DOCSLIB.ORG

Basic Elements of Neutron Inelastic Scattering

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Basic Elements of Neutron Inelastic Scattering 2012 NCNR Summer School on Fundamentals of Neutron Scattering Basic Elements of Neutron Inelastic Scattering Peter M. Gehring National Institute of Standards and Technology NIST Center for Neutron Research Gaithersburg, MD USA Φs hω Outline 1. Introduction - Motivation - Types of Scattering 2. The Neutron - Production and Moderation - Wave/Particle Duality 3. Basic Elements of Neutron Scattering - The Scattering Length, b - Scattering Cross Sections - Pair Correlation Functions - Coherent and Incoherent Scattering - Neutron Scattering Methods (( )) (( )) (( )) (( )) 4. Summary of Scattering Cross Sections ω0 ≠ 0 (( )) (( )) (( )) (( )) - Elastic (Bragg versus Diffuse) (( )) (( )) (( )) (( )) - Quasielastic (Diffusion) - Inelastic (Phonons) ω (( )) (( )) (( )) (( )) Motivation Structure and Dynamics The most important property of any material is its underlying atomic / molecular structure (structure dictates function). Bi2Sr2CaCu2O8+δ In addition the motions of the constituent atoms (dynamics) are extremely important because they provide information about the interatomic potentials. An ideal method of characterization would be one that can provide detailed information about both structure and dynamics. Types of Scattering How do we “see”? Thus scattering We see something when light scatters from it. conveys information! Light is composed of electromagnetic waves. λ ~ 4000 A – 7000 A However, the details of what we see are ultimately limited by the wavelength. Types of Scattering The tracks of a compact disk act as a diffraction grating, producing a separation of the colors of white light. From this one can determine the nominal distance between tracks on a CD, which is 1.6 x 10-6 meters = 16,000 Angstroms. To characterize materials we must determine the underlying structure. We do this by using d the material as a diffraction grating. Problem: Distances between atoms in materials o are of order Angstroms à light is inadequate. λLight >> d ~ 4 A Moreover, most materials are opaque to light. Types of Scattering To “see” atomic structure, we require a probe with a wavelength λ ~ length scale of interest. X-rays EM - wave Some candidates … Electrons Charged particle Neutrons Neutral particle Types of Scattering Which one should we choose? If we wish only to determine relative atomic positions, then we should choose x-rays almost every time. 1. Relatively cheap 2. Sources are ubiquitous à easy access 3. Fluxes are extremely high à can study small samples However … Types of Scattering Nucleus X-rays are electromagnetic radiation. Thus they scatter from the atomic electrons. Electrons Consequences: Low-Z elements Elements with similar X-rays are strongly attenuated are hard to see. atomic numbers have as they pass through the walls very little contrast. of furnaces, cryostats, etc. Hydrogen Cobalt Nickel ?? (Z = 1) (Z = 27) (Z = 28) Types of Scattering What about electrons? Electrons are charged particles à they see both the atomic electrons and nuclear protons at the same time. 1. Relatively cheap 2. Sources are not uncommon à good access 3. Fluxes are extremely high à can study tiny crystals 4. Very small wavelengths à more information However … Types of Scattering Electrons have some deficiencies too ... Requires very Radiation damage Magnetic structures are hard to thin samples. is a concern. determine because electrons are deflected by the internal magnetic fields. Types of Scattering What about neutrons? Advantages Disadvantages Wavelengths easily varied Neutrons are expensive to match atomic spacings to produce à access is not as easy Zero charge à not strongly