DOCSLIB.ORG

Lecture 23 Spectroscopy and Atomic Models

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Lecture 23 Spectroscopy and Atomic Models LECTURE 23 SPECTROSCOPY AND ATOMIC MODELS Instructor: Kazumi Tolich Lecture 23 2 ¨ 29.1 Spectroscopy ¨ 29.2 Atoms ¤ The first nuclear physics experiment ¤ Using the nuclear model ¨ 29.3 Bohr’s model of atomic quantization ¨ 29.4 The Bohr hydrogen atom ¤ The stationary states of the hydrogen atom ¤ Hydrogen atom energy levels ¤ The hydrogen spectrum 29.1 Spectroscopy / demo ¨ A spectrum is recorded in a spectrometer. ¨ Self-luminous objects emit a continuous spectrum that depends on the temperature. ¨ Individual atoms produce atomic spectrum, a discrete spectrum with spectral lines. ¨ Gases also absorb discrete wavelengths. ¨ Demo: line spectra Quiz 29.1-1 ¨ These spectra are from the same element. Which is an emission spectrum, which an absorption spectrum? A. Top is emission; bottom absorption. B. Top is absorption; bottom emission. C. Can’t tell without knowing the element. Quiz 29.1-1 answer ¨ Top is emission; bottom absorption. ¨ Every wavelength that is absorbed by the gas is also emitted, but not every emitted wavelength is absorbed. Spectroscopy ¨ Balmer formula represents the wavelengths of the spectral lines of hydrogen. 91.1 nm � = 1 1 − �* �* ¤ where � = 1, 2, 3, … and � can be any integer and � > �. 29.2 Atoms - the raisin-cake model of the atom 7 ¨ J. J. Thomson, soon after discovering electrons, proposed the raisin-cake model of the atom (“plum-pudding model” actually). ¤ It was known that electrons are much smaller and less massive than atoms. ¨ The first observations that atoms have an inner structure came from beta rays and alpha rays emitted from uranium crystal. ¤ Beta rays are high-speed electrons emitted by uranium. ¤ Alpha rays (now called alpha particles) consist of helium nuclei, with mass � = 6.64 ×106*7 kg, emitted at high speed from a sample. 29.2 The first nuclear physics experiment 8 ¨ The discovery of large-angle scattering of alpha particles led to the nuclear model of the atom in which negative electrons orbit a small, massive, positive nucleus. 29.2 Using the nuclear model 9 ¨ In the nuclear model, an atom has a nucleus with positively charged protons and neutral neutrons, and negatively charged electrons are orbiting around it. ¨ Protons and neutrons are both much more massive than electrons. ¨ Orbiting electrons are very light and can be easily knocked off, creating a positive ion. Quiz: 29.3-1 10 ¨ Is there something wrong with the nuclear model (like a miniature solar system) of the atom? If so, what is wrong? Choose all that apply. A. No. Everything is fine with the model. B. Yes. Nothing is providing orbiting electrons the centripetal force. C. Yes. Orbiting electrons would collapse into the nucleus in a very short time. D. Yes. The frequency of radiation emitted by an orbiting electron would not agree with the emission spectra. Quiz: 29.3-1 answer 11 ¨ Yes. Orbiting electrons would collapse into the nucleus in a very short time. ¨ Yes. The frequency of radiation emitted by an orbiting electron would not agree with the emission spectra. ¨ The coulomb force by the nucleus is providing orbiting electrons the centripetal force. ¨ The frequency of radiation emitted by a continuously radiating electron would have a continuous spectrum, rather than the individual frequencies that are actually observed. 29.3 Bohr’s model of atomic quantization 12 ¨ Bohr model of the atom: ¤ An electron in an atom can exist only in a stationary state. ¤ Each stationary state has a discrete well- defined energy. ¤ An atom can undergo a transition by emitting or absorbing a photon with an energy equal to the difference in the energies of the states: �9:;<;= = �> − �? = ℎ�. ¤ An atom can be exited by absorbing energy in collision (collisional excitation). Quiz: 29.3-2 ¨ An atom has the energy levels shown. A photon with a wavelength of 620 nm has an energy of 2.0 eV. Do you expect to see a spectral line with wavelength of 620 nm in this atom’s absorption spectrum? A. Yes B. No C. There’s not enough information to tell. Quiz: 29.3-2 answer ¨ No ¨ Absorption occurs from the ground state, in which nearly all the atoms are. ¨ No quantum jump from the ground state has ∆�C<;D = 2.0 eV. ¨ Every wavelength that is emitted by gas is not absorbed. Emission transitions Absorption transitions Quiz: 29.3-3 ¨ An atom has the energy levels shown. A beam of electrons with 5.5 eV kinetic energy collides with a gas of these atoms in the ground state. How many spectral lines will be seen? Quiz: 29.3-3 answer ¨ An atom has the energy levels shown. A beam of electrons with 5.5 eV kinetic energy collides with a gas of these atoms in the ground state. How many spectral lines will be seen? ¨ 3 ¨ A 5.5 eV electron can excite either the � = 2 or the � = 3 energy level. Quiz: 29.4-1 17 ¨ De Broglie showed that the allowed orbits of the Bohr model correspond to standing matter wave of the electrons. What is the relationship between the wavelengths of the electrons in an atom and the circumferences of the allowed orbits? A. The circumference must be an integer multiple of �. E B. The circumference must be an odd integer multiple of . * C. There is not relationship between the circumference and �. Quiz: 29.4-1 answer 18 ¨ The circumference must be an integer multiple of �. ¨ The circumference of an allowed orbit is 2�� = ��, � = 1, 2, 3, ⋯. 