DOCSLIB.ORG

5. Atomic Radiation Processes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
5. Atomic Radiation Processes 5. Atomic radiation processes Einstein coefficients for absorption and emission oscillator strength line profiles: damping profile, collisional broadening, Doppler broadening continuous absorption and scattering 1 2 A. Line transitions Einstein coefficients probability that a photon in frequency interval in the solid angle range is absorbed by an atom in the energy level El with a resulting transition El à Eu per second: atomic property ~ no. of incident probability for probability for photons absorption of with photon with probability for absorption transition l à u profile Blu: Einstein coefficient for absorption 3 Einstein coefficients similarly for stimulated emission Bul: Einstein coefficient for stimulated emission and for spontaneous emission Aul: Einstein coefficient for spontaneous emission 4 Einstein coefficients, absorption and emission coefficients Number of absorptions & stimulated emissions dF dV = dF ds Iν in dV per second: ds absorbed energy in dV per second: stimulated emission counted as negative absorption and also (using definition of intensity): Absorption and emission coefficients are a function of Einstein coefficients, occupation numbers and line broadening for the spontaneously emitted energy: 5 Relations between Einstein coefficients Einstein coefficients are atomic properties à do not depend on thermodynamic state of matter We can assume TE: From the Boltzmann formula: for hν/kT << 1: for T à ∞ 0 6 Relations between Einstein coefficients for T à ∞ Note: Einstein coefficients atomic quantities. That means any relationship that holds in a special thermodynamic situation (such as T very large) must be generally valid. only one Einstein coefficient needed 7 Oscillator strength Quantum mechanics The Einstein coefficients can be calculated by quantum mechanics + classical electrodynamics calculation. Eigenvalue problem using using wave function: Consider a time-dependent perturbation such as an external iωt electromagnetic field (light wave) E(t) = E0 e . The potential of the time dependent perturbation on the atom is: d: dipol operator with transition probability 8 Oscillator strength The result is flu: oscillator strength (dimensionless) classical result from electrodynamics = 0.02654 cm2/s Classical electrodynamics electron quasi-elastically bound to nucleus and oscillates within outer electric field as E. Equation of motion (damped harmonic oscillator): ma = damping force + restoring force + EM force the electron oscillates preferentially at resonance (incoming radiation ν = ν ) damping 0 constant resonant The damping is caused, because the de- and accelerated electron radiates (natural) frequency 9 Classical cross section and oscillator strength Calculating the power absorbed by the oscillator, the integrated “classical” absorption coefficient and cross section, and the absorption line profile are found: 2 σ cl: classical ¼e nl: number tot L,cl cl density of cross section integrated over the line profile ·º dº = nl = nl ¾tot m c absorbers (cm2/s) Z e 1 °/4¼ '(º)dº = [Lorentz (damping) line profile] ¼ (º º )2 + (°/4¼)2 ¡ 0 oscillator strength flu is quantum mechanical correction to classical result (effective number of classical oscillators, ≈ 1 for strong resonance lines) From (neglecting stimulated emission) 10 Oscillator strength absorption cross section; dimension is cm2 Oscillator strength (f-value) is different for each atomic transition Values are determined empirically in the laboratory or by elaborate numerical atomic physics calculations Semi-analytical calculations possible in simplest cases, e.g. hydrogen g: Gaunt factor Hα: f=0.6407 Hβ: f=0.1193 Hγ: f=0.0447 11 Line profiles line profiles contain information on physical conditions of the gas and chemical abundances analysis of line profiles requires knowledge of distribution of opacity with frequency several mechanisms lead to line broadening (no infinitely sharp lines) - natural damping: finite lifetime of atomic levels - collisional (pressure) broadening: impact vs quasi-static approximation - Doppler broadening: convolution of velocity distribution with atomic profiles 12 1. Natural damping profile finite lifetime of atomic levels à line width NATURAL LINE BROADENING OR RADIATION DAMPING -8 t = 1 / Aul (¼ 10 s in