X-Ray interactions With Superheavy Atoms. Pavlo Baranov Queens College Advisor: John Rehr August 18 th, 2016

Transcription

1 X-Ray interactions With Superheavy Atoms Pavlo Baranov Queens College Advisor: John Rehr August 18 th,

2 Table of Contents Introduction XAFS Theory Project 1: XANES of element Z = 130 Thomson Scattering Cross Section & Thomas-Fermi model Project 2: Thomas-Fermi model to predict densities Future Work 2

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4 Superheavy Elements Start from Z = 104 Have very short half-lives Made artificially Created in a particle accelerator Particle Accelerator, 4

5 Extended Periodic Table, 5

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7 Island of Stability The idea that heavy elements near the isotope 300 Ubn (element 120) with near the magic number of protons and neutrons will be much more stable. Island of Stability, 7

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9 XAFS X-Ray Absorption Fine Structure XAFS tells us how x-rays are absorbed by a system of atoms, including free atoms, molecules and solids at energies around the core-level binding energies of the atom. XAFS depends on the atomic structure and electronic and vibrational properties of the material; therefore, XAFS can be calculated for every element on the periodic table. XAFS can be used to characterize materials, including atomic and electronic structure. Absorption coefficient µ, I = I 0 e µt Beer s Law. µ f i d f 2 δ(e f E i ħω) - Fermi s Golden Rule. 9

10 Photoelectric Effect Fermi Level 10

11 EXAFS Extended X-Ray Absorption Fine Structure Edges are the sharp rises in absorption at certain energies. They occur at roughly the binding energy of each core-level electron. EXAFS is what is happening well above the edges. EXAFS Equation χ k = j N j f j (k)e 2k2 σ j 2 kr j 2 sin[2kr j + σ j (k)] 11

12 XANES X-Ray Absorption Near Edge Structure XANES is typically within 30 ev of the main absorption edge. XANES can be used as a fingerprint to identify the presence of a particular chemical species. XANES and EXAFS, 12

13 FEFF9 FEFF9, 13

14 mu 1.80E+00 Uranium Dioxide UO 2 UO2 L3 Edge XANES 1.60E E E E E E E E-01 E. A. Hudson, J. J. Rehr, J. J. Bucher, Multiple-scattering calculations of the uranium L3-edge x-ray-absorption near-edge structure, Physical Review B, E omega 14

15 mu Erbium Oxide Er 2 O 3 Er2O3 L3 Edge XANES 1.60E E E E E E E E-01 Hiroyuki Asakura, Tetsuya Shishido, Kentaro Teramura, and Tsunehiro Tanaka, Local Structure and L1- and L3-Edge X-ray Absorption Near Edge Structure of Late Lanthanide Elements (Ho, Er, Yb) in Their Complex Oxides, J. Phys. Chem. C 2015, 119, E omega 15

16 mu Americium Dioxide AmO 2 AmO2 L3 Edge XANES 1.80E E E E E E E E E-01 Tsuyoshi Nishi, Masami Nakada, Akinori Itoh, Chikashi Suzuki, Masaru Hirata, Mitsuo Akabori, EXAFS and XANES Studies of Americium Dioxide with fluorite structure, J. Of Nuclear Materials, E omega 16

17 XANES of Untrinilium (Utn2) 17

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19 Thomson Scattering The elastic scattering of X-rays from free electrons. The atomic scattering factor f 0 = Z n=1 0 4πr 2 ρ n (r) sin(qr) dr qr Momentum transfer q = 4πsin(θ B) λ Thomson Scattering, /bf/thomson_scattering_geometry.png 19

20 Thomas Fermi model n = [2(φ φ 0)] 3/2 3π 2 r = xbz 1/3, b = φ r = Z4/3 b χ(x) x Thomas Fermi equation x 1/2 d2 χ dx 2 = χ3/2 TF density n r = Z 2 f( rz1/3 b ), f x = 32 9π 3 (χ x )3/2 20

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23 Future Work Calculation of phase shifts using FEFF9 Comparison to WKB approximation Developing a model to calculate radii for superheavy molecules. 23

24 Acknowledgments Thank you to professor John Rehr, Joshua Kas, and Fernando Vila for their guidance through my projects. Thank you to Ron Musgrave for the machine shop lessons. Thank you to REU coordinators and the NSF. 24

25 References J. J. Rehr, R. C. Albers, Theoretical Approaches to X-ray Absorption Fine Structure, Reviews of Modern Physics, Vol. 72, No. 3, 2000 Pekka Pyykko, A suggested Periodic Table up to Z 172, based on Dirac-Fock calculations on atoms and ions, Phys. Chem. Chem. Phys., 2011,13, Hiroyuki Asakura, Tetsuya Shishido, Kentaro Teramura, and Tsunehiro Tanaka, Local Structure and L1- and L3-Edge X-ray Absorption Near Edge Structure of Late Lanthanide Elements (Ho, Er, Yb) in Their Complex Oxides, J. Phys. Chem. C 2015, 119, Tsuyoshi Nishi, Masami Nakada, Akinori Itoh, Chikashi Suzuki, Masaru Hirata, Mitsuo Akabori, EXAFS and XANES Studies of Americium Dioxide with fluorite structure, J. Of Nuclear Materials, 2007 E. A. Hudson, J. J. Rehr, J. J. Bucher, Multiple-scattering calculations of the uranium L3-edge x-ray-absorption near-edge structure, Physical Review B, 1995 Matthew Newville, Fundamentals of XAFS, Consortium for Advanced Radiation Sources, 2004 J. Kas, Theory and Calculation of X-Ray Absorption, V. L. Eletskii, V.S. Popov, The Thomas-Fermi method for Z>137, Zh. Eksp. Teor. Fiz. 73, , 1977 A. Messiah, Quantum Mechanics, Dover Publications Inc., Mineola, New York, 1999 L. D. Landau, E. M. Lifshitz, Quantum Mechanics, non-relativistic theory, Pergamon Press, Oxford, New York, Beijing, Frankfurt, Sao Paulo, Sydney, Tokyo, Toronto, 1977 Gwyndaf Evans, Classical X-ray scattering, Ray Wong, Josh Alamillo, EXAFS: Theory,