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Coalescence of binary neutron stars gives rise to kilonova, thermal emission powered by radioactive decays of newly synthesized r-process nuclei. Observational properties of kilonova are largely affected by bound-bound opacities of r-process elements. It is, thus, important to understand atomic properties of heavy elements to link the observed signals with nucleosynthesis of neutron star mergers. In this paper, we introduce the latest status of kilonova modeling by focusing on the aspects of atomic physics. We perform systematic atomic structure calculations of r-process elements to understand element-to-element variation in the opacities. We demonstrate that the properties of the atomic structure of heavy elements are imprinted in the opacities of the neutron star merger ejecta and consequently in the kilonova light curves and spectra. Using this latest opacity dataset, we briefly discuss implications for GW170817, expected diversity of kilonova emission, and prospects for element identification in kilonova spectra.

Lanthanide elements play important roles as an opacity source in the ejected material from neutron star mergers. Accurate and complete atomic data are necessary to evaluate the opacities and to analyze the observed data. In this paper, we perform extended, ab-initio atomic calculations from Pr II (Z=59) to Gd II (Z=64). By using multiconfiguration Dirac-Hartree-Fock and relativistic configuration-interaction methods, implemented in the general-purpose relativistic atomic structure package GRASP2K, we calculate the energy levels and transition data of electric dipole transitions. These computations are based on strategies (with small variations) of Nd II published by Gaigalas et al. (2019). Accuracy of data is evaluated by comparing computed energy levels with the NIST database or other works. For the energy levels, we obtain the average relative accuracy of 8%, 12%, 6%, 8%, and 7% for Pr II, Pm II, Sm II, Eu II, and Gd II ions, respectively as compared with the NIST data. Accuracy of energy transfer to the wavelength as 3%, 14% and 11% for Pr II, Eu II and Gd II. Our computed E1 type transition probabilities are in good agreement with experimental values presented by other authors especially for strong transitions., 20 pages, 14 tables, 11 figures

In this work, we continue large-scale ab initio computations for single ionized lanthanides. Extended atomic calculations for the set of ions from Pr ii (Z = 59) to Gd ii (Z = 64) have been performed in our previous work. In this study, ions from Tb ii (Z = 65) to Yb ii (Z = 70) are analyzed. By employing the same multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods that are implemented in the general-purpose relativistic atomic structure package GRASP2018, the energy levels and transition data of electric dipole (E1) transitions are computed. These computations are based on the strategies (with small variations) of Paper I. Accuracy of data is evaluated by comparing the computed energy levels with the data provided by the National Institute of Standards and Technology (NIST) database and with data from various methods. We obtain the average accuracy in the energy level compared with the NIST database: 6%, 5%, 4%, 5%, 3%, and 3% for Tb ii, Dy ii, Ho ii, Er ii, Tm ii, and Yb ii, respectively. We also provide extensive comparison of transition probabilities and wavelengths. Our results reach the average accuracy of transition wavelengths: 9%, 9%, 9%, 3%, 4%, and 11% for Tb ii, Dy ii, Ho ii, Er ii, Tm ii, and Yb ii, respectively.

The JJ2LSJ program, which is important not only for the GRASP2K package but for the atom theory in general, is presented. The program performs the transformation of atomic state functions (ASFs) from a jj-coupled CSF basis into an LSJ-coupled CSF basis. In addition, the program implements a procedure that assigns a unique label to all energy levels. Examples of how to use the JJ2LSJ program are given. Several cases are presented where there is a unique labeling problem.

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., 56 pages, 1 figure, Atomic Data and Nuclear Data Tables (2014)

