Alternative mathematical technique to determine LS spectral terms

Xu, Renjun; Dai, Zhenwen

doi:10.1088/0953-4075/39/16/007

Cited by 7 publications

(8 citation statements)

References 36 publications

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“…[8] For d 5 , f 7 and g 9 , they are consistent with R. Xu's results. [9] For f 7 , compared with Y. Xu's results, [10] the only difference is that their quadruple series for f 7 has H 10 terms both in their Table 4 and in their final results. We and R. Xu [9] find H 5 and F 5 terms instead of H 10 .…”

Section: Resultsmentioning

confidence: 95%

A generic procedure for determining atomic LS spectral terms and their LS eigenfunctions

Zhang

Bacalis

2009

Chinese Phys. B

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This paper develops a Fortran code which is capable to construct the simplest LS eigenfunctions for desired symmetry and determine all permitted atomic LS spectral terms under a given orbital occupancy by implementing and extending the Schaefer and Harris method. Examples (in some cases the most complete set to date) of multiple spectroscopic terms of LS coupling of atomic states for both non-equivalent and equivalent electronic configurations are given. It also corrects a few observed errors from the recent literature.

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Section: Resultsmentioning

confidence: 95%

A generic procedure for determining atomic LS spectral terms and their LS eigenfunctions

Zhang

Bacalis

2009

Chinese Phys. B

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“…Therefore, in these cases, the ℒ S coupling is achieved after the crystal field branching. (See Xu et al [23] for details on ℒ S coupling. )…”

Section: S2p Rixs With Kramers-heisenbergmentioning

confidence: 99%

1s2p RIXS Calculations for 3d Transition Metal Ions in Octahedral Symmetry

Zimmermann

Hunault

Groot

2018

Journal of Spectroscopy

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We present a series of 1s2p resonant inelastic X-ray scattering (RIXS) calculations for 3d transition metal ions in octahedral symmetry covering each ground state between 3d 0 and 3d 9 . The calculations are performed in octahedral (O h ) symmetry using the crystal field multiplet theory. We discuss the crystal field effects and the selection rules with respect to the 1s2p RIXS pre-edge and compare their final state energies with the corresponding 2p X-ray absorption spectrum (XAS). The calculations provide a detailed understanding of 1s2p RIXS and serve as a basis for the future analysis of experimental spectra and also as a starting point for calculations that add additional channels including the nonlocal peaks.

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“…The problem of listing the terms arising in a complex configuration can be solved from elementary group theory [50,51,52,53,54]. The number Q(S, L) of LS terms of a configuration ℓ N can be obtained from the relation…”

Section: Approximation Of the Coefficient G Ementioning

confidence: 99%

“…where X SLJ is any quantity depending on S, L and J, enables one to deal with the coupling of angular momenta L and S avoiding the use of coefficients of fractional parentage. One has ḡe = S,L,J L ′ ,J ′ Q(S, L ′ ) g e (S, L, J, L ′ , J ′ ) ǫ(L, L ′ , J, J ′ ), (54) where ǫ(L, L ′ , J, J ′ ) stands for the selection rules: L ′ = L, L − 1 or L + 1 avoiding L ′ = L = 0 and J ′ = J, J − 1 or J + 1 avoiding J ′ = J = 0. One has…”

Section: Approximation Of the Coefficient G Ementioning

confidence: 99%

Characterization of anomalous Zeeman patterns in complex atomic spectra

Pain

Gilleron

2012

Phys. Rev. A

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The modeling of complex atomic spectra is a difficult task, due to the huge number of levels and lines involved. In the presence of a magnetic field, the computation becomes even more difficult. The anomalous Zeeman pattern is a superposition of many absorption or emission profiles with different Zeeman relative strengths, shifts, widths, asymmetries and sharpnesses. We propose a statistical approach to study the effect of a magnetic field on the broadening of spectral lines and transition arrays in atomic spectra. In this model, the σ and π profiles are described using the moments of the Zeeman components, which depend on quantum numbers and Landé factors. A graphical calculation of these moments, together with a statistical modeling of Zeeman profiles as expansions in terms of Hermite polynomials are presented. It is shown that the procedure is more efficient, in terms of convergence and validity range, than the Taylor-series expansion in powers of the magnetic field which was suggested in the past. Finally, a simple approximate method to estimate the contribution of a magnetic field to the width of transition arrays is proposed. It relies on our recently published recursive technique for the numbering of LS-terms of an arbitrary configuration.

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Alternative mathematical technique to determine LS spectral terms

Cited by 7 publications

References 36 publications

A generic procedure for determining atomic LS spectral terms and their LS eigenfunctions

A generic procedure for determining atomic LS spectral terms and their LS eigenfunctions

1s2p RIXS Calculations for 3d Transition Metal Ions in Octahedral Symmetry

Characterization of anomalous Zeeman patterns in complex atomic spectra

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