arXiv subjects

M. Godefroid

Publications and source records attributed to M. Godefroid.

17 recordsLinked to original sources

arXiv2023

Nuclear charge radius of $^{26m}$Al and its implication for V$_{ud}$ in the quark-mixing matrix

Collinear laser spectroscopy was performed on the isomer of the aluminium isotope $^{26m}$Al. The measured isotope shift to $^{27}$Al in the $3s^{2}3p\;^{2}\!P^\circ_{3/2} \rightarrow 3s^{2}4s\;^{2}\!S_{1/2}$ atomic transition enabled the first experimental determination of the nuclear charge radius of $^{26m}$Al, resulting in $R_c$=\qty{3.130\pm.015}{\femto\meter}. This differs by 4.5 standard deviations from the extrapolated value used to calculate the isospin-symmetry breaking corrections in the superallowed $\beta$ decay of $^{26m}$Al. Its corrected $\mathcal{F}t$ value, important for the estimation of $V_{ud}$ in the CKM matrix, is thus shifted by one standard deviation to \qty{3071.4\pm1.0}{\second}.

nucl-ex↗

arXiv2023

Opacities of Singly and Doubly Ionised Neodymium and Uranium for Kilonova Emission Modeling

Even though the electromagnetic counterpart AT2017gfo to the binary neutron star merger GW170817 is powered by the radioactive decay of r-process nuclei, only few tentative identifications of light r-process elements have been made so far. One of the major limitations for the identification of heavy nuclei is incomplete or missing atomic data. While substantial progress has been made on lanthanide atomic data over the last few years, for actinides there has been less emphasis, with the first complete set of opacity data only recently published. We perform atomic structure calculations of neodymium $(Z=60)$ as well as the corresponding actinide uranium $(Z=92)$. Using two different codes (FAC and HFR) for the calculation of the atomic data, we investigate the accuracy of the calculated data (energy levels and electric dipole transitions) and their effect on kilonova opacities. For the FAC calculations, we optimise the local central potential and the number of included configurations and use a dedicated calibration technique to improve the agreement between theoretical and available experimental atomic energy levels (AELs). For ions with vast amounts of experimental data available, the presented opacities agree quite well with previous estimations. On the other hand, the optimisation and calibration method cannot be used for ions with only few available AELs. For these cases, where no experimental nor benchmarked calculations are available, a large spread in the opacities estimated from the atomic data obtained with the various atomic structure codes is observed.We find that the opacity of uranium is almost double the neodymium opacity.

astro-ph.HE↗

arXiv2020

High-resolution laser spectroscopy of $^{27-32}$Al

Hyperfine spectra of $^\text{27-32}$Al ($Z=13$) have been measured at the ISOLDE-CERN facility via collinear laser spectroscopy using the $3s^23p\ ^2\text{P}^\text{o} _{3/2}\rightarrow 3s^24s\ ^2\text{S}_{1/2}$ atomic transition. For the first time, mean-square charge radii of radioactive aluminum isotopes have been determined alongside the previously unknown magnetic dipole moment of $^{29}$Al and electric quadrupole moments of $^{29,30}$Al. A potentially reduced charge radius at $N=19$ may suggest an effect of the $N=20$ shell closure, which is visible in the Al chain, contrary to other isotopic chains in the $sd$ shell. The experimental results are compared to theoretical calculations in the framework of the valence-space in-medium similarity renormalization group using multiple sets of two and three-nucleon forces from chiral effective field theory. While the trend of experimental magnetic dipole and electric quadrupole moments is well reproduced, the absolute values are underestimated by theory, consistent with earlier studies. Moreover, both the scale and trend of the charge radii appear to be very sensitive to the chosen interaction.

nucl-ex↗

arXiv2020

Extended Calculations with Spectroscopic Accuracy: Energy Levels and Radiative Rates for O-like Ions between Ar XI and Cr XVII

