Lucio Cerrito Introduction to the Physics of Radiation and Detection
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Appendix A: Symbols and Prefixes
Appendix A: Symbols and Prefixes (Appendix A last revised November 2020) This appendix of the Author's Kit provides recommendations on prefixes, unit symbols and abbreviations, and factors for conversion into units of the International System. Prefixes Recommended prefixes indicating decimal multiples or submultiples of units and their symbols are as follows: Multiple Prefix Abbreviation 1024 yotta Y 1021 zetta Z 1018 exa E 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 10 deka da 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro μ 10-9 nano n 10-12 pico p 10-15 femto f 10-18 atto a 10-21 zepto z 10-24 yocto y Avoid using compound prefixes, such as micromicro for pico and kilomega for giga. The abbreviation of a prefix is considered to be combined with the abbreviation/symbol to which it is directly attached, forming with it a new unit symbol, which can be raised to a positive or negative power and which can be combined with other unit abbreviations/symbols to form abbreviations/symbols for compound units. For example: 1 cm3 = (10-2 m)3 = 10-6 m3 1 μs-1 = (10-6 s)-1 = 106 s-1 1 mm2/s = (10-3 m)2/s = 10-6 m2/s Abbreviations and Symbols Whenever possible, avoid using abbreviations and symbols in paragraph text; however, when it is deemed necessary to use such, define all but the most common at first use. The following is a recommended list of abbreviations/symbols for some important units. -
Basic Four-Momentum Kinematics As
L4:1 Basic four-momentum kinematics Rindler: Ch5: sec. 25-30, 32 Last time we intruduced the contravariant 4-vector HUB, (II.6-)II.7, p142-146 +part of I.9-1.10, 154-162 vector The world is inconsistent! and the covariant 4-vector component as implicit sum over We also introduced the scalar product For a 4-vector square we have thus spacelike timelike lightlike Today we will introduce some useful 4-vectors, but rst we introduce the proper time, which is simply the time percieved in an intertial frame (i.e. time by a clock moving with observer) If the observer is at rest, then only the time component changes but all observers agree on ✁S, therefore we have for an observer at constant speed L4:2 For a general world line, corresponding to an accelerating observer, we have Using this it makes sense to de ne the 4-velocity As transforms as a contravariant 4-vector and as a scalar indeed transforms as a contravariant 4-vector, so the notation makes sense! We also introduce the 4-acceleration Let's calculate the 4-velocity: and the 4-velocity square Multiplying the 4-velocity with the mass we get the 4-momentum Note: In Rindler m is called m and Rindler's I will always mean with . which transforms as, i.e. is, a contravariant 4-vector. Remark: in some (old) literature the factor is referred to as the relativistic mass or relativistic inertial mass. L4:3 The spatial components of the 4-momentum is the relativistic 3-momentum or simply relativistic momentum and the 0-component turns out to give the energy: Remark: Taylor expanding for small v we get: rest energy nonrelativistic kinetic energy for v=0 nonrelativistic momentum For the 4-momentum square we have: As you may expect we have conservation of 4-momentum, i.e. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
Decay Rates and Cross Section
Decay rates and Cross section Ashfaq Ahmad National Centre for Physics Outlines Introduction Basics variables used in Exp. HEP Analysis Decay rates and Cross section calculations Summary 11/17/2014 Ashfaq Ahmad 2 Standard Model With these particles we can explain the entire matter, from atoms to galaxies In fact all visible stable matter is made of the first family, So Simple! Many Nobel prizes have been awarded (both theory/Exp. side) 11/17/2014 Ashfaq Ahmad 3 Standard Model Why Higgs Particle, the only missing piece until July 2012? In Standard Model particles are massless =>To explain the non-zero mass of W and Z bosons and fermions masses are generated by the so called Higgs mechanism: Quarks and leptons acquire masses by interacting with the scalar Higgs field (amount coupling strength) 11/17/2014 Ashfaq Ahmad 4 Fundamental Fermions 1st generation 2nd generation 3rd generation Dynamics of fermions described by Dirac Equation 11/17/2014 Ashfaq Ahmad 5 Experiment and Theory It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t agree with experiment, it’s wrong. Richard P. Feynman A theory is something nobody believes except the person who made it, An experiment is something everybody believes except the person who made it. Albert Einstein 11/17/2014 Ashfaq Ahmad 6 Some Basics Mandelstam Variables In a two body scattering process of the form 1 + 2→ 3 + 4, there are 4 four-vectors involved, namely pi (i =1,2,3,4) = (Ei, pi) Three Lorentz Invariant variables namely s, t and u are defined. -
The International System of Units (SI)
NAT'L INST. OF STAND & TECH NIST National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 330 2001 Edition The International System of Units (SI) 4. Barry N. Taylor, Editor r A o o L57 330 2oOI rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Relativistic Kinematics & Dynamics Momentum and Energy