29.4 The stationary states of the hydrogen atom 19 ¨ The allowed radii of the electron’s orbit in a hydrogen atom is * �I = � �K ¤ � = 1, 2, 3, ⋯ ¤ �K = 0.0529 nm is the Bohr radius. ¨ The possible orbits are quantized. 29.4 Hydrogen atom energy levels 20 ¨ There is an energy level in a hydrogen atom corresponding to each allowed state radius. � 13.6 eV � = − M = − I �* �* ¤ � = 1, 2, 3, ⋯ Quiz: 29.4-2 21 ¨ How much energy in eV does it take to ionize a hydrogen atom in its ground state? Quiz: 29.4-2 answer 22 ¨ 13.6 eV ¨ When a hydrogen atom in the ground state absorbs 13.6 eV of energy, the electron makes a transition to � = ∞ state (ionization limit), which means that the electron is no longer associated to the nucleus. 29.4 The hydrogen spectrum ¨ The Bohr hydrogen atom with discrete energy levels correctly predicts the discrete spectrum of the hydrogen atom..
Load more

Recommended publications
  • Unit 1 Old Quantum Theory
    UNIT 1 OLD QUANTUM THEORY Structure Introduction Objectives li;,:overy of Sub-atomic Particles Earlier Atom Models Light as clectromagnetic Wave Failures of Classical Physics Black Body Radiation '1 Heat Capacity Variation Photoelectric Effect Atomic Spectra Planck's Quantum Theory, Black Body ~diation. and Heat Capacity Variation Einstein's Theory of Photoelectric Effect Bohr Atom Model Calculation of Radius of Orbits Energy of an Electron in an Orbit Atomic Spectra and Bohr's Theory Critical Analysis of Bohr's Theory Refinements in the Atomic Spectra The61-y Summary Terminal Questions Answers 1.1 INTRODUCTION The ideas of classical mechanics developed by Galileo, Kepler and Newton, when applied to atomic and molecular systems were found to be inadequate. Need was felt for a theory to describe, correlate and predict the behaviour of the sub-atomic particles. The quantum theory, proposed by Max Planck and applied by Einstein and Bohr to explain different aspects of behaviour of matter, is an important milestone in the formulation of the modern concept of atom. In this unit, we will study how black body radiation, heat capacity variation, photoelectric effect and atomic spectra of hydrogen can be explained on the basis of theories proposed by Max Planck, Einstein and Bohr. They based their theories on the postulate that all interactions between matter and radiation occur in terms of definite packets of energy, known as quanta. Their ideas, when extended further, led to the evolution of wave mechanics, which shows the dual nature of matter
    [Show full text]
  • Comparing the Emission Spectra of U and Th Hollow Cathode Lamps and a New U Line-List
    Astronomy & Astrophysics manuscript no. HCL_U_Th_Ull_S2018 c ESO 2018 October 1, 2018 Comparing the emission spectra of U and Th hollow cathode lamps and a new U line-list L. F. Sarmiento1,⋆, A. Reiners1, P. Huke1, F. F. Bauer1, E. W. Guenter2,3, U. Seemann1, and U. Wolter4 1 Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany 2 Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg, Germany 3 Instituto de Astrofísica de Canarias (IAC), 38205 La Laguna, Tenerife, Spain 4 Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany Received , 22 February 2018; accepted , 5 June 2018 ABSTRACT Context. Thorium hollow cathode lamps (HCLs) are used as frequency calibrators for many high resolution astronomical spectro- graphs, some of which aim for Doppler precision at the 1 m/s level. Aims. We aim to determine the most suitable combination of elements (Th or U, Ar or Ne) for wavelength calibration of astronomical spectrographs, to characterize differences between similar HCLs, and to provide a new U line-list. Methods. We record high resolution spectra of different HCLs using a Fourier transform spectrograph: (i) U-Ne, U-Ar, Th-Ne, and Th-Ar lamps in the spectral range from 500 to 1000 nm and U-Ne and U-Ar from 1000 to 1700 nm; (ii) we systematically compare the number of emission lines and the line intensity ratio for a set of 12 U-Ne HCLs; and (iii) we record a master spectrum of U-Ne to create a new U line-list. Results. Uranium lamps show more lines suitable for calibration than Th lamps from 500 to 1000 nm.
