Modified Relativistic Approach for Atomic Data CalculationModified Relativistic Approach for Atomic...
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Relativistic integral analogues Quasirelativistic Hartree-Fock Approach Summary Modified Relativistic Approach for Atomic Data Calculation Romas Kisielius VU Institute of Theoretical Physics and Astronomy Vilnius, Lithuania [email protected] ADAS Workshop 2009 R.Kisielius Modified relativistic approach
Transcript of Modified Relativistic Approach for Atomic Data CalculationModified Relativistic Approach for Atomic...
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
Modified Relativistic Approachfor Atomic Data Calculation
Romas Kisielius
VU Institute of Theoretical Physics and AstronomyVilnius, [email protected]
ADAS Workshop 2009
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
Outlook
1 Relativistic integral analoguesMethodChanges to standard R-matrix codesResults
2 Quasirelativistic Hartree-Fock ApproachMethodEnergy Level SpectraTransition Line Spectra
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
Outlook
1 Relativistic integral analoguesMethodChanges to standard R-matrix codesResults
2 Quasirelativistic Hartree-Fock ApproachMethodEnergy Level SpectraTransition Line Spectra
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Outlook
1 Relativistic integral analoguesMethodChanges to standard R-matrix codesResults
2 Quasirelativistic Hartree-Fock ApproachMethodEnergy Level SpectraTransition Line Spectra
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Relativistic Integral Analogues
A relation for multipole integral
Mk (n1l1, n2l2) =12
∑j1j2
[j1, j2]{
j1 j2 kl2 l1 1/2
}2
Mk (n1l1j1, n2l2j2)
A non-relativistic multipole integral
Mk (n1l1, n2l2) =
∫ ∞0
dr Pn1l1 r k Pn2l2
A relativistic multipole integral
Mk (n1l1j1, n2l2j2) =
∫ ∞0
dr r k[Pn1l1j1 Pn2l2j2 + Qn1 l̄1j1 Qn2 l̄2j2
]R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Relativistic Integral Analogues
A relation for multipole integral
Mk (n1l1, n2l2) =12
∑j1j2
[j1, j2]{
j1 j2 kl2 l1 1/2
}2
Mk (n1l1j1, n2l2j2)
A non-relativistic multipole integral
Mk (n1l1, n2l2) =
∫ ∞0
dr Pn1l1 r k Pn2l2
A relativistic multipole integral
Mk (n1l1j1, n2l2j2) =
∫ ∞0
dr r k[Pn1l1j1 Pn2l2j2 + Qn1 l̄1j1 Qn2 l̄2j2
]R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Relativistic Integral Analogues
A relation for multipole integral
Mk (n1l1, n2l2) =12
∑j1j2
[j1, j2]{
j1 j2 kl2 l1 1/2
}2
Mk (n1l1j1, n2l2j2)
A non-relativistic multipole integral
Mk (n1l1, n2l2) =
∫ ∞0
dr Pn1l1 r k Pn2l2
A relativistic multipole integral
Mk (n1l1j1, n2l2j2) =
∫ ∞0
dr r k[Pn1l1j1 Pn2l2j2 + Qn1 l̄1j1 Qn2 l̄2j2
]R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Outlook
1 Relativistic integral analoguesMethodChanges to standard R-matrix codesResults
2 Quasirelativistic Hartree-Fock ApproachMethodEnergy Level SpectraTransition Line Spectra
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Changes in standard R-matrix codes
Amendments to R-matrix flow
Start from relativistic R-matrix version (DARC)GRASP → DSTG0 → DSTG1/ORB/INTFollow with non-relativistic R-matrix (RmaX)AUTOSTRUCTURE → STG1 →STG2 → STGHFinish with intermediate coupling frame transformationmethod (ICFT)STGICF → STGFTest on electron-impact excitation of 2s2 - 2s2p 3S1
transitionV.Jonauskas et al., J.Phys B 38 (2005) L79-L85
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Changes in standard R-matrix codes
Amendments to R-matrix flow
Start from relativistic R-matrix version (DARC)GRASP → DSTG0 → DSTG1/ORB/INTFollow with non-relativistic R-matrix (RmaX)AUTOSTRUCTURE → STG1 →STG2 → STGHFinish with intermediate coupling frame transformationmethod (ICFT)STGICF → STGFTest on electron-impact excitation of 2s2 - 2s2p 3S1
transitionV.Jonauskas et al., J.Phys B 38 (2005) L79-L85
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Changes in standard R-matrix codes
Amendments to R-matrix flow
Start from relativistic R-matrix version (DARC)GRASP → DSTG0 → DSTG1/ORB/INTFollow with non-relativistic R-matrix (RmaX)AUTOSTRUCTURE → STG1 →STG2 → STGHFinish with intermediate coupling frame transformationmethod (ICFT)STGICF → STGFTest on electron-impact excitation of 2s2 - 2s2p 3S1
transitionV.Jonauskas et al., J.Phys B 38 (2005) L79-L85
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Changes in standard R-matrix codes
Amendments to R-matrix flow
Start from relativistic R-matrix version (DARC)GRASP → DSTG0 → DSTG1/ORB/INTFollow with non-relativistic R-matrix (RmaX)AUTOSTRUCTURE → STG1 →STG2 → STGHFinish with intermediate coupling frame transformationmethod (ICFT)STGICF → STGFTest on electron-impact excitation of 2s2 - 2s2p 3S1
transitionV.Jonauskas et al., J.Phys B 38 (2005) L79-L85
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Changes in standard R-matrix codes
Amendments to R-matrix flow
Start from relativistic R-matrix version (DARC)GRASP → DSTG0 → DSTG1/ORB/INTFollow with non-relativistic R-matrix (RmaX)AUTOSTRUCTURE → STG1 →STG2 → STGHFinish with intermediate coupling frame transformationmethod (ICFT)STGICF → STGFTest on electron-impact excitation of 2s2 - 2s2p 3S1
transitionV.Jonauskas et al., J.Phys B 38 (2005) L79-L85
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Outlook
1 Relativistic integral analoguesMethodChanges to standard R-matrix codesResults
2 Quasirelativistic Hartree-Fock ApproachMethodEnergy Level SpectraTransition Line Spectra
