A new theoretical insight into the spectroscopic properties of polonium and astatine atoms Pascal Quinet Spectroscopie Atomique et Physique des Atomes.

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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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] ?° ?154471 6p 43P3P07514.696p 3 ( 4 S)8s 5 S° ?255465.36 6p 43P3P116831.61[odd] ?° ?2 ?55923 6p 41D1D221679.116p 3 ( 4 S)8s 2 S° ?1 ?56268.34 6p 3 ( 4 S)7s 5 S°239081.196p 3 ( 2 D)7S 3 D° ?1 ?57078.05 6p 3 ( 4 S)7s 3 S°140802.706p 3 ( 4 S)8p 5 P ?359290.61 6p 41S1S0427186p 3 ( 4 S)8p?1 or 259354.47 6p 3 ( 4 S)7p 5 P ?3 ?50681.286p 3 ( 4 S)7d° ?2 ?59469.66 6p 3 ( 4 S)7p??50934.896p 3 ( 4 S)8p?1 or 259583.06 6p 3 ( 4 S)7p?1 or 251636.42[odd] ?° ?1 or 261818 6p 3 ( 4 S)6d 5 D° ?251713.096p 3 ( 4 S)9p 5 P ?3 ?62680.99 6p 3 ( 4 S)6d 5 D° ?352098.936p 3 ( 4 S)9p?1 or 262703.96 6p 3 ( 4 S)6d° ?152532.126p 3 ( 4 S)9p ??1 or 262806 6p 3 ( 4 S)6d° ?253027.616p 3 ( 4 S)8d° ?1 or 262885.19 [odd] ?° ?1537626p 3 ( 4 S)8d° ?1 or 262959.49 [odd] ?° ?154250.266p 3 ( 4 S)10p ??1 or 264451 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 Experimental spectrum and energy levels of astatine Config.TermJE (cm -1 ) 6p 52 P°3/20.0 6p 4 ( 3 P)7s 4P4P5/244549.3 6p 4 ( 3 P)7s 4P4P3/246233.6 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 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 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 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 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 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 10596 states 10910 states 196 states594 states

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015 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 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 43P3P20.000278% 6p 4 3 P20% 6p 4 1 D 6p 43P3P07514.697516055% 6p 4 3 P43% 6p 4 1 S 6p 43P3P116831.6116833198% 6p 4 3 P 6p 41D1D221679.1121680278% 6p 4 1 D20% 6p 4 3 P 6p 41S1S04271842717054% 6p 4 1 S43% 6p 4 3 P 6p 3 ( 4 S)7p 5 P ?3 ?50681.2850773134% 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??50934.8950838240% 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 251636.4251641352% 6p 3 ( 4 S)7p 5 P31% 6p 3 ( 2 P)7p 3 D8% 6p 3 ( 2 D)7p 3 F 51896131% 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 2 P)7p 3 S 52853238% 6p 3 ( 4 S)7p 3 P17% 6p 3 ( 2 P)7p 1 D13% 6p 3 ( 2 P)7p 3 P 53847055% 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 (P.Quinet@ulg.ac.be) | 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 43P3P20.000278% 6p 4 3 P20% 6p 4 1 D 6p 43P3P07514.697516055% 6p 4 3 P43% 6p 4 1 S 6p 43P3P116831.6116833198% 6p 4 3 P 6p 41D1D221679.1121680278% 6p 4 1 D20% 6p 4 3 P 6p 41S1S04271842717054% 6p 4 1 S43% 6p 4 3 P 6p 3 ( 4 S)7p 5 P ?3 ?50681.2850773134% 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??50934.8950838240% 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 251636.4251641352% 6p 3 ( 4 S)7p 5 P31% 6p 3 ( 2 P)7p 3 D8% 6p 3 ( 2 D)7p 3 F 51896131% 6p 3 ( 4 S)7p 3 P19% 6p 3 ( 4 S)7p 5 P16% 6p 3 ( 2 P)7p 3 S 52853238% 6p 3 ( 4 S)7p 3 P17% 6p 3 ( 2 P)7p 1 D13% 6p 3 ( 2 P)7p 3 P 53847055% 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 = 159242.80Te5p 3 ( 4 S)6p 5 PJ = 154160.09 [Experimental data] J = 259287.82 [Experimental data] J = 254199.12 J = 359391.31J = 354535.35

