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

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 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 | BriX Workshop, Liège, 27 – 28 May 2015 Some properties of polonium and astatine atoms Polonium (Po) Astatine (At) Atomic number :84 Ground electronic configuration :[Xe]4f 14 5d 10 6s 2 6p 4 Excited electronic configurations :[Xe]4f 14 5d 10 6s 2 6p 3 nl (nl = 6d, 7s, 7p, 7d, …) Known isotopes :42 (A = 186 – 227) Longest half-life :103 years ( 209 Po) Atomic number :85 Ground electronic configuration :[Xe]4f 14 5d 10 6s 2 6p 5 Excited electronic configurations :[Xe]4f 14 5d 10 6s 2 6p 4 nl (nl = 6d, 7s, 7p, 7d, …) Known isotopes :32 (A = 191, 193 – 223) Longest half-life :8.1 hours ( 210 At)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Experimental spectrum and energy levels of polonium Config.TermJE (cm -1 )Config.TermJE (cm -1 ) 6p 43P3P20.00[odd] ?° ? p 43P3P p 3 ( 4 S)8s 5 S° ? p 43P3P [odd] ?° ?2 ? p 41D1D p 3 ( 4 S)8s 2 S° ?1 ? p 3 ( 4 S)7s 5 S° p 3 ( 2 D)7S 3 D° ?1 ? p 3 ( 4 S)7s 3 S° p 3 ( 4 S)8p 5 P ? p 41S1S p 3 ( 4 S)8p?1 or p 3 ( 4 S)7p 5 P ?3 ? p 3 ( 4 S)7d° ?2 ? p 3 ( 4 S)7p?? p 3 ( 4 S)8p?1 or p 3 ( 4 S)7p?1 or [odd] ?° ?1 or p 3 ( 4 S)6d 5 D° ? p 3 ( 4 S)9p 5 P ?3 ? p 3 ( 4 S)6d 5 D° ? p 3 ( 4 S)9p?1 or p 3 ( 4 S)6d° ? p 3 ( 4 S)9p ??1 or p 3 ( 4 S)6d° ? p 3 ( 4 S)8d° ?1 or [odd] ?° ? p 3 ( 4 S)8d° ?1 or [odd] ?° ? p 3 ( 4 S)10p ??1 or G.W. Charles, J.O.S.A. 56, 1292 (1966)  97 spectral lines in the region – nm [NIST Atomic Spectra Database (

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Experimental spectrum and energy levels of polonium Config.TermJE (cm -1 )Config.TermJE (cm -1 ) 6p 43P3P20.00[odd] ?° ? p 43P3P p 3 ( 4 S)8s 5 S° ? p 43P3P [odd] ?° ?2 ? p 41D1D p 3 ( 4 S)8s 2 S° ?1 ? p 3 ( 4 S)7s 5 S° p 3 ( 2 D)7S 3 D° ?1 ? p 3 ( 4 S)7s 3 S° p 3 ( 4 S)8p 5 P ? p 41S1S p 3 ( 4 S)8p?1 or p 3 ( 4 S)7p 5 P ?3 ? p 3 ( 4 S)7d° ?2 ? p 3 ( 4 S)7p?? p 3 ( 4 S)8p?1 or p 3 ( 4 S)7p?1 or [odd] ?° ?1 or p 3 ( 4 S)6d 5 D° ? p 3 ( 4 S)9p 5 P ?3 ? p 3 ( 4 S)6d 5 D° ? p 3 ( 4 S)9p?1 or p 3 ( 4 S)6d° ? p 3 ( 4 S)9p ??1 or p 3 ( 4 S)6d° ? p 3 ( 4 S)8d° ?1 or [odd] ?° ? p 3 ( 4 S)8d° ?1 or [odd] ?° ? p 3 ( 4 S)10p ??1 or G.W. Charles, J.O.S.A. 56, 1292 (1966)  97 spectral lines in the region – nm [NIST Atomic Spectra Database (

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Experimental spectrum and energy levels of polonium Config.TermJE (cm -1 )Config.TermJE (cm -1 ) 6p 43P3P20.00[odd] ?° ? p 43P3P p 3 ( 4 S)8s 5 S° ? p 43P3P [odd] ?° ?2 ? p 41D1D p 3 ( 4 S)8s 2 S° ?1 ? p 3 ( 4 S)7s 5 S° p 3 ( 2 D)7S 3 D° ?1 ? p 3 ( 4 S)7s 3 S° p 3 ( 4 S)8p 5 P ? p 41S1S p 3 ( 4 S)8p?1 or p 3 ( 4 S)7p 5 P ?3 ? p 3 ( 4 S)7d° ?2 ? p 3 ( 4 S)7p?? p 3 ( 4 S)8p?1 or p 3 ( 4 S)7p?1 or [odd] ?° ?1 or p 3 ( 4 S)6d 5 D° ? p 3 ( 4 S)9p 5 P ?3 ? p 3 ( 4 S)6d 5 D° ? p 3 ( 4 S)9p?1 or p 3 ( 4 S)6d° ? p 3 ( 4 S)9p ??1 or p 3 ( 4 S)6d° ? p 3 ( 4 S)8d° ?1 or [odd] ?° ? p 3 ( 4 S)8d° ?1 or [odd] ?° ? p 3 ( 4 S)10p ??1 or G.W. Charles, J.O.S.A. 56, 1292 (1966)  97 spectral lines in the region – nm [NIST Atomic Spectra Database (