Physics 106a, Caltech | 3 December, 2019 Lecture 18 { Relativistic kinematics & dynamics Momentum and energy Our discussion of 4-vectors in general led us to the energy-momentum 4-vector p with components in some inertial frame (E; ~p) = (mγu; mγu~u) with ~u the velocity of the particle in that inertial 2 −1=2 1 2 frame and γu = (1 − u ) . The length-squared of the 4-vector is (since u = 1) p2 = m2 = E2 − p2 (1) where the last expression is the evaluation in some inertial frame and p = j~pj. In conventional units this is E2 = p2c2 + m2c4 : (2) For a light particle (photon) m = 0 and so E = p (going back to c = 1). Thus the energy-momentum 4-vector for a photon is E(1; n^) withn ^ the direction of propagation. This is consistent with the quantum expressions E = hν; ~p = (h/λ)^n with ν the frequency and λ the wave length, and νλ = 1 (the speed of light) We are led to the expression for the relativistic 3-momentum and energy m~u m ~p = p ;E = p : (3) 1 − u2 1 − u2 Note that ~u = ~p=E. The frame independent statement that the energy-momentum 4-vector is conserved leads to the conservation of this 3-momentum and energy in each inertial frame, with the new implication that mass can be converted to and from energy. Since (E; ~p) form the components of a 4-vector they transform between inertial frames in the same way as (t; ~x), i.e. in our standard configuration 0 px = γ(px − vE) (4) 0 py = py (5) 0 pz = pz (6) 0 E = γ(E − vpx) (7) and the inverse 0 0 px = γ(px + vE ) (8) 0 py = py (9) 0 pz = pz (10) 0 0 E = γ(E + vpx) (11) These reduce to the Galilean expressions for small particle speeds and small transformation speeds. -
Relativistic Kinematics of Particle Interactions Introduction
le kin rel.tex Relativistic Kinematics of Particle Interactions byW von Schlipp e, March2002 1. Notation; 4-vectors, covariant and contravariant comp onents, metric tensor, invariants. 2. Lorentz transformation; frequently used reference frames: Lab frame, centre-of-mass frame; Minkowski metric, rapidity. 3. Two-b o dy decays. 4. Three-b o dy decays. 5. Particle collisions. 6. Elastic collisions. 7. Inelastic collisions: quasi-elastic collisions, particle creation. 8. Deep inelastic scattering. 9. Phase space integrals. Intro duction These notes are intended to provide a summary of the essentials of relativistic kinematics of particle reactions. A basic familiarity with the sp ecial theory of relativity is assumed. Most derivations are omitted: it is assumed that the interested reader will b e able to verify the results, which usually requires no more than elementary algebra. Only the phase space calculations are done in some detail since we recognise that they are frequently a bit of a struggle. For a deep er study of this sub ject the reader should consult the monograph on particle kinematics byByckling and Ka jantie. Section 1 sets the scene with an intro duction of the notation used here. Although other notations and conventions are used elsewhere, I present only one version which I b elieveto b e the one most frequently encountered in the literature on particle physics, notably in such widely used textb o oks as Relativistic Quantum Mechanics by Bjorken and Drell and in the b o oks listed in the bibliography. This is followed in section 2 by a brief discussion of the Lorentz transformation. -
Comparing Many-Body Approaches Against the Helium Atom Exact Solution
SciPost Phys. 6, 040 (2019) Comparing many-body approaches against the helium atom exact solution Jing Li1,2, N. D. Drummond3, Peter Schuck1,4,5 and Valerio Olevano1,2,6? 1 Université Grenoble Alpes, 38000 Grenoble, France 2 CNRS, Institut Néel, 38042 Grenoble, France 3 Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom 4 CNRS, LPMMC, 38042 Grenoble, France 5 CNRS, Institut de Physique Nucléaire, IN2P3, Université Paris-Sud, 91406 Orsay, France 6 European Theoretical Spectroscopy Facility (ETSF) ? [email protected] Abstract Over time, many different theories and approaches have been developed to tackle the many-body problem in quantum chemistry, condensed-matter physics, and nuclear physics. Here we use the helium atom, a real system rather than a model, and we use the exact solution of its Schrödinger equation as a benchmark for comparison between methods. We present new results beyond the random-phase approximation (RPA) from a renormalized RPA (r-RPA) in the framework of the self-consistent RPA (SCRPA) originally developed in nuclear physics, and compare them with various other approaches like configuration interaction (CI), quantum Monte Carlo (QMC), time-dependent density- functional theory (TDDFT), and the Bethe-Salpeter equation on top of the GW approx- imation. Most of the calculations are consistently done on the same footing, e.g. using the same basis set, in an effort for a most faithful comparison between methods. Copyright J. Li et al. Received 15-01-2019 This work is licensed under the Creative Commons Accepted 21-03-2019 Check for Attribution 4.0 International License. -
Introduction to Numerical Projects Format for Electronic Delivery Of
Introduction to numerical projects Here follows a brief recipe and recommendation on how to write a report for each project. • Give a short description of the nature of the problem and the eventual numerical methods you have used. • Describe the algorithm you have used and/or developed. Here you may find it con- venient to use pseudocoding. In many cases you can describe the algorithm in the program itself. • Include the source code of your program. Comment your program properly. • If possible, try to find analytic solutions, or known limits in order to test your program when developing the code. • Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes. • Try to evaluate the reliabilty and numerical stability/precision of your results. If pos- sible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc. • Try to give an interpretation of you results in your answers to the problems. • Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you’ve made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it. We do appreciate your comments. • Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don’t properly remember what a previous test version of your program did. -
