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A new theoretical insight into the spectroscopic properties of polonium and astatine atoms

Gain a new perspective on the spectroscopic attributes of polonium and astatine atoms through a comprehensive analysis of their properties, energy levels, theoretical calculations, and experimental spectra.

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A new theoretical insight into the spectroscopic properties of polonium and astatine atoms

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  1. A new theoretical insight into the spectroscopic properties of polonium and astatine atoms Pascal Quinet Spectroscopie Atomique et Physique des Atomes Froids, Université de Liège & Astrophysique et Spectroscopie, Université de Mons

  2. Plan of the talk • Some properties of polonium and astatine atoms • Experimental spectrum and energy levels of polonium • Experimental spectrum and energy levels of astatine • Theoretical approach • Atomic structure calculations in polonium • Atomic structure calculations in astatine • Summary and conclusions Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  3. Some properties of polonium and astatine atoms Polonium (Po) Astatine (At) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  4. Experimental spectrum and energy levels of polonium G.W. Charles, J.O.S.A. 56, 1292 (1966)  97 spectral lines in the region 213.9 – 861.9 nm [NIST Atomic Spectra Database (http://www.nist.gov/pml/data/asd.cfm)] Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  5. Experimental spectrum and energy levels of polonium G.W. Charles, J.O.S.A. 56, 1292 (1966)  97 spectral lines in the region 213.9 – 861.9 nm [NIST Atomic Spectra Database (http://www.nist.gov/pml/data/asd.cfm)] Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  6. Experimental spectrum and energy levels of polonium G.W. Charles, J.O.S.A. 56, 1292 (1966)  97 spectral lines in the region 213.9 – 861.9 nm [NIST Atomic Spectra Database (http://www.nist.gov/pml/data/asd.cfm)] Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  7. Experimental spectrum and energy levels of astatine R. McLaughlin, J.O.S.A. 54, 965 (1964)  2 spectral lines at 216.225 and 224.401 nm [NIST Atomic Spectra Database (http://www.nist.gov/pml/data/asd.cfm)] Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  8. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Based on the Schrödinger equation (atom with N electrons) with Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  9. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Based on the Schrödinger equation (atom with N electrons) with Central field approximation  One-electron wavefunctions Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  10. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Based on the Schrödinger equation (atom with N electrons) with Central field approximation  One-electron wavefunctions Atomic wavefunctions (Slater determinant) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  11. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Hartree-Fock equations Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  12. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Hartree-Fock equations Resolution of Hartree-Fock equations (self-consistent field) Starting Pi(ri)  Calculate potentials  Solve HF equations  New Pi(ri) Same as before ? NO YES STOP Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  13. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Multiconfiguration approach (Slater-Condon) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  14. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Multiconfiguration approach (Slater-Condon) Relativistic effects Included perturbationaly (spin-orbit, mass-velocity, Darwin term) Good agreement with fully relativistic methods Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  15. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Multiconfiguration approach (Slater-Condon) Relativistic effects Included perturbationaly (spin-orbit, mass-velocity, Darwin term) Good agreement with fully relativistic methods Ab initio or semi-empirical approach Experimental energy levels can be used to optimize the radial parameters (configuration average energies, electrostatic interaction integrals, spin-orbit parameters) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  16. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Multiconfiguration approach (Slater-Condon) Example : Po (6p4 – 6p36d transitions) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  17. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Multiconfiguration approach (Slater-Condon) Example : Po (6p4 – 6p36d transitions) Intravalence correlation (single excitations up to n=6, l=3) Even parity 4f145d106s26p4 4f145d106s26p35f 4f145d106s26p36f 4f145d106s26p26d2 Odd parity 4f145d106s26p36d 4f145d106s26p26d5f 4f145d106s26p26d6f Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  18. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Multiconfiguration approach (Slater-Condon) Core-valence correlation (single excitations from 4f, 5d, 6s) Example : Po (6p4 – 6p36d transitions) Even parity 4f145d106s6p46d 4f145d106s6p36d5f 4f145d106s6p36d6f 4f145d96s26p46d 4f145d96s26p36d5f 4f145d96s26p36d6f 4f135d106s26p5 4f135d106s26p45f 4f135d106s26p46f 4f135d106s26p36d2 Odd parity 4f145d106s6p5 4f145d106s6p45f 4f145d106s6p46f 4f145d106s6p36d2 4f145d96s26p5 4f145d96s26p45f 4f145d96s26p46f 4f145d96s26p36d2 4f135d106s26p46d 4f135d106s26p36d5f 4f135d106s26p36d6f Intravalence correlation (single excitations up to n=6, l=3) Even parity 4f145d106s26p4 4f145d106s26p35f 4f145d106s26p36f 4f145d106s26p26d2 Odd parity 4f145d106s26p36d 4f145d106s26p26d5f 4f145d106s26p26d6f Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  19. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Multiconfiguration approach (Slater-Condon) Core-valence correlation (single excitations from 4f, 5d, 6s) Example : Po (6p4 – 6p36d transitions) Even parity 4f145d106s6p46d 4f145d106s6p36d5f 4f145d106s6p36d6f 4f145d96s26p46d 4f145d96s26p36d5f 4f145d96s26p36d6f 4f135d106s26p5 4f135d106s26p45f 4f135d106s26p46f 4f135d106s26p36d2 Odd parity 4f145d106s6p5 4f145d106s6p45f 4f145d106s6p46f 4f145d106s6p36d2 4f145d96s26p5 4f145d96s26p45f 4f145d96s26p46f 4f145d96s26p36d2 4f135d106s26p46d 4f135d106s26p36d5f 4f135d106s26p36d6f Intravalence correlation (single excitations up to n=6, l=3) Even parity 4f145d106s26p4 4f145d106s26p35f 4f145d106s26p36f 4f145d106s26p26d2 Odd parity 4f145d106s26p36d 4f145d106s26p26d5f 4f145d106s26p26d6f 196 states 594 states Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  20. Theoretical approach Pseudo-relativistic Hartree-Fock (HFR) method (R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981) Multiconfiguration approach (Slater-Condon) Core-valence correlation (single excitations from 4f, 5d, 6s) Example : Po (6p4 – 6p36d transitions) Even parity 4f145d106s6p46d 4f145d106s6p36d5f 4f145d106s6p36d6f 4f145d96s26p46d 4f145d96s26p36d5f 4f145d96s26p36d6f 4f135d106s26p5 4f135d106s26p45f 4f135d106s26p46f 4f135d106s26p36d2 Odd parity 4f145d106s6p5 4f145d106s6p45f 4f145d106s6p46f 4f145d106s6p36d2 4f145d96s26p5 4f145d96s26p45f 4f145d96s26p46f 4f145d96s26p36d2 4f135d106s26p46d 4f135d106s26p36d5f 4f135d106s26p36d6f Intravalence correlation (single excitations up to n=6, l=3) Even parity 4f145d106s26p4 4f145d106s26p35f 4f145d106s26p36f 4f145d106s26p26d2 Odd parity 4f145d106s26p36d 4f145d106s26p26d5f 4f145d106s26p26d6f 10596 states 10910 states 196 states 594 states Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  21. Theoretical approach Core-polarization corrections (HFR+CPOL method) (see e.g. Quinet et al., M.N.R.A.S. 307, 934, 1999; Quinet et al., J. Alloys Compd 344, 255, 2002) Core-polarization model potential Intravalence correlation considered within a configuration interaction expansion Core-valence correlation represented by a core-polarization model potential depending on two parameters (dipole polarizability ad and cut-off radius rc) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  22. Theoretical approach Core-polarization corrections (HFR+CPOL method) (see e.g. Quinet et al., M.N.R.A.S. 307, 934, 1999; Quinet et al., J. Alloys Compd 344, 255, 2002) Core-polarization model potential Intravalence correlation considered within a configuration interaction expansion Core-valence correlation represented by a core-polarization model potential depending on two parameters (dipole polarizability ad and cut-off radius rc) Corrected dipole radial integral replaced by Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  