QUANTUM ELECTRODYNAMICS Greiner Greiner Quantum Mechanics Mechanics I an Introduction 3Rd Edition (In Preparation)
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Relativistic Quantum Mechanics Walter Greiner Pdf
Relativistic quantum mechanics walter greiner pdf Continue The German physicist Walter Greiner (October 29, 1935-October 6, 2016) was a German theoretical physicist. His research interests lay in atomic physics, heavy ion physics, nuclear physics, particle physics (especially in quantum electrodynamics and quantum chromodynamics). He is known for his series of books on theoretical physics, especially in Germany, but all over the world. Greiner's biography was born on October 29, 1935, in Neuenbau, Sonnenberg, Germany. He studied physics at the University of Frankfurt (University of Goethe in Frankfurt), received a bachelor's degree in physics, a master's degree in 1960 with a thesis on plasma reactors and a doctorate in 1961 from the University of Freiburg under the direction of Hans Marshall, with a thesis on nuclear polarization in μ-mesic atoms. From 1962 to 1964, he was an assistant professor at the University of Maryland and then a research fellow at the University of Freiburg, 1964. Beginning in 1965, he became a professor at the Institute of Theoretical Physics at the University of Goethe in Frankfurt until 1995. Greiner has been a visiting professor at many universities and laboratories, including Florida State University, the University of Virginia, the University of California, the University of Melbourne, Vanderbilt University, Yale University, the Oak Ridge National Laboratory, and the Los Alamos National Laboratory. In 2003, together with Wolf Singer, he was founding director of the Frankfurt Institute for Advanced Studies (FIAS) and lectured and seminared on particle physics. Died 6 October 2016 at the age of 80. After his death, several books and articles in honor of Walter Greiner were published. -
Compton Scattering from the Deuteron at Low Energies
SE0200264 LUNFD6-NFFR-1018 Compton Scattering from the Deuteron at Low Energies Magnus Lundin Department of Physics Lund University 2002 W' •sii" Compton spridning från deuteronen vid låga energier (populärvetenskaplig sammanfattning på svenska) Vid Compton spridning sprids fotonen elastiskt, dvs. utan att förlora energi, mot en annan partikel eller kärna. Kärnorna som användes i detta försök består av en proton och en neutron (sk. deuterium, eller tungt väte). Kärnorna bestrålades med fotoner av kända energier och de spridda fo- tonerna detekterades mha. stora Nal-detektorer som var placerade i olika vinklar runt strålmålet. Försöket utfördes under 8 veckor och genom att räkna antalet fotoner som kärnorna bestålades med och antalet spridda fo- toner i de olika detektorerna, kan sannolikheten för att en foton skall spridas bestämmas. Denna sannolikhet jämfördes med en teoretisk modell som beskriver sannolikheten för att en foton skall spridas elastiskt mot en deuterium- kärna. Eftersom protonen och neutronen består av kvarkar, vilka har en elektrisk laddning, kommer dessa att sträckas ut då de utsätts för ett elek- triskt fält (fotonen), dvs. de polariseras. Värdet (sannolikheten) som den teoretiska modellen ger, beror på polariserbarheten hos protonen och neu- tronen i deuterium. Genom att beräkna sannolikheten för fotonspridning för olika värden av polariserbarheterna, kan man se vilket värde som ger bäst överensstämmelse mellan modellen och experimentella data. Det är speciellt neutronens polariserbarhet som är av intresse, och denna kunde bestämmas i detta arbete. Organization Document name LUND UNIVERSITY DOCTORAL DISSERTATION Department of Physics Date of issue 2002.04.29 Division of Nuclear Physics Box 118 Sponsoring organization SE-22100 Lund Sweden Author (s) Magnus Lundin Title and subtitle Compton Scattering from the Deuteron at Low Energies Abstract A series of three Compton scattering experiments on deuterium have been performed at the high-resolution tagged-photon facility MAX-lab located in Lund, Sweden. -
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 -
1 PROF. CHHANDA SAMANTA, Phd PAPERS in PEER REVIEWED INTERNATIONAL JOURNALS: 1. C. Samanta, T. A. Schmitt, “Binding, Bonding A
