Opacity calculations in four to nine times ionized Pr, Nd, and Pm atoms for the spectral analysis of kilonovae

Abstract

New atomic data for radiative transitions in Pr V–X, Nd V–X and Pm V–X were determined by means of large-scale calculations involving three independent theoretical methods, i.e. the pseudo-relativistic Hartree-Fock method including core-polarization corrections (HFR+CPOL), the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, and the configuration interaction many-body perturbation theory (CI+MBPT) implemented in the AMBiT program. This multi-platform approach allowed us to estimate the reliability of the results obtained and to extract a large amount of energy levels, wavelengths, transition probabilities and oscillator strengths for the determination of opacities required for the analysis of the spectra emitted in the early phases of kilonovae following neutron star mergers, i.e. for typical conditions corresponding to temperatures T > 20000 K, a density ρ = 10−10 g cm−3 and a time after the merger t = 0.1 day. Our radiative parameters were compared in detail with the few experimental data published so far and their impact on the calculated opacities, in terms of atomic computation strategy, was also examined.

Pseudo-Relativistic Hartree–Fock and Fully Relativistic Dirac–Hartree–Fock Calculations of Radiative Parameters in the Fifth Spectrum of Lutetium (Lu V)

“…This opacity, which is a key parameter for the determination of the kilonova light curve, i.e., the evolution of light intensity as a function of time, can only be reliably estimated by the knowledge of the most accurate atomic data possible for a sufficient number of spectral lines belonging to the elements of interest, in different ionization stages. Applications to the opacity determination of the new radiative parameters computed in our work for Lu V transitions are also discussed in the present paper, which is part of our systematic investigation of moderately ionized lanthanides already started with recent similar works on atomic and opacity calculations in La V-X [10], Ce V-X [11], Pr V-X, Nd V-X, and Pm V-X [12] ions.…”

“…The first method used for modeling the atomic structure and computing the radiative parameters in Lu V was the pseudo-relativistic Hartree-Fock (HFR) approach developed by Cowan [5], using the suite of codes RCN, RCN2 and RCG adapted by the Atomic Physics and Astrophysics group of Mons University for the atomic structure calculations in heavy elements [13]. Configuration interaction was considered by explicitly including in the calculations the 4f 13 , 4f 12 6p, 4f 12 7p, 4f 12 8p, 4f 12 5f, 4f 12 6f, 4f 12 7f, 4f 12 8f, 4f 11 5d 2 , 4f 11 6s 2 , 4f 11 6p 2 , 4f 11 5d6s, 5p 5 4f 14 , 5p 5 4f 13 6p odd-parity configurations, and the 4f 12 6s, 4f 12 7s, 4f 12 8s, 4f 12 5d, 4f 12 6d, 4f 12 7d, 4f 12 8d, 4f 12 5g, 4f 12 6g, 4f 12 7g, 4f 12 8g, 4f 11 6s6p, 4f 11 5d6p, 5p 5 4f 13 6s and 5p 5 4f 13 5d even-parity configurations. These configurations represent the majority of those lying (and overlapping) below the Lu V ionization potential, as shown in Figures 2 and 3, where their energy ranges, estimated from Monoconfigurational HFR calculations, are plotted for odd and even parities, respectively.…”

“…The first (and most complete) experimental analysis of the Lu V spectrum dates back to 1978 with the paper by Kaufman and Sugar [2] in which 419 lines were classified as transitions among 136 energy levels belonging to the 4f 13 , 4f 12 5d, 4f 12 6s and 4f 12 6p configurations on the basis of observations made from a sliding spark discharge using a 10.7 m normal incidence spectrograph in the range of 500-2100 Å. Calculated energy levels and eigenvectors, obtained with a limited configuration interaction model utilizing the Racah algebra techniques [3] and a semi-empirical adjustment of radial integrals, were also reported in this paper.…”

Statistical RTA simulations of atomic data for astrophysical opacity modeling in the context of kilonova emission

“…In order to compute these opacities, we used exactly the same procedure as the one employed in all our aforementioned papers (such as Carvajal Gallego et al (2021Gallego et al ( , 2022aGallego et al ( , 2022bGallego et al ( , 2023aGallego et al ( , 2023b). As a reminder, in a dynamic environment that expands rapidly, such as the one observed in the ejecta from neutron star mergers, the bound-bound transitions can be evaluated using the expansion formalism (Karp et al 1977, Eastman and Pinto 1993, Kasen et al 2006 according to which the contributions of a large number of lines to the monochromatic opacity are approximated by a discretization involving the summation of lines falling within a spectral width, while the radiative transfer is considered by the Sobolev (1960) approximation.…”

“…They are of particular interest in the study of earlyphase kilonovae (i.e. a few hours after the merger) and have been considered in recent works, among which are those we published for La V-X (Carvajal Gallego et al 2022a), Ce V-X (Carvajal Gallego et al 2022b), Pr-Nd-Pm V-X (Carvajal Gallego et al 2023), Sm V-X (Carvajal Gallego et al 2023a) and recently all the remaining lanthanides from the V to the VII charge state (Carvajal Gallego et al 2023b). All the calculations in the latter studies were performed with theoretical computational methods such as relativistic Hartree-Fock (HFR) (Cowan 1981) and multi-configuration Dirac Hartree-Fock (Froese Fischer et al 2019).…”