23. Atomic structure calculations in polonium Journal of Quantitative Spectroscopy and Radiative Transfer 145 (2014) 153 - 159 Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  24. Atomic structure calculations in polonium Pseudo-relativistic Hartree-Fock models considered in the present work Intravalence interactions within 6p3nl Single excitations from 6p Double excitations from 6p Single excitations from 6s Double excitations from 6s Core-polarization up to 5d Model A : 6s26p4 + 6s26p3nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s26p2nln’l’ Model C : Model B + 6s26pnln’l’n’’l’’ Model D : Model C + 6s6p4nl + 6s6p3nln’l’ Model E : Model D + 6p6 + 6p5nl + 6p4nln’l’ Model F : Model E + [1s2 … 5d10] core-polarization (Po6+ core : ad = 2.00 a.u., rc = 1.17 a.u.) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  25. Atomic structure calculations in polonium Pseudo-relativistic Hartree-Fock models considered in the present work Model A : 6s26p4 + 6s26p3nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s26p2nln’l’ Model C : Model B + 6s26pnln’l’n’’l’’ Model D : Model C + 6s6p4nl + 6s6p3nln’l’ Model E : Model D + 6p6 + 6p5nl + 6p4nln’l’ Model F : Model E + [1s2 … 5d10] core-polarization (Po6+ core : ad = 2.00 a.u., rc = 1.17 a.u.) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  26. Atomic structure calculations in polonium Pseudo-relativistic Hartree-Fock models considered in the present work Model A : 6s26p4 + 6s26p3nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s26p2nln’l’ Model C : Model B + 6s26pnln’l’n’’l’’ Model D : Model C + 6s6p4nl + 6s6p3nln’l’ Model E : Model D + 6p6 + 6p5nl + 6p4nln’l’ Model F : Model E + [1s2 … 5d10] core-polarization (Po6+ core : ad = 2.00 a.u., rc = 1.17 a.u.) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  27. Atomic structure calculations in polonium Even-parity energy levels Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  28. Atomic structure calculations in polonium Even-parity energy levels Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  29. Atomic structure calculations in polonium Even-parity energy levels Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  30. Atomic structure calculations in polonium Even-parity energy levels Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  31. Atomic structure calculations in polonium Odd-parity energy levels Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  32. Atomic structure calculations in polonium Odd-parity energy levels Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  33. Atomic structure calculations in polonium Radiative transitions (transition probabilities and oscillator strengths) E fik with Aki in s-1, DEki in cm-1, l in Å Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  34. Atomic structure calculations in polonium Radiative transitions (transition probabilities and oscillator strengths) Model A : 6s26p4 + 6s26p3nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s26p2nln’l’ Model C : Model B + 6s26pnln’l’n’’l’’ Model D : Model C + 6s6p4nl + 6s6p3nln’l’ Model E : Model D + 6p6 + 6p5nl + 6p4nln’l’ Model F : Model E + [1s2 … 5d10] core-polarization (Po6+ core : ad = 2.00 a.u., rc = 1.17 a.u.) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  35. Atomic structure calculations in polonium Radiative transitions Model A : 6s26p4 + 6s26p3nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s26p2nln’l’ Model C : Model B + 6s26pnln’l’n’’l’’ Model D : Model C + 6s6p4nl + 6s6p3nln’l’ Model E : Model D + 6p6 + 6p5nl + 6p4nln’l’ Model F : Model E + [1s2 … 5d10] core-polarization (Po6+ core : ad = 2.00 a.u., rc = 1.17 a.u.) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  36. Atomic structure calculations in polonium Radiative transitions (oscillator strengths and transition probabilities) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  37. Atomic structure calculations in polonium Comparison with experiment Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  38. Atomic structure calculations in astatine Up to very recently… R. McLaughlin, J.O.S.A. 54, 965 (1964) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  39. Atomic structure calculations in astatine New experimental analyses (laser spectroscopy – ionization potential) S. Rothe et al., Nature Commun. 