Extended Calculations of Energy Levels and Transition Rates of Nd ii-iv Ions for Application to Neutron Star Mergers

Abstract

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.

Laboratory studies of Vacuum Ultra-Violet (VUV) emission spectra of heavy element ions

“…Furthermore, reliable semi-empirical radiative transition probabilities and Landé factors can be derived from parametric calculations based on experimental energies (see below). In Nd IV, a comparison of gA values (weighted probability for spontaneous emission) from Cowan's code parametric calculations (Arab et al 2019) and from a more sophisticated semi-empirical calculation (Enzonga Yoca & Quinet 2014) fitting the same experimental energies agree within 10%, whereas the full relativistic ab initio values of gA may deviate by a factor 2 (Gaigalas et al 2019).…”

“…Although ab initio theoretical calculations provide a great amount of atomic data needed, experimental studies remain essential. For instance, in Nd IV, a recent full relativistic ab initio calculation (Gaigalas et al 2019) led to calculated wavelengths with deviations within 20% from the experimental ones (Wyart et al 2007). Indeed, a precision of 10 -6 on VUV wavelengths can only be achieved by experimental measurements.…”

Numerical Procedures for Relativistic Atomic Structure Calculations

“…This formula requires the evaluation of the derivative of a function. For a numerical grid of equally spaced points, the derivative could be approximated using Stirling's formula for seven (7) adjacent grid points, three on each side,…”

“…Benchmark calculations for opacity applications where extensive data are needed, not necessarily of high accuracy, have been reported by Gaigalas et al [7]. Multiconfiguration Dirac-Hartree-Fock calculations were performed in connection with the analysis of data from the coalescence of a binary neutron star that gave rise to electromagnetic emission powered by radioactive decays of r-process nuclei.…”

The Application of Electromagnetic Sensors for Determination of Cherenkov Cone Inside and in the Vicinity of the Detector Volume in Any Environment Known

“…Sensors 2021, 21, 992 2 of 18 The theoretical limit of GZK is applicable to protons emitted by cosmic radiation. In the case of neutrinos, the GZK limit does not apply [7].…”