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 intoA new theoretical insight intothe spectroscopic propertiesthe spectroscopic propertiesof polonium and astatine atomsof 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 ([email protected]) | 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


Some properties of polonium and astatine atoms

Polonium (Po)

Astatine (At)

Atomic number : 84Ground electronic configuration : [Xe]4f145d106s26p4

Excited electronic configurations : [Xe]4f145d106s26p3nl(nl = 6d, 7s, 7p, 7d, …)

Known isotopes : 42 (A = 186 – 227)Longest half-life : 103 years (209Po)

Atomic number : 85Ground electronic configuration : [Xe]4f145d106s26p5

Excited electronic configurations : [Xe]4f145d106s26p4nl(nl = 6d, 7s, 7p, 7d, …)

Known isotopes : 32 (A = 191, 193 – 223)Longest half-life : 8.1 hours (210At)



Config. Term J E (cm-1) Config. Term J E (cm-1)6p4 3P 2 0.00 [odd] ? ° ? 1 544716p4 3P 0 7514.69 6p3(4S)8s 5S° ? 2 55465.366p4 3P 1 16831.61 [odd] ? ° ? 2 ? 559236p4 1D 2 21679.11 6p3(4S)8s 2S° ? 1 ? 56268.346p3(4S)7s 5S° 2 39081.19 6p3(2D)7S 3D° ? 1 ? 57078.056p3(4S)7s 3S° 1 40802.70 6p3(4S)8p 5P ? 3 59290.616p4 1S 0 42718 6p3(4S)8p ? 1 or 2 59354.476p3(4S)7p 5P ? 3 ? 50681.28 6p3(4S)7d ° ? 2 ? 59469.666p3(4S)7p ? ? 50934.89 6p3(4S)8p ? 1 or 2 59583.066p3(4S)7p ? 1 or 2 51636.42 [odd] ? ° ? 1 or 2 618186p3(4S)6d 5D° ? 2 51713.09 6p3(4S)9p 5P ? 3 ? 62680.996p3(4S)6d 5D° ? 3 52098.93 6p3(4S)9p ? 1 or 2 62703.966p3(4S)6d ° ? 1 52532.12 6p3(4S)9p ? ? 1 or 2 628066p3(4S)6d ° ? 2 53027.61 6p3(4S)8d ° ? 1 or 2 62885.19[odd] ? ° ? 1 53762 6p3(4S)8d ° ? 1 or 2 62959.49[odd] ? ° ? 1 54250.26 6p3(4S)10p ? ? 1 or 2 64451

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)]










Experimental spectrum and energy levels of astatine

Config. Term J E (cm-1)6p5 2P° 3/2 0.06p4(3P)7s 4P 5/2 44549.36p4(3P)7s 4P 3/2 46233.6

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)]


Theoretical approachPseudo-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)

EH with

ij ijii

N

i r

e

r

Ze

mH

0

2

0

22

2

1 442




EH with

ij ijii

N

i r

e

r

Ze

mH

0

2

0

22

2

1 442

Central field approximation One-electron wavefunctions

)(),()(1

)( ,2/1 σqslsl mlmnlmnlm YrP

r




EH with

ij ijii

N

i r

e

r

Ze

mH

0

2

0

22

2

1 442

Central field approximation One-electron wavefunctions

)(),()(1

)( ,2/1 σqslsl mlmnlmnlm YrP

r

Atomic wavefunctions (Slater determinant)

)(...)()(

............

)(...)()(

)(...)()(

!

1),...,,(

21

22221

11211

21

NNNN

N

N

NN

qqq

qqq

qqq

qqq



Hartree-Fock equations

)()(4)()(

)(4

)()(42

)1(

2

0

2*

0

22

0

2

2

2

2

22

iiiijjij

jijjmmij

iijij

jjij

iiii

ii

i

rPErPdr

erPrP

rPdr

erPrP

r

Ze

mr

ll

dr

d

m

jsis



Hartree-Fock equations

Resolution of Hartree-Fock equations (self-consistent field)

)()(4)()(

)(4

)()(42

)1(

2

0

2*

0

22

0

2

2

2

2

22

iiiijjij

jijjmmij

iijij

jjij

iiii

ii

i

rPErPdr

erPrP

rPdr

erPrP

r

Ze

mr

ll

dr

d

m

jsis

Starting Pi(ri) Calculate potentials Solve HF equations New Pi(ri)

Same as before ?