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Experimental spectrum and energy levels of astatine Config.TermJE (cm -1 ) 6p 52 P°3/20.0 6p 4 ( 3 P)7s 4P4P5/ p 4 ( 3 P)7s 4P4P3/ R. McLaughlin, J.O.S.A. 54, 965 (1964)  2 spectral lines at and nm [NIST Atomic Spectra Database (

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 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 | BriX Workshop, Liège, 27 – 28 May 2015 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 | BriX Workshop, Liège, 27 – 28 May 2015 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 | BriX Workshop, Liège, 27 – 28 May 2015 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 | BriX Workshop, Liège, 27 – 28 May 2015 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 P i (r i )  Calculate potentials  Solve HF equations  New P i (r i ) Same as before ? STOP NO YES

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 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 | BriX Workshop, Liège, 27 – 28 May 2015 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 | BriX Workshop, Liège, 27 – 28 May 2015 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 Ab initio or semi-empirical approach Included perturbationaly (spin-orbit, mass-velocity, Darwin term) Good agreement with fully relativistic methods 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 | BriX Workshop, Liège, 27 – 28 May 2015 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 (6p 4 – 6p 3 6d transitions)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 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 (6p 4 – 6p 3 6d transitions) Intravalence correlation (single excitations up to n=6, l=3) Even parity 4f 14 5d 10 6s 2 6p 4 4f 14 5d 10 6s 2 6p 3 5f 4f 14 5d 10 6s 2 6p 3 6f 4f 14 5d 10 6s 2 6p 2 6d 2 Odd parity 4f 14 5d 10 6s 2 6p 3 6d 4f 14 5d 10 6s 2 6p 2 6d5f 4f 14 5d 10 6s 2 6p 2 6d6f

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 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 (6p 4 – 6p 3 6d transitions) Intravalence correlation (single excitations up to n=6, l=3) Even parity 4f 14 5d 10 6s 2 6p 4 4f 14 5d 10 6s 2 6p 3 5f 4f 14 5d 10 6s 2 6p 3 6f 4f 14 5d 10 6s 2 6p 2 6d 2 Odd parity 4f 14 5d 10 6s 2 6p 3 6d 4f 14 5d 10 6s 2 6p 2 6d5f 4f 14 5d 10 6s 2 6p 2 6d6f Core-valence correlation (single excitations from 4f, 5d, 6s) Even parity 4f 14 5d 10 6s6p 4 6d 4f 14 5d 10 6s6p 3 6d5f 4f 14 5d 10 6s6p 3 6d6f 4f 14 5d 9 6s 2 6p 4 6d 4f 14 5d 9 6s 2 6p 3 6d5f 4f 14 5d 9 6s 2 6p 3 6d6f 4f 13 5d 10 6s 2 6p 5 4f 13 5d 10 6s 2 6p 4 5f 4f 13 5d 10 6s 2 6p 4 6f 4f 13 5d 10 6s 2 6p 3 6d 2 Odd parity 4f 14 5d 10 6s6p 5 4f 14 5d 10 6s6p 4 5f 4f 14 5d 10 6s6p 4 6f 4f 14 5d 10 6s6p 3 6d 2 4f 14 5d 9 6s 2 6p 5 4f 14 5d 9 6s 2 6p 4 5f 4f 14 5d 9 6s 2 6p 4 6f 4f 14 5d 9 6s 2 6p 3 6d 2 4f 13 5d 10 6s 2 6p 4 6d 4f 13 5d 10 6s 2 6p 3 6d5f 4f 13 5d 10 6s 2 6p 3 6d6f

