New experimental and theoretical energy levels, lifetimes, and oscillator strengths in singly ionised zirconium

¹ Division of Astrophysics, Department of Physics, Lund University, Box 43, 221 00 Lund, Sweden
² Material Science and Applied Mathematics, Malmö University, 205 06 Malmö, Sweden
³ Division of Atomic Physics, Department of Physics, Lund University, Box 118, 221 00, Lund, Sweden
⁴ Physique Atomique et Astrophysique, Université de Mons, 7000 Mons, Belgium
⁵ IPNAS, Université de Liège, 4000 Liège, Belgium

^★ Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 8 September 2025
Accepted: 9 November 2025

Abstract

Context. Neutron-capture elements are believed to make up almost all elements heavier than iron in the periodic table. By studying the abundance of these elements throughout the Galaxy, it is possible to put constraints on how and where neutron-capture processes occur. Determining elemental abundances is made possible through the correct interpretation and modelling of astrophysical spectra. Key ingredients for this, in turn, are accurate and complete sets of atomic data.

Aims. We investigate the spectrum of singly ionised zirconium with the aim of reporting level energies and radiative lifetimes for previously experimentally unknown high-lying even 4d²6s and 4d²5d levels, as well as improved energies for odd 4d²5p and 4d5s5p levels. We also aim to provide wavelengths, branching fractions, and oscillator strengths (log gf values) for lines from these upper even 4d²6s and 4d²5d levels.

Methods. The energies, wavelengths, and branching fractions were derived from hollow cathode spectra recorded with a Fourier transform spectrometer. The radiative lifetimes were measured using a two-step laser-induced fluorescence technique. Theoretical calculations using the pseudo-relativistic Hartree-Fock method, modified to account for core polarisation effects, were also performed and show good general agreement with the experimental results.

Results. We report for the first time level energies and radiative lifetimes for 19 high-lying even 4d²6s and 4d²5d levels and improved energies for odd 15 4d²5p and 4d5s5p levels in Zr II. We also report wavelengths, branching fractions, and oscillator strengths for 79 lines from upper levels of 4d²6s and 4d²5d.