ω = E and wave vector kp= . Thus K≡=(,)ω kP is a 4-vector. The phase φ of the plane wave at any space-time location X= (, tx ) is then φω=−( ,k ) ⋅ (, tx ) =−⋅ K X (A-10) and is a Lorentz invariant. Changing reference frames will result in a Lorentz transformation of the components of the wave’s 4-vector K : this is the origin of the Doppler shift 3 of the wave frequency and wavelength, as well as a change in its direction of propagation (see the next section). Assume the new reference frame moves with velocity β ; the component of k parallel to β is then kk|| =⋅=ββ kcos θ, where θ is the angle between k and β . From the Lorentz transformation (A-4) the wave frequency ω′ (time-like component of K′) in the moving frame is: Doppler shift formula ω′ = γω( − βkk|| )( = γω −⋅ β ) (A-11) In the case of a photon ω = k , and the Doppler shift formula is ωω′ = γ(1 − β cos θ ) .
Load more

Recommended publications
  • 10. Collisions • Use Conservation of Momentum and Energy and The
    10. Collisions • Use conservation of momentum and energy and the center of mass to understand collisions between two objects. • During a collision, two or more objects exert a force on one another for a short time: -F(t) F(t) Before During After • It is not necessary for the objects to touch during a collision, e.g. an asteroid flied by the earth is considered a collision because its path is changed due to the gravitational attraction of the earth. One can still use conservation of momentum and energy to analyze the collision. Impulse: During a collision, the objects exert a force on one another. This force may be complicated and change with time. However, from Newton's 3rd Law, the two objects must exert an equal and opposite force on one another. F(t) t ti tf Dt From Newton'sr 2nd Law: dp r = F (t) dt r r dp = F (t)dt r r r r tf p f - pi = Dp = ò F (t)dt ti The change in the momentum is defined as the impulse of the collision. • Impulse is a vector quantity. Impulse-Linear Momentum Theorem: In a collision, the impulse on an object is equal to the change in momentum: r r J = Dp Conservation of Linear Momentum: In a system of two or more particles that are colliding, the forces that these objects exert on one another are internal forces. These internal forces cannot change the momentum of the system. Only an external force can change the momentum. The linear momentum of a closed isolated system is conserved during a collision of objects within the system.
    [Show full text]
  • Mesons Modeled Using Only Electrons and Positrons with Relativistic Onium Theory Ray Fleming [email protected]
    All mesons modeled using only electrons and positrons with relativistic onium theory Ray Fleming [email protected] All mesons were investigated to determine if they can be modeled with the onium model discovered by Milne, Feynman, and Sternglass with only electrons and positrons. They discovered the relativistic positronium solution has the mass of a neutral pion and the relativistic onium mass increases in steps of me/α and me/2α per particle which is consistent with known mass quantization. Any pair of particles or resonances can orbit relativistically and particles and resonances can collocate to form increasingly complex resonances. Pions are positronium, kaons are pionium, D mesons are kaonium, and B mesons are Donium in the onium model. Baryons, which are addressed in another paper, have a non-relativistic nucleon combined with mesons. The results of this meson analysis shows that the compo- sition, charge, and mass of all mesons can be accurately modeled. Of the 220 mesons mod- eled, 170 mass estimates are within 5 MeV/c2 and masses of 111 of 121 D, B, charmonium, and bottomonium mesons are estimated to within 0.2% relative error. Since all mesons can be modeled using only electrons and positrons, quarks and quark theory are unnecessary. 1. Introduction 2. Method This paper is a report on an investigation to find Sternglass and Browne realized that a neutral pion whether mesons can be modeled as combinations of (π0), as a relativistic electron-positron pair, can orbit a only electrons and positrons using onium theory. A non-relativistic particle or resonance in what Browne companion paper on baryons is also available.
