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

When considering some complex lanthanide ions characterized by a half-filled 4f subshell, the atomic structure Hamiltonian matrix sizes are so large that their diagonalization is challenging and therefore the atomic data of these ions are only used to compute the expansion opacity of a kilonova with difficulty. To avoid this problem, we propose a statistical simulation method to compute kilonova expansion opacities based on the resolved transition array (RTA) method of Bauche et al (1991 Phys. Rev. A 44 5707). The atomic structure relativistic Hartree-Fock (HFR) method has been employed to compute the radial integrals necessary for our statistical RTA simulations where the atomic data are randomly drawn using their corresponding statistical distributions and to determine the exact expansion opacities where the atomic data are obtained by the diagonalization of the Hamiltonian matrix. The statistical RTA simulations carried out for two specific ions, i.e. Sm VIII and Eu VI, for which it is still possible to diagonalize the Hamiltonian matrix, reproduce well the expansion opacities computed using HFR atomic data. Based on this good agreements, the statistical RTA method was used to compute the expansion opacity of Dy VIII, which is determined through diagonalization with difficulty. The proposed statistical RTA simulation method allows the computation of reliable astrophysical expansion opacities which are of paramount importance for kilonova light curve modeling and spectral analysis.