STOP

NOYES



Multiconfiguration approach (Slater-Condon)

bkb

b

k a




Relativistic effects

bkb

b

k a

Included perturbationaly (spin-orbit, mass-velocity, Darwin term)

Good agreement with fully relativistic methods




Relativistic effects

Ab initio or semi-empirical approach

bkb

b

k a

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)




Example : Po (6p4 – 6p36d transitions)

bkb

b

k a





bkb

b

k a

Intravalence correlation(single excitations up to n=6, l=3)

Even parity4f145d106s26p4

4f145d106s26p35f4f145d106s26p36f4f145d106s26p26d2

Odd parity4f145d106s26p36d4f145d106s26p26d5f4f145d106s26p26d6f





bkb

b

k a





Core-valence correlation (single excitations from 4f, 5d, 6s)

Even parity4f145d106s6p46d4f145d106s6p36d5f4f145d106s6p36d6f4f145d96s26p46d4f145d96s26p36d5f4f145d96s26p36d6f4f135d106s26p5


Odd parity4f145d106s6p5


4f145d96s26p5


4f135d106s26p46d4f135d106s26p36d5f4f135d106s26p36d6f





bkb

b

k a










4f145d96s26p5



196 states

594 states





bkb

b

k a










4f145d96s26p5



10596 states

10910 states

196 states

594 states


Theoretical approachCore-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 rc)

n

i ci

idP rr

rV

1322

2

1 )(2

1

ji cjci

jidP rrrr

rrV

2/322222 )])([(

.


Theoretical approachCore-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 rc)

n

i ci

idP rr

rV

1322

2

1 )(2

1

ji cjci

jidP rrrr

rrV

2/322222 )])([(

.

0

'' )()( drrPrrP lnnl replaced by

0

''2/322)(

)(1)( drrP

rrrrP ln

c

dnl


Atomic structure calculations in poloniumJournal of Quantitative Spectroscopy and Radiative Transfer 145 (2014) 153 - 159



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 : d = 2.00 a.u., rc = 1.17 a.u.)

Pseudo-relativistic Hartree-Fock models considered in the present work

Intravalence interactionswithin 6p3nl

Single excitations from 6p

Double excitations from 6p

Single excitations from 6s

Double excitations from 6s

Core-polarization up to 5d





















Experiment (NIST) Theory (This work)

Config. Term J E (cm-1) E(cm-1) J 1st component 2nd component 3rd component

6p4 3P 2 0.00 0 2 78% 6p4 3P 20% 6p4 1D

6p4 3P 0 7514.69 7516 0 55% 6p4 3P 43% 6p4 1S

6p4 3P 1 16831.61 16833 1 98% 6p4 3P

6p4 1D 2 21679.11 21680 2 78% 6p4 1D 20% 6p4 3P

6p4 1S 0 42718 42717 0 54% 6p4 1S 43% 6p4 3P

6p3(4S)7p 5P ? 3 ? 50681.28 50773 1 34% 6p3(4S)7p 5P 16% 6p3(4S)7p 3P 15% 6p3(2P)7p 3P

6p3(4S)7p ? ? 50934.89 50838 2 40% 6p3(4S)7p 5P 15% 6p3(2P)7p 3D 13% 6p3(2P)7p 3P

6p3(4S)7p ? 1 or 2 51636.42 51641 3 52% 6p3(4S)7p 5P 31% 6p3(2P)7p 3D 8% 6p3(2D)7p 3F