    [Show full text]
  • B2.IV Nuclear and Particle Physics
    B2.IV Nuclear and Particle Physics A.J. Barr February 13, 2014 ii Contents 1 Introduction 1 2 Nuclear 3 2.1 Structure of matter and energy scales . 3 2.2 Binding Energy . 4 2.2.1 Semi-empirical mass formula . 4 2.3 Decays and reactions . 8 2.3.1 Alpha Decays . 10 2.3.2 Beta decays . 13 2.4 Nuclear Scattering . 18 2.4.1 Cross sections . 18 2.4.2 Resonances and the Breit-Wigner formula . 19 2.4.3 Nuclear scattering and form factors . 22 2.5 Key points . 24 Appendices 25 2.A Natural units . 25 2.B Tools . 26 2.B.1 Decays and the Fermi Golden Rule . 26 2.B.2 Density of states . 26 2.B.3 Fermi G.R. example . 27 2.B.4 Lifetimes and decays . 27 2.B.5 The flux factor . 28 2.B.6 Luminosity . 28 2.C Shell Model § ............................. 29 2.D Gamma decays § ............................ 29 3 Hadrons 33 3.1 Introduction . 33 3.1.1 Pions . 33 3.1.2 Baryon number conservation . 34 3.1.3 Delta baryons . 35 3.2 Linear Accelerators . 36 iii CONTENTS CONTENTS 3.3 Symmetries . 36 3.3.1 Baryons . 37 3.3.2 Mesons . 37 3.3.3 Quark flow diagrams . 38 3.3.4 Strangeness . 39 3.3.5 Pseudoscalar octet . 40 3.3.6 Baryon octet . 40 3.4 Colour . 41 3.5 Heavier quarks . 43 3.6 Charmonium . 45 3.7 Hadron decays . 47 Appendices 48 3.A Isospin § ................................ 49 3.B Discovery of the Omega § ......................
    [Show full text]
  • Ions, Protons, and Photons As Signatures of Monopoles
    universe Article Ions, Protons, and Photons as Signatures of Monopoles Vicente Vento Departamento de Física Teórica-IFIC, Universidad de Valencia-CSIC, 46100 Burjassot (Valencia), Spain; [email protected] Received: 8 October 2018; Accepted: 1 November 2018; Published: 7 November 2018 Abstract: Magnetic monopoles have been a subject of interest since Dirac established the relationship between the existence of monopoles and charge quantization. The Dirac quantization condition bestows the monopole with a huge magnetic charge. The aim of this study was to determine whether this huge magnetic charge allows monopoles to be detected by the scattering of charged ions and protons on matter where they might be bound. We also analyze if this charge favors monopolium (monopole–antimonopole) annihilation into many photons over two photon decays. 1. Introduction The theoretical justification for the existence of classical magnetic poles, hereafter called monopoles, is that they add symmetry to Maxwell’s equations and explain charge quantization. Dirac showed that the mere existence of a monopole in the universe could offer an explanation of the discrete nature of the electric charge. His analysis leads to the Dirac Quantization Condition (DQC) [1,2] eg = N/2, N = 1, 2, ..., (1) where e is the electron charge, g the monopole magnetic charge, and we use natural units h¯ = c = 1 = 4p#0. Monopoles have been a subject of experimental interest since Dirac first proposed them in 1931. In Dirac’s formulation, monopoles are assumed to exist as point-like particles and quantum mechanical consistency conditions lead to establish the value of their magnetic charge. Because of of the large magnetic charge as a consequence of Equation (1), monopoles can bind in matter [3].