PROF. CHHANDA SAMANTA, PhD PAPERS IN PEER REVIEWED INTERNATIONAL JOURNALS: 1. C. Samanta, T. A. Schmitt, “Binding, bonding and charge symmetry breaking in Λ- hypernuclei”, arXiv:1710.08036v2 [nucl-th] (to be published) 2. T. A. Schmitt, C. Samanta, “A-dependence of -bond and charge symmetry energies”, EPJ Web Conf. 182, 03012 (2018) 3. Chhanda Samanta, Superheavy Nuclei to Hypernuclei: A Tribute to Walter Greiner, EPJ Web Conf. 182, 02107 (2018) 4. C. Samanta with X Qiu, L Tang, C Chen, et al., “Direct measurements of the lifetime of medium-heavy hypernuclei”, Nucl. Phys. A973, 116 (2018); arXiv:1212.1133 [nucl-ex] 5. C. Samanta with with S. Mukhopadhyay, D. Atta, K. Imam, D. N. Basu, “Static and rotating hadronic stars mixed with self-interacting fermionic Asymmetric Dark Matter”, The European Physical Journal C.77:440 (2017); arXiv:1612.07093v1 6. C. Samanta with R. Honda, M. Agnello, J. K. Ahn et al, “Missing-mass spectroscopy with 6 − + 6 the Li(π ,K )X reaction to search for ΛH”, Phys. Rev. C 96, 014005 (2017); arXiv:1703.00623v2 [nucl-ex] 7. C. Samanta with T. Gogami, C. Chen, D. Kawama et al., “Spectroscopy of the neutron-rich 7 hypernucleus He from electron scattering”, Phys. Rev. C94, 021302(R) (2016); arXiv:1606.09157 8. C. Samanta with T. Gogami, C. Chen, D. Kawama,et al., ”High Resolution Spectroscopic 10 Study of ΛBe”, Phys. Rev. C93, 034314(2016); arXiv:1511.04801v1[nucl-ex] 9. C. Samanta with L. Tang, C. Chen, T. Gogami et al., “The experiments with the High 12 Resolution Kaon Spectrometer at JLab Hall C and the new spectroscopy of ΛB hypernuclei, Phys. -
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 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 -
Nuclear Models:Shell Structure and the Extension of the Periodic System- Walter Greiner, Joachim
FUNDAMENTALS OF PHYSICS – Vol. III - Nuclear Models:Shell Structure And The Extension Of The Periodic System- Walter Greiner, Joachim. A. Maruhn, and Thomas Bürvenich NUCLEAR MODELS: SHELL STRUCTURE AND THE EXTENSION OF THE PERIODIC SYSTEM Walter Greiner, Joachim. A. Maruhn, and Thomas Bürvenich Institut für Theoretische Physik, J.W. Goethe-Universität, Frankfurt, Germany Keywords: superheavy elements, nuclear fission, cold valleys, magic numbers, cluster radioactivity, hyper nuclei, antimatter production, structure of the vacuum Contents 1. Introduction 2. Cold valleys in the potential 3. Shell structure in the superheavy region 4. Asymmetric and superasymmetric fission – cluster radioactivity 5. Fission observed with the gamma-sphere: long living nuclear molecules 6. Extension of the periodic system into the sections of hyper- and antimatter 7. Concluding remarks – outlook Glossary Bibliography Biographical Sketches Summary The extension of the periodic system into various new areas is investigated. Experiments for the synthesis of superheavy elements and the predictions of magic numbers are reviewed. Different ways of nuclear decay are discussed like cluster radioactivity, cold fission and cold multifragmentation, including the recent discovery of the triple fission of 252 Cf . Further on, investigations on hypernuclei and the possible production of antimatter-clusters in heavy ion collisions are reported. Various versions of the meson field theory serve as effective field theories as the basis of modern nuclear structure and suggest structure in the vacuum which might be important for the production of hyper- and antimatter. A perspective for future research is given. 1. IntroductionUNESCO – EOLSS There are fundamental questions in science, like e.g. “how did life emerge” or “how does our brain work”SAMPLE and others. -
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. -
Stefan Schramm Mirko Schäfer Editors New Horizons in Fundamental Physics FIAS Interdisciplinary Science Series
FIAS Interdisciplinary Science Series Series Editor: Walter Greiner Stefan Schramm Mirko Schäfer Editors New Horizons in Fundamental Physics FIAS Interdisciplinary Science Series Editor-in-chief Walter Greiner, Frankfurt am Main, Germany Editorial Board Ernst Bamberg, Frankfurt am Main, Germany Marc Thilo Figge, Jena, Germany Thomas Haberer, Heidelberg, Germany Volker Lindenstruth, Frankfurt am Main, Germany Joachim Reinhardt, Frankfurt, Germany Klaus Schulten, Urbana, USA Wolf Singer, Frankfurt am Main, Germany Horst Stöcker, Darmstadt, Germany The Frankfurt Institute for Advanced Studies (FIAS) is an independent research institute pursuing cutting-edge theoretical research in the areas of physics, life-science and chemistry, neuroscience, and computer