51896 1 31% 6p3(4S)7p 3P 19% 6p3(4S)7p 5P 16% 6p3(2P)7p 3S

52853 2 38% 6p3(4S)7p 3P 17% 6p3(2P)7p 1D 13% 6p3(2P)7p 3P

53847 0 55% 6p3(4S)7p 3P 19% 6p3(2P)7p 1S 12% 6p3(2D)7p 3P

Even-parity energy levels





6p4 3P 2 0.00 0 2 78% 6p4 3P 20% 6p4 1D

6p4 3P 0 7514.69 7516 0 55% 6p4 3P 43% 6p4 1S

6p4 3P 1 16831.61 16833 1 98% 6p4 3P

6p4 1D 2 21679.11 21680 2 78% 6p4 1D 20% 6p4 3P

6p4 1S 0 42718 42717 0 54% 6p4 1S 43% 6p4 3P




51896 1 31% 6p3(4S)7p 3P 19% 6p3(4S)7p 5P 16% 6p3(2P)7p 3S

52853 2 38% 6p3(4S)7p 3P 17% 6p3(2P)7p 1D 13% 6p3(2P)7p 3P

53847 0 55% 6p3(4S)7p 3P 19% 6p3(2P)7p 1S 12% 6p3(2D)7p 3P






6p4 3P 2 0.00 0 2 78% 6p4 3P 20% 6p4 1D

6p4 3P 0 7514.69 7516 0 55% 6p4 3P 43% 6p4 1S

6p4 3P 1 16831.61 16833 1 98% 6p4 3P

6p4 1D 2 21679.11 21680 2 78% 6p4 1D 20% 6p4 3P

6p4 1S 0 42718 42717 0 54% 6p4 1S 43% 6p4 3P




51896 1 31% 6p3(4S)7p 3P 19% 6p3(4S)7p 5P 16% 6p3(2P)7p 3S

52853 2 38% 6p3(4S)7p 3P 17% 6p3(2P)7p 1D 13% 6p3(2P)7p 3P

53847 0 55% 6p3(4S)7p 3P 19% 6p3(2P)7p 1S 12% 6p3(2D)7p 3P






6p4 3P 2 0.00 0 2 78% 6p4 3P 20% 6p4 1D

6p4 3P 0 7514.69 7516 0 55% 6p4 3P 43% 6p4 1S

6p4 3P 1 16831.61 16833 1 98% 6p4 3P

6p4 1D 2 21679.11 21680 2 78% 6p4 1D 20% 6p4 3P

6p4 1S 0 42718 42717 0 54% 6p4 1S 43% 6p4 3P




51896 1 31% 6p3(4S)7p 3P 19% 6p3(4S)7p 5P 16% 6p3(2P)7p 3S

52853 2 38% 6p3(4S)7p 3P 17% 6p3(2P)7p 1D 13% 6p3(2P)7p 3P

53847 0 55% 6p3(4S)7p 3P 19% 6p3(2P)7p 1S 12% 6p3(2D)7p 3P


Se 4p3(4S)5p 5P J = 1 59242.80 Te 5p3(4S)6p 5P J = 1 54160.09[Experimental data] J = 2 59287.82 [Experimental data] J = 2 54199.12

J = 3 59391.31 J = 3 54535.35





6p3(4S)7s 5S° 2 39081.19 38837 2 52% 6p3(4S)7s 5S 32% 6p3(2P)7s 3P 9% 6p3(2D)7s 3D


6p3(4S)6d 5D° ? 2 51713.09 51846 2 28% 6p3(4S)6d 5D 18% 6p3(4S)6d 3D 15% 6p3(2P)6d 3D

6p3(4S)6d 5D° ? 3 52098.93 52213 3 47% 6p3(4S)6d 5D 17% 6p3(2P)6d 3D 14% 6p3(2P)6d 3F

6p3(4S)6d ° ? 1 52532.12 52375 1 44% 6p3(4S)6d 5D 17% 6p3(2P)6d 3P 12% 6p3(2P)6d 3D

52835 4 53% 6p3(4S)6d 5D 31% 6p3(2P)6d 3F 8% 6p3(2D)6d 3G

6p3(4S)6d ° ? 2 53027.61 52863 2 26% 6p3(4S)6d 3D 21% 6p3(4S)6d 5D 6% 6p3(2D)6d 3P

52904 0 54% 6p3(4S)6d 5D 30% 6p3(2P)6d 3P 7% 6p3(2D)6d 3P

54000 3 46% 6p3(4S)6d 3D 20% 6p3(2P)6d 1F 11% 6p3(2D)6d 3G

[odd] ? ° ? 1 54250.26 54316 1 44% 6p3(4S)6d 3D 16% 6p3(2P)6d 1P 10% 6p3(2P)6d 3P

[odd] ? ° ? 2 ? 55923.80 56107 2 37% 6p3(2D)7s 3D 36% 6p3(4S)7s 5S 16% 6p3(2D)7s 1D

6p3(2D)7S 3D° ? 1 ? 57078.05 57321 1 46% 6p3(2D)7s 3D 36% 6p3(4S)7s 3S 3% 6p3(4S)7d 3D

6p3(4S)7d ° ? 2 ? 59469.66 59456 2 30% 6p3(4S)7d 5D 20% 6p3(4S)7d 3D 14% 6p3(2P)7d 3D

Odd-parity energy levels







6p3(4S)6d 5D° ? 2 51713.09 51846 2 28% 6p3(4S)6d 5D 18% 6p3(4S)6d 3D 15% 6p3(2P)6d 3D