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 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 (6p 4 – 6p 3 6d transitions) Intravalence correlation (single excitations up to n=6, l=3) Even parity 4f 14 5d 10 6s 2 6p 4 4f 14 5d 10 6s 2 6p 3 5f 4f 14 5d 10 6s 2 6p 3 6f 4f 14 5d 10 6s 2 6p 2 6d 2 Odd parity 4f 14 5d 10 6s 2 6p 3 6d 4f 14 5d 10 6s 2 6p 2 6d5f 4f 14 5d 10 6s 2 6p 2 6d6f Core-valence correlation (single excitations from 4f, 5d, 6s) Even parity 4f 14 5d 10 6s6p 4 6d 4f 14 5d 10 6s6p 3 6d5f 4f 14 5d 10 6s6p 3 6d6f 4f 14 5d 9 6s 2 6p 4 6d 4f 14 5d 9 6s 2 6p 3 6d5f 4f 14 5d 9 6s 2 6p 3 6d6f 4f 13 5d 10 6s 2 6p 5 4f 13 5d 10 6s 2 6p 4 5f 4f 13 5d 10 6s 2 6p 4 6f 4f 13 5d 10 6s 2 6p 3 6d 2 Odd parity 4f 14 5d 10 6s6p 5 4f 14 5d 10 6s6p 4 5f 4f 14 5d 10 6s6p 4 6f 4f 14 5d 10 6s6p 3 6d 2 4f 14 5d 9 6s 2 6p 5 4f 14 5d 9 6s 2 6p 4 5f 4f 14 5d 9 6s 2 6p 4 6f 4f 14 5d 9 6s 2 6p 3 6d 2 4f 13 5d 10 6s 2 6p 4 6d 4f 13 5d 10 6s 2 6p 3 6d5f 4f 13 5d 10 6s 2 6p 3 6d6f 196 states594 states

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 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 (6p 4 – 6p 3 6d transitions) Intravalence correlation (single excitations up to n=6, l=3) Even parity 4f 14 5d 10 6s 2 6p 4 4f 14 5d 10 6s 2 6p 3 5f 4f 14 5d 10 6s 2 6p 3 6f 4f 14 5d 10 6s 2 6p 2 6d 2 Odd parity 4f 14 5d 10 6s 2 6p 3 6d 4f 14 5d 10 6s 2 6p 2 6d5f 4f 14 5d 10 6s 2 6p 2 6d6f Core-valence correlation (single excitations from 4f, 5d, 6s) Even parity 4f 14 5d 10 6s6p 4 6d 4f 14 5d 10 6s6p 3 6d5f 4f 14 5d 10 6s6p 3 6d6f 4f 14 5d 9 6s 2 6p 4 6d 4f 14 5d 9 6s 2 6p 3 6d5f 4f 14 5d 9 6s 2 6p 3 6d6f 4f 13 5d 10 6s 2 6p 5 4f 13 5d 10 6s 2 6p 4 5f 4f 13 5d 10 6s 2 6p 4 6f 4f 13 5d 10 6s 2 6p 3 6d 2 Odd parity 4f 14 5d 10 6s6p 5 4f 14 5d 10 6s6p 4 5f 4f 14 5d 10 6s6p 4 6f 4f 14 5d 10 6s6p 3 6d 2 4f 14 5d 9 6s 2 6p 5 4f 14 5d 9 6s 2 6p 4 5f 4f 14 5d 9 6s 2 6p 4 6f 4f 14 5d 9 6s 2 6p 3 6d 2 4f 13 5d 10 6s 2 6p 4 6d 4f 13 5d 10 6s 2 6p 3 6d5f 4f 13 5d 10 6s 2 6p 3 6d6f states states 196 states594 states

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 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  d and cut-off radius r c )

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 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 Corrected dipole radial integral Intravalence correlation considered within a configuration interaction expansion Core-valence correlation represented by a core-polarization model potential depending on two parameters (dipole polarizability  d and cut-off radius r c ) replaced by

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Journal of Quantitative Spectroscopy and Radiative Transfer 145 (2014)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Model A : 6s 2 6p 4 + 6s 2 6p 3 nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s 2 6p 2 nln’l’ Model C : Model B + 6s 2 6pnln’l’n’’l’’ Model D : Model C + 6s6p 4 nl + 6s6p 3 nln’l’ Model E : Model D + 6p 6 + 6p 5 nl + 6p 4 nln’l’ Model F : Model E + [1s 2 … 5d 10 ] core-polarization (Po 6+ core :  d = 2.00 a.u., r c = 1.17 a.u.) Pseudo-relativistic Hartree-Fock models considered in the present work Intravalence interactions within 6p 3 nl Single excitations from 6p Double excitations from 6p Single excitations from 6s Double excitations from 6s Core-polarization up to 5d

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Model A : 6s 2 6p 4 + 6s 2 6p 3 nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s 2 6p 2 nln’l’ Model C : Model B + 6s 2 6pnln’l’n’’l’’ Model D : Model C + 6s6p 4 nl + 6s6p 3 nln’l’ Model E : Model D + 6p 6 + 6p 5 nl + 6p 4 nln’l’ Model F : Model E + [1s 2 … 5d 10 ] core-polarization (Po 6+ core :  d = 2.00 a.u., r c = 1.17 a.u.) Pseudo-relativistic Hartree-Fock models considered in the present work