H atom 2 à 1): finite lifetime with respect to spontaneous emission Δ E t ≥ h/2π uncertainty principle Δν1/2 = Γ / 2π 2 Δλ1/2 = Δν1/2λ /c line broadening -4 e.g. Ly α: Δλ1/2 = 1.2 10 A -4 1 ¡/4¼ Hα: Δλ1/2 = 4.6 10 A '(º) = ¼ (º º )2 + (¡/4¼)2 ¡ 0 Lorentzian profile 13 Natural damping profile resonance line excited line natural line broadening is important for strong lines (resonance lines) at low densities (no additional broadening mechanisms) e.g. Ly α in interstellar medium but also in stellar atmospheres 14 2. Collisional broadening radiating atoms are perturbed by the electromagnetic field of neighbour atoms, ions, electrons, molecules energy levels are temporarily modified through the Stark - effect: perturbation is a function of separation absorber-perturber energy levels affected à line shifts, asymmetries & broadening n ΔE(t) = h Δν = C/r (t) r: distance to perturbing atom a) impact approximation: radiating atoms are perturbed by passing particles at distance r(t). Duration of collision << lifetime in level à lifetime shortened à line broader in all cases a Lorentzian profile is obtained (but with larger total Γ than only natural damping) b) quasi-static approximation: applied when duration of collisions >> life time in level à consider stationary distribution of perturbers 15 Collisional broadening n = 2 linear Stark effect ΔE ~ F for levels with degenerate angular momentum (e.g. HI, HeII) field strength F ~ 1/r2 à ΔE ~ 1/r2 important for H I lines, in particular in hot stars (high number density of free electrons and ions). However , for ion collisional broadening the quasi-static broadening is also important for strong lines (see below) à Γe ~ ne n = 3 resonance broadening atom A perturbed by atom A’ of same species important in cool stars, e.g. Balmer lines in the Sun à Γ ~ n à ΔE ~ 1/r3 e e 16 Collisional broadening n = 4 quadratic Stark effect ΔE ~ F2 field strength F ~ 1/r2 à ΔE ~ 1/r4 (no dipole moment) - important for metal ions broadened by e in hot stars à Lorentz profile with Γe ~ ne n = 6 van der Waals broadening atom A perturbed by atom B Γ important in cool stars, e.g. Na perturbed by H in the Sun à e ~ ne 17 Quasi-static approximation tperturbation >> τ = 1/Aul à perturbation practically constant during emission or absorption atom radiates in a statistically fluctuating field produced by ‘quasi-static’ perturbers, e.g. slow-moving ions given a distribution of perturbers à field at location of absorbing or emitting atom statistical frequency of particle distribution à probability of fields of different strength (each producing an energy shift ΔE = h Δν) à field strength distribution function à line broadening Linear Stark effect of H lines can be approximated to 0st order in this way 18 Quasi-static approximation for hydrogen line broadening Line broadening profile function determined by probability function for electric field caused by all other particles as seen by the radiating atom. W(F) dF: probability that field seen by radiating atom is F For calculating W(F)dF we use as a first step the nearest-neighbor approximation: main effect from nearest particle 19 Quasi-static approximation – nearest neighbor approximation assumption: main effect from nearest particle (F ~ 1/r2) we need to calculate the probability that nearest neighbor is in the distance range (r,r+dr) = probability that none is at distance < r and one is in (r,r+dr) Integral equation for W(r) differentiating à differential equation relative probability for particle in shell (r,r+dr) probability for no particle in (0,r) N: particle density Differential equation Normalized solution 20 Linear Stark effect: Quasi-static approximation mean interparticle distance: normal field strength: F r 2 note: at high particle density à large F define: ¯ = = 0 0 F { r } à stronger broadening 0 from W(r) dr à W(β) dβ: Stark broadened line profile in the wings, not Δλ-2 as for natural or impact broadening 21 Quasi-static approximation – advanced theory complete treatment of an ensemble of particles: Holtsmark theory + interaction among perturbers (Debye shielding of the potential at distances > Debye length) Holtsmark (1919), 2¯ 1 y3/2 W(¯) = e¡ y sin(¯y)dy Chandrasekhar (1943, Phys. Rev. 15, 1) ¼ Z0 Ecker (1957, Zeitschrift f. Physik, 148, 593 & 149,245) 4/3 2¯± 1 ±g(y) 2/3 W(¯) = e¡ y sin(± ¯y)dy ¼ 0 number of particles Z inside Debye sphere 2 3/2 1 1 5/2 g(y) = y (1 z¡ sinz)z¡ dz 3 ¡ Zy 1/2 T Debye length, field of ion vanishes D = 4.8 cm beyond D ne 4¼ ± = D3N number of particles inside Debye sphere Mihalas, 78! 3 22 3. Doppler broadening radiating atoms have thermal velocity Maxwellian distribution: Doppler effect: atom with velocity v emitting at frequency , observed at frequency : 23 Doppler broadening Define the velocity component along the line of sight: The Maxwellian distribution for this component is: thermal velocity if we observe at v, an atom with velocity component ξ absorbs at ν′ in its frame if v/c <<1 à line center 24 Doppler broadening line profile for v = 0 à profile for v ≠ 0 New line profile: convolution profile function in rest velocity distribution frame function 25 Doppler broadening: sharp line approximation : Doppler width of the line thermal velocity Approximation 1: assume a sharp line – half width of profile function <<
Load more

Recommended publications
  • 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]
  • Physics 305, Fall 2008 Problem Set 8 Due Thursday, December 3
    Physics 305, Fall 2008 Problem Set 8 due Thursday, December 3 1. Einstein A and B coefficients (25 pts): This problem is to make sure that you have read and understood Griffiths 9.3.1. Consider a system that consists of atoms with two energy levels E1 and E2 and a thermal gas of photons. There are N1 atoms with energy E1, N2 atoms with energy E2 and the energy density of photons with frequency ! = (E2 − E1)=~ is W (!). In thermal equilbrium at temperature T , W is given by the Planck distribution: ~!3 1 W (!) = 2 3 : π c exp(~!=kBT ) − 1 According to Einstein, this formula can be understood by assuming the following rules for the interaction between the atoms and the photons • Atoms with energy E1 can absorb a photon and make a transition to the excited state with energy E2; the probability per unit time for this transition to take place is proportional to W (!), and therefore given by Pabs = B12W (!) for some constant B12. • Atoms with energy E2 can make a transition to the lower energy state via stimulated emission of a photon. The probability per unit time for this to happen is Pstim = B21W (!) for some constant B21. • Atoms with energy E2 can also fall back into the lower energy state via spontaneous emission. The probability per unit time for spontaneous emission is independent of W (!). Let's call this probability Pspont = A21 : A21, B21, and B12 are known as Einstein coefficients. a. Write a differential equation for the time dependence of the occupation numbers N1 and N2.
    [Show full text]
  • Inis: Terminology Charts
    IAEA-INIS-13A(Rev.0) XA0400071 INIS: TERMINOLOGY CHARTS agree INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, AUGUST 1970 INISs TERMINOLOGY CHARTS TABLE OF CONTENTS FOREWORD ... ......... *.* 1 PREFACE 2 INTRODUCTION ... .... *a ... oo 3 LIST OF SUBJECT FIELDS REPRESENTED BY THE CHARTS ........ 5 GENERAL DESCRIPTOR INDEX ................ 9*999.9o.ooo .... 7 FOREWORD This document is one in a series of publications known as the INIS Reference Series. It is to be used in conjunction with the indexing manual 1) and the thesaurus 2) for the preparation of INIS input by national and regional centrea. The thesaurus and terminology charts in their first edition (Rev.0) were produced as the result of an agreement between the International Atomic Energy Agency (IAEA) and the European Atomic Energy Community (Euratom). Except for minor changesq the terminology and the interrela- tionships btween rms are those of the December 1969 edition of the Euratom Thesaurus 3) In all matters of subject indexing and ontrol, the IAEA followed the recommendations of Euratom for these charts. Credit and responsibility for the present version of these charts must go to Euratom. Suggestions for improvement from all interested parties. particularly those that are contributing to or utilizing the INIS magnetic-tape services are welcomed. These should be addressed to: The Thesaurus Speoialist/INIS Section Division of Scientific and Tohnioal Information International Atomic Energy Agency P.O. Box 590 A-1011 Vienna, Austria International Atomic Energy Agency Division of Sientific and Technical Information INIS Section June 1970 1) IAEA-INIS-12 (INIS: Manual for Indexing) 2) IAEA-INIS-13 (INIS: Thesaurus) 3) EURATOM Thesaurusq, Euratom Nuclear Documentation System.