Interact weakly with matter à attenuated by furnaces, etc. often require large samples Magnetic dipole moment à Available fluxes are low can study magnetic structures compared to those for x-rays Nuclear interaction à can see low-Z elements easily like H à good for the study of biomolecules and polymers. Nuclear interaction is simple Low energies à Let’s consider à scattering is easy to model Non-destructive probe neutrons … The Neutron “If the neutron did not exist, it would need to be invented.” Bertram Brockhouse 1994 Nobel Laureate in Physics -27 mn= 1.675x10 kg The Neutron Q = 0 S = ½ h µn= -1.913 µN 1926: de Broglie Relation λ = h/p = h/mnv o o λ = 1 A λ = 9 A v = 4000 m/s v = 440 m/s E = 82 meV E = 1 meV Neutron Production Neutrons not bound to a nucleus decay via - the weak force at a rate characterized by a n à p + e + νe lifetime of ~ 888 seconds (15 minutes). A useful source of neutrons requires a nuclear process by which bound neutrons can be freed from n the nuclei of atoms and that is easily sustainable. There are two such processes, spallation and fission … Spallation Neutron Production Fission by Fission t Nuclear fission is used in power 235 236 * and research reactors. 92U143 + n →[ 92U144 ] → X +Y + 2.44n A liquid medium (D2O, or heavy water) is used to moderate the fast fission neutrons to room temperature (2 MeV à 50 meV). The fission process and moderator are confined by a large containment vessel. Neutron 2 3 (-m v /2kBT) Moderation Maxwellian Distribution Φ ~ v e Liquid Hydrogen 25 K 6 5 Heavy Water (D2O) 4 3 Hot Graphite 300 K 2 1 2000 K 0 0 5 10 15 “Fast” neutrons: v = 20,000 km/sec Neutron velocity v (km/sec) Wave - Particle de Broglie Relation λ = h/mnv Duality Fast Neutron, ~ 0.00002 nm V ~ 20,000,000 m/sec Thermal Neutron, ~ 0.2 nm V ~ 2,000 m/sec Cold Neutron, V ~ 200 m/sec ~ 2 nm Basics of Neutron Scattering Neutron scattering experiments measure the flux Φs of neutrons scattered by a sample into a detector as a function of the change in neutron wave vector (Q) and energy (hω). Q h = neutrons Φs( , ω) sec–cm2 Momentum Energy 2 2 ki kf hk = h(2π/λ) hωn = h kn /2m hQ = hki - hkf hω = hωi - hωf 2θ The expressions for the scattered neutron flux Φs involve the positions and motions of atomic nuclei or unpaired electron spins. provides information = f{r (t), r (t), S (t), S (t)} Φs Φs i j i j about all of these quantities! Neutron Scattering These “cross sections” are what we measure Cross Sections experimentally. Consider an incident neutron beam 2 with flux Φi (neutrons/sec/cm ) and We define three cross sections: wave vector ki on a non-absorbing sample. σ = Total cross section d σ = Differential cross section d kf Ω d2 Partial differential σ = dΩdEf cross section 2 Φi ki Neutron Scattering What are the physical meanings of these three cross sections? Cross Sections σ Total # of neutrons scattered per second / Φi. dσ Total # of neutrons scattered per second into dΩ / dΩ Φi. dΩ (Diffraction à structure. Signal is summed over all energies.) d2σ Total # of neutrons scattered per second into dΩ with a final energy between Ef and dEf / dΩ dEf Φi. dΩ dEf (Inelastic scattering à dynamics. Small, but contains much info.) Neutron Scattering What are the relative sizes of the cross sections? Cross Sections dσ d2σ Clearly: σ = dΩ = dΩ dEf dΩ dΩ dEf dσ d2σ Thus: σ >> >> dΩ dΩ dEf 2 dσ . d σ σ d Ω dΩ dEf d d2σ Typically, σ ~ 106 x dΩ dΩ dEf Elastic vs Inelastic Note that both of these d2σ cases are described by … Scattering dΩ dEf d Elastic (k =k ) ≠ σ i f dΩ Elastic Scattering: • Change in neutron energy = 0 sinθ = (Q/2)/k • Probes changes in momentum kf θ Q = 2ksinθ = 4πsinθ/λ only θ ki Inelastic (ki≠kf) Inelastic Scattering: • Change in neutron energy ≠ 0 • Probes changes in both kf kf Q Q momentum and energy 