LECTURE NOTES. Ay/Ge 132 ATOMIC AND MOLECULAR PROCESSES IN ASTRONOMY AND PLANETARY SCIENCE. Geoffrey A. Blake. Fall term 2016 Caltech

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1 LECTURE NOTES Ay/Ge 132 ATOMIC AND MOLECULAR PROCESSES IN ASTRONOMY AND PLANETARY SCIENCE Geoffrey A. Blake Fall term 2016 Caltech Acknowledgment Part of these notes are based on lecture notes from the courses: Ge 132: Atomic and Molecular Processes... by E.F. van Dishoeck, Caltech Ay 522: Astronomical Spectroscopy by J.H. Black, University of Arizona Ay 209: Interstellar Medium by A. Dalgarno, Harvard University 1

2 CONTENTS CONTENTS..... INTRODUCTION... PART 1: ATOMS I. THE HYDROGEN ATOM A. Quantum Mechanical Formulation Energies Wave Functions Spin Hydrogen like atoms Higher order terms a. Spin orbit term... 7 b. Velocity dependence e-mass c. Darwin term d. Lamb shift e. Hyperfine structure B. Classical Atoms II. N ELECTRON ATOMS Wave Functions Configurations Term Diagrams a. LS coupling b. jj coupling c. Examples (i) Helium (ii) Alkali Atoms (iii) Other Species III. ATOMS AND RADIATION Definitions; Einstein Coefficients Multipole Expansion Radiation Field Selection Rules Transition Probabilities a. Electric Dipole b. Magnetic Dipole c. Electric Quadrupole d. Sum Rules e. Determination Example: C II Intercombination Transitions Two Photon Emission Example: O I IV. PHOTOIONIZATION AND RECOMBINATION A. Photoionization Hydrogen Helium a. Direct Photoionization b. Autoionization i i vi

3 3. Other Elements Inner Shell Ionizations B. Recombination Hydrogen Helium a. Radiative Recombination b. Dielectronic Recombination Other Species C. Accidental Resonance Fluorescence a. Bowen Fluorescence for O III b. H Ly β and O I c. H Ly β and Mg II D. Absorption and Emission of Line Radiation V. COLLISIONAL PROCESSES Classical Collision Theory a. Scattering by a Center of Force b. Rutherford Formula Quantum Theory a. Cross Section for Elastic Scattering b. Partial Wave Expansion c. Scattering by a Hard Sphere d. Inelastic Collisions Electron Hydrogen Scattering Collisional Excitation of Other Species Electron Impact Ionization Charge Transfer Processes VI. ATOMIC APPLICATIONS H in the Solar Photosphere Ionized Regions of the Interstellar Medium a. Photoionized Regions (i) Structure of Nebulae (ii) Thermal Balance (iii) Spectra of Nebulae (iv) Temperature Diagnostics (v) Electron Density Diagnostics (vi) Abundance Determinations (vii) X ray Nebulae b. Collisionally ionized Regions (i) Hot Coronal Gas (ii) Galactic Halo (iii) Nova and Supernova Remnants Solar Corona Active Galactic Nuclei, Starbursts (Near & Far) Terrestrial Atmosphere Planetary Atmospheres a. General Features b. Nitrogen in Titan s Atmosphere c. Io s Plasma Torus ii

4 PART 2: MOLECULES VII. OVERVIEW OF MOLECULAR STRUCTURE Born Oppenheimer Approximation Calculation of Electronic Energies a. H + 2 ion b. H 2 molecule Nuclear Motion a. Vibration b. Rotation Nomenclature a. Labeling b. Diatomic Molecules c. Polyatomic Molecules; Symmetry VIII. ROTATIONAL SPECTROSCOPY Classification Linear Rotor a. Energy Expression b. Selection Rules c. Nuclear Spin Statistics d. Higher order Terms (i) Λ doubling (ii) Spin orbit Interaction (iii) Hyperfine Structure e. Examples Symmetric Top Molecules Spherical Top Molecules Asymmetric Top Molecules IX. VIBRATIONAL SPECTROSCOPY Diatomic Molecules a. Energy Levels and Selection Rules b. Vibration rotation Spectroscopy c. Examples (i) H (ii) OH Polyatomic Molecules a. Group Vibrations b. Selection Rules c. Vibration rotation Spectroscopy (i) Linear Molecules (ii) Symmetric Top Molecules (iii) Spherical Top Molecules (iv) Asymmetric Top Molecules d. Anharmonicity e. Examples X. ELECTRONIC SPECTROSCOPY Rovibronic Energy Levels Selection Rules; Franck Condon Principle iii

5 3. Examples a. O b. CH Rotational Structure XI. MOLECULAR PROCESSES Photodissociation a. Mechanisms (i) Direct Photodissociation (ii) Predissociation (iii) Coupled States Photodissociation (iv) Spontaneous Radiative Dissociation b. Cross sections c. Photodissociation Rates d. Radiation Fields (i) Background Interstellar Field (ii) Lyman α Radiation (iii) Cosmic Ray Induced Photons (iv) Solar Radiation Field e. Isotopic Photodissociation f. Additional Considerations g. Photoionization Dissociative Recombination a. Mechanisms b. Rate Coefficients c. Example: H d. Product Branching Ratios e. Astrophysical Considerations Chemical Reactions a. Neutral Neutral Reactions b. Ion Molecule Reactions (i) Reaction Rates (ii) Isotope Fractionation c. Charge Transfer Processes d. Negative Ion Reactions Collision Induced Dissociation Radiative Association a. Mechanisms b. Rate Coefficients Three Body Formation a. Formation of Grains b. Example: Green Light of Night Sky XII. MOLECULAR APPLICATIONS The Early Universe a. Molecule Formation: z b. Molecules as Coolants: z c. Observations: z Comets a. Introduction iv

6 b. Observations c. Models Supernova Chemistry a. Introduction b. Chemistry in the Core of SN 1987A c. Chemistry in the Envelope of SN 1987A Molecular Clouds a. Diffuse Interstellar Clouds b. Dense Interstellar Clouds (i) Observations (Gas & Ice) (ii) Molecular Excitation; Line/Band Formation (iii) Chemistry Near/Mid-IR Spectroscopy of Triton/Pluto Spectroscopy of Planetary Atmospheres a. The Jovian Planets (i) Typical State (ii) SL9/Jupiter Impact Spectra b. The Terrestrial Planets (i) Whole Disk Spectra (ii) Imaging, Limb Sounding Spectra APPENDIX.... A1 Fundamental Constants etc A1-3 Examples of Terms from p 2 Configuration..... A4 Summary Notation Atoms... A5 Selection Rules... A6-7 Table of Ionization Potentials A8 Boltzmann & Saha Equations A9 Selection Rules Revisited.... A10 LTE Analysis of CO Lines A11-13 v

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