    [Show full text]
  • Doppler-Free Spectroscopy
    Doppler-Free Spectroscopy MIT Department of Physics (Dated: November 29, 2012) Traditionally, optical spectroscopy had been performed by dispersing the light emitted by excited matter, or by dispersing the light transmitted by an absorber. Alternatively, if one has available a tunable monochromatic source (such as certain lasers), a spectrum can be measured one wave- length at a time' by measuring light intensity (fluorescence or transmission) as a function of the wavelength of the tunable source. In either case, physically important structures in such spectra are often obscured by the Doppler broadening of spectral lines that comes from the thermal motion of atoms in the matter. In this experiment you will make use of an elegant technique known as Doppler-free saturated absorption spectroscopy that circumvents the problem of Doppler broaden- ing. This experiment acquaints the student with saturated absorption laser spectroscopy, a common application of non-linear optics. You will use a diode laser system to measure hyperfine splittings 2 2 85 87 in the 5 S1=2 and 5 P3=2 states of Rb and Rb. I. PREPARATORY PROBLEMS II. LASER SAFETY 1. Suppose you are interested in small variations in You will be using a medium low power (≈ 40 mW) wavelength, ∆λ, about some wavelength, λ. What near-infrared laser in this experiment. The only real is the expression for the associated small variations damage it can do is to your eyes. Infrared lasers are es- in frequency, ∆ν? Now, assuming λ = 780nm (as is pecially problematic because the beam is invisible. You the case in this experiment), what is the conversion would be surprised how frequently people discover they factor between wavelength differences (∆λ) and fre- have a stray beam or two shooting across the room.
    [Show full text]
  • Fundamentals of Radiative Transfer
    RADIATIVE PROCESSE S IN ASTROPHYSICS GEORGE B. RYBICKI, ALAN P. LIGHTMAN Copyright 0 2004 WY-VCHVerlag GmbH L Co. KCaA FUNDAMENTALS OF RADIATIVE TRANSFER 1.1 THE ELECTROMAGNETIC SPECTRUM; ELEMENTARY PROPERTIES OF RADIATION Electromagnetic radiation can be decomposed into a spectrum of con- stituent components by a prism, grating, or other devices, as was dis- covered quite early (Newton, 1672, with visible light). The spectrum corresponds to waves of various wavelengths and frequencies, related by Xv=c, where v is the frequency of the wave, h is its wavelength, and c-3.00~10" cm s-I is the free space velocity of light. (For waves not traveling in a vacuum, c is replaced by the appropriate velocity of the wave in the medium.) We can divide the spectrum up into various regions, as is done in Figure 1.1. For convenience we have given the energy E = hv and temperature T= E/k associated with each wavelength. Here h is Planck's constant = 6.625 X erg s, and k is Boltzmann's constant = 1.38 X erg K-I. This chart will prove to be quite useful in converting units or in getting a quick view of the relevant magnitude of quantities in a given portion of the spectrum. The boundaries between different regions are somewhat arbitrary, but conform to accepted usage. 1 2 Fundamentals of Radiatiw Transfer -6 -5 -4 -3 -2 -1 0 1 2 1 I 1 I I I I 1 1 log A (cm) Wavelength I I I I I log Y IHr) Frequency 0 -1 -2 -3 -4 -5 -6 I I I I I I I log Elev) Energy 43 21 0-1 I I 1 I I I log T("K)Temperature Y ray X-ray UV Visible IR Radio Figum 1.1 The electromagnetic spctnun.
    [Show full text]
  • Acknowledgements Acknowl
    1277 Acknowledgements Acknowl. A.1 The Properties of Light by Helen Wächter, Markus W. Sigrist by Richard Haglund The authors thank a number of coworkers for their The author thanks Prof. Emil Wolf for helpful discus- valuable input, notably R. Bartlome, Dr. C. Fischer, sions, and gratefully acknowledges the financial support D. Marinov, Dr. J. Rey, M. Stahel, and Dr. D. Vogler. of a Senior Scientist Award from the Alexander von The financial support by the Swiss National Science Humboldt Foundation and of the Medical Free-Electron Foundation and ETH Zurich for the isotopomer studies Laser program of the Department of Defense (Con- is gratefully acknowledged. tract F49620-01-1-0429) during the preparation of this chapter. by Jürgen Helmcke In writing the chapter on frequency-stabilized lasers, A.4 Nonlinear Optics the author has greatly benefited from fruitful coopera- by Aleksei Zheltikov, Anne L’Huillier, Ferenc Krausz tion and helpful discussions with his colleagues at PTB, We acknowledge the support of the European Com- in particular with Drs. Fritz Riehle, Harald Schnatz, munity’s Human Potential Programme under contract Uwe Sterr, and Harald Telle. Special thanks belong to HPRN-CT-2000-00133 (ATTO) and the Swedish Sci- Dr. Fritz Riehle for his careful and critical reading of the ence Council. manuscript. Part of the work discussed in this chapter was supported by the Deutsche Forschungsgemeinschaft A.5 Optical Materials and Their Properties (DFG) under SFB 407. by Klaus Bonrad The author of Sect. 5.9.2 is grateful to Dr. Thomas C.12 Femtosecond Laser Pulses: Däubler, Dr. Dirk Hertel, and Dr.