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Model A : 6s 2 6p 4 + 6s 2 6p 3 nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s 2 6p 2 nln’l’ Model C : Model B + 6s 2 6pnln’l’n’’l’’ Model D : Model C + 6s6p 4 nl + 6s6p 3 nln’l’ Model E : Model D + 6p 6 + 6p 5 nl + 6p 4 nln’l’ Model F : Model E + [1s 2 … 5d 10 ] core-polarization (Po 6+ core :  d = 2.00 a.u., r c = 1.17 a.u.) Pseudo-relativistic Hartree-Fock models considered in the present work

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Experiment (NIST)Theory (This work) Config.TermJE (cm -1 ) J1 st component2 nd component3 rd component 6p 43P3P % 6p 4 3 P20% 6p 4 1 D 6p 43P3P % 6p 4 3 P43% 6p 4 1 S 6p 43P3P % 6p 4 3 P 6p 41D1D % 6p 4 1 D20% 6p 4 3 P 6p 41S1S % 6p 4 1 S43% 6p 4 3 P 6p 3 ( 4 S)7p 5 P ?3 ? % 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 4 S)7p 3 P15% 6p 3 ( 2 P)7p 3 P 6p 3 ( 4 S)7p?? % 6p 3 ( 4 S)7p 5 P15% 6p 3 ( 2 P)7p 3 D13% 6p 3 ( 2 P)7p 3 P 6p 3 ( 4 S)7p?1 or % 6p 3 ( 4 S)7p 5 P31% 6p 3 ( 2 P)7p 3 D8% 6p 3 ( 2 D)7p 3 F % 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 2 P)7p 3 S % 6p 3 ( 4 S)7p 3 P17% 6p 3 ( 2 P)7p 1 D13% 6p 3 ( 2 P)7p 3 P % 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 2 P)7p 1 S12% 6p 3 ( 2 D)7p 3 P Even-parity energy levels

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Experiment (NIST)Theory (This work) Config.TermJE (cm -1 ) J1 st component2 nd component3 rd component 6p 43P3P % 6p 4 3 P20% 6p 4 1 D 6p 43P3P % 6p 4 3 P43% 6p 4 1 S 6p 43P3P % 6p 4 3 P 6p 41D1D % 6p 4 1 D20% 6p 4 3 P 6p 41S1S % 6p 4 1 S43% 6p 4 3 P 6p 3 ( 4 S)7p 5 P ?3 ? % 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 4 S)7p 3 P15% 6p 3 ( 2 P)7p 3 P 6p 3 ( 4 S)7p?? % 6p 3 ( 4 S)7p 5 P15% 6p 3 ( 2 P)7p 3 D13% 6p 3 ( 2 P)7p 3 P 6p 3 ( 4 S)7p?1 or % 6p 3 ( 4 S)7p 5 P31% 6p 3 ( 2 P)7p 3 D8% 6p 3 ( 2 D)7p 3 F % 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 2 P)7p 3 S % 6p 3 ( 4 S)7p 3 P17% 6p 3 ( 2 P)7p 1 D13% 6p 3 ( 2 P)7p 3 P % 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 2 P)7p 1 S12% 6p 3 ( 2 D)7p 3 P Even-parity energy levels

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Experiment (NIST)Theory (This work) Config.TermJE (cm -1 ) J1 st component2 nd component3 rd component 6p 43P3P % 6p 4 3 P20% 6p 4 1 D 6p 43P3P % 6p 4 3 P43% 6p 4 1 S 6p 43P3P % 6p 4 3 P 6p 41D1D % 6p 4 1 D20% 6p 4 3 P 6p 41S1S % 6p 4 1 S43% 6p 4 3 P 6p 3 ( 4 S)7p 5 P ?3 ? % 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 4 S)7p 3 P15% 6p 3 ( 2 P)7p 3 P 6p 3 ( 4 S)7p?? % 6p 3 ( 4 S)7p 5 P15% 6p 3 ( 2 P)7p 3 D13% 6p 3 ( 2 P)7p 3 P 6p 3 ( 4 S)7p?1 or % 6p 3 ( 4 S)7p 5 P31% 6p 3 ( 2 P)7p 3 D8% 6p 3 ( 2 D)7p 3 F % 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 2 P)7p 3 S % 6p 3 ( 4 S)7p 3 P17% 6p 3 ( 2 P)7p 1 D13% 6p 3 ( 2 P)7p 3 P % 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 2 P)7p 1 S12% 6p 3 ( 2 D)7p 3 P Even-parity energy levels