4, 1835 (2013) S. Raeder et al., Hyperfine Interact. 227, 77 (2014) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  40. Atomic structure calculations in astatine New experimental analyses (laser spectroscopy – ionization potential) S. Rothe et al., Nature Commun. 4, 1835 (2013) S. Raeder et al., Hyperfine Interact. 227, 77 (2014) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  41. Atomic structure calculations in astatine Pseudo-relativistic Hartree-Fock models Model A : 6s26p5 + 6s26p4nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s26p3nln’l’ Model C : Model B + 6s26p2nln’l’n’’l’’ Model D : Model C + 6s6p5nl + 6s6p4nln’l’ Model E : Model D + 6p6nl + 6p5nln’l’ Model F : Model E + [1s2 … 5d10] core-polarization (At7+ core : ad = 1.8 a.u., rc = 1.12 a.u.) Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  42. Atomic structure calculations in astatine Energy levels within the 6p47p configuration Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  43. Atomic structure calculations in astatine Energy levels within the 6p47p configuration Experiment Theory (Raeder et al. 2014) (This work) 58805.0 (J=3/2) 58778 (J=3/2) 57298 (J=1/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57274 (J=7/2) 57157.1 (J=5/2) 57158 (J=5/2) 56103 (J=5/2) 55969 (J=3/2) Not to scale ! Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  44. Atomic structure calculations in astatine Energy levels within the 6p47p configuration Experiment Theory (Raeder et al. 2014) (This work) 58805.0 (J=3/2) 58778 (J=3/2) 57298 (J=1/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57274 (J=7/2) 57157.1 (J=5/2) 57158 (J=5/2) 56103 (J=5/2) 55969 (J=3/2) Not to scale ! Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  45. Atomic structure calculations in astatine Energy levels within the 6p47p configuration Rothe et al. (2013); Raeder et al. (2014) Experiment Theory (Raeder et al. 2014) (This work) 6p47p 58805.0 (J=3/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57157.1 (J=5/2) 58805.0 (J=3/2) 58778 (J=3/2) 57298 (J=1/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57274 (J=7/2) 57157.1 (J=5/2) 57158 (J=5/2) 6p47s 46233.64 (J=3/2) 44549.28 (J=5/2) 56103 (J=5/2) 55969 (J=3/2) Not to scale ! Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  46. Atomic structure calculations in astatine Energy levels within the 6p47p configuration Rothe et al. (2013); Raeder et al. (2014) Experiment Theory (Raeder et al. 2014) (This work) 6p47p 58805.0 (J=3/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57157.1 (J=5/2) 58805.0 (J=3/2) 58778 (J=3/2) 57298 (J=1/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57274 (J=7/2) 57157.1 (J=5/2) 57158 (J=5/2) 6p47s 46233.64 (J=3/2) 44549.28 (J=5/2) 56103 (J=5/2) 55969 (J=3/2) Not to scale ! Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  47. Atomic structure calculations in astatine Energy levels within the 6p47p configuration Rothe et al. (2013); Raeder et al. (2014) Experiment Theory (Raeder et al. 2014) (This work) 6p47p 58805.0 (J=3/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57157.1 (J=5/2) 58805.0 (J=3/2) 58778 (J=3/2) == 1/2 == 7/2 57298 (J=1/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57274 (J=7/2) 57157.1 (J=5/2) 57158 (J=5/2) 6p47s 46233.64 (J=3/2) 44549.28 (J=5/2) 56103 (J=5/2) 55969 (J=3/2) Not to scale ! Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  48. Atomic structure calculations in astatine Energy levels within the 6p47p configuration Rothe et al. (2013); Raeder et al. (2014) Experiment Theory (Raeder et al. 2014) (This work) 6p47p 58805.0 (J=3/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57157.1 (J=5/2) 58805.0 (J=3/2) 58778 (J=3/2) == 1/2 == 7/2 57298 (J=1/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57274 (J=7/2) 57157.1 (J=5/2) 57158 (J=5/2) 6p47s 46233.64 (J=3/2) 44549.28 (J=5/2) 56103 (J=5/2) 55969 (J=3/2) Not to scale ! Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  49. Atomic structure calculations in astatine Classification of experimentally observed energy levels Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

  50. Atomic structure calculations in astatine Classification of experimentally observed energy levels Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015

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