    [Show full text]
  • Saturated Absorption Spectroscopy
    Ph 76 ADVANCED PHYSICS LABORATORY —ATOMICANDOPTICALPHYSICS— Saturated Absorption Spectroscopy I. BACKGROUND One of the most important scientificapplicationsoflasersisintheareaofprecisionatomicandmolecular spectroscopy. Spectroscopy is used not only to better understand the structure of atoms and molecules, but also to define standards in metrology. For example, the second is defined from atomic clocks using the 9192631770 Hz (exact, by definition) hyperfine transition frequency in atomic cesium, and the meter is (indirectly) defined from the wavelength of lasers locked to atomic reference lines. Furthermore, precision spectroscopy of atomic hydrogen and positronium is currently being pursued as a means of more accurately testing quantum electrodynamics (QED), which so far is in agreement with fundamental measurements to ahighlevelofprecision(theoryandexperimentagreetobetterthanapartin108). An excellent article describing precision spectroscopy of atomic hydrogen, the simplest atom, is attached (Hänsch et al.1979). Although it is a bit old, the article contains many ideas and techniques in precision spectroscopy that continue to be used and refined to this day. Figure 1. The basic saturated absorption spectroscopy set-up. Qualitative Picture of Saturated Absorption Spectroscopy — 2-Level Atoms. Saturated absorp- tion spectroscopy is one simple and frequently-used technique for measuring narrow-line atomic spectral features, limited only by the natural linewidth Γ of the transition (for the rubidium D lines Γ 6 MHz), ≈ from an atomic vapor with large Doppler broadening of ∆νDopp 1 GHz. To see how saturated absorp- ∼ tion spectroscopy works, consider the experimental set-up shown in Figure 1. Two lasers are sent through an atomic vapor cell from opposite directions; one, the “probe” beam, is very weak, while the other, the “pump” beam, is strong.
    [Show full text]
  • Astronomy 700: Radiation. 1 Basic Radiation Properties
    Astronomy 700: Radiation. 1 Basic Radiation Properties 1.1 Basic definitions Fundamental importance to Astronomy: Almost exclusive carrier of information Radiation: Energy transport by electromagnetic fields Other forms of energy transport: cosmic rays • stochastic transport (micro: conduction, macro: convection) • gravitational waves • bulk transport (organized flows) • plasma waves • ... • Transport time variability (see section of E&M) → 1.1.1 The spectrum The most natural description of electromagnetic radiation is through Fourier decomposition into waves: f(~r, t) f(~k,ν) (1.1) ↔ where E is some variable describing the radiation field. Question: Why is this so natural? As we will shortly see, electromagnetic radiation naturally decomposes into waves with wave- length λ and frequency ν 1 Often, it is convenient to write the wave vector ~k =2πk/λˆ and angular frequency ω =2πν. In vacuum, group and phase velocity of those waves are equal: 10 1 λν = ∂ω/∂k c 2.99792... 10 cms− (1.2) ≡ ≡ × Fourier decomposition allows us to describe the local spectrum of the radiation at a fixed point in space as the Fourier transform ∞ f f(ν)= dtei2πνtf(t) (1.3) F ≡ Z−∞ and the inverse Fourier transform 1 ∞ i2πνt − f f(t)= dνe− f(ν) (1.4) F ≡ Z−∞ Without going into any details on Lebesque integration, it is worth pointing out the following identity: The inverse Fourier transform of a delta function in frequency is ∞ 1 i2πνt i2πν0t − δ(ν ν )= dνe− δ(ν ν )= e− (1.5) F − 0 − 0 Z−∞ i2πν0 t Thus, the Fourier transform of e− is ∞ i2πν0t i2π(ν ν0)t e− = dte − = δ(ν ν ) (1.6) F − 0 Z−∞ as one would expect for a decomposition into a spectrum of different exponentials.