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Experiment (NIST)Theory (This work) Config.TermJE (cm -1 ) J1 st component2 nd component3 rd component 6p 43P3P % 6p 4 3 P20% 6p 4 1 D 6p 43P3P % 6p 4 3 P43% 6p 4 1 S 6p 43P3P % 6p 4 3 P 6p 41D1D % 6p 4 1 D20% 6p 4 3 P 6p 41S1S % 6p 4 1 S43% 6p 4 3 P 6p 3 ( 4 S)7p 5 P ?3 ? % 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 4 S)7p 3 P15% 6p 3 ( 2 P)7p 3 P 6p 3 ( 4 S)7p?? % 6p 3 ( 4 S)7p 5 P15% 6p 3 ( 2 P)7p 3 D13% 6p 3 ( 2 P)7p 3 P 6p 3 ( 4 S)7p?1 or % 6p 3 ( 4 S)7p 5 P31% 6p 3 ( 2 P)7p 3 D8% 6p 3 ( 2 D)7p 3 F % 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 2 P)7p 3 S % 6p 3 ( 4 S)7p 3 P17% 6p 3 ( 2 P)7p 1 D13% 6p 3 ( 2 P)7p 3 P % 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 2 P)7p 1 S12% 6p 3 ( 2 D)7p 3 P Even-parity energy levels Se4p 3 ( 4 S)5p 5 PJ = Te5p 3 ( 4 S)6p 5 PJ = [Experimental data] J = [Experimental data] J = J = J =

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Experiment (NIST)Theory (This work) Config.TermJE (cm -1 ) J1 st component2 nd component3 rd component 6p 3 ( 4 S)7s 5 S° % 6p 3 ( 4 S)7s 5 S32% 6p 3 ( 2 P)7s 3 P9% 6p 3 ( 2 D)7s 3 D 6p 3 ( 4 S)7s 3 S° % 6p 3 ( 4 S)7s 3 S22% 6p 3 ( 2 P)7s 1 P20% 6p 3 ( 2 D)7s 3 D 6p 3 ( 4 S)6d 5 D° ? % 6p 3 ( 4 S)6d 5 D18% 6p 3 ( 4 S)6d 3 D15% 6p 3 ( 2 P)6d 3 D 6p 3 ( 4 S)6d 5 D° ? % 6p 3 ( 4 S)6d 5 D17% 6p 3 ( 2 P)6d 3 D14% 6p 3 ( 2 P)6d 3 F 6p 3 ( 4 S)6d° ? % 6p 3 ( 4 S)6d 5 D17% 6p 3 ( 2 P)6d 3 P12% 6p 3 ( 2 P)6d 3 D % 6p 3 ( 4 S)6d 5 D31% 6p 3 ( 2 P)6d 3 F8% 6p 3 ( 2 D)6d 3 G 6p 3 ( 4 S)6d° ? % 6p 3 ( 4 S)6d 3 D21% 6p 3 ( 4 S)6d 5 D6% 6p 3 ( 2 D)6d 3 P % 6p 3 ( 4 S)6d 5 D30% 6p 3 ( 2 P)6d 3 P7% 6p 3 ( 2 D)6d 3 P % 6p 3 ( 4 S)6d 3 D20% 6p 3 ( 2 P)6d 1 F11% 6p 3 ( 2 D)6d 3 G [odd] ?° ? % 6p 3 ( 4 S)6d 3 D16% 6p 3 ( 2 P)6d 1 P10% 6p 3 ( 2 P)6d 3 P [odd] ?° ?2 ? % 6p 3 ( 2 D)7s 3 D36% 6p 3 ( 4 S)7s 5 S16% 6p 3 ( 2 D)7s 1 D 6p 3 ( 2 D)7S 3 D° ?1 ? % 6p 3 ( 2 D)7s 3 D36% 6p 3 ( 4 S)7s 3 S3% 6p 3 ( 4 S)7d 3 D 6p 3 ( 4 S)7d° ?2 ? % 6p 3 ( 4 S)7d 5 D20% 6p 3 ( 4 S)7d 3 D14% 6p 3 ( 2 P)7d 3 D Odd-parity energy levels