2θ 2θ ki ki Energy loss (hω>0) Energy gain (hω<0) Scattering From Consider the simplest case: A fixed, isolated nucleus. a Single Nucleus The scattered (final) neutron Ψ is a spherical wave: λ ∼ 2 Α ikr Ψf(r) ~ (-b/r)e QUESTIONS: 1. The scattering is elastic (ki = kf = k). Why? x 2. The scattering is isotropic. Why? The incident neutron Ψi is a plane wave: Nucleus ikx 1 fm = 10-15 m Ψi(r) ~ e (k = 2π/λ) Scattering From ANSWERS: a Single Nucleus 1. The scattering is elastic because the nucleus is fixed, so no energy can be transferred to it from the neutron (ignoring any excitations of the nucleus itself). 2. A basic result of diffraction theory states: if waves of any kind scatter from an object of a size << λ, then the scattered waves are spherically symmetric. (This is also known as s-wave scattering.) N << λ V(r) = 2πh2 b (r-r ) ( mn ) j δ j Σ j=1 ~ 10-15 m << 10-10 m The details of V(r) are unimportant – V(r) can be described by a scalar parameter b that depends Fermi Pseudopotential only the choice of nucleus and isotope! Scattering From The Neutron Scattering Length - b a Single Nucleus The parameter b is known as the X-rays neutron “scattering length” and has units of length ~ 10-12 cm. Z It is independent of neutron energy. Neutrons It is (usually) a real number; imaginary for absorption ... It corresponds to the b varies randomly with Z and isotope à “form factor” for x- allows access to atoms that are usually ray scattering. unseen by x-rays. Scattering From We can easily calculate σ for a single, fixed nucleus: a Single Nucleus . Def. σ Φi = Total number of neutrons scattered per second by the nucleus. v = Velocity of neutrons (elastic à same before and after scattering). dA v 2 Total number of neutrons scattered per second through dA. v dA |Ψf| = 2 2 2 2 2 . v dA |Ψf| = v(r dΩ)(b/r) = v b dΩ = v 4πb = σ Φi dσ Since = v | |2 = v à = 2 Try calculating Φi Ψi σ 4πb dΩ Scattering From What if many atoms are present? Many Nuclei Scattering from Scattering from one nucleus many nuclei Scattered neutron Ψf is a spherical wave: Constructive interference The incident neutron Ψi is a plane wave: Get strong scattering in some directions, but not in others.
Load more

Recommended publications
  • Part B. Radiation Sources Radiation Safety
    Part B. Radiation sources Radiation Safety 1. Interaction of electrons-e with the matter −31 me = 9.11×10 kg ; E = m ec2 = 0.511 MeV; qe = -e 2. Interaction of photons-γ with the matter mγ = 0 kg ; E γ = 0 eV; q γ = 0 3. Interaction of neutrons-n with the matter −27 mn = 1.68 × 10 kg ; En = 939.57 MeV; qn = 0 4. Interaction of protons-p with the matter −27 mp = 1.67 × 10 kg ; Ep = 938.27 MeV; qp = +e Note: for any nucleus A: mass number – nucleons number A = Z + N Z: atomic number – proton (charge) number N: neutron number 1 / 35 1. Interaction of electrons with the matter Radiation Safety The physical processes: 1. Ionization losses inelastic collisions with orbital electrons 2. Bremsstrahlung losses inelastic collisions with atomic nuclei 3. Rutherford scattering elastic collisions with atomic nuclei Positrons at nearly rest energy: annihilation emission of two 511 keV photons 2 / 35 1. Interaction of electrons with1.E+02 the matter Radiation Safety ) 1.E+03 -1 Graphite – Z = 6 .g 2 1.E+01 ) Lead – Z = 82 -1 .g 2 1.E+02 1.E+00 1.E+01 1.E-01 1.E+00 collision 1.E-02 radiative collision 1.E-01 stopping pow er (MeV.cm total radiative 1.E-03 stopping pow er (MeV.cm total 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E-02 energy (MeV) 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 Electrons – stopping power 1.E+02 energy (MeV) S 1 dE ) === -1 Copper – Z = 29 ρρρ ρρρ dl .g 2 1.E+01 S 1 dE 1 dE === +++ ρρρ ρρρ dl coll ρρρ dl rad 1 dE 1.E+00 : mass stopping power (MeV.cm 2 g.