    [Show full text]
  • Fundamentals of Spectroscopy for Optical Remote Sensing Course
    Fundamentals of Spectroscopy for Optical Remote Sensing Course Outline 2013 (Draft) Part I. Introduction to Quantum Physics Chapter 1. Quantum Concepts and Experimental Facts 1.1. Blackbody Radiation and Planck’s Radiation Law [Textbook “Laser Spectroscopy” Sections 2.1 – 2.4, Corney’s book Section 1.1] 1.2. Photoelectric Effect and Quantized Energy [Textbook Section 4.5.4, Corney’s book Section 1.2] 1.3. Compton Effect and Quantized Momentum 1.4. Hydrogen Spectra and Discrete Energy Levels [Textbook Section 4.1, Corney’s book Section 1.3] 1.5. Bohr’s Model [Corney’s book Sections 1.4-1.8] Chapter 2. Wave-Particle Duality [Dirac’s The Principles of Quantum Mechanics, and Cohen-Tannoudji’s Quantum Mechanics, vol. I and II] 2.1. Wave Behavior of Light 2.2. Single Photon Experiment 2.3. Wave-Particle Duality of Light 2.4. Wave-Particle Duality of Material Particles 2.5. de Broglie Relationship Chapter 3. Basics of Quantum Mechanics (Postulates, Principles, and Mathematic Formalism) [Cohen-Tannoudji’s Quantum Mechanics, vol. I and II] 3.1. Postulates of Quantum Mechanics 3.2. Principle of Superposition of States 3.3. Principle of Motion – Schrödinger Equation 3.4. Principle of Uncertainty – Indeterminacy 3.5. Dirac Notation and Representations 3.6. Solutions to Eigenvalue Equation and Schrödinger Equation Part II. Fundamentals of Atomic Spectroscopy Chapter 4. Introduction to Atomic Structure and Atomic Spectra Chapter 5. Atomic Structure 5.1. Atomic Structure Overview 5.2. Atomic Structure for Hydrogen Atom and Hydrogen-like Ions 1. Hydrogen energy eigenvalues and eigenstate in Coulomb Potential 2.
    [Show full text]
  • Introduction to Astrophysical Spectra Solar Spectropolarimetry: from Virtual to Real Observations 2019
    Introduction to Astrophysical Spectra Solar spectropolarimetry: From virtual to real observations 2019 Jorrit Leenaarts ([email protected]) Jaime de la Cruz Rodr´ıguez([email protected]) 1 Contents Preface 4 1 Introduction 5 2 Solid angle 6 3 Radiation, intensity and flux 7 3.1 Basic properties of radiation . 7 3.2 Definition of intensity . 7 3.3 Additional radiation quantities . 9 3.4 Flux from a uniformly bright sphere . 11 4 Radiative transfer 12 4.1 Definitions . 12 4.2 The radiative transfer equation . 14 4.3 Formal solution of the transport equation . 16 4.4 Radiation from a homogeneous medium . 17 4.5 Radiation from an optically thick medium . 19 5 Radiation in thermodynamic equilibrium 22 5.1 Black-body radiation . 22 5.2 Transfer equation and source function in thermodynamic equi- librium . 24 6 Matter in thermodynamic equilibrium 25 7 Matter/radiation interaction 26 7.1 Bound-bound transitions . 27 7.2 Einstein relations . 29 7.3 Emissivity and extinction coefficient . 31 7.4 Source function . 33 8 Line broadening 33 8.1 Broadening processes . 34 8.2 Combining broadening mechanisms . 36 8.3 Line widths as a diagnostic . 40 2 9 Bound-free transitions 40 10 Other radiative processes 43 10.1 Elastic scattering . 45 10.2 The H− ion ............................ 46 11 Rate equations 46 11.1 General theory . 46 11.2 The two-level atom . 47 11.3 A three-level atom as a density diagnostic . 49 11.4 A three-level atom as a temperature diagnostic . 52 12 Exercises 53 3 Preface These are a fraction of the lecture notes for the Solarnet Summer School - Solar spectropolarimetry: From virtual to real observations.