science. A central aim of FIAS is to foster interdisciplinary co-operation and to provide a common platform for the study of the structure and dynamics of complex systems, both animate and inanimate. FIAS closely cooperates with the science faculties of Goethe University (Frankfurt) and with various experimentally oriented research centers in the vicinity. The series is meant to highlight the work of researchers at FIAS and its partner institutions, illustrating current progress and also reflecting on the historical development of science. The series comprises monographs on specialized current research topics, reviews summarizing the state of research in more broadly-framed areas, and volumes of conferences organized by FIAS. More information about this series at http://www.springer.com/series/10781 -
Fundamental Study of Compton Scattering Tomography
FUNDAMENTAL STUDY OF COMPTON SCATTERING TOMOGRAPHY R. XIAO, S. SATO, C. UYAMAf, and T. NAKAMURAJ Department of Biophysical Engineering, Faculty of Engineering Science, Osaka University \ Department of Investigative Radiology, National Cardiovascular Center Research Institute \Cyclotron and Radioisotope Center, Tohoku University 1. Introduction Compton scattering tomography is an imaging technique that forms tomographic im ages corresponding to distribution of electron densities in an X-rays or 7-rays1 irradiating object by measuring Compton scattered photons emitted out of it. Because of its advan tage of free choice of measurement geometry, Compton scattering tomography is useful for inspection of defects inside huge objects in industry where X-rays or 7-rays can hardly pen etrate the objects[l]. For medical usage, Compton scattered rays are used for densitometry of bone or other tissues. Compton scattering tomographic images, in which densities of body other than attenuation coefficients of body can be shown, are meaningful for medical diagnoses. Before building a real Compton scattering tomography system for medical applica tions, we made some fundamental observations upon Compton scattering imaging process through Monte Carlo simulation in order to testify feasibility of the imaging and to seek for an available scheme of system design. EGS4 code system[2] is used for simulation of transport processes of photons in an imaged object. Multiple scattering, one of factors that influence quantity of Compton scattering images, is evaluated here. Some methods to overcome multiple scattering are proposed and their effects are discussed below. 2. Principle of Compton scattering tomography A beam of X-rays or 7-rays attenuates in its intensity by interactions of photoelectric absorption, Compton scattering, Rayleigh scattering and electron-positron pair production while it is passing through an object. -
Lecture 18 Quantum Electrodynamics
Lecture 18 Quantum Electrodynamics Quantum Electrodynamics (QED) describes a U(1) gauge theory coupled to a fermion, e.g. the electron, muon or any other charged particle. As we saw previously the lagrangian for such theory is 1 L = ¯(iD6 − m) − F F µν ; (18.1) 4 µν where the covariant derivative is defined as Dµ (x) = (@µ + ieAµ(x)) (x) ; (18.2) resulting in 1 L = ¯(i6@ − m) − F F µν − eA ¯γµ ; (18.3) 4 µν µ where the last term is the interaction lagrangian and thus e is the photon-fermion cou- pling. We would like to derive the Feynman rules for this theory, and then compute the amplitudes and cross sections for some interesting processes. 18.1 Feynman Rules for QED In addition to the rules for the photon and fermion propagator, we now need to derive the Feynman rule for the photon-fermion vertex. One way of doing this is to use the generating functional in presence of linearly coupled external sources Z ¯ R 4 µ ¯ ¯ iS[ ; ;Aµ]+i d xfJµA +¯η + ηg Z[η; η;¯ Jµ] = N D D DAµ e : (18.4) 1 2 LECTURE 18. QUANTUM ELECTRODYNAMICS From it we can derive a three-point function with an external photon, a fermion and an antifermion. This is given by 3 3 (3) (−i) δ Z[η; η;¯ Jµ] G (x1; x2; x3) = ; (18.5) Z[0; 0; 0] δJ (x )δη(x )δη¯(x ) µ 1 2 3 Jµ,η;η¯=0 which, when we expand in the interaction term, results in 1 Z ¯ G(3)(x ; x ; x ) = D ¯ D DA eiS0[ ; ;Aµ]A (x ) ¯(x ) (x ) 1 2 3 Z[0; 0; 0] µ µ 1 2 3 Z 4 ¯ ν × 1 − ie d yAν(y) (y)γ (y) + ::: Z 4 ν = (+ie) d yDF µν(x1 − y)Tr [SF(x3 − y)γ SF(x2 − y)] ; (18.6) where S0 is the free action, obtained from the first two terms in (18.3).