Coalescence of binary neutron star give rise to electromagnetic emission, kilonova, powered by radioactive decays of r-process nuclei. Observations of kilonova associated with GW170817 provided unique opportunity to study the heavy element synthesis in the Universe. However, atomic data of r-process elements to decipher the light curves and spectral features of kilonova are not fully constructed yet. In this paper, we perform extended atomic calculations of neodymium (Nd, Z=60) to study the impact of accuracies in atomic calculations to the astrophysical opacities. By employing multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction methods, we calculate energy levels and transition data of electric dipole transitions for Nd II, Nd III, and Nd IV ions. Compared with previous calculations, our new results provide better agreement with the experimental data. The accuracy of energy levels was achieved in the present work 10 %, 3 % and 11 % for Nd II, Nd III and Nd IV, respectively, comparing with the NIST database. We confirm that the overall properties of the opacity are not significantly affected by the accuracies of the atomic calculations. The impact to the Planck mean opacity is up to a factor of 1.5, which affects the timescale of kilonova at most 20 %. However, we find that the wavelength dependent features in the opacity are affected by the accuracies of the calculations. We emphasize that accurate atomic calculations, in particular for low-lying energy levels, are important to provide predictions of kilonova light curves and spectra., Comment: 24 pages, 9 figures, The Astrophysical Journal Supplement Series, in press

Energies, E1, M1, E2, M2 transition rates, line strengths, oscillator strengths, and lifetimes from relativistic configuration interaction calculations are reported for the states of the (1s2)2s22p, 2s2p2, and 2p3 configurations in all boron-like ions between N III and Zn XXVI. Valence, core–valence, and core–core correlation effects were accounted for through single–double multireference (SD-MR) expansions to increasing sets of active orbitals.

Large-scale multiconfiguration Hartree–Fock and Dirac–Fock calculations have been performed for the ground configuration, [Kr]4d104f4, energy levels of the W24+ ion. The relativistic corrections were taken into account in the quasirelativistic Breit–Pauli and fully relativistic Breit (taking into account QED effects) approximations. The role of correlation, relativistic, and QED corrections is discussed. Line strengths, oscillator strengths, and transition probabilities in the Coulomb and Babushkin gauges are presented for the electric quadrupole (E2) transitions among these levels. The magnetic dipole transitions are also investigated. Dependence of the E2 transition probabilities on the gauge condition of the electromagnetic field potential is studied as well.

Energies, electric dipole, magnetic dipole, and electric quadrupole transition rates, hyperfine structures, and Lande g J factors from relativistic configuration interaction calculations are reported for the states of the (1s2)2s22p2, 2s2p3, and 2p4 configurations in all carbon-like ions between F IV and Ni XXIII. Valence, core–valence, and core–core correlation effects were accounted for through single/double-excitation-multireference expansions to increasing sets of active orbitals. The calculated energy levels generally agree within a few hundred cm−1 with the experimentally compiled results, and the Babushkin (length), and Coulomb (velocity) forms of transition rates agree within less than 1% for a majority of the allowed transitions.

The fully relativistic multiconfiguration Dirac--Hartree--Fock method is used to compute excitation energies and lifetimes for the 143 lowest states of the $3s^23p^3$, $3s3p^4$, $3s^23p^23d$, $3s3p^33d$, $3p^5$, $3s^23p3d^2$ configurations in P-like ions from Cr X to Zn XVI. Multipole (E1, M1, E2, M2) transition rates, line strengths, oscillator strengths, and branching fractions among these states are also given. Valence-valence and core-valence electron correlation effects are systematically accounted for using large basis function expansions. Computed excitation energies are compared with the NIST ASD and CHIANTI compiled values and previous calculations. The mean average absolute difference, removing obvious outliers, between computed and observed energies for the 41 lowest identified levels in Fe XII is only 0.057 \%, implying that the computed energies are accurate enough to aid identification of new emission lines from the sun and other astrophysical sources. The amount of energy and transition data of high accuracy is significantly increased for several P-like ions of astrophysics interest, where experimental data are still very scarce.

Energy levels, radiative transition wavelengths and probabilities have been studied for the W$^{26+}$ ion using multiconfiguration Dirac-Fock and Dirac-Fock-Slater methods. Corona and collisional-radiative models have been applied to determine lines and corresponding configurations in a low-density electron beam ion trap (EBIT) plasma. Correlation effects for the $4f^{2}$, $4d^{9}4f^{3}$, $4f5l$ ($l=0,...,4$), $4fng$ ($n=5, 6, 7$) configurations have been estimated by presenting configuration interaction strengths. It was determined that correlation effects are important for the $4f5s \rightarrow 4f^{2}$ transitions corresponding to weak electric octupole transitions in a single-configuration approach. Correlation effects influence the $4f5d \rightarrow 4f^{2}$ transitions by increasing transition probabilities by an order of magnitude. Identification of some lines observed in fusion plasma has been proposed. Spectra modeling shows strong increase of lines originating from the $4f5s \rightarrow 4f^{2}$ transitions. Other transitions from the $10-30$ nm region can be of interest for the EBIT plasma., Comment: 22pages including 8 figures and 3 tables. Supplementary data available from stacks.iop.org/jpb/48/135003/mmedia

