🔬 atomic physics

Experimental Ni II Oscillator Strengths for Transitions from $3d^84d$ to $3d^84p$ Levels Measured Using High-resolution Fourier Transform Spectroscopy

This study presents the first experimentally measured oscillator strengths for 174 Ni II transitions between $3d^84d$ and $3d^84p$ levels, derived from high-resolution Fourier transform spectroscopy and branching fractions, to provide definitive atomic data that improves upon existing theoretical calculations.

Original authors: Ruijie Chen, Christian P. Clear, Gillian Nave, Juliet C. Pickering

Published 2026-09-14

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CC BY 4.0

Original authors: Ruijie Chen, Christian P. Clear, Gillian Nave, Juliet C. Pickering

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Stars are not just distant points of light; they are vast laboratories where the elements that make up our world are forged and transformed. To understand how these cosmic engines work, how they evolve, and what they are made of, astronomers rely on a precise map of light. When starlight passes through a prism or a spectrometer, it splits into a rainbow, but this rainbow is not smooth. It is crisscrossed by dark and bright lines, each one a fingerprint left by a specific atom or ion absorbing or emitting light at a very particular color. For the iron-group elements, which are abundant in the universe and crucial to the opacity of stellar atmospheres, these fingerprints are incredibly dense and complex. Among them, singly ionized nickel, known as Ni II, is a key player. However, for decades, the map of these fingerprints has been incomplete. While scientists knew how the lower-energy atoms behaved, the behavior of nickel atoms in higher, more excited energy states remained a mystery, leaving a gap in our ability to accurately measure the chemical composition of stars and supernovae.

A team of researchers has now filled in a significant portion of this missing map by measuring the light emitted by nickel ions in a high-energy state that had never been experimentally quantified before. Working with specialized equipment at Imperial College London and the National Institute of Standards and Technology, the scientists created a controlled environment using hollow cathode lamps filled with nickel and helium gas. By running an electric current through this gas, they excited the nickel atoms, causing them to glow. They then captured the light from these glowing atoms using high-resolution spectrometers, instruments capable of separating light into its individual colors with extreme precision. The goal was to measure the brightness of specific lines of light emitted as the nickel atoms dropped from a high-energy state, specifically the 3d84d configuration, down to a slightly lower state, the 3d84p configuration.

The process required more than just taking a picture of the light. The researchers had to determine how much of the total light emitted by a single excited nickel atom went into each specific color line. This is known as the branching fraction. Imagine a single drop of water falling from a height and splitting into many smaller streams; the researchers needed to measure exactly how much water went down each stream. To do this, they recorded the spectra multiple times under different conditions to ensure the lines were not distorted by the equipment or by the atoms absorbing their own light. They calibrated their measurements against standard lamps to ensure the intensity of every color was recorded accurately. By combining these measured proportions with known or calculated lifetimes of the excited states—essentially how long an atom stays in that high-energy state before dropping down—they were able to calculate the absolute probability of each transition.

The result is a new, experimentally verified set of data for 174 distinct lines of light. For 19 of these lines, the data is entirely based on direct laboratory measurement, representing the first time these specific values have been determined experimentally. For the remaining lines, the team combined their new measurements of light proportions with theoretical calculations of how long the atoms live in their excited states to derive absolute values. The team found that for the strongest lines, their new measurements align very well with the most recent theoretical predictions, giving them confidence in the accuracy of the data. However, for the fainter, weaker lines, the theoretical calculations showed more scatter and less agreement with the new measurements, suggesting that while theory is a powerful tool, it still struggles to predict the behavior of the most subtle atomic transitions without experimental guidance.

This work provides the first fully experimental branching fractions and oscillator strengths for transitions from these high-lying nickel energy levels. By offering a more complete and accurate set of numbers, the study allows astronomers to interpret the light from distant stars, supernovae, and quasars with greater precision. When the light from a dying star or a distant galaxy is analyzed, these new data points will help scientists determine the exact amount of nickel present, leading to a clearer understanding of how stars evolve and how the heavy elements in the universe are created. The researchers have made their full list of measurements available for the scientific community, ensuring that this new chapter in the story of nickel can be used to refine our models of the cosmos.