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | 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°239081.1938837252% 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°140802.7040551143% 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° ?251713.0951846228% 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° ?352098.9352213347% 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° ?152532.1252375144% 6p 3 ( 4 S)6d 5 D17% 6p 3 ( 2 P)6d 3 P12% 6p 3 ( 2 P)6d 3 D 52835453% 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° ?253027.6152863226% 6p 3 ( 4 S)6d 3 D21% 6p 3 ( 4 S)6d 5 D6% 6p 3 ( 2 D)6d 3 P 52904054% 6p 3 ( 4 S)6d 5 D30% 6p 3 ( 2 P)6d 3 P7% 6p 3 ( 2 D)6d 3 P 54000346% 6p 3 ( 4 S)6d 3 D20% 6p 3 ( 2 P)6d 1 F11% 6p 3 ( 2 D)6d 3 G [odd] ?° ?154250.2654316144% 6p 3 ( 4 S)6d 3 D16% 6p 3 ( 2 P)6d 1 P10% 6p 3 ( 2 P)6d 3 P [odd] ?° ?2 ?55923.8056107237% 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 ?57078.0557321146% 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 ?59469.6659456230% 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 ) 175.1990.00J=2 (even)57078.05J=1 (odd)-0.853.11E+8 178.8150.00J=2 (even)55923.80J=2 (odd)-0.369.26E+8 184.3310.00J=2 (even)54250.26J=1 (odd)-0.813.05E+8 188.5810.00J=2 (even)53027.61J=2 (odd)-0.151.33E+9 190.3600.00J=2 (even)52532.12J=1 (odd)-1.981.90E+7 191.9430.00J=2 (even)52098.93J=3 (odd)-0.614.44E+8 201.6977514.69J=0 (even)57078.05J=1 (odd)-1.191.08E+8 213.9027514.69J=0 (even)54250.26J=1 (odd)-0.268.05E+8 222.0677514.69J=0 (even)52532.12J=1 (odd)-1.267.43E+7 234.46116831.61J=1 (even)59469.66J=2 (odd)-1.871.64E+7 245.0080.00J=2 (even)40802.70J=1 (odd)-0.098.96E+8 248.39416831.61J=1 (even)57078.05J=1 (odd)-0.216.72E+8 255.72916831.61J=1 (even)55923.80J=2 (odd)-1.147.46E+7 255.8010.00J=2 (even)39081.19J=2 (odd)-0.423.84E+8 264.53821679.11J=2 (even)59469.66J=2 (odd)-1.542.74E+7 276.19216831.61J=1 (even)53027.61J=2 (odd)-1.215.38E+7 280.02616831.61J=1 (even)52532.12J=1 (odd)-1.969.21E+6 282.41121679.11J=2 (even)57078.05J=1 (odd)-1.116.60E+7 286.60116831.61J=1 (even)51713.09J=2 (odd)-1.801.29E+7 291.93121679.11J=2 (even)55923.80J=2 (odd)-1.145.79E+7 300.3217514.69J=0 (even)40802.70J=1 (odd)-0.801.16E+8 306.93121679.11J=2 (even)54250.26J=1 (odd)-2.363.13E+6 324.02421679.11J=2 (even)52532.12J=1 (odd)-1.858.79E+6 328.63821679.11J=2 (even)52098.93J=3 (odd)-2.144.52E+6 417.05216831.61J=1 (even)40802.70J=1 (odd)-1.491.23E+7 574.48521679.11J=2 (even)39081.19J=2 (odd)-2.624.70E+5 696.18442718.00J=0 (even)57078.05J=1 (odd)-2.464.94E+5 796.26239081.19J=2 (odd)51636.42J=3 (even)0.523.62E+8 843.38739081.19J=2 (odd)50934.89J=2 (even)0.271.77E+8 861.82639081.19J=2 (odd)50681.28J=1 (even)-0.078.03E+7 986.68340802.70J=1 (odd)50934.89J=2 (even)-0.452.52E+7