Photoelectric Effect Prac
Name ___________________. Photoelectric Effect Prac 1. The threshold frequency in a photoelectric experiment is most closely related to the A) brightness of the incident light B) thickness of the photoemissive metal C) area of the photoemissive metal D) work function of the photoemissive metal 2. When a source of dim orange light shines on a photosensitive metal, no photoelectrons are ejected from its surface. What could be done to increase the likelihood of producing photoelectrons? A) Replace the orange light source with a red light source. B) Replace the orange light source with a higher frequency light source. C) Increase the brightness of the orange light source. D) Increase the angle at which the photons of orange light strike the metal. 3. The threshold frequency for a photoemissive surface is hertz. Which color light, if incident upon the surface, may produce photoelectrons? A) blue B) green C) yellow D) red 4. The threshold frequency of a metal surface is in the violet light region. What type of radiation will cause photoelectrons to be emitted from the metal's surface? A) infrared light B) red light C) ultraviolet light D) radio waves 5. Photons with an energy of 7.9 electron-volts strike a zinc plate, causing the emission of photoelectrons with a maximum kinetic energy of 4.0 electronvolts. The work function of the zinc plate is A) 11.9 eV B) 7.9 eV C) 3.9 eV D) 4.0 eV 6. The threshold frequency for a photoemissive surface is 1.0 × 1014 hertz. What is the work function of the surface? A) 1.0 × 10–14 J B) 6.6 × 10–20 J C) 6.6 × 10–48 J D) 2.2 × 10–28 J 7. -
Measurement of the Mass of the Higgs Boson in the Two Photon Decay Channel with the CMS Experiment
Facolt`adi Scienze Matematiche Fisiche e Naturali Ph.D. Thesis Measurement of the mass of the Higgs Boson in the two photon decay channel with the CMS experiment. Candidate Thesis advisors Shervin Nourbakhsh Dott. Riccardo Paramatti Dott. Paolo Meridiani Matricola 1106418 Year 2012/2013 Contents Introduction i 1 Standard Model Higgs and LHC physics 1 1.1 StandardModelHiggsboson.......................... 1 1.1.1 Overview ................................ 2 1.1.2 Spontaneous symmetry breaking and the Higgs boson . 3 1.1.3 Higgsbosonproduction ........................ 5 1.1.4 Higgsbosondecays ........................... 5 1.1.5 Higgs boson property study in the two photon final state . 6 1.2 LHC ....................................... 11 1.2.1 The LHC layout............................. 12 1.2.2 Machineoperation ........................... 13 1.2.3 LHC physics (proton-proton collision) . 15 2 Compact Muon Solenoid Experiment 17 2.1 Detectoroverview................................ 17 2.1.1 Thecoordinatesystem . 18 2.1.2 Themagnet ............................... 18 2.1.3 Trackersystem ............................. 19 2.1.4 HadronCalorimeter. 21 2.1.5 Themuonsystem............................ 22 2.2 Electromagnetic Calorimeter . 24 2.2.1 Physics requirements and design goals . 24 I Contents II 2.2.2 ECAL design............................... 24 2.3 Triggeranddataacquisition . 26 2.3.1 CalorimetricTrigger . 27 2.4 CMS simulation ................................. 28 3 Electrons and photons reconstruction and identification 32 3.1 Energy measurement in ECAL ......................... 32 3.2 Energycalibration ............................... 33 3.2.1 Responsetimevariation . 34 3.2.2 Intercalibrations. 36 3.3 Clusteringandenergycorrections . 38 3.4 Algorithmic corrections to electron and photon energies ........... 39 3.4.1 Parametric electron and photon energy corrections . ....... 40 3.4.2 MultiVariate (MVA) electron and photon energy corrections . 41 3.5 Photonreconstruction ............................ -
9081872 Physics Jan. 01
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION PHYSICS Tuesday, January 23, 2001 — 9:15 a.m. to 12:15 p.m., only The answer paper is stapled in the center of this examination booklet. Open the examination book- let, carefully remove the answer paper, and close the examination booklet. Then fill in the heading on your answer paper. All of your answers are to be recorded on the separate answer paper. For each question in Part I and Part II, decide which of the choices given is the best answer. Then on the answer paper, in the row of numbers for that question, circle with pencil the number of the choice that you have selected. The sample below is an example of the first step in recording your answers. SAMPLE: 1 2 3 4 If you wish to change an answer, erase your first penciled circle and then circle with pencil the num- ber of the answer you want. After you have completed the examination and you have decided that all of the circled answers represent your best judgment, signal a proctor and turn in all examination material except your answer paper. Then and only then, place an X in ink in each penciled circle. Be sure to mark only one answer with an X in ink for each question. No credit will be given for any question with two or more X’s marked. The sample below indicates how your final choice should be marked with an X in ink. SAMPLE: 1 2 3 4 For questions in Part III, record your answers in accordance with the directions given in the exami- nation booklet.