Effect of third- and fourth-order moments on the modeling of Unresolved Transition Arrays

The impact of the third (skewness) and fourth (kurtosis) reduced centered moments on the statistical modeling of E1 lines in complex atomic spectra is investigated through the use of Gram-Charlier, Normal Inverse Gaussian and Generalized Gaussian distributions. It is shown that the modeling of unresolved transition arrays with non-Gaussian distributions may reveal more detailed structures, due essentially to the large value of the kurtosis. In the present work, focus is put essentially on the Generalized Gaussian, the power of the argument in the exponential being constrained by the kurtosis value. The relevance of the new statistical line distribution is checked by comparisons with smoothed detailed line-by-line calculations and through the analysis of 2p-3d transitions of recent laser or Z-pinch absorption measurements. The issue of calculating high-order moments is also discussed (Racah algebra, Jucys graphical method, semi-empirical approach ...).Comment: submitted to High Energy Density Physic

Hybrid atomic models for spectroscopic plasma diagnostics

We propose a hybrid approach to treating atomic structure and rates in collisional-radiative models, combining the completeness of highly averaged models with the accuracy of detailed models. The hybrid scheme supplements a small subset of coronally accessible fine structure levels with a complete set of configuration- and superconfiguration-averaged levels and produces spectra based on transitions among a mix of fine-structure and relativistic configuration-averaged levels. Convenient expressions are given for obtaining rates between the fine structure and averaged levels and a technique for propagating configuration interaction from the fine structure calculations to configuration averages is described. We present results from a trial hybrid model of germanium which demonstrate the accuracy of the hybrid model for charge state distributions and spectra

Chaos and localization in the wavefunctions of complex atoms NdI, PmI and SmI

Wavefunctions of complex lanthanide atoms NdI, PmI and SmI, obtained via multi-configuration Dirac-Fock method, are analyzed for density of states in terms of partial densities, strength functions ($F_k(E)$), number of principal components ($\xi_2(E)$) and occupancies (\lan n_\alpha \ran^E) of single particle orbits using embedded Gaussian orthogonal ensemble of one plus two-body random matrix ensembles [EGOE(1+2)]. It is seen that density of states are in general multi-modal, $F_k(E)$'s exhibit variations as function of the basis states energy and $\xi_2(E)$'s show structures arising from localized states. The sources of these departures from EGOE(1+2) are investigated by examining the partial densities, correlations between $F_k(E)$, $\xi_2(E)$ and \lan n_\alpha \ran^E and also by studying the structure of the Hamiltonian matrices. These studies point out the operation of EGOE(1+2) but at the same time suggest that weak admixing between well separated configurations should be incorporated into EGOE(1+2) for more quantitative description of chaos and localization in NdI, PmI and SmI.Comment: There are 9 figure

A Holder Continuous Nowhere Improvable Function with Derivative Singular Distribution

We present a class of functions $\mathcal{K}$ in $C^0(\R)$ which is variant of the Knopp class of nowhere differentiable functions. We derive estimates which establish \mathcal{K} \sub C^{0,\al}(\R) for 0<\al<1 but no $K \in \mathcal{K}$ is pointwise anywhere improvable to C^{0,\be} for any \be>\al. In particular, all $K$'s are nowhere differentiable with derivatives singular distributions. $\mathcal{K}$ furnishes explicit realizations of the functional analytic result of Berezhnoi. Recently, the author and simulteously others laid the foundations of Vector-Valued Calculus of Variations in $L^\infty$ (Katzourakis), of $L^\infty$-Extremal Quasiconformal maps (Capogna and Raich, Katzourakis) and of Optimal Lipschitz Extensions of maps (Sheffield and Smart). The "Euler-Lagrange PDE" of Calculus of Variations in $L^\infty$ is the nonlinear nondivergence form Aronsson PDE with as special case the $\infty$-Laplacian. Using $\mathcal{K}$, we construct singular solutions for these PDEs. In the scalar case, we partially answered the open $C^1$ regularity problem of Viscosity Solutions to Aronsson's PDE (Katzourakis). In the vector case, the solutions can not be rigorously interpreted by existing PDE theories and justify our new theory of Contact solutions for fully nonlinear systems (Katzourakis). Validity of arguments of our new theory and failure of classical approaches both rely on the properties of $\mathcal{K}$.Comment: 5 figures, accepted to SeMA Journal (2012), to appea