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Experiment (NIST)Theory (This work) Config.TermJE (cm -1 ) J1 st component2 nd component3 rd component 6p 3 ( 4 S)7s 5 S° % 6p 3 ( 4 S)7s 5 S32% 6p 3 ( 2 P)7s 3 P9% 6p 3 ( 2 D)7s 3 D 6p 3 ( 4 S)7s 3 S° % 6p 3 ( 4 S)7s 3 S22% 6p 3 ( 2 P)7s 1 P20% 6p 3 ( 2 D)7s 3 D 6p 3 ( 4 S)6d 5 D° ? % 6p 3 ( 4 S)6d 5 D18% 6p 3 ( 4 S)6d 3 D15% 6p 3 ( 2 P)6d 3 D 6p 3 ( 4 S)6d 5 D° ? % 6p 3 ( 4 S)6d 5 D17% 6p 3 ( 2 P)6d 3 D14% 6p 3 ( 2 P)6d 3 F 6p 3 ( 4 S)6d° ? % 6p 3 ( 4 S)6d 5 D17% 6p 3 ( 2 P)6d 3 P12% 6p 3 ( 2 P)6d 3 D % 6p 3 ( 4 S)6d 5 D31% 6p 3 ( 2 P)6d 3 F8% 6p 3 ( 2 D)6d 3 G 6p 3 ( 4 S)6d° ? % 6p 3 ( 4 S)6d 3 D21% 6p 3 ( 4 S)6d 5 D6% 6p 3 ( 2 D)6d 3 P % 6p 3 ( 4 S)6d 5 D30% 6p 3 ( 2 P)6d 3 P7% 6p 3 ( 2 D)6d 3 P % 6p 3 ( 4 S)6d 3 D20% 6p 3 ( 2 P)6d 1 F11% 6p 3 ( 2 D)6d 3 G [odd] ?° ? % 6p 3 ( 4 S)6d 3 D16% 6p 3 ( 2 P)6d 1 P10% 6p 3 ( 2 P)6d 3 P [odd] ?° ?2 ? % 6p 3 ( 2 D)7s 3 D36% 6p 3 ( 4 S)7s 5 S16% 6p 3 ( 2 D)7s 1 D 6p 3 ( 2 D)7S 3 D° ?1 ? % 6p 3 ( 2 D)7s 3 D36% 6p 3 ( 4 S)7s 3 S3% 6p 3 ( 4 S)7d 3 D 6p 3 ( 4 S)7d° ?2 ? % 6p 3 ( 4 S)7d 5 D20% 6p 3 ( 4 S)7d 3 D14% 6p 3 ( 2 P)7d 3 D Odd-parity energy levels

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Radiative transitions (transition probabilities and oscillator strengths) E f ik with A ki in s -1,  E ki in cm -1, in Å

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Model A : 6s 2 6p 4 + 6s 2 6p 3 nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s 2 6p 2 nln’l’ Model C : Model B + 6s 2 6pnln’l’n’’l’’ Model D : Model C + 6s6p 4 nl + 6s6p 3 nln’l’ Model E : Model D + 6p 6 + 6p 5 nl + 6p 4 nln’l’ Model F : Model E + [1s 2 … 5d 10 ] core-polarization (Po 6+ core :  d = 2.00 a.u., r c = 1.17 a.u.) Radiative transitions (transition probabilities and oscillator strengths)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Radiative transitions Model A : 6s 2 6p 4 + 6s 2 6p 3 nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s 2 6p 2 nln’l’ Model C : Model B + 6s 2 6pnln’l’n’’l’’ Model D : Model C + 6s6p 4 nl + 6s6p 3 nln’l’ Model E : Model D + 6p 6 + 6p 5 nl + 6p 4 nln’l’ Model F : Model E + [1s 2 … 5d 10 ] core-polarization (Po 6+ core :  d = 2.00 a.u., r c = 1.17 a.u.)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Radiative transitions (oscillator strengths and transition probabilities) (nm) a Lower level (cm -1 ) b Upper level (cm -1 ) b log gfgA (s -1 ) J=2 (even) J=1 (odd) E J=2 (even) J=2 (odd) E J=2 (even) J=1 (odd) E J=2 (even) J=2 (odd) E J=2 (even) J=1 (odd) E J=2 (even) J=3 (odd) E J=0 (even) J=1 (odd) E J=0 (even) J=1 (odd) E J=0 (even) J=1 (odd) E J=1 (even) J=2 (odd) E J=2 (even) J=1 (odd) E J=1 (even) J=1 (odd) E J=1 (even) J=2 (odd) E J=2 (even) J=2 (odd) E J=2 (even) J=2 (odd) E J=1 (even) J=2 (odd) E J=1 (even) J=1 (odd) E J=2 (even) J=1 (odd) E J=1 (even) J=2 (odd) E J=2 (even) J=2 (odd) E J=0 (even) J=1 (odd) E J=2 (even) J=1 (odd) E J=2 (even) J=1 (odd) E J=2 (even) J=3 (odd) E J=1 (even) J=1 (odd) E J=2 (even) J=2 (odd) E J=0 (even) J=1 (odd) E J=2 (odd) J=3 (even) E J=2 (odd) J=2 (even) E J=2 (odd) J=1 (even) E J=1 (odd) J=2 (even) E+7

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in polonium Comparison with experiment

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Up to very recently… R. McLaughlin, J.O.S.A. 54, 965 (1964) Config.TermJE (cm -1 ) 6p 52 P°3/20.0 6p 4 ( 3 P)7s 4P4P5/ p 4 ( 3 P)7s 4P4P3/

