Efficient methods for calculating the number of states, levels and lines in atomic configurations

Gilleron, F.; Pain, Jean‐Christophe

doi:10.1016/j.hedp.2009.04.007

Cited by 26 publications

(45 citation statements)

References 10 publications

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“…and M J,min = −M J,max [54]. In that case, the excess of J values is equal to the excess of M J values [55].…”

Section: Propensity Rulementioning

confidence: 99%

Regularities and symmetries in atomic structure and spectra

Pain¹

2013

High Energy Density Physics

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The use of statistical methods for the description of complex quantum systems was primarily motivated by the failure of a line-by-line interpretation of atomic spectra. Such methods reveal regularities and trends in the distributions of levels and lines. In the past, much attention was paid to the distribution of energy levels (Wigner surmise, random-matrix model...). However, information about the distribution of the lines (energy and strength) is lacking. Thirty years ago, Learner found empirically an unexpected law: the logarithm of the number of lines whose intensities lie between 2 k I0 and 2 k+1 I0, I0 being a reference intensity and k an integer, is a decreasing linear function of k. In the present work, the fractal nature of such an intriguing regularity is outlined and a calculation of its fractal dimension is proposed. Other peculiarities are also presented, such as the fact that the distribution of line strengths follows Benford's law of anomalous numbers, the existence of additional selection rules (PH coupling), the symmetry with respect to a quarter of the subshell in the spinadapted space (LL coupling) and the odd-even staggering in the distribution of quantum numbers, pointed out by Bauche and Cossé.

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“…and M J,min = −M J,max [54]. In that case, the excess of J values is equal to the excess of M J values [55].…”

Section: Propensity Rulementioning

confidence: 99%

Regularities and symmetries in atomic structure and spectra

Pain¹

2013

High Energy Density Physics

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“…Less attention has been paid to the consequences of treating large ensembles of energy levels as simple states void of internal structure in plasmas far from equilibrium. We might expect these consequences to be most obvious in the screened hydrogenic models whose superconfigurations can represent tens of thousands of fine structure levels [35]; this will be the focus of the present paper.…”

Section: Introductionmentioning

confidence: 94%

Superconfiguration widths and their effects on atomic models

Hansen

Bauche

Bauche‐Arnoult

2011

High Energy Density Physics

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“…This led us to develop efficient algorithms for the numbering of LS terms and J levels. 9 We have also extended the statistical modelling of the distribution of quantum states in order to better describe configurations having open sub-shells with a large angular momentum.…”

Section: Hybrid Approachmentioning

confidence: 99%

Opacity of germanium and silicon in ICF plasmas

et al. 2013

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Because germanium and silicon may be used as dopants in the ablator of ignition target, the knowledge of their opacities is crucial. We have calculated the opacity by using two approaches. The first one utilizes a detailed line calculation in which the atomic database is provided by the MCDF code. A lineshape code was then adapted to the calculation of opacity profiles. Because the calculation time is prohibitive when the number of lines is huge, a second approach, combining detailed line calculations and statistical calculations is used. This approach necessitates much smaller calculation than the first one and is then well suited for extensive calculations. The monochromatic opacity and the Rosseland and Planck mean opacities are calculated for various relevant densities and temperatures.

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Efficient methods for calculating the number of states, levels and lines in atomic configurations

Cited by 26 publications

References 10 publications

Regularities and symmetries in atomic structure and spectra

Regularities and symmetries in atomic structure and spectra

Superconfiguration widths and their effects on atomic models

Opacity of germanium and silicon in ICF plasmas

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