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Electron-impact excitation C2+
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Electron-impact excitation Fe22+
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodChanges to standard R-matrix codesResults
Electron-impact excitation W70+
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Outlook
1 Relativistic integral analoguesMethodChanges to standard R-matrix codesResults
2 Quasirelativistic Hartree-Fock ApproachMethodEnergy Level SpectraTransition Line Spectra
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
General form of QRHF equations
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Main Distinctions
No statistical potentials are used. Only conventionalself-consistent filed direct V (nl |r) and exchange X (nl |r)potentials in QRHFThe finite size of nucleus is considered determiningpotential U(r)The mass-velocity term splits into two partsNo two-electron potentials in the numeratorOnly direct part of V (nl |r) in denominator of the contactinteractionContact interaction woth nucleus is defined both fors-electrons and p-electrons
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Main Distinctions
No statistical potentials are used. Only conventionalself-consistent filed direct V (nl |r) and exchange X (nl |r)potentials in QRHFThe finite size of nucleus is considered determiningpotential U(r)The mass-velocity term splits into two partsNo two-electron potentials in the numeratorOnly direct part of V (nl |r) in denominator of the contactinteractionContact interaction woth nucleus is defined both fors-electrons and p-electrons
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Main Distinctions
No statistical potentials are used. Only conventionalself-consistent filed direct V (nl |r) and exchange X (nl |r)potentials in QRHFThe finite size of nucleus is considered determiningpotential U(r)The mass-velocity term splits into two partsNo two-electron potentials in the numeratorOnly direct part of V (nl |r) in denominator of the contactinteractionContact interaction woth nucleus is defined both fors-electrons and p-electrons
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Main Distinctions
No statistical potentials are used. Only conventionalself-consistent filed direct V (nl |r) and exchange X (nl |r)potentials in QRHFThe finite size of nucleus is considered determiningpotential U(r)The mass-velocity term splits into two partsNo two-electron potentials in the numeratorOnly direct part of V (nl |r) in denominator of the contactinteractionContact interaction woth nucleus is defined both fors-electrons and p-electrons
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Main Distinctions
No statistical potentials are used. Only conventionalself-consistent filed direct V (nl |r) and exchange X (nl |r)potentials in QRHFThe finite size of nucleus is considered determiningpotential U(r)The mass-velocity term splits into two partsNo two-electron potentials in the numeratorOnly direct part of V (nl |r) in denominator of the contactinteractionContact interaction woth nucleus is defined both fors-electrons and p-electrons
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Main Distinctions
No statistical potentials are used. Only conventionalself-consistent filed direct V (nl |r) and exchange X (nl |r)potentials in QRHFThe finite size of nucleus is considered determiningpotential U(r)The mass-velocity term splits into two partsNo two-electron potentials in the numeratorOnly direct part of V (nl |r) in denominator of the contactinteractionContact interaction woth nucleus is defined both fors-electrons and p-electrons
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Outlook
1 Relativistic integral analoguesMethodChanges to standard R-matrix codesResults
2 Quasirelativistic Hartree-Fock ApproachMethodEnergy Level SpectraTransition Line Spectra
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Energy Levels for W II
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Outlook
1 Relativistic integral analoguesMethodChanges to standard R-matrix codesResults
2 Quasirelativistic Hartree-Fock ApproachMethodEnergy Level SpectraTransition Line Spectra
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
MethodEnergy Level SpectraTransition Line Spectra
Transition probabilities for W II
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
Summary
Method of Relativistic Integral Analogues (ARI) for electronscattering calculationQuasirelativistic Hartree-Fock (QRHF) approach fordiscete spectra
Acknowledgments
V.JonauskasP. BogdanovichR.KarpuskieneO.Rancova
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
Summary
Method of Relativistic Integral Analogues (ARI) for electronscattering calculationQuasirelativistic Hartree-Fock (QRHF) approach fordiscete spectra
Acknowledgments
V.JonauskasP. BogdanovichR.KarpuskieneO.Rancova
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
Summary
Method of Relativistic Integral Analogues (ARI) for electronscattering calculationQuasirelativistic Hartree-Fock (QRHF) approach fordiscete spectra
Acknowledgments
V.JonauskasP. BogdanovichR.KarpuskieneO.Rancova
R.Kisielius Modified relativistic approach
Relativistic integral analoguesQuasirelativistic Hartree-Fock Approach
Summary
THANK YOU
R.Kisielius Modified relativistic approach