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015 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 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 4P4P5/244549.3 6p 4 ( 3 P)7s 4P4P3/246233.6

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | 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 (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration 58805.0 (J=3/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57157.1 (J=5/2) 58778 (J=3/2) 57298 (J=1/2) 57274 (J=7/2) 57158 (J=5/2) 56103 (J=5/2) 55969 (J=3/2) Not to scale ! Experiment Theory (Raeder et al. 2014) (This work)

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration 58805.0 (J=3/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57157.1 (J=5/2) 58778 (J=3/2) 57298 (J=1/2) 57274 (J=7/2) 57158 (J=5/2) 56103 (J=5/2) 55969 (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 46233.64 (J=3/2) 44549.28 (J=5/2) 6p 4 7p 58805.0 (J=3/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57157.1 (J=5/2)

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | BriX Workshop, Liège, 27 – 28 May 2015 Atomic structure calculations in astatine Energy levels within the 6p 4 7p configuration 58805.0 (J=3/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57157.1 (J=5/2) 58778 (J=3/2) 57298 (J=1/2) 57274 (J=7/2) 57158 (J=5/2) 56103 (J=5/2) 55969 (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 46233.64 (J=3/2) 44549.28 (J=5/2) 6p 4 7p 58805.0 (J=3/2) 57276.7 (J=7/2) 57267.8 (J=1/2) 57157.1 (J=5/2) == 1/2 == 7/2

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | 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 44549.28(even)5/278% 6p 4 ( 3 P)7s 4 P20% 6p 4 ( 1 D)7s 2 D 46233.64(even)3/260% 6p 4 ( 3 P)7s 2 P23% 6p 4 ( 1 D)7s 2 D15% 6p 4 ( 3 P)7s 4 P 57157.10(odd)5/243% 6p 4 ( 3 P)7p 2 D35% 6p 4 ( 3 P)7p 4 P11% 6p 4 ( 1 D)7p 2 D 57267.80(odd)7/277% 6p 4 ( 3 P)7p 4 D22% 6p 4 ( 1 D)7p 2 F 57276.70(odd)1/237% 6p 4 ( 3 P)7p 2 S24% 6p 4 ( 1 D)7p 2 P24% 6p 4 ( 3 P)7p 2 P 58805.00(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 (P.Quinet@ulg.ac.be) | 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 ) 216.2250.00J=3/2 (odd)46233.64J=3/2 (even)-0.071.21E+9 224.4010.00J=3/2 (odd)44549.28J=5/2 (even)-0.941.53E+8 701.27944549.28J=5/2 (even)58805.00J=3/2 (odd)-0.681.83E+8 786.03944549.28J=5/2 (even)57267.80J=7/2 (odd)0.431.72E+8 792.94044549.28J=5/2 (even)57157.10J=5/2 (odd)-0.144.50E+7 795.24046233.64J=3/2 (even)58805.00J=3/2 (odd)-0.075.74E+7 905.29846233.64J=3/2 (even)57276.70J=1/2 (odd)-0.173.10E+7 915.21046233.64J=3/2 (even)57157.10J=5/2 (odd)0.095.46E+7 Radiative transitions (oscillator strengths, transition probabilities)

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | 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 71708.7 cm -1 71376.7 cm -1 70055.4 cm -1 69615.1 cm -1 6p 4 np

