Regularities in the distribution of oscillator strengths of lines in spectra of alkali metal atoms and their isoelectronic ions

Sarandaev, E. V.; Салахов, М. Х.; Fishman, I. S.

doi:10.1016/0022-4073(95)00098-6

Cited by 2 publications

(4 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, the enhancement of some transitions and the near-forbidenness of the other transitions indicate the existence of an additional selection rule [47]. Let us consider the operator A (10) = b(ℓs) † × a (ℓ ′ s) † (10) ,…”

Section: Propensity Rulementioning

confidence: 99%

“…The selection rule for the dipole transition amplitude follows from the relation between the operator A (10) and the radiative dipole transition operator D (1) in the second quantization representation for the considered transition ℓ N +1 ℓ ′N ′ → ℓ N ℓ ′N ′ +1 :…”

Section: Propensity Rulementioning

confidence: 99%

“…The only distribution invariant when a constant is added is the uniform distribution U . This means that in the interval [1,10]:…”

Section: Scale Invariancementioning

confidence: 99%

“…transitions of the kind nℓ → n ′ ℓ ′ with n ′ = n + 1, ℓ = n − 1 and ℓ ′ = n ′ − 1 = n (for instance 1s → 2p, 2p → 3d, 3d → 4f ). The hydrogenic expression of the oscillator strength (Gordon's formula) reads [10,11]:…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Regularities and symmetries in atomic structure and spectra

Pain¹

2013

High Energy Density Physics

View full text Add to dashboard Cite

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.

show abstract

Section: Propensity Rulementioning

confidence: 99%

Section: Propensity Rulementioning

confidence: 99%

“…The only distribution invariant when a constant is added is the uniform distribution U . This means that in the interval [1,10]:…”

Section: Scale Invariancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations