The nuclear level density (NLD) is a fundamental measure of the complex structure of atomic nuclei at relatively high energies. Here we present the first model-independent measurement of the absolute partial NLD for a short-lived nucleus. For this purpose we adapt the recently introduced “shape method” for $\beta$-decay experiments, providing the shape of the $\gamma$-ray strength function for exotic nuclei. In this work, we show that combining the shape method with the $\beta$-Oslo technique allows for the extraction of the NLD of the populated states without the need for theoretical input. This development opens the way for the extraction of experimental NLDs far from stability with major implications in astrophysical and other applications. We benchmark our approach using data for the stable ${}^{76}\mathrm{Ge}$ nucleus, finding excellent agreement with previous experimental results. In addition, we present new experimental data and determine the absolute partial level density for the short-lived ${}^{88}\mathrm{Kr}$ nucleus. Our results suggest a fivefold increase in the NLD for the case of ${}^{88}\mathrm{Kr}$, compared to the recommended values from semimicroscopic Hartree-Fock Bogoliubov calculations recommended by the RIPL3 nuclear data library. However, our results are in good agreement with other semimicroscopic level density models. We demonstrate the impact of our method on the ${}^{87}\mathrm{Kr}(n,\gamma$) neutron capture rate and show that our experimental uncertainties for NLDs fulfill the requirements needed for astrophysical calculations predicting $r$-process abundances.

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• Beta decay
• Energy levels
• Nuclear astrophysics
• Thermal & statistical models