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

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

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Pseudo-relativistic Hartree-Fock models Model A : 6s 2 6p 5 + 6s 2 6p 4 nl (nl = 7s, 7p, 6d, 7d, 5f, 6f) Model B : Model A + 6s 2 6p 3 nln’l’ Model C : Model B + 6s 2 6p 2 nln’l’n’’l’’ Model D : Model C + 6s6p 5 nl + 6s6p 4 nln’l’ Model E : Model D + 6p 6 nl + 6p 5 nln’l’ Model F : Model E + [1s 2 … 5d 10 ] core-polarization (At 7+ core :  d = 1.8 a.u., r c = 1.12 a.u.)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration (J=3/2) (J=7/2) (J=1/2) (J=5/2) (J=3/2) (J=1/2) (J=7/2) (J=5/2) (J=5/2) (J=3/2) Not to scale ! Experiment Theory (Raeder et al. 2014) (This work)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration (J=3/2) (J=7/2) (J=1/2) (J=5/2) (J=3/2) (J=1/2) (J=7/2) (J=5/2) (J=5/2) (J=3/2) Not to scale ! Experiment Theory (Raeder et al. 2014) (This work)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration (J=3/2) (J=7/2) (J=1/2) (J=5/2) (J=3/2) (J=1/2) (J=7/2) (J=5/2) (J=5/2) (J=3/2) Not to scale ! Experiment Theory (Raeder et al. 2014) (This work) Rothe et al. (2013); Raeder et al. (2014) 6p 4 7s (J=3/2) (J=5/2) 6p 4 7p (J=3/2) (J=7/2) (J=1/2) (J=5/2)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration (J=3/2) (J=7/2) (J=1/2) (J=5/2) (J=3/2) (J=1/2) (J=7/2) (J=5/2) (J=5/2) (J=3/2) Not to scale ! Experiment Theory (Raeder et al. 2014) (This work) Rothe et al. (2013); Raeder et al. (2014) 6p 4 7s (J=3/2) (J=5/2) 6p 4 7p (J=3/2) (J=7/2) (J=1/2) (J=5/2)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration (J=3/2) (J=7/2) (J=1/2) (J=5/2) (J=3/2) (J=1/2) (J=7/2) (J=5/2) (J=5/2) (J=3/2) Not to scale ! Experiment Theory (Raeder et al. 2014) (This work) Rothe et al. (2013); Raeder et al. (2014) 6p 4 7s (J=3/2) (J=5/2) 6p 4 7p (J=3/2) (J=7/2) (J=1/2) (J=5/2) == 1/2 == 7/2

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration (J=3/2) (J=7/2) (J=1/2) (J=5/2) (J=3/2) (J=1/2) (J=7/2) (J=5/2) (J=5/2) (J=3/2) Not to scale ! Experiment Theory (Raeder et al. 2014) (This work) Rothe et al. (2013); Raeder et al. (2014) 6p 4 7s (J=3/2) (J=5/2) 6p 4 7p (J=3/2) (J=7/2) (J=1/2) (J=5/2) == 1/2 == 7/2

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Classification of experimentally observed energy levels E(cm -1 )J1 st component2 nd component3 rd component 0.00(odd)3/298% 6p 5 2 P (even)5/278% 6p 4 ( 3 P)7s 4 P20% 6p 4 ( 1 D)7s 2 D (even)3/260% 6p 4 ( 3 P)7s 2 P23% 6p 4 ( 1 D)7s 2 D15% 6p 4 ( 3 P)7s 4 P (odd)5/243% 6p 4 ( 3 P)7p 2 D35% 6p 4 ( 3 P)7p 4 P11% 6p 4 ( 1 D)7p 2 D (odd)7/277% 6p 4 ( 3 P)7p 4 D22% 6p 4 ( 1 D)7p 2 F (odd)1/237% 6p 4 ( 3 P)7p 2 S24% 6p 4 ( 1 D)7p 2 P24% 6p 4 ( 3 P)7p 2 P (odd)3/242% 6p 4 ( 3 P)7p 2 P21% 6p 4 ( 3 P)7p 4 S12% 6p 4 ( 1 D)7p 2 D

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Classification of experimentally observed energy levels E(cm -1 )J1 st component2 nd component3 rd component 0.00(odd)3/298% 6p 5 2 P (even)5/278% 6p 4 ( 3 P)7s 4 P20% 6p 4 ( 1 D)7s 2 D (even)3/260% 6p 4 ( 3 P)7s 2 P23% 6p 4 ( 1 D)7s 2 D15% 6p 4 ( 3 P)7s 4 P (odd)5/243% 6p 4 ( 3 P)7p 2 D35% 6p 4 ( 3 P)7p 4 P11% 6p 4 ( 1 D)7p 2 D (odd)7/277% 6p 4 ( 3 P)7p 4 D22% 6p 4 ( 1 D)7p 2 F (odd)1/237% 6p 4 ( 3 P)7p 2 S24% 6p 4 ( 1 D)7p 2 P24% 6p 4 ( 3 P)7p 2 P (odd)3/242% 6p 4 ( 3 P)7p 2 P21% 6p 4 ( 3 P)7p 4 S12% 6p 4 ( 1 D)7p 2 D