6p3(4S)6d 5D° ? 3 52098.93 52213 3 47% 6p3(4S)6d 5D 17% 6p3(2P)6d 3D 14% 6p3(2P)6d 3F

6p3(4S)6d ° ? 1 52532.12 52375 1 44% 6p3(4S)6d 5D 17% 6p3(2P)6d 3P 12% 6p3(2P)6d 3D

52835 4 53% 6p3(4S)6d 5D 31% 6p3(2P)6d 3F 8% 6p3(2D)6d 3G

6p3(4S)6d ° ? 2 53027.61 52863 2 26% 6p3(4S)6d 3D 21% 6p3(4S)6d 5D 6% 6p3(2D)6d 3P

52904 0 54% 6p3(4S)6d 5D 30% 6p3(2P)6d 3P 7% 6p3(2D)6d 3P

54000 3 46% 6p3(4S)6d 3D 20% 6p3(2P)6d 1F 11% 6p3(2D)6d 3G

[odd] ? ° ? 1 54250.26 54316 1 44% 6p3(4S)6d 3D 16% 6p3(2P)6d 1P 10% 6p3(2P)6d 3P

[odd] ? ° ? 2 ? 55923.80 56107 2 37% 6p3(2D)7s 3D 36% 6p3(4S)7s 5S 16% 6p3(2D)7s 1D

6p3(2D)7S 3D° ? 1 ? 57078.05 57321 1 46% 6p3(2D)7s 3D 36% 6p3(4S)7s 3S 3% 6p3(4S)7d 3D

6p3(4S)7d ° ? 2 ? 59469.66 59456 2 30% 6p3(4S)7d 5D 20% 6p3(4S)7d 3D 14% 6p3(2P)7d 3D

Odd-parity energy levels



Radiative transitions (transition probabilities and oscillator strengths)

2)1(

36

2)1(

320

44

12

)(100261.2

12

)(

3

64

kkiik

ki

kkiik

kiki

JPJJ

E

JPJJ

E

h

aeA

E

kii

kik A

J

Jf

15

2

106702.612

12

fik

with Aki in s-1, Eki in cm-1, in Å









Radiative transitions (transition probabilities and oscillator strengths)



Radiative transitions








Atomic structure calculations in poloniumRadiative transitions (oscillator strengths and transition probabilities)

(nm)a Lower level (cm-1)b Upper level (cm-1)b log gf gA (s-1)175.199 0.00 J=2 (even) 57078.05 J=1 (odd) -0.85 3.11E+8178.815 0.00 J=2 (even) 55923.80 J=2 (odd) -0.36 9.26E+8184.331 0.00 J=2 (even) 54250.26 J=1 (odd) -0.81 3.05E+8188.581 0.00 J=2 (even) 53027.61 J=2 (odd) -0.15 1.33E+9190.360 0.00 J=2 (even) 52532.12 J=1 (odd) -1.98 1.90E+7191.943 0.00 J=2 (even) 52098.93 J=3 (odd) -0.61 4.44E+8201.697 7514.69 J=0 (even) 57078.05 J=1 (odd) -1.19 1.08E+8213.902 7514.69 J=0 (even) 54250.26 J=1 (odd) -0.26 8.05E+8222.067 7514.69 J=0 (even) 52532.12 J=1 (odd) -1.26 7.43E+7234.461 16831.61 J=1 (even) 59469.66 J=2 (odd) -1.87 1.64E+7245.008 0.00 J=2 (even) 40802.70 J=1 (odd) -0.09 8.96E+8248.394 16831.61 J=1 (even) 57078.05 J=1 (odd) -0.21 6.72E+8255.729 16831.61 J=1 (even) 55923.80 J=2 (odd) -1.14 7.46E+7255.801 0.00 J=2 (even) 39081.19 J=2 (odd) -0.42 3.84E+8264.538 21679.11 J=2 (even) 59469.66 J=2 (odd) -1.54 2.74E+7276.192 16831.61 J=1 (even) 53027.61 J=2 (odd) -1.21 5.38E+7280.026 16831.61 J=1 (even) 52532.12 J=1 (odd) -1.96 9.21E+6282.411 21679.11 J=2 (even) 57078.05 J=1 (odd) -1.11 6.60E+7286.601 16831.61 J=1 (even) 51713.09 J=2 (odd) -1.80 1.29E+7291.931 21679.11 J=2 (even) 55923.80 J=2 (odd) -1.14 5.79E+7300.321 7514.69 J=0 (even) 40802.70 J=1 (odd) -0.80 1.16E+8306.931 21679.11 J=2 (even) 54250.26 J=1 (odd) -2.36 3.13E+6324.024 21679.11 J=2 (even) 52532.12 J=1 (odd) -1.85 8.79E+6328.638 21679.11 J=2 (even) 52098.93 J=3 (odd) -2.14 4.52E+6417.052 16831.61 J=1 (even) 40802.70 J=1 (odd) -1.49 1.23E+7574.485 21679.11 J=2 (even) 39081.19 J=2 (odd) -2.62 4.70E+5696.184 42718.00 J=0 (even) 57078.05 J=1 (odd) -2.46 4.94E+5796.262 39081.19 J=2 (odd) 51636.42 J=3 (even) 0.52 3.62E+8843.387 39081.19 J=2 (odd) 50934.89 J=2 (even) 0.27 1.77E+8861.826 39081.19 J=2 (odd) 50681.28 J=1 (even) -0.07 8.03E+7986.683 40802.70 J=1 (odd) 50934.89 J=2 (even) -0.45 2.52E+7