    [Show full text]
  • 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
    [Show full text]
  • Particles and Deep Inelastic Scattering
    Heidi Schellman Northwestern Particles and Deep Inelastic Scattering Heidi Schellman Northwestern University HUGS - JLab - June 2010 June 2010 HUGS 1 Heidi Schellman Northwestern k’ k q P P’ A generic scatter of a lepton off of some target. kµ and k0µ are the 4-momenta of the lepton and P µ and P 0µ indicate the target and the final state of the target, which may consist of many particles. qµ = kµ − k0µ is the 4-momentum transfer to the target. June 2010 HUGS 2 Heidi Schellman Northwestern Lorentz invariants k’ k q P P’ 2 2 02 2 2 2 02 2 2 2 The 5 invariant masses k = m` , k = m`0, P = M , P ≡ W , q ≡ −Q are invariants. In addition you can define 3 Mandelstam variables: s = (k + P )2, t = (k − k0)2 and u = (P − k0)2. 2 2 2 2 s + t + u = m` + M + m`0 + W . There are also handy variables ν = (p · q)=M , x = Q2=2Mµ and y = (p · q)=(p · k). June 2010 HUGS 3 Heidi Schellman Northwestern In the lab frame k’ k θ q M P’ The beam k is going in the z direction. Confine the scatter to the x − z plane. µ k = (Ek; 0; 0; k) P µ = (M; 0; 0; 0) 0µ 0 0 0 k = (Ek; k sin θ; 0; k cos θ) qµ = kµ − k0µ June 2010 HUGS 4 Heidi Schellman Northwestern In the lab frame k’ k θ q M P’ 2 2 2 s = ECM = 2EkM + M − m ! 2EkM 2 0 0 2 02 0 t = −Q = −2EkEk + 2kk cos θ + mk + mk ! −2kk (1 − cos θ) 0 ν = (p · q)=M = Ek − Ek energy transfer to target 0 y = (p · q)=(p · k) = (Ek − Ek)=Ek the inelasticity P 02 = W 2 = 2Mν + M 2 − Q2 invariant mass of P 0µ June 2010 HUGS 5 Heidi Schellman Northwestern In the CM frame k’ k q P P’ The beam k is going in the z direction.
    [Show full text]
  • Chemical Applications of Inelastic X-Ray Scattering
    BNL- 68406 CHEMICAL APPLICATIONS OF INELASTIC X-RAY SCATTERING H. Hayashi and Y. Udagawa Research Institute for Scientific Measurements Tohoku University Sendai, 980-8577, Japan J.-M. Gillet Structures, Proprietes et Modelisation des Solides UMR8580 Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France W.A. Caliebe and C.-C. Kao National Synchrotron Light Source Brookhaven National Laboratory Upton, New York, 11973-5000, USA August 2001 National Synchrotron Light Source Brookhaven National Laboratory Operated by Brookhaven Science Associates Upton, NY 11973 Under Contract with the United States Department of Energy Contract Number DE-AC02-98CH10886 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy; completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. Th.e views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. CHEMICAL APPLICATIONS OF INELASTIC X-RAY SCATTERING H.
