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Beck, Donald R.; Cai, Ziyong

doi:10.1103/physreva.41.301

Cited by 31 publications

(14 citation statements)

References 27 publications

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“…The virtuals are chosen to be relativistic screened hydrogenic functions to avoid potential problems [7] [10].…”

Section: Introduction and Theorymentioning

confidence: 99%

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Theoretical lifetimes of Nb iiz4d35G3o
Beck
¹
,
Datta
²

1995
Phys. Rev. A
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Using relativistic configuration-interaction wave functions, we have obtained length and velocity f values for all lower J =2, 3,4 (4d+Ss) levels connected to the z 4d Sp 63, and D3 levels. Our lifetime results for length and velocity operators are~('63) =5.16 and 6.S3 ns, respectively, and~( D3) =4.67 and S.60 ns, respectively. These are in good agreement with the experimental values of 5.8 -6.2 and 5.0 ns. As we find for hyperfine structure, the 4d, 4d 5s interactions are important in generating accurate lifetime and f-value results. PACS number(s): 32.70.Cs, 31.25.v, 31.30.Jv

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“…The virtuals are chosen to be relativistic screened hydrogenic functions to avoid potential problems [7] [10].…”

Section: Introduction and Theorymentioning

confidence: 99%

“…Once the wave functions are created, the electric dipole transition probabilities between levels are obtained using the formalism outlined earlier [7] which is based on the work of Grant [12]. We calculate in both the length and the velocity gauges, using the experimental [9] excitation energies.…”

Section: Introduction and Theorymentioning

confidence: 99%

Theoretical lifetimes of Nb iiz4d35G3o
Beck
¹
,
Datta
²

1995
Phys. Rev. A
Self Cite
9
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4
0
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“…This is done using the methods of King et al [23], which over the years have been made several thousand times more efficient by the author [24] by making maximum use of symmetry [25]. The latest step has to been to implement a "one-pass" calculation which computes all 12 × 22 = 264 Fe II transitions for the cost of one (for optical transitions).…”

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confidence: 99%

Ab InitioElectric Dipolefvalues for Fe II (3d⁶4s + 3d⁷)J= 9/2 → 3d⁶4pJ= 9/2 Transitions

Beck¹

2005

Phys. Scr.

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“…The f -values are constructed from available formulae [17], using computer programs created by Beck and co-workers [18].…”

Section: A "Sum" Over F-values Approachmentioning

confidence: 99%

Improved RCI techniques for atomic 4fⁿexcitation energies and polarizabilities

Beck¹,

Pan²

2010

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We propose an efficient method by which previously computationally expensive, but moderately important, pair correlation effects can be incorporated into f n excitation energies. Application is to Gd IV. Secondly, we extend two methods of obtaining static and tensor dipole polarizabilities and apply them to the Ni II ground state. The first uses the sum over f -values approach, and the second is variational. Calculation of Excitation Energies for Lanthanides and ActinidesOur long term computational interest has been to develop (when necessary) and apply the relativistic configuration interaction (RCI) method to predict properties of complicated atoms and ions -specifically, for transition metals, lanthanides and actinides.Triply ionized lanthanide and actinide ions appear as impurities in condensed matter systems where they can serve as centers of lasing activity [1], play a role in MRI medicine as endohedral metallofullerenes (e.g. Gd 3 N-C 80 ) [2], appear as important constituents of high temperature super-conductors, etc. There also has been interest in the free Gd IV ion as a possible means of detecting an electron electric dipole moment [3].Experimentally, only a few of the low lying excitation energies within the f n configuration are generally known [4,5] from measurements made in the condensed phase. Dipole transition energies f n -f n−1 d are generally not known experimentally, as the d levels in the solid are not very well localized [5]. It also may be noted that most prevalent charge state of the lanthanide/actinide ion in the solid is 3 + [5]. Computationally, these excitation energies are also difficult to obtain [6]. The calculations require the use of a relativistic Hamiltonian (Dirac-Breit) and a correlated wavefunction having at least a first order form, i.e. one that includes all the differentially important single and double subshell excitations from a set of reference functions. At present, a reasonable ab initio accuracy goal for excitations within f n would be to position all levels to ∼1000 cm −1 relative to the ground state. Our recent Gd IV [6] achieved 1257 cm −1 , and we improve this to 838 cm −1 here, accompanied by a drop in calculation time of 67%.

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Relativistic many-body methodology of electric dipole oscillator strengths with application toTl+6s2

Cited by 31 publications

References 27 publications

Theoretical lifetimes of Nb iiz4d35G3o
Beck
¹
,
Datta
²

1995
Phys. Rev. A
Self Cite
9
1
4
0
View full text Add to dashboard Cite

Theoretical lifetimes of Nb iiz4d35G3o
Beck
¹
,
Datta
²

1995
Phys. Rev. A
Self Cite
9
1
4
0
View full text Add to dashboard Cite

Ab InitioElectric Dipolefvalues for Fe II (3d⁶4s + 3d⁷)J= 9/2 → 3d⁶4pJ= 9/2 Transitions

Improved RCI techniques for atomic 4fⁿexcitation energies and polarizabilities

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Relativistic many-body methodology of electric dipole oscillator strengths with application toTl+6s2

Cited by 31 publications

References 27 publications

Theoretical lifetimes of Nb iiz4d35G3oBeck1, Datta2 1995Phys. Rev. ASelf Cite9140View full textAdd to dashboardCite

Theoretical lifetimes of Nb iiz4d35G3oBeck1, Datta2 1995Phys. Rev. ASelf Cite9140View full textAdd to dashboardCite

Ab InitioElectric Dipolefvalues for Fe II (3d64s + 3d7)J= 9/2 → 3d64pJ= 9/2 Transitions

Improved RCI techniques for atomic 4fnexcitation energies and polarizabilities

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Theoretical lifetimes of Nb iiz4d35G3o
Beck
¹
,
Datta
²

1995
Phys. Rev. A
Self Cite
9
1
4
0
View full text Add to dashboard Cite

Theoretical lifetimes of Nb iiz4d35G3o
Beck
¹
,
Datta
²

1995
Phys. Rev. A
Self Cite
9
1
4
0
View full text Add to dashboard Cite

Ab InitioElectric Dipolefvalues for Fe II (3d⁶4s + 3d⁷)J= 9/2 → 3d⁶4pJ= 9/2 Transitions

Improved RCI techniques for atomic 4fⁿexcitation energies and polarizabilities