    [Show full text]
  • Mössbauer Spectroscopy 9.1 Recoil Free Resonance Absorption
    Chapter 9, page 1 9 Mössbauer Spectroscopy 9.1 Recoil free resonance absorption Robert Wood published in 1905 an article "Resonance Radiation of Sodium Vapor" (see Literature) and reported that if a bulb containing pure sodium vapor was illuminated by light from a sodium flame, the vapor emitted a yellow light which spectroscopic analysis showed to be identical with the exciting light, in other words, the two D lines. Sodium is liquid above 98 °C, boiling point 883 °C, thus a remarkable vapor pressure exists, if sodium is heated by the Fig. 9.1: Wood's apparatus for the Bunsen burner above 200 °C. Wood used the name resonance radiation of the sodium "resonance radiation" for the effect of identical D lines. absorbed radiation and fluorescence radiation. Now we use the term "resonance absorption" instead. Since 1900 γ-rays were known as a highly energetic monochromatic radiation, but the anticipated γ-ray resonance fluorescence failed to occur. Werner Kuhn succeeded in publishing such an experiment that don't work and argued in 1929: "The (third) influence, reducing the absorption, arises from the emission process of the γ-rays. The emitting atom will suffer recoil due to the projection of the γ-ray. The wavelength of the radiation is therefore shifted to the red; the emission line is displaced relative to the absorption line.... It is thus possible that by a large γ-shift, the whole emission line is brought out of the absorption region”. (see Literature, Kuhn) Intensity In the case of γ-radiation the atoms suffer recoil, which is not significant for radiation in the visible range, were the recoil energy is small compared with the linewidth of the h δν1/2 radiation (times h), see Fig.
    [Show full text]
  • Discrete-Continuous and Classical-Quantum
    Under consideration for publication in Math. Struct. in Comp. Science Discrete-continuous and classical-quantum T. Paul C.N.R.S., D.M.A., Ecole Normale Sup´erieure Received 21 November 2006 Abstract A discussion concerning the opposition between discretness and continuum in quantum mechanics is presented. In particular this duality is shown to be present not only in the early days of the theory, but remains actual, featuring different aspects of discretization. In particular discreteness of quantum mechanics is a key-stone for quantum information and quantum computation. A conclusion involving a concept of completeness linking dis- creteness and continuum is proposed. 1. Discrete-continuous in the old quantum theory Discretness is obviously a fundamental aspect of Quantum Mechanics. When you send white light, that is a continuous spectrum of colors, on a mono-atomic gas, you get back precise line spectra and only Quantum Mechanics can explain this phenomenon. In fact the birth of quantum physics involves more discretization than discretness : in the famous Max Planck’s paper of 1900, and even more explicitly in the 1905 paper by Einstein about the photo-electric effect, what is really done is what a computer does: an integral is replaced by a discrete sum. And the discretization length is given by the Planck’s constant. This idea will be later on applied by Niels Bohr during the years 1910’s to the atomic model. Already one has to notice that during that time another form of discretization had appeared : the atomic model. It is astonishing to notice how long it took to accept the atomic hypothesis (Perrin 1905).