    [Show full text]
  • Relative Merits and Limiting Factors for X-Ray and Electron Microscopy of Thick, Hydrated Organic Materials (2020 Revised Version)
    Relative merits and limiting factors for x-ray and electron microscopy of thick, hydrated organic materials (2020 revised version) Ming Du1, and Chris Jacobsen2;3;4;∗ 1Department of Materials Science and Engineering, Northwestern University, 2145 Sheridan Road, Evanston IL 60208, USA 2Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Argonne IL 60439, USA 3Department of Physics & Astronomy, Northwestern University, 2145 Sheridan Road, Evanston IL 60208, USA 4Chemistry of Life Processes Institute, Northwestern University, 2170 Campus Drive, Evanston IL 60208, USA ∗Corresponding author; Email: [email protected] Abstract Electron and x-ray microscopes allow one to image the entire, unlabeled structure of hydrated mate- rials at a resolution well beyond what visible light microscopes can achieve. However, both approaches involve ionizing radiation, so that radiation damage must be considered as one of the limits to imaging. Drawing upon earlier work, we describe here a unified approach to estimating the image contrast (and thus the required exposure and corresponding radiation dose) in both x-ray and electron microscopy. This approach accounts for factors such as plural and inelastic scattering, and (in electron microscopy) the use of energy filters to obtain so-called \zero loss" images. As expected, it shows that electron microscopy offers lower dose for specimens thinner than about 1 µm (such as for studies of macromolecules, viruses, bacteria and archaebacteria, and thin sectioned material), while x-ray microscopy offers superior charac- teristics for imaging thicker specimen such as whole eukaryotic cells, thick-sectioned tissues, and organs. The required radiation dose scales strongly as a function of the desired spatial resolution, allowing one to understand the limits of live and frozen hydrated specimen imaging.
    [Show full text]
  • Theory of Inelastic Lepton-Nucleus Scattering Granddon D
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1988 Theory of inelastic lepton-nucleus scattering Granddon D. Yen Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Nuclear Commons Recommended Citation Yen, Granddon D., "Theory of inelastic lepton-nucleus scattering " (1988). Retrospective Theses and Dissertations. 9746. https://lib.dr.iastate.edu/rtd/9746 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS The most advanced technology has been used to photo­ graph and reproduce this manuscript from the microfilm master. UMI films the original text directly from the copy submitted. Thus, some dissertation copies are in typewriter face, while others may be from a computer printer. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyrighted material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are re­ produced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each oversize page is available as one exposure on a standard 35 mm slide or as a IT x 23" black and white photographic print for an additional charge.
    [Show full text]
  • Cross Sections for Neutron Inelastic Scattering and (N, 2N) Processes
    AE-88 00 Cross Sections for Neutron Inelastic 00 w < Scattering and (n, 2n) Processes. A Review of Available Experimental and Theoretical Data. M. Leimdörfer, E. Bock and L Arkeryd AKTIEBOLAGET ATOMENERGI STOCKHOLM SWEDEN 1962 AE-88 CROSS SECTIONS FOR NEUTRON INELASTIC SCATTERING AND ( n, 2n ) PROCESSES A Review of Available Experimental and Theoretical Data by M. Leimdörfer, E. Bock and L. Arkeryd Summary: A survey of the present state of knowledge on (n, n') and (n, 2n) reactions has been performed. The result is presented in the form of a main index to references on all elements and several special indices to different theoretical ways of approach, such as the direct-interaction concept, the continuum model (including level density theories), the discrete-level statistical model (Hauser-Feshbach), with a subsection on the optical model, 486 references accompanied with abstracts giving essential information pertaining to the field are supplied in the report. It is intended to keep this review up to date by regular issue of supplements. The abstracts have been arranged alphabetically according to the name of the first author. Printed and distributed in October 1962. Contents: Foreword page I Introduction I - V Main Coordinate Index Arranged According to Elements and Publishing Year VI - XXIV Subject Indices XXV - XXVI Author Index XXVII - XXXV Abstracts 1 - 486 A first edition of this report was issued as VDIT-50 (RFA-74) in Fehruary 1962. In the present, revised, edition such publica- tions as have appeared since the issue of the former report have been included, simultaneously as the.organization has been improved and, we hope, most of the inevitable printing errors have been removed.