    [Show full text]
  • The Physics of a Car Collision by Andrew Zimmerman Jones, Thoughtco.Com on 09.10.19 Word Count 947 Level MAX
    The physics of a car collision By Andrew Zimmerman Jones, ThoughtCo.com on 09.10.19 Word Count 947 Level MAX Image 1. A crash test dummy sits inside a Toyota Corolla during the 2017 North American International Auto Show in Detroit, Michigan. Crash test dummies are used to predict the injuries that a human might sustain in a car crash. Photo by: Jim Watson/AFP/Getty Images During a car crash, energy is transferred from the vehicle to whatever it hits, be it another vehicle or a stationary object. This transfer of energy, depending on variables that alter states of motion, can cause injuries and damage cars and property. The object that was struck will either absorb the energy thrust upon it or possibly transfer that energy back to the vehicle that struck it. Focusing on the distinction between force and energy can help explain the physics involved. Force: Colliding With A Wall Car crashes are clear examples of how Newton's Laws of Motion work. His first law of motion, also referred to as the law of inertia, asserts that an object in motion will stay in motion unless an external force acts upon it. Conversely, if an object is at rest, it will remain at rest until an unbalanced force acts upon it. Consider a situation in which car A collides with a static, unbreakable wall. The situation begins with car A traveling at a velocity (v) and, upon colliding with the wall, ending with a velocity of 0. The force of this situation is defined by Newton's second law of motion, which uses the equation of This article is available at 5 reading levels at https://newsela.com.
    [Show full text]
  • A Study of the Effects of Pair Production and Axionlike Particle
    Washington University in St. Louis Washington University Open Scholarship Arts & Sciences Electronic Theses and Dissertations Arts & Sciences Summer 8-15-2016 A Study of the Effects of Pair Production and Axionlike Particle Oscillations on Very High Energy Gamma Rays from the Crab Pulsar Avery Michael Archer Washington University in St. Louis Follow this and additional works at: https://openscholarship.wustl.edu/art_sci_etds Recommended Citation Archer, Avery Michael, "A Study of the Effects of Pair Production and Axionlike Particle Oscillations on Very High Energy Gamma Rays from the Crab Pulsar" (2016). Arts & Sciences Electronic Theses and Dissertations. 828. https://openscholarship.wustl.edu/art_sci_etds/828 This Dissertation is brought to you for free and open access by the Arts & Sciences at Washington University Open Scholarship. It has been accepted for inclusion in Arts & Sciences Electronic Theses and Dissertations by an authorized administrator of Washington University Open Scholarship. For more information, please contact [email protected]. WASHINGTON UNIVERSITY IN ST. LOUIS Department of Physics Dissertation Examination Committee: James Buckley, Chair Francesc Ferrer Viktor Gruev Henric Krawzcynski Michael Ogilvie A Study of the Effects of Pair Production and Axionlike Particle Oscillations on Very High Energy Gamma Rays from the Crab Pulsar by Avery Michael Archer A dissertation presented to the Graduate School of Arts and Sciences of Washington University in partial fulfillment of the requirements for the degree of Doctor of Philosophy August 2016 Saint Louis, Missouri copyright by Avery Michael Archer 2016 Contents List of Tablesv List of Figures vi Acknowledgments xvi Abstract xix 1 Introduction1 1.1 Gamma-Ray Astronomy............................. 1 1.2 Pulsars......................................