    [Show full text]
  • Stark Broadening of Spectral Lines in Plasmas
    atoms Stark Broadening of Spectral Lines in Plasmas Edited by Eugene Oks Printed Edition of the Special Issue Published in Atoms www.mdpi.com/journal/atoms Stark Broadening of Spectral Lines in Plasmas Stark Broadening of Spectral Lines in Plasmas Special Issue Editor Eugene Oks MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editor Eugene Oks Auburn University USA Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Atoms (ISSN 2218-2004) in 2018 (available at: https://www.mdpi.com/journal/atoms/special issues/ stark broadening plasmas) For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03897-455-0 (Pbk) ISBN 978-3-03897-456-7 (PDF) Cover image courtesy of Eugene Oks. c 2018 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editor ...................................... vii Preface to ”Stark Broadening of Spectral Lines in Plasmas” ..................... ix Eugene Oks Review of Recent Advances in the Analytical Theory of Stark Broadening of Hydrogenic Spectral Lines in Plasmas: Applications to Laboratory Discharges and Astrophysical Objects Reprinted from: Atoms 2018, 6, 50, doi:10.3390/atoms6030050 ...................
    [Show full text]
  • A 2-Ghz Discrete-Spectrum Waveband-Division Microscopic Imaging System
    Optics Communications 338 (2015) 22–26 Contents lists available at ScienceDirect Optics Communications journal homepage: www.elsevier.com/locate/optcom A 2-GHz discrete-spectrum waveband-division microscopic imaging system Fangjian Xing, Hongwei Chen n, Cheng Lei, Minghua Chen, Sigang Yang, Shizhong Xie Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Electronic Engineering, Tsinghua University, Beijing 100084, P.R. China article info abstract Article history: Limited by dispersion-induced pulse overlap, the frame rate of serial time-encoded amplified microscopy Received 26 June 2014 is confined to the megahertz range. Replacing the ultra-short mode-locked pulse laser by a multi-wa- Received in revised form velength source, based on waveband-division technique, a serial time stretch microscopic imaging sys- 1 September 2014 tem with a line scan rate of in the gigahertz range is proposed and experimentally demonstrated. In this Accepted 4 September 2014 study, we present a surface scanning imaging system with a record line scan rate of 2 GHz and 15 pixels. Available online 22 October 2014 Using a rectangular spectrum and a sufficiently large wavelength spacing for waveband-division, the Keywords: resulting 2D image is achieved with good quality. Such a superfast imaging system increases the single- Real-time imaging shot temporal resolution towards the sub-nanosecond regime. Ultrafast & 2014 Elsevier B.V. All rights reserved. Discrete spectrum Wavelength-to-space-to-time mapping GHz imaging 1. Introduction elements with a broadband mode-locked laser to achieve ultrafast single pixel imaging. An important feature of STEAM is the spec- Most of the current research in optical microscopic imaging trum of the broadband laser source.
    [Show full text]
  • Quantitative Analysis of Cerium-Gallium Alloys Using a Hand-Held Laser Induced Breakdown Spectroscopy Device
    atoms Article Quantitative Analysis of Cerium-Gallium Alloys Using a Hand-Held Laser Induced Breakdown Spectroscopy Device Ashwin P. Rao 1 , Matthew T. Cook 2 , Howard L. Hall 2,3 and Michael B. Shattan 1,* 1 Air Force Institute of Technology, 2950 Hobson Way, WPAFB, OH 45433, USA 2 Institute for Nuclear Security, University of Tennessee, Knoxville, TN 37996, USA 3 Department of Nuclear Engineering, University of Tennessee, Knoxville, TN 37996, USA * Correspondence: michael.shattan@afit.edu Received: 26 July 2019; Accepted: 20 August 2019; Published: 22 August 2019 Abstract: A hand-held laser-induced breakdown spectroscopy device was used to acquire spectral emission data from laser-induced plasmas created on the surface of cerium-gallium alloy samples with Ga concentrations ranging from 0–3 weight percent. Ionic and neutral emission lines of the two constituent elements were then extracted and used to generate calibration curves relating the emission line intensity ratios to the gallium concentration of the alloy. The Ga I 287.4-nm emission line was determined to be superior for the purposes of Ga detection and concentration determination. A limit of detection below 0.25% was achieved using a multivariate regression model of the Ga I 287.4-nm line ratio versus two separate Ce II emission lines. This LOD is considered a conservative estimation of the technique’s capability given the type of the calibration samples available and the low power (5 mJ per 1-ns pulse) and resolving power (l/Dl = 4000) of this hand-held device. Nonetheless, the utility of the technique is demonstrated via a detailed mapping analysis of the surface Ga distribution of a Ce-Ga sample, which reveals significant heterogeneity resulting from the sample production process.
