ATOMIC SPECTROSCOPY and OPACITY” • 3 Weeks Lecture Course • Textbook: ”Atomic Astrophysics and Spectroscopy” -A.K
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”ATOMIC SPECTROSCOPY AND OPACITY” • 3 Weeks Lecture Course • Textbook: ”Atomic Astrophysics and Spectroscopy” -A.K. Pradhan and S.N. Nahar (Cambridge, 2011) SULTANA N. NAHAR Department of Astronomy The Ohio State University Columbus, Ohio, USA Email: naharastronomy.ohio-state.edu Web: www.astronomy.ohio-state.edu/∼nahar Physics Department Cairo University, Giza, Egypt February 16 - March 7, 2013 Support: DOE, NSF, OSC, Cairo University 1 ”ATOMIC SPECTROSCOPY AND OPACITY” • 3 Weeks Lecture Course • Textbook: ”Atomic Astrophysics and Spectroscopy” (AAS) -A.K. Pradhan and S.N. Nahar (Cambridge, 2011) Lecture Topics: Week 1: • Physics and Astronomy Connection i) Elements and Spectroscopy ii) Opacity and Observations iii) The Sun and Evolution of Spectroscopy iv) Electron and Photon Distribution Functions v) The Plasma Universe • Atomic Structure and Spectroscopy i) Hydrogen - Single electron energy and wave functions ii) Quantum numbers n,l,m, s, parity iii) Spectral lines - Rydberg formula Week 2: • Atomic Structure, Computation with SUPERSTRUCTURE & Atomic Processes i) Multi-election Systems - Angular Sates ii) Angular Couplings, Quantum Defects iii) Hartee-Fock Approximation iv) Central Field Approximations v) Dirac Equation, Breit-Pauli Approximation, Dirac-Fock 2 Approximation vi) Atomic Processes of Plasma Opacity Week 3: • Plasma Opacity, R-matrix Calculations for Atomic Processes i) Autoionization and Resonances and Opacity ii) Plasma Opacity iii) Close-Coupling Approximation and R-matrix Method iv) R-matrix Calculations 3 i) Elements and Spectroscopy: ELEMENTS (Key Information) • Periodic TableP E R I O D ofI C T elements A B L E (Ref. NIST) Group 1 Atomic Properties of the Elements 18 IA VIIIA 2S 1S 1 1/2 Frequently used fundamental physical constants Physics Standard Reference 2 0 For the most accurate values of these and other constants, visit physics.nist.gov/constants Laboratory Data Group 1 H 1 second = 9 192 631 770 periods of radiation corresponding to the transition physics.nist.gov www.nist.gov/srd He Hydrogen 133 Helium 1.00794 between the two hyperfine levels of the ground state of Cs 4.002602 -1 2 1s 2 speed of light in vacuum c 299 792 458 m s (exact) Solids 13 14 15 16 17 1s -34 13.5984 IIA Planck constant h 6.6261 × 10 J s ( /2 ) IIIA IVA VA VIA VIIA 24.5874 -19 Liquids 2S 1S elementary charge e 1.6022 × 10 C 2P° 3P 4S° 3P 2P° 1S 3 1/2 4 0 -31 Gases 5 1/2 6 0 7 3/2 8 2 9 3/2 10 0 electron mass me 9.1094 × 10 kg 2 Li Be mec 0.5110 MeV Artificially B C N O F Ne 2 Lithium Beryllium -27 Boron Carbon Nitrogen Oxygen Fluorine Neon proton mass mp 1.6726 × 10 kg Prepared 6.941 9.012182 10.811 12.0107 14.0067 15.9994 18.9984032 20.1797 2 2 2 fine-structure constant 1/137.036 2 2 2 2 2 2 2 3 2 2 4 2 2 5 2 2 6 -1 1s 2s 2p 1s 2s 1s 1s 2s 1s 2s 1s 2s 1s 2s Rydberg constant R 10 973 732 m 2p 2s 2p 1s 2s 2p 2p 2p 5.3917 9.3227 8.2980 11.2603 14.5341 13.6181 17.4228 21.5645 R c 3.289 842 × 1015 Hz 2S 1S 2P 3P 4S 3P 2P 1S 11 1/2 12 0 R hc 13.6057 eV 13 1/2° 14 0 15 3/2° 16 2 17 3/2° 18 0 - - Na Mg Boltzmann constant k 1.3807 × 10 23 J K 1 Al Si P S Cl Ar 3 Sodium Magnesium Aluminum Silicon Phosphorus Sulfur Chlorine Argon 22.989770 24.3050 26.981538 28.0855 30.973761 32.065 35.453 39.948 2 3 4 5 6 7 8 9 10 11 12 2 2 2 2 3 2 4 2 5 2 6 [Ne]3s [Ne]3s [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p 5.1391 7.6462 IIIB IVB VB VIB VIIB VIII IB IIB 5.9858 8.1517 10.4867 10.3600 12.9676 15.7596 2 1 2 3 4 7 6 5 4 3 2 1 2 3 4 3 2 1 19 S1/2 20 S0 21 D3/2 22 F2 23 F3/2 24 S3 25 S5/2 26 D4 27 F9/2 28 F4 29 S1/2 30 S0 31 P1/2° 32 P0 33 S3/2° 34 P2 35 P3/2° 36 S0 K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 4 Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton 