Isotope Shifts in Beryllium-, Boron-, Carbon-, and Nitrogen-like Ions from Relativistic Configuration Interaction Calculations

Energy levels, normal and specific mass shift parameters as well as electronic densities at the nucleus are reported for numerous states along the beryllium, boron, carbon, and nitrogen isoelectronic sequences. Combined with nuclear data, these electronic parameters can be used to determine values of level and transition isotope shifts. The calculation of the electronic parameters is done using first-order perturbation theory with relativistic configuration interaction wave functions that account for valence, core-valence and core-core correlation effects as zero-order functions. Results are compared with experimental and other theoretical values, when available.Comment: 56 pages, 1 figure, Atomic Data and Nuclear Data Tables (2014

Ab initio calculations of the {33}S 3p4 3P_J and {33}S- / {37,35}Cl 3p5 2Po_J hyperfine structures

We present highly correlated multi-configuration Hartree-Fock (MCHF) calculations of the hyperfine structure of the 3p5 2Po_J levels of {33}S- and {35,37}Cl. We obtain a good agreement with observation. The hyperfine structure of the neutral sulfur {33}S 3p4 3P_J lowest multiplet that has never been measured to the knowledge of the authors, is also estimated theoretically. We discuss some interesting observations made on the description of the atomic core in MCHF theory.Comment: 14 pages, 2 figures (10 subfigures

Entanglement Equivalence of NN-qubit Symmetric States

We study the interconversion of multipartite symmetric $N$-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local operation (ILO), then they belong necessarily to the separable, W, or GHZ entanglement class, establishing a practical method of discriminating subsets of entanglement classes. Furthermore, we prove that there always exists a symmetric ILO connecting any pair of symmetric $N$-qubit states equivalent under SLOCC, simplifying the requirements for experimental implementations of local interconversion of those states.Comment: Minor correction

Exploring Biorthonormal Transformations of Pair-Correlation Functions in Atomic Structure Variational Calculations

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core-valence correlation effects. This in turn leads to huge numbers of CSFs, many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the MCHF method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double- excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional CAS-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations

Confluence reduction for Markov automata

Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude

Multiconfiguration electron density function for the ATSP2K-package

A new ATSP2K module is presented for evaluating the electron density function of any multiconfiguration Hartree-Fock or configuration interaction wave function in the non relativistic or relativistic Breit-Pauli approximation. It is first stressed that the density function is not a priori spherically symmetric in the general open shell case. Ways of building it as a spherical symmetric function are discussed, from which the radial electron density function emerges. This function is written in second quantized coupled tensorial form for exploring the atomic spherical symmetry. The calculation of its expectation value is performed using the angular momentum theory in orbital, spin, and quasispin spaces, adopting a generalized graphical technique. The natural orbitals are evaluated from the diagonalization of the density matrix

CH in stellar atmospheres: an extensive linelist

The advent of high-resolution spectrographs and detailed stellar atmosphere modelling has strengthened the need for accurate molecular data. Carbon-enhanced metal-poor (CEMP) stars spectra are interesting objects with which to study transitions from the CH molecule. We combine programs for spectral analysis of molecules and stellar-radiative transfer codes to build an extensive CH linelist, including predissociation broadening as well as newly identified levels. We show examples of strong predissociation CH lines in CEMP stars, and we stress the important role played by the CH features in the Bond-Neff feature depressing the spectra of barium stars by as much as 0.2 magnitudes in the $\lambda=$3000 -- 5500 \AA\ range. Because of the extreme thermodynamic conditions prevailing in stellar atmospheres (compared to the laboratory), molecular transitions with high energy levels can be observed. Stellar spectra can thus be used to constrain and improve molecular data.Comment: 33pages, 15 figures, accepted in A&A external data available at http://www.astro.ulb.ac.be/~spectrotools

Prototyping symbolic execution engines for interpreted languages

Symbolic execution is being successfully used to automatically test statically compiled code. However, increasingly more systems and applications are written in dynamic interpreted languages like Python. Building a new symbolic execution engine is a monumental effort, and so is keeping it up-to-date as the target language evolves. Furthermore, ambiguous language specifications lead to their implementation in a symbolic execution engine potentially differing from the production interpreter in subtle ways. We address these challenges by flipping the problem and using the interpreter itself as a specification of the language semantics. We present a recipe and tool (called Chef) for turning a vanilla interpreter into a sound and complete symbolic execution engine. Chef symbolically executes the target program by symbolically executing the interpreter's binary while exploiting inferred knowledge about the program's high-level structure. Using Chef, we developed a symbolic execution engine for Python in 5 person-days and one for Lua in 3 person-days. They offer complete and faithful coverage of language features in a way that keeps up with future language versions at near-zero cost. Chef-produced engines are up to 1000 times more performant than if directly executing the interpreter symbolically without Chef

Extended Calculations of Spectroscopic Data: Energy Levels, Lifetimes and Transition rates for O-like ions from Cr XVII to Zn XXIII

Employing two state-of-the-art methods, multiconfiguration Dirac--Hartree--Fock and second-order many-body perturbation theory, the excitation energies and lifetimes for the lowest 200 states of the $2s^2 2p^4$, $2s 2p^5$, $2p^6$, $2s^2 2p^3 3s$, $2s^2 2p^3 3p$, $2s^2 2p^3 3d$, $2s 2p^4 3s$, $2s 2p^4 3p$, and $2s 2p^4 3d$ configurations, and multipole (electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2)) transition rates, line strengths, and oscillator strengths among these states are calculated for each O-like ion from Cr XVII to Zn XXIII. Our two data sets are compared with the NIST and CHIANTI compiled values, and previous calculations. The data are accurate enough for identification and deblending of new emission lines from the sun and other astrophysical sources. The amount of data of high accuracy is significantly increased for the $n = 3$ states of several O-like ions of astrophysics interest, where experimental data are very scarce

Trace Spaces: an Efficient New Technique for State-Space Reduction

State-space reduction techniques, used primarily in model-checkers, all rely on the idea that some actions are independent, hence could be taken in any (respective) order while put in parallel, without changing the semantics. It is thus not necessary to consider all execution paths in the interleaving semantics of a concurrent program, but rather some equivalence classes. The purpose of this paper is to describe a new algorithm to compute such equivalence classes, and a representative per class, which is based on ideas originating in algebraic topology. We introduce a geometric semantics of concurrent languages, where programs are interpreted as directed topological spaces, and study its properties in order to devise an algorithm for computing dihomotopy classes of execution paths. In particular, our algorithm is able to compute a control-flow graph for concurrent programs, possibly containing loops, which is "as reduced as possible" in the sense that it generates traces modulo equivalence. A preliminary implementation was achieved, showing promising results towards efficient methods to analyze concurrent programs, with very promising results compared to partial-order reduction techniques