    [Show full text]
  • Inelastic Scattering of Electrons in Solids
    Scanning Electron Microscopy Volume 1982 Number 1 1982 Article 2 1982 Inelastic Scattering of Electrons in Solids C. J. Powell National Bureau of Standards Follow this and additional works at: https://digitalcommons.usu.edu/electron Part of the Biology Commons Recommended Citation Powell, C. J. (1982) "Inelastic Scattering of Electrons in Solids," Scanning Electron Microscopy: Vol. 1982 : No. 1 , Article 2. Available at: https://digitalcommons.usu.edu/electron/vol1982/iss1/2 This Article is brought to you for free and open access by the Western Dairy Center at DigitalCommons@USU. It has been accepted for inclusion in Scanning Electron Microscopy by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. Electron Beam Interactions With Solids (Pp. 19-3 I) SEM, Inc., AMF O'Hare (Chicago), IL 60666, U.S.A. INELASTIC SCATTERING OF ELECTRONS IN SOLIDS* C.J. POWELL Surface Science Division, National Bureau of Standards Washington, DC 20234 Tel. 301-921-2188 *Contribution of the National Bureau of Standards, not sub­ ject to copyright. ABSTRACT 1. INTRODUCTION The principal mechanisms and available data for the in­ Electrons incident on a solid or generated internally within elastic scatter ing of electrons in solids are reviewed. The pro­ a solid can be scattered elastically (with a change of momen­ cesses relevant for electron-probe microanalysis, electron tum but without change of energy) or inelastically (with a energy-loss spectroscopy, Auger-electron spectroscopy, and change of energy). This article reviews the principal mechan­ x-ray photoelectron spectroscopy are described and examples isms and available data for the inelastic scattering of elec­ of relevant electron energy-loss data are shown .
    [Show full text]
  • Introduction to Deep Inelastic Scattering: Past and Present
    Introduction to Deep Inelastic Scattering: past and present 24/03/2012 Joël Feltesse - DIS 2012 1 Outlook • Glorious surprises at SLAC • High precision fixed target data and new themes (Spin and Nuclear effects) • Discoveries from HERA • High precision and extension of the field • Conclusions 24/03/2012 Joël Feltesse - DIS 2012 2 Deep Inelastic Scattering Lepton-Nucleon Scattering Large MX = Inelastic Large Q2 = Deep 24/03/2012 Joël Feltesse - DIS 2012 3 Two major surprises observed in late 1967 at SLAC Very weak Q2 dependence Scaling at non asymptotic low Q2 values [W.K.H. Panovsky, HEP Vienna,1968] 24/03/2012 Joël Feltesse - DIS 2012 4 Why was it such a surprise? 24/03/2012 Joël Feltesse - DIS 2012 5 Before 1967 elastic scattering experiments (Hofstater) had demonstrated that the proton is not a point but an extensive structure (Dick Taylor, Nobel Prize Lecture) (almost) Nobody expected that the study of the continuum at high W would be so crucial in the history of high energy physics. At DESY, Brasse et al. did notice in june 1967 a surprising slow Q 2 dependence at high W that they tentatively attributed to resonances of high angular momentum. (F. Brasse et al. , DESY, 1967) Joël Feltesse - DIS 2012 6 Bjorken as lone prophet Formal desciption of scaling but « a more physical description is without question needed » (Bjorken, 1966) We can understand the sum rules in a very simple way (Bjorken, 1967). We suppose that the nucleon consists of a certain number of ‘ elementary constituents ’ « It will be of interest to look at very large
    [Show full text]
  • Deep Inelastic Scattering of Polarized Electrons by Polarized 3He and The
    SLACPUB Septemb er Deep Inelastic Scattering of Polarized Electrons by Polarized He and the Study of the Neutron Spin Structure The E Collab oration PL Anthony RG Arnold HR Band H Borel PE Bosted V Breton GD Cates TE Chupp FS Dietrich J Dunne R Erbacher J Fellbaum H Fonvieille R Gearhart R Holmes EW Hughes JR Johnson D Kawall C Kepp el SE Kuhn RM LombardNelsen J Marroncle T Maruyama W Meyer ZE Meziani H Middleton J Morgenstern NR Newbury GG Petratos R Pitthan R Prep ost Y Roblin SE Ro ck SH Rokni G Shapiro T Smith PA Souder M Sp engos F Staley LM Stuart ZM Szalata Y Terrien AK Thompson JL White M Wo o ds J Xu CC Young G Zapalac American University Washington DC LPC INPCNRS Univ Blaise Pascal F Aubiere