Corona modeling of spectral lines for the W27+ ion is performed. Energy levels and radiative transition probabilities are calculated using GRASP2K and FAC codes. Electron-impact excitation rates are studied in the distorted wave approximation and are taken proportional to the electric dipole line strengths.

Analysis of energy levels and radiative transition probabilities for the W27+ ion is performed using multiconfiguration Dirac-Fock method. Configuration interaction strength has been used to determine the influence of correlation effects.

No lines have been observed for transitions between the doublet and quartet levels of B i. Consequently, energy levels based on observation for the latter are obtained through extrapolation of wavelengths along the isoelectronic sequence for the $2{s}^{2}2p$ ${\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}^{o}$ -- $2s2{p}^{2}$ ${\phantom{\rule{0.16em}{0ex}}}^{4}{P}_{5/2}$ transition. In this paper, accurate theoretical excitation energies from a partitioned-correlation-function-interaction (PCFI) method are reported for B i that include both relativistic effects in the Breit-Pauli approximation and a finite mass correction. Results are compared with extrapolated values from observed data. For B i our estimate of the excitation energy 28 959 $\ifmmode\pm\else\textpm\fi{}$ 5 cm${}^{\ensuremath{-}1}$ is in better agreement with the values obtained by Edl\'en et al. (1969) than those reported by Kramida and Ryabtsev (2007). Our method is validated by applying the same procedure to the separation of these levels in C ii.

Usually it is accepted that the probabilities of the electric-multipole electron transitions are rapidly decreasing functions of their multipolarity. Therefore while calculating the probabilities of electronic transitions between the configurations of certain chosen parities, it seems sufficient to take into account the first nonzero term, i.e., to consider the electron transitions of lowest multipolarity permitted by the exact selection rules. This paper aims at verifying this assumption on the example of electric-octupole transitions in ${\mathrm{W}}^{24+}$ ion. For this purpose the large-scale multiconfiguration Hartree-Fock and Dirac-Fock calculations have been performed for the configurations [Kr]$4{d}^{10}4{f}^{4}$ and [Kr]$4{d}^{10}4{f}^{3}5s$ energy levels of ${\mathrm{W}}^{24+}$ ion. The relativistic corrections were taken into account in the quasirelativistic Breit-Pauli and fully relativistic Breit (taking into account QED effects) approximations. The role of correlation, relativistic, and QED corrections is discussed. Line strengths, oscillator strengths, and transition probabilities in Coulomb and Babushkin gauges are presented for $E1$ and $E3$ transitions among these levels.

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., Comment: 22 pages, no figures, submitted to J. Phys. B

We aim at demonstrating the feasibility of accurate theoretical studies of atoms and ions having complex electronic configurations, open f shell included, by combining the second quantization method in coupled tensorial form with a quasispin technique, leading to triple tensors (in orbital, spin, and quasispin spaces). The large-scale nonrelativistic and relativistic calculations of the 977 lowest energy levels of W{sup 24+}, accounting for correlation, relativistic, and quantum electrodynamics effects, demonstrate the high efficacy of the methods used. The accuracy of the LS- and jj-coupling schemes is discussed as well. The wavelengths of electric dipole transitions, their line strengths and transition probabilities, as well as the lifetimes of some lowest excited levels are also calculated. The authors hope that the success in theoretical studies of such complex ions will stimulate relevant experimental research, encouraging yet further progress in the theory.

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., Comment: 35 pages, 6 tables and 10 figures

XXVII International Conference on Photonic, Electronic and Atomic Collisions Belfast, (Northern Ireland, UK), July 27 – August 2, 2011.