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine  (nm) Lower level (cm -1 )Upper level (cm -1 )log gfgA (s -1 ) J=3/2 (odd) J=3/2 (even) E J=3/2 (odd) J=5/2 (even) E J=5/2 (even) J=3/2 (odd) E J=5/2 (even) J=7/2 (odd) E J=5/2 (even) J=5/2 (odd) E J=3/2 (even) J=3/2 (odd) E J=3/2 (even) J=1/2 (odd) E J=3/2 (even) J=5/2 (odd) E+7 Radiative transitions (oscillator strengths, transition probabilities)

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Identification of new high lying odd-parity energy levels S. Raeder et al., Hyperfine Interact. 227, 77 (2014) Odd-parity levels cm cm cm cm -1 6p 4 np

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Identification of new high lying odd-parity energy levels S. Raeder et al., Hyperfine Interact. 227, 77 (2014) Odd-parity levels cm cm cm cm -1 6p 4 np 6p 4 14p 6p 4 13p 6p 4 12p 6p 4 11p 6p 4 10p 6p 4 9p 6p 4 8p 6p 4 7p Theory Experiment

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Identification of new high lying odd-parity energy levels E(cm -1 )J1 st component2 nd component3 rd component (odd)5/241% 6p 4 ( 3 P)9p 2 D36% 6p 4 ( 3 P)9p 4 P14% 6p 4 ( 3 P)9p 2 D (odd)3/243% 6p 4 ( 3 P)9p 2 P20% 6p 4 ( 3 P)9p 4 S12% 6p 4 ( 1 D)9p 2 D (odd)5/241% 6p 4 ( 3 P)10p 2 D36% 6p 4 ( 3 P)10p 4 P14% 6p 4 ( 3 P)10p 2 D (odd)3/243% 6p 4 ( 3 P)10p 2 P20% 6p 4 ( 3 P)10p 4 S12% 6p 4 ( 1 D)10p 2 D

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Identification of new high lying odd-parity energy levels E(cm -1 )J1 st component2 nd component3 rd component (odd)5/241% 6p 4 ( 3 P)9p 2 D36% 6p 4 ( 3 P)9p 4 P14% 6p 4 ( 3 P)9p 2 D (odd)3/243% 6p 4 ( 3 P)9p 2 P20% 6p 4 ( 3 P)9p 4 S12% 6p 4 ( 1 D)9p 2 D (odd)5/241% 6p 4 ( 3 P)10p 2 D36% 6p 4 ( 3 P)10p 4 P14% 6p 4 ( 3 P)10p 2 D (odd)3/243% 6p 4 ( 3 P)10p 2 P20% 6p 4 ( 3 P)10p 4 S12% 6p 4 ( 1 D)10p 2 D  E ion = cm -1 R At = cm -1 (A = 210) Quantum defect 

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Estimated energy level values in the 6p 4 ( 3 P)np Rydberg series Config.Level  Estim. (cm -1 )Obs. (cm -1 )Config.Level  Estim. (cm -1 )Obs. (cm -1 ) 6p 4 ( 3 P)8p 2 D 5/ p 4 ( 3 P)19p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)9p 2 D 5/ p 4 ( 3 P)20p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)10p 2 D 5/ p 4 ( 3 P)21p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)11p 2 D 5/ p 4 ( 3 P)22p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)12p 2 D 5/ p 4 ( 3 P)23p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)13p 2 D 5/ p 4 ( 3 P)24p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)14p 2 D 5/ p 4 ( 3 P)25p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)15p 2 D 5/ p 4 ( 3 P)26p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)16p 2 D 5/ p 4 ( 3 P)27p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)17p 2 D 5/ p 4 ( 3 P)28p 2 D 5/ P 3/ P 3/ p 4 ( 3 P)18p 2 D 5/ p 4 ( 3 P)29p 2 D 5/ P 3/ P 3/

Université de Liège Pascal Quinet | BriX Workshop, Liège, 27 – 28 May 2015 Summary and conclusions  Theoretical investigation of polonium and astatine atomic structures  Pseudo-relativistic Hartree-Fock method  Polonium : - Spectroscopic designation of 6p 3 7p, 6p 3 6d, 6p 3 7s and 6p 3 7d energy levels - Radiative transition parameters for 31 spectral lines in the wavelength region 175 – 987 nm  Astatine : - Spectroscopic designation of 4 levels belonging to 6p 4 7p - Radiative transition parameters for 8 spectral lines in the wavelength region 216 – 915 nm - Identification of 4 new levels in 6p 4 9p and 6p 4 10p configurations - Predicted energies for levels within the 6p 4 np Rydberg series

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