Alternative Mathematical Technique to Determine LS Spectral Terms

We presented an alternative computational method for determining the permitted LS spectral terms arising from $l^N$ electronic configurations. This method makes the direct calculation of LS terms possible. Using only basic algebra, we derived our theory from LS-coupling scheme and Pauli exclusion principle. As an application, we have performed the most complete set of calculations to date of the spectral terms arising from $l^N$ electronic configurations, and the representative results were shown. As another application on deducing LS-coupling rules, for two equivalent electrons, we deduced the famous Even Rule; for three equivalent electrons, we derived a new simple rule.Comment: Submitted to Phys. Rev.

Electron recombination with multicharged ions via chaotic many-electron states

We show that a dense spectrum of chaotic multiply-excited eigenstates can play a major role in collision processes involving many-electron multicharged ions. A statistical theory based on chaotic properties of the eigenstates enables one to obtain relevant energy-averaged cross sections in terms of sums over single-electron orbitals. Our calculation of the low-energy electron recombination of Au$^{25+}$ shows that the resonant process is 200 times more intense than direct radiative recombination, which explains the recent experimental results of Hoffknecht {\em et al.} [J. Phys. B {\bf 31}, 2415 (1998)].Comment: 9 pages, including 1 figure, REVTe

Calculations of parity nonconserving s-d transitions in Cs, Fr, Ba II, and Ra II

We have performed ab initio mixed-states and sum-over-states calculations of parity nonconserving (PNC) electric dipole (E1) transition amplitudes between s-d electron states of Cs, Fr, Ba II, and Ra II. For the lower states of these atoms we have also calculated energies, E1 transition amplitudes, and lifetimes. We have shown that PNC E1 transition amplitudes between s-d states can be calculated to high accuracy. Contrary to the Cs 6s-7s transition, in these transitions there are no strong cancelations between different terms in the sum-over-states approach. In fact, there is one dominating term which deviates from the sum by less than 20%. This term corresponds to an s-p_{1/2} weak matrix element, which can be calculated to better than 1%, and a p_{1/2}-d_{3/2} E1 transition amplitude, which can be measured. Also, the s-d amplitudes are about four times larger than the corresponding s-s transitions. We have shown that by using a hybrid mixed-states/sum-over-states approach the accuracy of the calculations of PNC s-d amplitudes could compete with that of Cs 6s-7s if p_{1/2}-d_{3/2} E1 amplitudes are measured to high accuracy.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

Isotope shift in the electron affinity of chlorine

The specific mass shift in the electron affinity between ^{35}Cl and ^{37}Cl has been determined by tunable laser photodetachment spectroscopy to be -0.51(14) GHz. The isotope shift was observed as a difference in the onset of the photodetachment process for the two isotopes. In addition, the electron affinity of Cl was found to be 29138.59(22) cm^{-1}, giving a factor of 2 improvement in the accuracy over earlier measurements. Many-body calculations including lowest-order correlation effects demonstrates the sensitivity of the specific mass shift and show that the inclusion of higher-order correlation effects would be necessary for a quantitative description.Comment: 16 pages, 6 figures, LaTeX2e, amsmat

Measurement of XUV-absorption spectra of ZnS radiatively heated foils

Time-resolved absorption of zinc sulfide (ZnS) and aluminum in the XUV-range has been measured. Thin foils in conditions close to local thermodynamic equilibrium were heated by radiation from laser-irradiated gold spherical cavities. Analysis of the aluminum foil radiative hydrodynamic expansion, based on the detailed atomic calculations of its absorption spectra, showed that the cavity emitted flux that heated the absorption foils corresponds to a radiation temperature in the range 55 60 eV. Comparison of the ZnS absorption spectra with calculations based on a superconfiguration approach identified the presence of species Zn6+ - Zn8+ and S5+ - S6+. Based on the validation of the radiative source simulations, experimental spectra were then compared to calculations performed by post-processing the radiative hydrodynamic simulations of ZnS. Satisfying agreement is found when temperature gradients are accounted for