    [Show full text]
  • Emission Mössbauer Spectroscopy at ISOLDE/CERN
    Emission Mössbauer Spectroscopy at ISOLDE/CERN Torben Esmann Mølholt ISOLDE Seminar, 25. Nov. 2015 Outline Experimental setup at ISOLDE Brief on the Mössbauer spectroscopy technique Examples and Results Future/ongoing measurements 2 Acknowledgements The Mössbauer collaboration at ISOLDE/CERN, >30 active members with new members (2014) from China, Russia, Bulgaria, Austria, Spain: Four experiments Existing members New members 2014 (IS-501, IS-576, IS-578, I-161) 3 Emission Mössbauer Spectroscopy at ISOLDE/CERN http://e-ms.web.cern.ch/ GLM (GPS) LA1-2 (HRS) 4 119In RILIS 2014 2015 57Mn 119 RILIS In 15 μSi/h - 57Mn 10 μSi/h - RILIS 5 μSi/h - 0 μSi/h - 5 Mössbauer Experimental setup Implantation chamber Incoming 60 keV beam Sample Faraday cup Be window Mössbauer drive with resonance detector Container: 25 mbar acetone • Intensity (~1×108 atoms/s) • High statistics spectrum (5 – 10 min.) •On-line (short lived) •Collections for Off-line (long lived) 6 •Hours - days Mössbauer Experimental setup Sample holder •Temperature range 90 – 700 K • Measurements at different emission angles • Applied magnetic field (Bext ≤ 0.6 T) 7 Mössbauer Experimental setup Sample holder • Quenching: Implant at high temperature Measure at low temperature (off-line) 8 Mössbauer Experimental setup Resonance detector - G. Weyer, Mössbauer Eff. Meth., 10 (1976) 301 PPAD: Parallel Plate Avalanche Detector - Single line resonance detector. 0.1 cps (~0.1 µCi) – 50k cps (~500 mCi) 9 Mössbauer spectroscopy technique 10 40-60 keV Ion-implantation of Mössbauer Probe Emission
    [Show full text]
  • Quantum Mechanics in One Dimension
    Solved Problems on Quantum Mechanics in One Dimension Charles Asman, Adam Monahan and Malcolm McMillan Department of Physics and Astronomy University of British Columbia, Vancouver, British Columbia, Canada Fall 1999; revised 2011 by Malcolm McMillan Given here are solutions to 15 problems on Quantum Mechanics in one dimension. The solutions were used as a learning-tool for students in the introductory undergraduate course Physics 200 Relativity and Quanta given by Malcolm McMillan at UBC during the 1998 and 1999 Winter Sessions. The solutions were prepared in collaboration with Charles Asman and Adam Monaham who were graduate students in the Department of Physics at the time. The problems are from Chapter 5 Quantum Mechanics in One Dimension of the course text Modern Physics by Raymond A. Serway, Clement J. Moses and Curt A. Moyer, Saunders College Publishing, 2nd ed., (1997). Planck's Constant and the Speed of Light. When solving numerical problems in Quantum Mechanics it is useful to note that the product of Planck's constant h = 6:6261 × 10−34 J s (1) and the speed of light c = 2:9979 × 108 m s−1 (2) is hc = 1239:8 eV nm = 1239:8 keV pm = 1239:8 MeV fm (3) where eV = 1:6022 × 10−19 J (4) Also, ~c = 197:32 eV nm = 197:32 keV pm = 197:32 MeV fm (5) where ~ = h=2π. Wave Function for a Free Particle Problem 5.3, page 224 A free electron has wave function Ψ(x; t) = sin(kx − !t) (6) •Determine the electron's de Broglie wavelength, momentum, kinetic energy and speed when k = 50 nm−1.