Cedex France University of California and LBL Berkeley CA California Institute of Technology Pasadena CA hep-ex/9610007 14 Oct 1996 Centre dEtudes de Saclay DAPNIASPhN F GifsurYvette France Kent State University Kent OH Lawrence Livermore National Lab oratory Livermore CA University of Michigan Ann Arb or MI National Institute of Standards and Technology Gaithersburg MD Old Dominion University Norfolk VA Princeton University Princeton NJ Stanford Linear Accelerator Center Stanford CA Stanford University Stanford CA Syracuse University Syracuse NY Work supp orted by Department of Energy contract DEACSF Temple University Philadelphia PA University of Wisconsin Madison WI Abstract The neutron longitudinal and transverse
    [Show full text]
  • Deep Inelastic Scattering (DIS)
    Deep Inelastic Scattering (DIS) Ingo Schienbein Laboratoire de Physique UGA/LPSC Grenoble Campus Subatomique et de Cosmologie Universitaire CTEQ School on QCD and Electroweak Phenomenology Monday, October 8, 12 EAOM LPSC, Serge Kox, 20/9/2012 Mayaguez, Puerto Rico, USA 18-28 June 2018 Tuesday 19 June 18 Disclaimer This lecture has profited a lot from the following resources: • The text book by Halzen&Martin, Quarks and Leptons • The text book by Ellis, Stirling & Webber, QCD and Collider Physics • The lecture on DIS at the CTEQ school in 2012 by F. Olness • The lecture on DIS given by F. Gelis Saclay in 2006 Tuesday 19 June 18 Lecture 1 1. Kinematics of Deep Inelastic Scattering 2. Cross sections for inclusive DIS (photon exchange) 3. Longitudinal and Transverse Structure functions 4. CC and NC DIS 5. Bjorken scaling 6. The Parton Model 7. Which partons? 8. Structure functions in the parton model Tuesday 19 June 18 1. Kinematics of Deep Inelastic Scattering Tuesday 19 June 18 What is inside nucleons? ‣ Basic idea: smash a well known probe on a nucleon or nucleus in order to try to figure out what is inside ‣ Photons are well suited for that purpose because their interactions are well understood ‣ Deep inelastic scattering: collision between an electron and a nucleon or nucleus by exchange of a virtual photon Note: the virtual photon is spacelike: q 2 < 0 e- • q 2 2 2 2 • Deep: Q = -q >> MN ~1 GeV X 2≣ 2 2 p , A • Inelastic: W MX > MN ‣ Variant: collision with a neutrino, by exchange of a Z0 or W± Tuesday 19 June 18 18 Masses in deep inelastic scattering Kinematic variables Figure 2.1: Kinematics of DIS in the single exchange boson approximation.
    [Show full text]
  • Lec13 Inelastic-Scattering.Pdf
    Inelastic Scattering Ken Voss, Ocean Optics Summer class, 2017 Introduction Remember your freshman physics class and all that time you spent learning about collisions? Two types of collisions: elastic and in-elastic. What was the difference? Introduction Remember your freshman physics class and all that time you spent learning about collisions? Two types of collisions: elastic and in-elastic. What was the difference? Elastic collisions conserved Kinetic energy and momentum, inelastic just momentum….was energy lost? Introduction So elastic scattering: photons come in and out of the process with the same energy (wavelength) In-elastic scattering: photons come in with one wavelength and leave with another wavelength. (remember Compton scattering of photons?). Difference between this and fluorescence is basically a short intermediate time for the event (which leads to other effects). prepared samples (see Fig. 1). All measurements were when recording Raman and luminescence spectra. done at a temperature of 21°C. This background-correcting spectrum was sub- A schematic for the experimental setup is shown in tracted from the raw experimental data. In the case Fig. 1. Laser light of wavelength 532 nm with a of Raman spectra, a straight line has been fitted in polarization controlled through the λ∕2 waveplate the spectral region from 700 to 745 nm. This straight was reflected by a dichroic mirror and focused onto line is shown in Fig. 2 and has been also subtracted the sample by a microscope objective. The degree from the spectrum. This subtraction has affected the of linear polarization of the incoming laser light is final estimate for the scattering coefficient by less at least better than 99.9%.
    [Show full text]