    [Show full text]
  • 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
    [Show full text]
  • Arxiv:1809.04815V2 [Physics.Hist-Ph] 28 Jan 2020
    Who discovered positron annihilation? Tim Dunker∗ (Dated: 29 January 2020) In the early 1930s, the positron, pair production, and, at last, positron annihila- tion were discovered. Over the years, several scientists have been credited with the discovery of the annihilation radiation. Commonly, Thibaud and Joliot have received credit for the discovery of positron annihilation. A conversation between Werner Heisenberg and Theodor Heiting prompted me to examine relevant publi- cations, when these were submitted and published, and how experimental results were interpreted in the relevant articles. I argue that it was Theodor Heiting— usually not mentioned at all in relevant publications—who discovered positron annihilation, and that he should receive proper credit. arXiv:1809.04815v2 [physics.hist-ph] 28 Jan 2020 ∗ tdu {at} justervesenet {dot} no 2 I. INTRODUCTION There is no doubt that the positron was discovered by Carl D. Anderson (e.g. Anderson, 1932; Hanson, 1961; Leone and Robotti, 2012) after its theoretical prediction by Paul A. M. Dirac (Dirac, 1928, 1931). Further, it is undoubted that Patrick M. S. Blackett and Giovanni P. S. Occhialini discovered pair production by taking photographs of electrons and positrons created from cosmic rays in a Wilson cloud chamber (Blackett and Occhialini, 1933). The answer to the question who experimentally discovered the reverse process—positron annihilation—has been less clear. Usually, Frédéric Joliot and Jean Thibaud receive credit for its discovery (e.g., Roqué, 1997, p. 110). Several of their contemporaries were enganged in similar research. In a letter correspondence with Werner Heisenberg Heiting and Heisenberg (1952), Theodor Heiting (see Appendix A for a rudimentary biography) claimed that it was he who discovered positron annihilation.
    [Show full text]
  • Is It Time for a New Paradigm in Physics?
    Vigier IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1251 (2019) 012024 doi:10.1088/1742-6596/1251/1/012024 Is it time for a new paradigm in physics? Shukri Klinaku University of Prishtina Sheshi Nëna Terezë, Prishtina, Kosovo [email protected] Abstract. The fact that the two main pillars of modern Physics are incompatible with each other; the fact that some unsolved problems have accumulated in Physics; and, in particular, the fact that Physics has been invaded by weird concepts (as if we were in the Middle Ages); these facts are quite sufficient to confirm the need for a new paradigm in Physics. But the conclusion that a new paradigm is needed is not sufficient, without an answer to the question: is there sufficient sources and resources to construct a new paradigm in Physics? I consider that the answer to this question is also yes. Today, Physics has sufficient material in experimental facts, theoretical achievements and human and technological potential. So, there is the need and opportunity for a new paradigm in Physics. The core of the new paradigm of Physics would be the nature of matter. According to this new paradigm, Physics should give up on wave-particle dualism, should redefine waves, and should end the mystery about light and its privilege in Physics. The consequences of this would make Physics more understandable, and - more importantly - would make it capable of solving current problems and opening up new perspectives in exploring nature and the universe. 1. Introduction Quantum Physics and the theory of relativity are the ‘two main pillars’ of modern Physics.
    [Show full text]
  • Pkoduction of RELATIVISTIC ANTIHYDROGEN ATOMS by PAIR PRODUCTION with POSITRON CAPTURE*
    SLAC-PUB-5850 May 1993 (T/E) PkODUCTION OF RELATIVISTIC ANTIHYDROGEN ATOMS BY PAIR PRODUCTION WITH POSITRON CAPTURE* Charles T. Munger and Stanley J. Brodsky Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 .~ and _- Ivan Schmidt _ _.._ Universidad Federico Santa Maria _. - .Casilla. 11 O-V, Valparaiso, Chile . ABSTRACT A beam of relativistic antihydrogen atoms-the bound state (Fe+)-can be created by circulating the beam of an antiproton storage ring through an internal gas target . An antiproton that passes through the Coulomb field of a nucleus of charge 2 will create e+e- pairs, and antihydrogen will form when a positron is created in a bound rather than a continuum state about the antiproton. The - cross section for this process is calculated to be N 4Z2 pb for antiproton momenta above 6 GeV/c. The gas target of Fermilab Accumulator experiment E760 has already produced an unobserved N 34 antihydrogen atoms, and a sample of _ N 760 is expected in 1995 from the successor experiment E835. No other source of antihydrogen exists. A simple method for detecting relativistic antihydrogen , - is -proposed and a method outlined of measuring the antihydrogen Lamb shift .g- ‘,. to N 1%. Submitted to Physical Review D *Work supported in part by Department of Energy contract DE-AC03-76SF00515 fSLAC’1 and in Dart bv Fondo National de InvestiPaci6n Cientifica v TecnoMcica. Chile. I. INTRODUCTION Antihydrogen, the simplest atomic bound state of antimatter, rf =, (e+$, has never. been observed. A 1on g- sought goal of atomic physics is to produce sufficient numbers of antihydrogen atoms to confirm the CPT invariance of bound states in quantum electrodynamics; for example, by verifying the equivalence of the+&/2 - 2.Py2 Lamb shifts of H and I?.