Using the multiconfiguration Dirac-Hartree-Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the main 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 in O-like Ions between Ar XI ($Z = 18$) and Cr XVII ($Z = 24$) is provided. Our data set is compared with the NIST compiled values and previous calculations. The data are accurate enough for identification and deblending of new emission lines from hot astrophysical and laboratory plasmas. The amount of data of high accuracy is significantly increased for the $n = 3$ states of several O-like ions, where experimental data are very scarce.

physics.atom-ph↗

arXiv2020

Large-scale multiconfiguration Dirac-Hartree-Fock calculations for astrophysics: n=4 levels in P-like ions from Mn~XI to Ni~XIV

Using the multiconfiguration Dirac-Hartree-Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the lowest 546 (623, 701, 745) states of the $3p^4 3d$, $3s 3p^2 3d^2$, $3s 3p^3 4p$, $3s 3p^4$, $3s^2 3d^3$, $3s^2 3p^2 3d$, $3s^2 3p^2 4d$, $3s^2 3p^2 4s$, $3p^3 3d^2$, $3p^5$, $3s 3p 3d^3$, $3s 3p^3 3d$, $3s 3p^3 4s$, $3s^2 3p 3d^2$, %$3s^2 3p^2 4f$, $3s^2 3p^2 4p$, $3s^2 3p^3$ configurations in Mn~XI (Fe~XII, Co~XIII, Ni~XIV) is provided. The comparison between calculated excitation energies for the $n=4$ states and available experimental values for Fe XII indicate that the calculations are highly accurate, with uncertainties of only a few hundred cm$^{-1}$. Lines from these states are prominent in the soft X-rays. With the present calculations, several recent new identifications are confirmed. Other identifications involving $3p^2 4d$ levels in Fe~XII that were found questionable are discussed and a few new assignments are recommended. As some $n=4$ states of the other ions also show large discrepancies between experimental and calculated energies, we reassess their identification. The present study provides highly accurate atomic data for the $n=4$ states of P-like ions of astrophysical interest, for which experimental data are scarce.

physics.atom-ph↗

arXiv2019

Large-scale multiconfiguration Dirac-Hartree-Fock calculations for astrophysics: Cl-like ions from Cr~VIII to Zn~XIV

We use the multiconfiguration Dirac-Hartree-Fock (MCDHF) method combined with the relativistic configuration interaction (RCI) approach (GRASP2K) to provide a consistent set of transition energies and radiative transition data for the lower $n =3$ states in all Cl-like ions of astrophysical importance, from \ion{Cr}{8} to \ion{Zn}{14}. We also provide excitation energies calculated for \mbox{Fe X} using the many-body perturbation theory (MBPT, implemented within FAC). The comparison of the present MCDHF results with MBPT and with the available experimental energies indicates that the theoretical excitation energies are highly accurate, with uncertainties of only a few hundred cm$^{-1}$. Detailed comparisons for Fe~X and Ni~XII highlight discrepancies in the experimental energies found in the literature. Several new identifications are proposed.

physics.atom-ph↗

arXiv2014

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.

astro-ph.SR↗

arXiv2014

Hyperfine structures and Land\'e $g_J$-factors for $n=2$ states in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations

Energy levels, hyperfine interaction constants, and Land\'e $g_J$-factors are reported for n=2 states in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations. Valence, core-valence, and core-core correlation effects are taken into account through single and double-excitations from multireference expansions to increasing sets of active orbitals. A systematic comparison of the calculated hyperfine interaction constants is made with values from the available literature.

physics.atom-ph↗

arXiv2014

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.

physics.atom-ph↗

arXiv2013

Theoretical study of the isotope effects on the detachment thresholds of Si$^-$

The isotope effects in Si$^-$ bound levels are studied using the multi-configuration Hartree-Fock ab initio approach. Large scale calculations are carried out for the $3p^3\ ^4S^o,\, ^2D^o$ and $^2P^o$ multiplets of Si$^-$ and the $3p^2\ ^3P$ multiplet of Si. We predict an anomalous isotope shift on the electron affinity, dominated by the specific mass shift, with a value of $IS(^e\!\!A)= -0.66(6)$ m$^{-1}$ for the ($30-28$) isotope pair. We also report hyperfine structure parameters for the studied multiplets. Finally, we provide the values of level electric field gradients at the nucleus that could be of interest in a study of the metastable silicon isotopes. Relativistic corrections are estimated using non-relativistic orbitals in the Breit-Pauli and fully relativistic frameworks.