39.0983 40.078 44.955910 47.867 50.9415 51.9961 54.938049 55.845 58.933200 58.6934 63.546 65.409 69.723 72.64 74.92160 78.96 79.904 83.798 Period 2 2 2 2 3 2 5 5 2 6 2 7 2 8 2 10 10 2 10 2 10 2 2 10 2 3 10 2 4 10 2 5 10 2 6 [Ar]4s [Ar]4s [Ar]3d4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p 4.3407 6.1132 6.5615 6.8281 6.7462 6.7665 7.4340 7.9024 7.8810 7.6398 7.7264 9.3942 5.9993 7.8994 9.7886 9.7524 11.8138 13.9996 2 1 2 3 6 7 6 5 4 1 2 1 2 3 4 3 2 1 37 S1/2 38 S0 39 D3/2 40 F2 41 D1/2 42 S3 43 S5/2 44 F5 45 F9/2 46 S0 47 S1/2 48 S0 49 P1/2° 50 P0 51 S3/2° 52 P2 53 P3/2° 54 S0 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 5 Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon 85.4678 87.62 88.90585 91.224 92.90638 95.94 (98) 101.07 102.90550 106.42 107.8682 112.411 114.818 118.710 121.760 127.60 126.90447 131.293 2 2 2 2 4 5 5 2 7 8 10 10 10 2 10 2 10 2 2 10 2 3 10 2 4 10 2 5 10 2 6 [Kr]5s [Kr]5s [Kr]4d5s [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s [Kr]4d [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p 4.1771 5.6949 6.2173 6.6339 6.7589 7.0924 7.28 7.3605 7.4589 8.3369 7.5762 8.9938 5.7864 7.3439 8.6084 9.0096 10.4513 12.1298 2 1 3 4 5 6 5 4 3 2 1 2 3 4 3 2 1 55 S1/2 56 S0 72 F2 73 F3/2 74 D0 75 S5/2 76 D4 77 F9/2 78 D3 79 S1/2 80 S0 81 P1°/2 82 P0 83 S3°/2 84 P2 85 P3°/2 86 S0 Cs Ba Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 6 Cesium Barium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon 132.90545 137.327 178.49 180.9479 183.84 186.207 190.23 192.217 195.078 196.96655 200.59 204.3833 207.2 208.98038 (209) (210) (222) 2 14 2 2 14 3 2 14 4 2 14 5 2 14 6 2 14 7 2 14 9 14 10 14 10 2 2 3 4 5 6 [Xe]6s [Xe]6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Hg]6p [Hg]6p [Hg]6p [Hg]6p [Hg]6p [Hg]6p 3.8939 5.2117 6.8251 7.5496 7.8640 7.8335 8.4382 8.9670 8.9588 9.2255 10.4375 6.1082 7.4167 7.2855 8.414 10.7485 2 1 3 87 S1/2 88 S0 104 F2 ? 105 106 107 108 109 110 111 112 114 116 Fr Ra Rf Db Sg Bh Hs Mt Uun Uuu Uub Uuq Uuh 7 Francium Radium Rutherfordium Dubnium Seaborgium Bohrium Hassium Meitnerium Ununnilium Unununium Ununbium Ununquadium Ununhexium (223) (226) (261) (262) (266) (264) (277) (268) (281) (272) (285) (289) (292) 2 14 2 2 [Rn]7s [Rn]7s [Rn]5f 6d 7s ? 4.0727 5.2784 6.0 ? 2 1 4 5 6 7 8 9 6 5 4 3 2 1 2 Atomic Ground-state s 57 D3/2 58 G°4 59 I9/2° 60 I4 61 H°5/2 62 F0 63 S°7/2 64 D°2 65 H°15/2 66 I8 67 I15/2° 68 H6 69 F°7/2 70 S0 71 D3/2 Number Level e d i n 1 a La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu h Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Symbol 58 G°4 t n 138.9055 140.116 140.90765 144.24 (145) 150.36 151.964 157.25 158.92534 162.500 164.93032 167.259 168.93421 173.04 174.967 a 2 2 3 2 4 2 5 2 6 2 7 2 7 2 9 2 10 2 11 2 12 2 13 2 14 2 14 2 L [Xe]5d6s [Xe]4f5d6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 5d6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 5d6s Name Ce 5.5769 5.5387 5.473 5.5250 5.582 5.6437 5.6704 6.1498 5.8638 5.9389 6.0215 6.1077 6.1843 6.2542 5.4259 Cerium 2 3 4 5 6 7 8 9 6 5 4 3 2 1 2 89 D3/2 90 F2 91 K11/2 92 L°6 93 L11/2 94 F0 95 S7/2° 96 D°2 97 H°15/2 98 I8 99 I15/2° 100 H6 101 F°7/2 102 S0 103 P°1/2? 140.116 s Atomic e † 2 d Weight [Xe]4f5d6s i n Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr i 5.5387 t Actinium Thorium Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium c (227) 232.0381 231.03588 238.02891 (237) (244) (243) (247) (247) (251) (252) (257) (258) (259) (262) A 2 2 2 2 2 3 2 4 2 6 2 7 2 7 2 9 2 10 2 11 2 12 2 13 2 14 2 14 2 Ground-state Ionization [Rn]6d7s [Rn]6d 7s [Rn]5f 6d7s [Rn]5f 6d7s [Rn]5f 6d7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 6d7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s 7p? Configuration Energy (eV) 5.17 6.3067 5.89 6.1941 6.2657 6.0260 5.9738 5.9914 6.1979 6.2817 6.42 6.50 6.58 6.65 4.9 ? † Based upon 12C.