The nuclear level-density (NLD) model, a nuclear-structure input used to calculate neutron-capture rates, was associated with different rare-earth abundance patterns in simulations of neutron-star-merger outflows, with the clearest contrasts in the cold case. The comparison examined how information encoded in NLDs related to rare-earth peak formation and to the sensitivity of final abundances to neutron-capture rates. In runs using microscopic NLD models, a model-generated peak appeared at mass numbers 170 to 180 in all three scenarios. The associated effect was largest in cold runs, smaller in hot/cold runs and smallest in hot runs.
Three simulated outflows
The study used SkyNet to evolve more than 7000 nuclides under three parameterized neutron-star-merger dynamical-ejecta conditions. The hot setup had an electron fraction, Ye, of 0.18, entropy of 30 kB per baryon and a 70-millisecond timescale. The hot/cold setup used Ye of 0.2, entropy of 20 kB per baryon and a 10-millisecond timescale. The cold setup used Ye of 0.2, entropy of 10 kB per baryon and a 3-millisecond timescale.
Six nuclear models, shared inputs
Researchers recalculated the neutron-capture rates with TALYS 1.96 for nuclei with proton numbers from 45 to 87. The range included the magic proton numbers 50 and 82 and excluded actinides. The six NLD models were divided between phenomenological BFM, CTM and GSM models and microscopic HFBCS+stat., HFB+comb. and THFB+comb. models. The calculations kept the other listed nuclear inputs common.
FRDM2012 supplied binding and separation energies. The default Kopecky-Uhl generalized Lorentzian gamma-strength model stayed fixed, and default JINA Reaclib rates were used for other reactions. The six NLD choices were then compared through modeled final abundances and neutron-capture sensitivity.
Where the modeled patterns separated
The reported abundance differences appeared in distinct mass regions. Near mass number 164, differences appeared in the cold and hot/cold calculations, while hot final abundances were almost unaffected. The model-generated feature at mass numbers 170 to 180 appeared in all three scenarios, but its effect decreased from cold to hot/cold to hot.
A closer comparison of BFM and HFBCS+stat. showed how the NLD patterns differed. HFBCS+stat. had higher NLDs for even-even nuclei and lower NLDs for odd-odd nuclei than BFM. In the cold scenario, its modeled flow reached even-proton and even-even chains earlier. The rare-earth peak formed earlier and was temporarily enhanced in that comparison.
The researchers also swapped NLD inputs by mass-number class. Replacing only the even-A NLDs reproduced nearly the full abundance difference between the complete BFM and HFBCS+stat. runs. Replacing only the odd-A NLDs mainly changed the region from mass numbers 170 to 180.
Sensitivity depended on the region
To examine rate sensitivity, the study used an F-metric test. It perturbed one neutron-capture rate at a time by a factor of f = 3 and compared deviations in final abundances. In the cold scenario, the sensitivity map separated into two approximate regions. Regime I, roughly 15 to 30 neutrons from stability, retained strong nucleon odd-even sensitivity. Regime II, roughly 7 to 15 neutrons from stability, showed smoother oscillations and higher sensitivity. The boundaries were approximate and environment-dependent.
The pattern varied with the NLD model. In cold Regime I, BFM sensitivity was highest for odd-even nuclei, intermediate for even-A nuclei and lowest for even-odd nuclei. HFBCS+stat. instead showed higher sensitivity for nuclei with even neutron number than for those with odd neutron number, with a weaker dependence on proton parity. Across the wider comparison, phenomenological models showed paired proton-and-neutron odd-even oscillations. Microscopic models showed different even-even and odd-odd sensitivities and ultimately no proton odd-even sensitivity variation.
The astrophysical scenario also mattered to the sensitivity pattern. In hot runs, all models showed a clear odd-neutron effect in Regime I, while Regime II had lower and distinct sensitivity. The hot/cold sensitivity results were not shown because they closely resembled the cold results. The remaining model runs were internally consistent within the phenomenological and microscopic classes.
A result tied to the model setup
The authors interpret mostly sub-order-of-magnitude changes in individual capture rates as collectively associated with a global redirection of the modeled nucleosynthesis pathway. They recommend unified microscopic inputs.
The analysis covered three representative outflow conditions and six tested NLD models. It kept FRDM2012 binding and separation energies, the default Kopecky-Uhl generalized Lorentzian model and default JINA Reaclib rates for other reactions in common. The reported sensitivity pattern came from the f = 3 perturbation setup.
The work is an arXiv v1 preprint dated 26 August 2026. Its acknowledgments report support from the Chinese Academy of Sciences Project for Young Scientists in Basic Research, YSBR-099, and the Key Laboratory of Nuclear Data Foundation, JCKY2025201C154.
Paper data and sources
Original title: Impact of Nuclear Level Density on $r$-Process Rare-Earth Peak Nucleosynthesis
Authors: Hang Xu, Peng-Xiang Du, Jian Li, Dong-Liang Fang
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: 10.3847/1538-4357/ae9d64
Original paper · Full text