Comparison with experiment


Atomic structure calculations in astatineUp to very recently…

R. McLaughlin, J.O.S.A. 54, 965 (1964)Config. Term J E (cm-1)6p5 2P° 3/2 0.06p4(3P)7s 4P 5/2 44549.36p4(3P)7s 4P 3/2 46233.6



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)



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)


Atomic structure calculations in astatinePseudo-relativistic Hartree-Fock models



Model C : Model B + 6s26p2nln’l’n’’l’’


Model E : Model D + 6p6nl + 6p5nln’l’

Model F : Model E + [1s2 … 5d10] core-polarization (At7+ core : d = 1.8 a.u., rc = 1.12 a.u.)


Atomic structure calculations in astatineEnergy levels within the 6p47p 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)



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 !




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 !


Rothe et al. (2013); Raeder et al. (2014)

6p47s

46233.64 (J=3/2)44549.28 (J=5/2)

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)

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 !



6p47s

46233.64 (J=3/2)44549.28 (J=5/2)

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)

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 !



6p47s

46233.64 (J=3/2)44549.28 (J=5/2)

6p47p

58805.0 (J=3/2)

57276.7 (J=7/2)57267.8 (J=1/2)

57157.1 (J=5/2)

== 1/2== 7/2



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 !



6p47s

46233.64 (J=3/2)44549.28 (J=5/2)

6p47p

58805.0 (J=3/2)

57276.7 (J=7/2)57267.8 (J=1/2)

57157.1 (J=5/2)

== 1/2== 7/2


Atomic structure calculations in astatineClassification of experimentally observed energy levels

E(cm-1) J 1st component 2nd component 3rd component

0.00 (odd) 3/2 98% 6p5 2P

44549.28 (even) 5/2 78% 6p4(3P)7s 4P 20% 6p4(1D)7s 2D

46233.64 (even) 3/2 60% 6p4(3P)7s 2P 23% 6p4(1D)7s 2D 15% 6p4(3P)7s 4P

57157.10 (odd) 5/2 43% 6p4(3P)7p 2D 35% 6p4(3P)7p 4P 11% 6p4(1D)7p 2D

57267.80 (odd) 7/2 77% 6p4(3P)7p 4D 22% 6p4(1D)7p 2F

57276.70 (odd) 1/2 37% 6p4(3P)7p 2S 24% 6p4(1D)7p 2P 24% 6p4(3P)7p 2P

58805.00 (odd) 3/2 42% 6p4(3P)7p 2P 21% 6p4(3P)7p 4S 12% 6p4(1D)7p 2D


Atomic structure calculations in astatineClassification of experimentally observed energy levels


0.00 (odd) 3/2 98% 6p5 2P

44549.28 (even) 5/2 78% 6p4(3P)7s 4P 20% 6p4(1D)7s 2D

46233.64 (even) 3/2 60% 6p4(3P)7s 2P 23% 6p4(1D)7s 2D 15% 6p4(3P)7s 4P

57157.10 (odd) 5/2 43% 6p4(3P)7p 2D 35% 6p4(3P)7p 4P 11% 6p4(1D)7p 2D

57267.80 (odd) 7/2 77% 6p4(3P)7p 4D 22% 6p4(1D)7p 2F

57276.70 (odd) 1/2 37% 6p4(3P)7p 2S 24% 6p4(1D)7p 2P 24% 6p4(3P)7p 2P




(nm) Lower level (cm-1) Upper level (cm-1) log gf gA (s-1)

