A new theoretical insight in A new theoretical insight in the spectroscopic properties the spectroscopic properties of polonium and astatine ato of polonium and astatine ato Pascal Quinet Spectroscopie Atomique et Physique des Atomes Froids, Université de Liège & Astrophysique et Spectroscopie, Université de Mons
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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 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
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Some properties of polonium and astatine atoms
Polonium (Po)
Astatine (At)
Atomic number : 84Ground electronic configuration : [Xe]4f145d106s26p4
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 ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
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)]
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
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
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
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
Central field approximation One-electron wavefunctions
)(),()(1
)( ,2/1 σqslsl mlmnlmnlm YrP
r
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
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
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
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-relativistic Hartree-Fock (HFR) method(R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981)
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
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-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)
)()(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
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-relativistic Hartree-Fock (HFR) method(R.D. Cowan, The Theory of Atomic Structure and Spectra, Univ. California Press, Berkeley, 1981)
Multiconfiguration approach (Slater-Condon)
bkb
b
k a
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-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
bkb
b
k a
Included perturbationaly (spin-orbit, mass-velocity, Darwin term)
Good agreement with fully relativistic methods
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-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
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)
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-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)
bkb
b
k a
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-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)
bkb
b
k a
Intravalence correlation(single excitations up to n=6, l=3)
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-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)
bkb
b
k a
Intravalence correlation(single excitations up to n=6, l=3)
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-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)
bkb
b
k a
Intravalence correlation(single excitations up to n=6, l=3)
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Theoretical approachPseudo-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)
bkb
b
k a
Intravalence correlation(single excitations up to n=6, l=3)
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
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 )])([(
.
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
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
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Atomic structure calculations in poloniumJournal of Quantitative Spectroscopy and Radiative Transfer 145 (2014) 153 - 159
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Atomic structure calculations in polonium
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
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Atomic structure calculations in polonium
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
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Atomic structure calculations in polonium
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
Université de Liège Pascal Quinet ([email protected]) | BriX Workshop, Liège, 27 – 28 May 2015
Atomic structure calculations in polonium
Experiment (NIST) Theory (This work)
Config. Term J E (cm-1) E(cm-1) J 1st component 2nd component 3rd component
Université de Liège Pascal Quinet ([email protected]) | 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 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