physics.atom-ph↗

arXiv2013

A Partitioned Correlation Function Interaction approach for describing electron correlation in atoms

Traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis (OB). For atoms with complicated shell structures, a large OB is needed to saturate all the electron correlation effects. The large OB leads to massive configuration state function (CSF) expansions that are difficult to handle. We show that it is possible to relax the orthonormality restriction on the OB and break down the originally large calculations to a set of smaller ones that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The mixing coefficients of the PCFs are fixed from a small generalized eigenvalue problem. The required matrices are computed using a biorthonormal transformation technique. The new method, called partitioned correlation function interaction (PCFI), converges rapidly and gives total energies that are lower than the ordinary ones (MCHF and CI). Considering Li I, we show that by dedicating a PCF to the single excitations from the core highly improves the convergence patterns of the hyperfine parameters. Collecting the optimized PCFs to correct the MR function, the variational degrees of freedom in the relative mixing coefficients of the CSFs building the PCFs are inhibited. These constraints lead to small off-sets in computed properties other than total energy, with respect to the correct values. By (partially) deconstraining the mixing coefficients one converges to the correct limits and keeps the important advantage in the convergence rates. Reducing ultimately each PCF to a single CSF with its own OB leads to a non-orthogonal CI approach. Various perspectives of the new method are given.

physics.atom-ph↗

arXiv2011

Tensorial form and matrix elements of the relativistic nuclear recoil operator

Within the lowest-order relativistic approximation ($\sim v^2/c^2$) and to first order in $m_e/M$, the tensorial form of the relativistic corrections of the nuclear recoil Hamiltonian is derived, opening interesting perspectives for calculating isotope shifts in the multiconfiguration Dirac-Hartree-Fock framework. Their calculation is illustrated for selected Li-, B- and C-like ions. The present work underlines the fact that the relativistic corrections to the nuclear recoil are definitively necessary for getting reliable isotope shift values.

physics.atom-ph↗

arXiv2009

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.

physics.atom-ph↗

arXiv2009

Entanglement Equivalence of $N$-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.

quant-ph↗

arXiv2009

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.

physics.atom-ph↗

arXiv2009

Operational Families of Entanglement Classes for Symmetric $N$-Qubit States

We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for all multipartite symmetric states in the general $N$-qubit case. For this purpose, we introduce 2 parameters playing a crucial role, namely the \emph{diversity degree} and the \emph{degeneracy configuration} of a symmetric state. Those parameters give rise to a simple method of identifying operational families of SLOCC entanglement classes of all symmetric $N$-qubit states, where the number of families grows as the partition function of the number of qubits.

quant-ph↗

arXiv2007

A Quantum Similarity Study of Atomic Density Functions: Insights from Information Theory and the Role of Relativistic Effects

A novel quantum similarity measure (QSM) is constructed based on concepts from information theory. In an application of QSM to atoms, the new QSM and its corresponding quantum similarity index (QSI) are evaluated throughout the periodic table, using the atomic electron densities and shape functions calculated in the Hartree-Fock approximation. The periodicity of Mendeleev's table is regained for the first time through the evaluation of a QSM. Evaluation of the information theory based QSI demonstrates, however, that the patterns of periodicity are lost due to the renormalization of the QSM, yielding chemically less appealing results for the QSI. A comparison of the information content of a given atom on top of a group with the information content of the elements in the subsequent rows reveals another periodicity pattern. Relativistic effects on the electronic density functions of atoms are investigated. Their importance is quantified in a QSI study by comparing for each atom, the density functions evaluated in the Hartree-Fock and Dirac-Fock approximations. The smooth decreasing of the relevant QSI along the periodic table illustrates in a quantitative way the increase of relativistic corrections with the nuclear charge.

physics.atom-ph↗