A novel approach for extracting model-independent nuclear level densities far from stability

The level density of quantum states in statistical mesoscopic systems is a critical input for various fields of physics, including nuclear physics, nuclear astrophysics, atomic physics and their applications. In atomic nuclei, the level density is a fundamental measure of their complex structure at relatively high energies. Here we present the first model-independent measurement of the absolute partial nuclear level density for a short-lived unstable nucleus. For this purpose, we introduce the ``Shape method'' to extract the shape of the $\gamma$-ray strength function. Combining the Shape method with the existing $\beta$-Oslo technique allows the extraction of the nuclear level density without the need for theoretical input. We benchmark the Shape method using results for the stable $^{76}$Ge nucleus, finding an excellent agreement to previous experimental results. We apply the Shape method to new experimental data on the short-lived $^{88}$Kr nucleus. Our method opens the door for measurements of the nuclear level density and $\gamma$-ray strength function far away from stability, a pivotal input required to understand the role of exotic nuclei in forming the cosmos.