216.225 0.00 J=3/2 (odd) 46233.64 J=3/2 (even) -0.07 1.21E+9

224.401 0.00 J=3/2 (odd) 44549.28 J=5/2 (even) -0.94 1.53E+8

701.279 44549.28 J=5/2 (even) 58805.00 J=3/2 (odd) -0.68 1.83E+8

786.039 44549.28 J=5/2 (even) 57267.80 J=7/2 (odd) 0.43 1.72E+8

792.940 44549.28 J=5/2 (even) 57157.10 J=5/2 (odd) -0.14 4.50E+7

795.240 46233.64 J=3/2 (even) 58805.00 J=3/2 (odd) -0.07 5.74E+7

905.298 46233.64 J=3/2 (even) 57276.70 J=1/2 (odd) -0.17 3.10E+7

915.210 46233.64 J=3/2 (even) 57157.10 J=5/2 (odd) 0.09 5.46E+7

Radiative transitions (oscillator strengths, transition probabilities)


Atomic structure calculations in astatineIdentification 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

6p4np



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

6p4np

6p414p6p413p6p412p6p411p6p410p

6p49p

6p48p

6p47p

Theory Experiment




69615.1 (odd) 5/2 41% 6p4(3P)9p 2D 36% 6p4(3P)9p 4P 14% 6p4(3P)9p 2D











4.55

4.36

4.61

4.36

2)( n

REE Ation

Eion = 75150.8 cm-1

RAt = 109737.02 cm-1 (A = 210)

Quantum defect


Atomic structure calculations in astatineEstimated energy level values in the 6p4(3P)np Rydberg series

Config. Level Estim. (cm-1) Obs. (cm-1) Config. Level Estim. (cm-1) Obs. (cm-1)6p4(3P)8p 2D5/2 4.58 65769 6p4(3P)19p 2D5/2 4.58 74623

2P3/2 4.36 66869 2P3/2 4.36 746396p4(3P)9p 2D5/2 4.58 69534 69615.1 6p4(3P)20p 2D5/2 4.58 74689

2P3/2 4.36 70054 70055.4 2P3/2 4.36 747026p4(3P)10p 2D5/2 4.58 71415 71376.7 6p4(3P)21p 2D5/2 4.58 74744

2P3/2 4.36 71701 71708.7 2P3/2 4.36 747546p4(3P)11p 2D5/2 4.58 72488 6p4(3P)22p 2D5/2 4.58 74789

2P3/2 4.36 72662 2P3/2 4.36 747986p4(3P)12p 2D5/2 4.58 73158 6p4(3P)23p 2D5/2 4.58 74827

2P3/2 4.36 73271 2P3/2 4.36 748356p4(3P)13p 2D5/2 4.58 73603 6p4(3P)24p 2D5/2 4.58 74860

2P3/2 4.36 73681 2P3/2 4.36 748666p4(3P)14p 2D5/2 4.58 73914 6p4(3P)25p 2D5/2 4.58 74888

2P3/2 4.36 73970 2P3/2 4.36 748936p4(3P)15p 2D5/2 4.58 74140 6p4(3P)26p 2D5/2 4.58 74912

2P3/2 4.36 74181 2P3/2 4.36 749166p4(3P)16p 2D5/2 4.58 74309 6p4(3P)27p 2D5/2 4.58 74932

2P3/2 4.36 74341 2P3/2 4.36 749376p4(3P)17p 2D5/2 4.58 74439 6p4(3P)28p 2D5/2 4.58 74951

2P3/2 4.36 74464 2P3/2 4.36 749546p4(3P)18p 2D5/2 4.58 74541 6p4(3P)29p 2D5/2 4.58 74967

2P3/2 4.36 74561 2P3/2 4.36 74970


Summary and conclusions

Theoretical investigation of polonium and astatine atomic structures

Pseudo-relativistic Hartree-Fock method

Polonium : - Spectroscopic designation of 6p37p, 6p36d, 6p37s and 6p37d energy levels - Radiative transition parameters for 31 spectral lines in the wavelength region 175 – 987 nm

Astatine : - Spectroscopic designation of 4 levels belonging to 6p47p - Radiative transition parameters for 8 spectral lines in the wavelength region 216 – 915 nm - Identification of 4 new levels in 6p49p and 6p410p configurations - Predicted energies for levels within the 6p4np Rydberg series

Thank you for your attention

Documents

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