    [Show full text]
  • Glossary of Terms Absorption Line a Dark Line at a Particular Wavelength Superimposed Upon a Bright, Continuous Spectrum
    Glossary of terms absorption line A dark line at a particular wavelength superimposed upon a bright, continuous spectrum. Such a spectral line can be formed when electromag- netic radiation, while travelling on its way to an observer, meets a substance; if that substance can absorb energy at that particular wavelength then the observer sees an absorption line. Compare with emission line. accretion disk A disk of gas or dust orbiting a massive object such as a star, a stellar-mass black hole or an active galactic nucleus. An accretion disk plays an important role in the formation of a planetary system around a young star. An accretion disk around a supermassive black hole is thought to be the key mecha- nism powering an active galactic nucleus. active galactic nucleus (agn) A compact region at the center of a galaxy that emits vast amounts of electromagnetic radiation and fast-moving jets of particles; an agn can outshine the rest of the galaxy despite being hardly larger in volume than the Solar System. Various classes of agn exist, including quasars and Seyfert galaxies, but in each case the energy is believed to be generated as matter accretes onto a supermassive black hole. adaptive optics A technique used by large ground-based optical telescopes to remove the blurring affects caused by Earth’s atmosphere. Light from a guide star is used as a calibration source; a complicated system of software and hardware then deforms a small mirror to correct for atmospheric distortions. The mirror shape changes more quickly than the atmosphere itself fluctuates.
    [Show full text]
  • Class 2: Operators, Stationary States
    Class 2: Operators, stationary states Operators In quantum mechanics much use is made of the concept of operators. The operator associated with position is the position vector r. As shown earlier the momentum operator is −iℏ ∇ . The operators operate on the wave function. The kinetic energy operator, T, is related to the momentum operator in the same way that kinetic energy and momentum are related in classical physics: p⋅ p (−iℏ ∇⋅−) ( i ℏ ∇ ) −ℏ2 ∇ 2 T = = = . (2.1) 2m 2 m 2 m The potential energy operator is V(r). In many classical systems, the Hamiltonian of the system is equal to the mechanical energy of the system. In the quantum analog of such systems, the mechanical energy operator is called the Hamiltonian operator, H, and for a single particle ℏ2 HTV= + =− ∇+2 V . (2.2) 2m The Schrödinger equation is then compactly written as ∂Ψ iℏ = H Ψ , (2.3) ∂t and has the formal solution iHt Ψ()r,t = exp − Ψ () r ,0. (2.4) ℏ Note that the order of performing operations is important. For example, consider the operators p⋅ r and r⋅ p . Applying the first to a wave function, we have (pr⋅) Ψ=−∇⋅iℏ( r Ψ=−) i ℏ( ∇⋅ rr) Ψ− i ℏ( ⋅∇Ψ=−) 3 i ℏ Ψ+( rp ⋅) Ψ (2.5) We see that the operators are not the same. Because the result depends on the order of performing the operations, the operator r and p are said to not commute. In general, the expectation value of an operator Q is Q=∫ Ψ∗ (r, tQ) Ψ ( r , td) 3 r .
    [Show full text]
  • Arxiv:Cond-Mat/0404626V1
    LA-UR-03-8735 Nuclear Magnetic Resonance Studies of δ-Stabilized Plutonium N. J. Curro Condensed Matter and Thermal Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, [email protected] L. Morales Nuclear Materials and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (Dated: July 14, 2018) Nuclear Magnetic Resonance studies of Ga stabilized δ-Pu reveal detailed information about the local distortions surrounding the Ga impurities as well as provides information about the local spin fluctuations experienced by the Ga nuclei. The Ga NMR spectrum is inhomogeneously broadened by a distribution of local electric field gradients (EFGs), which indicates that the Ga experiences local distortions from cubic symmetry. The Knight shift and spin lattice relaxation rate indicate that the Ga is dominantly coupled to the Fermi surface via core polarization, and is inconsistent with magnetic order or low frequency spin correlations. Introduction tuations of of the electron spin S relax the nuclei so fast that their signal is rendered invisible. On the other hand, The investigavtion of the low temperature properties the hyperfine coupling to the nuclei of the secondary el- of plutonium and its compounds has experienced a re- ement (Al, Ga or In) are typically one to three orders of naissance in recent years, and several important experi- magnitude smaller, so by measuring the secondary nuclei ments have revealed unusual correlated electron behavior one can gain considerable insight into the spin dynamics [1, 2, 3]. The 5f electrons in elemental plutonium are on of the system. the boundary between localized and itinerant behavior, One of the challenges facing band theorists calculating so that slight perturbations in the Pu-Pu spacing can give the electronic structure of δ-Pu is the role of the sec- rise to dramatic changes in the ground state character.
    [Show full text]