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | 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 71708.7 cm -1 71376.7 cm -1 70055.4 cm -1 69615.1 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 (P.Quinet@ulg.ac.be) | 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 69615.1(odd)5/241% 6p 4 ( 3 P)9p 2 D36% 6p 4 ( 3 P)9p 4 P14% 6p 4 ( 3 P)9p 2 D 70055.4(odd)3/243% 6p 4 ( 3 P)9p 2 P20% 6p 4 ( 3 P)9p 4 S12% 6p 4 ( 1 D)9p 2 D 71376.7(odd)5/241% 6p 4 ( 3 P)10p 2 D36% 6p 4 ( 3 P)10p 4 P14% 6p 4 ( 3 P)10p 2 D 71708.7(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 (P.Quinet@ulg.ac.be) | 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 69615.1(odd)5/241% 6p 4 ( 3 P)9p 2 D36% 6p 4 ( 3 P)9p 4 P14% 6p 4 ( 3 P)9p 2 D 70055.4(odd)3/243% 6p 4 ( 3 P)9p 2 P20% 6p 4 ( 3 P)9p 4 S12% 6p 4 ( 1 D)9p 2 D 71376.7(odd)5/241% 6p 4 ( 3 P)10p 2 D36% 6p 4 ( 3 P)10p 4 P14% 6p 4 ( 3 P)10p 2 D 71708.7(odd)3/243% 6p 4 ( 3 P)10p 2 P20% 6p 4 ( 3 P)10p 4 S12% 6p 4 ( 1 D)10p 2 D  4.55 4.36 4.61 4.36 E ion = 75150.8 cm -1 R At = 109737.02 cm -1 (A = 210) Quantum defect 

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | 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 5/2 4.58657696p 4 ( 3 P)19p 2 D 5/2 4.5874623 2 P 3/2 4.3666869 2 P 3/2 4.3674639 6p 4 ( 3 P)9p 2 D 5/2 4.586953469615.16p 4 ( 3 P)20p 2 D 5/2 4.5874689 2 P 3/2 4.367005470055.4 2 P 3/2 4.3674702 6p 4 ( 3 P)10p 2 D 5/2 4.587141571376.76p 4 ( 3 P)21p 2 D 5/2 4.5874744 2 P 3/2 4.367170171708.7 2 P 3/2 4.3674754 6p 4 ( 3 P)11p 2 D 5/2 4.58724886p 4 ( 3 P)22p 2 D 5/2 4.5874789 2 P 3/2 4.3672662 2 P 3/2 4.3674798 6p 4 ( 3 P)12p 2 D 5/2 4.58731586p 4 ( 3 P)23p 2 D 5/2 4.5874827 2 P 3/2 4.3673271 2 P 3/2 4.3674835 6p 4 ( 3 P)13p 2 D 5/2 4.58736036p 4 ( 3 P)24p 2 D 5/2 4.5874860 2 P 3/2 4.3673681 2 P 3/2 4.3674866 6p 4 ( 3 P)14p 2 D 5/2 4.58739146p 4 ( 3 P)25p 2 D 5/2 4.5874888 2 P 3/2 4.3673970 2 P 3/2 4.3674893 6p 4 ( 3 P)15p 2 D 5/2 4.58741406p 4 ( 3 P)26p 2 D 5/2 4.5874912 2 P 3/2 4.3674181 2 P 3/2 4.3674916 6p 4 ( 3 P)16p 2 D 5/2 4.58743096p 4 ( 3 P)27p 2 D 5/2 4.5874932 2 P 3/2 4.3674341 2 P 3/2 4.3674937 6p 4 ( 3 P)17p 2 D 5/2 4.58744396p 4 ( 3 P)28p 2 D 5/2 4.5874951 2 P 3/2 4.3674464 2 P 3/2 4.3674954 6p 4 ( 3 P)18p 2 D 5/2 4.58745416p 4 ( 3 P)29p 2 D 5/2 4.5874967 2 P 3/2 4.3674561 2 P 3/2 4.3674970

Université de Liège Pascal Quinet (P.Quinet@ulg.ac.be) | 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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A new theoretical insight into the spectroscopic properties of polonium and astatine atoms Pascal Quinet Spectroscopie Atomique et Physique des Atomes.

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A new theoretical insight into the spectroscopic properties of polonium and astatine atoms Pascal Quinet Spectroscopie Atomique et Physique des Atomes.

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Presentation on theme: "A new theoretical insight into the spectroscopic properties of polonium and astatine atoms Pascal Quinet Spectroscopie Atomique et Physique des Atomes."— Presentation transcript:

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