Technical Summary: Experimental Ni II Oscillator Strengths for Transitions from 3d⁸4d to 3d⁸4p Levels

Problem Statement
Accurate atomic data, specifically oscillator strengths (log(gf)), are fundamental for interpreting high-resolution astrophysical spectra and determining elemental abundances in stellar and galactic environments. While nickel (Ni II) is a critical iron-group element observed in diverse astrophysical systems, existing experimental data for Ni II have been largely restricted to transitions involving low-lying energy levels (specifically the 3d⁸4p – 3d⁸4s and 3d⁸4p – 3d⁹ arrays). There has been a significant lack of experimental transition probabilities for lines originating from higher-lying energy levels, such as the 3d⁸4d configuration. Consequently, modeling of plasmas involving these higher excitation potentials has relied heavily on theoretical calculations, which vary in accuracy and completeness.

Methodology
This study employs the branching fraction method to determine absolute oscillator strengths for Ni II transitions between the 3d⁸4d (upper) and 3d⁸4p (lower) configurations. The experimental procedure involved the following steps:

Spectroscopic Acquisition: High-resolution Fourier Transform Spectra (FTS) were recorded using Ni-He hollow cathode lamps. Measurements were conducted at two facilities: Imperial College London (IC) and the National Institute of Standards and Technology (NIST). Eight distinct spectra (labeled A–H) were acquired, covering wavenumber ranges from approximately 24,000 cm⁻¹ to 54,000 cm⁻¹ (200–395 nm).
Intensity Calibration: Relative line intensities were calibrated using deuterium (D₂) standard lamps, which were themselves calibrated by the Physikalisch-Technische Bundesanstalt (PTB). Spectrometer response functions were derived by comparing the measured D₂ spectra against their certified radiance.
Branching Fraction Determination: Integrated line intensities were obtained by fitting Voigt profiles to the observed spectra using the software Xgremlin. Experimental branching fractions (BF) were calculated for transitions originating from common upper levels, ensuring that the sum of observed transitions accounted for at least 95% of the total transition probability for 31 of the 35 observed upper levels.
Absolute Scale Normalization: To convert relative branching fractions into absolute transition probabilities ( $A_{ul}$ $A_{u l}$ ) and oscillator strengths ($gf$), the experimental BFs were combined with level lifetimes ( $\tau_u$ $τ_{u}$ ).
- For seven 3d⁸4d levels, experimental lifetimes measured by Hartman et al. (2017) were used.
- For the remaining 24 levels, theoretical lifetimes calculated by Clear et al. (2026) were utilized. The authors validated these theoretical lifetimes against experimental data for 3d⁸4p and 3d⁸4d levels, finding agreement within approximately 8%, which was adopted as the relative uncertainty for the theoretical values.
Uncertainty Analysis: Total uncertainties were derived by combining statistical errors from line fitting, intensity calibration uncertainties (estimated at 6.1% total), and scaling factors for spectra lacking a common reference line.

Key Contributions and Results
The primary contribution of this work is the provision of the first experimentally measured oscillator strengths for Ni II 3d⁸4d – 3d⁸4p transitions. The study reports:

174 Lines: Absolute oscillator strengths and transition probabilities were determined for 174 transitions originating from 31 upper levels.
Fully Experimental Data: For 19 lines originating from four specific upper levels, the results represent the first fully experimentally determined $gf$-values, as they combine experimental branching fractions with experimental lifetimes.
Semi-Empirical Data: For the remaining lines, oscillator strengths were placed on an absolute scale using the combination of experimental branching fractions and theoretically derived lifetimes.
Completeness: For 31 of the 35 observed upper levels, the observed transitions accounted for at least 95% of the predicted transition probability, ensuring reliable branching fractions. Four levels with lower completeness (<95%) were treated as branching ratios rather than absolute values.

Comparison with Theory
The authors compared their new experimental log(gf) values with three sets of theoretical calculations:

Clear et al. (2026): These calculations showed the best agreement with the new experimental data, particularly for strong lines (log(gf) > -1.0). The authors attribute this success to the fine-tuning of eigenvalues in the Clear et al. (2026) model using the most accurate experimental energy levels available.
Hartman et al. (2017) and Kurucz (2011): These calculations showed similar trends but exhibited greater scatter and larger discrepancies, particularly for weaker transitions and levels with significant configuration mixing.

Significance
The paper asserts that this work provides the first experimental branching fractions, transition probabilities, and oscillator strengths for Ni II 3d⁸4d – 3d⁸4p transitions. By supplying these data, the study enables more accurate chemical abundance determinations in astrophysical spectra using these specific transitions. The results illustrate the necessity of laboratory measurements to validate and improve theoretical atomic data, particularly for higher-lying energy levels where configuration mixing can reduce the accuracy of purely theoretical predictions. The data are intended to support the development of realistic synthetic spectra and photospheric models that account for non-LTE effects and 3D atmospheric structures.

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