Study of spectra for lanthanides atoms with relativistic many- body perturbation theory: Rydberg resonances

Theoretical Spectroscopy of Rare-Earth Elements: Spectra and Autoionization Resonances

“…In Refs. [32][33][34][35][36][37][38][39][40][41], it has been shown that two pairs of low-lying ionization Here ROD refers to re-orientation-type AS decay. The states 4f À1 5=2 6s 1=2 ðJ 12 ¼ 3Þnl are exposed simultaneously to BFD and ROD-decays.…”

“…In Refs. [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], it has been performed the detailed computing energies and widths of the autoionization resonances, Rydberg levels for ytterbium and thallium. The positions and widths of the autoionization states belonging to the 7s6p,6 p5d,6 p 2 and 5d 2 configurations were calculated using the method of relativistic perturbation theory (PT) with the model potential (MP) zeroth approximation .…”

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

“…The formalism is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov's exponents analysis, and surrogate data method, prediction models etc (see details in Refs. [6][7][8][9][10][11][12][13][14][15][16][17][18][19]). There are firstly presented the numerical data on topological and dynamical invariants of chaotic systems, in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov's exponents, Kolmogorov's entropy etc for laser (the semiconductor GaAs/GaAlAs laser with retarded feedback) systems dynamics in chaotic and hyperchaotic regimes.…”

“…In a general case, s(n) is any time series, particularly the amplitude level. Since processes resulting in the chaotic behaviour are fundamentally multivariate (look [18][19][20][21][22][23]), it is necessary to reconstruct phase space using as well as possible information contained in the s(n). Such a reconstruction results in a certain set of ddimensional vectors y(n) replacing the scalar measurements.…”

“…The statistical convergence tests together with surrogate data algorithm can provide the satisfactory significance of the investigated data regarding the state-space reconstruction. In Table 1 we present the main blocks of our universal chaos-geometric approach to computational studying a non-linear dynamics of the chaotic systems [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. 3.…”