    [Show full text]
  • 14 Shape of Spectral Lines
    II ⋅ Stellar Atmospheres Copyright (2003) George W. Collins, II 14 Shape of Spectral Lines . If we take the classical picture of the atom as the definitive view of the formation of spectral lines, we would conclude that these lines should be delta functions of frequency and appear as infinitely sharp black lines on the stellar spectra. However, many processes tend to broaden these lines so that the lines develop a characteristic shape or profile. Some of these effects originate in the quantum mechanical description of the atom itself. Others result from perturbations introduced by the neighboring particles in the gas. Still others are generated by the motions of the atoms giving rise to the line. These motions consist of the random thermal motion of the atoms themselves which are superimposed on whatever large scale motions may be present. The macroscopic motions may be highly ordered, as in the case of stellar rotation, or show a high degree of randomness such as is characteristic of turbulent flow. 348 14 ⋅ Shape of Spectral Lines In practice, all these effects are present and give the line its characteristic shape. The correct representation of these effects allows for the calculation of the observed line profile and in the process reveals a great deal about the conditions in the star that give rise to the spectrum. Of course the photons that give rise to the absorption lines in the stellar spectrum have their origins at different locations in the atmosphere. So the conditions giving rise to a spectral line are really an average of a range of conditions.
    [Show full text]
  • Sitzungsberichte Der Leibniz-Sozietät, Jahrgang 2003, Band 61
    SITZUNGSBERICHTE DER LEIBNIZ-SOZIETÄT Band 61 • Jahrgang 2003 trafo Verlag Berlin ISSN 0947-5850 ISBN 3-89626-462-1 Inhalt Heinz Kautzleben Hans-Jürgen Treder, die kosmische Physik und die Geo- und Kosmoswissenschaften >>> Herbert Hörz Kosmische Rätsel in philosophischer Sicht >>> Karl-Heinz Schmidt Die Lokale Galaxiengruppe >>> Helmut Moritz Epicycles in Modern Physics >>> Armin Uhlmann Raum-Zeit und Quantenphysik >>> Rainer Schimming Über Gravitationsfeldgleichungen 4. Ordnung >>> Werner Holzmüller Energietransfer und Komplementarität im kosmischen Geschehen >>> Klaus Strobach Mach'sches Prinzip und die Natur von Trägheit und Zeit >>> Fritz Gackstatter Separation von Raum und Zeit beim eingeschränkten Dreikörperproblem mit Anwendung bei den Resonanzphänomenen im Saturnring und Planetoidengürtel >>> Gerald Ulrich Fallende Katzen >>> Rainer Burghardt New Embedding of the Schwarzschild Geometry. Exterior Solution >>> Holger Filling und Ralf Koneckis Die Goldpunkte auf der frühbronzezeitlichen Himmelsscheibe von Nebra >>> Joachim Auth Hans-Jürgen Treder und die Humboldt-Universität zu Berlin >>> Thomas Schalk Hans-Jürgen Treder und die Förderung des wissenschaftlichen Nachwuchses >>> Wilfried Schröder Hans-Jürgen Treder und die kosmische Physik >>> Dieter B. Herrmann Quantitative Methoden in der Astronomiegeschichte >>> Gottfried Anger und Helmut Moritz Inverse Problems and Uncertainties in Science and Medicine >>> Ernst Buschmann Geodäsie: die Raum+Zeit-Disziplin im Bereich des Planeten Erde >>> Hans Scheurich Quantengravitation auf der Grundlage eines stringkollektiven Fermionmodells >>> Hans Scheurich Ein mathematisches Modell der Subjektivität >>> Hans-Jürgen Treder Anstelle eines Schlußwortes >>> Leibniz-Sozietät/Sitzungsberichte 61(2003)5, 5–16 Heinz Kautzleben Hans-Jürgen Treder, die kosmische Physik und die Geo- und Kosmoswissenschaften Laudatio auf Hans-Jürgen Treder anläßlich des Festkolloquiums am 02.10.2003 Das Kolloquium ist ein Geburtstagsgeschenk der Leibniz-Sozietät an ihr Mit- glied Hans-Jürgen Treder.
    [Show full text]