    [Show full text]
  • STRANGE MESON SPECTROSCOPY in Km and K$ at 11 Gev/C and CHERENKOV RING IMAGING at SLD *
    SLAC-409 UC-414 (E/I) STRANGE MESON SPECTROSCOPY IN Km AND K$ AT 11 GeV/c AND CHERENKOV RING IMAGING AT SLD * Youngjoon Kwon Stanford Linear Accelerator Center Stanford University Stanford, CA 94309 January 1993 Prepared for the Department of Energy uncer contract number DE-AC03-76SF005 15 Printed in the United States of America. Available from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, Virginia 22161. * Ph.D. thesis ii Abstract This thesis consists of two independent parts; development of Cherenkov Ring Imaging Detector (GRID) system and analysis of high-statistics data of strange meson reactions from the LASS spectrometer. Part I: The CIUD system is devoted to charged particle identification in the SLAC Large Detector (SLD) to study e+e- collisions at ,/Z = mzo. By measuring the angles of emission of the Cherenkov photons inside liquid and gaseous radiators, r/K/p separation will be achieved up to N 30 GeV/c. The signals from CRID are read in three coordinates, one of which is measured by charge-division technique. To obtain a N 1% spatial resolution in the charge- division, low-noise CRID preamplifier prototypes were developed and tested re- sulting in < 1000 electrons noise for an average photoelectron signal with 2 x lo5 gain. To help ensure the long-term stability of CRID operation at high efficiency, a comprehensive monitoring and control system was developed. This system contin- uously monitors and/or controls various operating quantities such as temperatures, pressures, and flows, mixing and purity of the various fluids.
    [Show full text]
  • Electron-Positron Pairs in Physics and Astrophysics
    Electron-positron pairs in physics and astrophysics: from heavy nuclei to black holes Remo Ruffini1,2,3, Gregory Vereshchagin1 and She-Sheng Xue1 1 ICRANet and ICRA, p.le della Repubblica 10, 65100 Pescara, Italy, 2 Dip. di Fisica, Universit`adi Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy, 3 ICRANet, Universit´ede Nice Sophia Antipolis, Grand Chˆateau, BP 2135, 28, avenue de Valrose, 06103 NICE CEDEX 2, France. Abstract Due to the interaction of physics and astrophysics we are witnessing in these years a splendid synthesis of theoretical, experimental and observational results originating from three fundamental physical processes. They were originally proposed by Dirac, by Breit and Wheeler and by Sauter, Heisenberg, Euler and Schwinger. For almost seventy years they have all three been followed by a continued effort of experimental verification on Earth-based experiments. The Dirac process, e+e 2γ, has been by − → far the most successful. It has obtained extremely accurate experimental verification and has led as well to an enormous number of new physics in possibly one of the most fruitful experimental avenues by introduction of storage rings in Frascati and followed by the largest accelerators worldwide: DESY, SLAC etc. The Breit–Wheeler process, 2γ e+e , although conceptually simple, being the inverse process of the Dirac one, → − has been by far one of the most difficult to be verified experimentally. Only recently, through the technology based on free electron X-ray laser and its numerous applications in Earth-based experiments, some first indications of its possible verification have been reached. The vacuum polarization process in strong electromagnetic field, pioneered by Sauter, Heisenberg, Euler and Schwinger, introduced the concept of critical electric 2 3 field Ec = mec /(e ).
    [Show full text]