Extracting model-independent nuclear level densities away from stability

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.

Figure 1

Left: Raw matrix of excitation energy vs $\gamma$-ray energy in SuN after population of ${}^{76}\mathrm{Ge}$. Right: Projections along the diagonal, $E_x-E_{\gamma }$, for three different energy bins (all in keV) $3900<E_x<4400$ (a), $4700<E_x<5100$ (b), $5500<E_x<5900$ (c). The peaks at 563 keV and 1108 keV correspond to decays into the states $2_1^{+}$ and $2_2^{+}$, respectively. The purple shaded areas were used to define a linear background under each peak.

Figure 2

$\gamma \mathrm{SF}$ (top) and total NLD (bottom) for ${}^{76}\mathrm{Ge}$. Results from the original publication [26] for ${}^{76}\mathrm{Ge}$ (blue bands) assume a specific level density $\rho \left(S_n\right)$ at the neutron separation energy from theory and systematics, whereas the present results (blue triangles) are model independent. In both cases the NLD populated in the experiment includes spins 0 through 4, assuming allowed $\beta$-decay transitions from the $2^{-}$ ground state of ${}^{76}\mathrm{Ga}$ and dipole $\gamma$-ray emission. Our results are also in good agreement with the NLD extracted from the particle evaporation method [42] (red circles, bottom). The $\gamma \mathrm{SF}$ is also compared to that of ${}^{74}\mathrm{Ge}$ extracted from the stable beam Oslo method [41] (pink circles, top) in a broader energy range.

Figure 3

Top: $\gamma \mathrm{SF}$ for ${}^{88}\mathrm{Kr}$ determined in this work using the shape method (blue triangles). Also shown is the $\gamma \mathrm{SF}$ using the $\beta$-Oslo technique (blue thin band, statistical uncertainties, only), transformed via Eq. (3) to best match the blue triangles. Our results are scaled to the literature data to guide the eye and allow a comparison of the general trend to data for ${}^{86}\mathrm{Kr}$ [45] (red circles) and to data for ${}^{87}\mathrm{Kr}$ (pink band) [27]. Bottom: Measured absolute partial level density for ${}^{88}\mathrm{Kr}$ (blue triangles) for the spins populated after $\beta$ decay from ${}^{88}\mathrm{Br}$. The blue band is a $1\sigma$ uncertainty range, see Sec. 5 for details. Recommended values from RIPL3 [11, 46] are shown as a black line, whereas two additional semimicroscopic models [10, 12] are shown in purple and orange solid lines, respectively (see text for details). The pink band shows model predictions [11], constrained via the known discrete levels, only.

Figure 4

Neutron-capture cross section ratios relative to values using the RIPL3 recommended level densities [46] (black solid line) in comparison to using the experimental level density from this work (blue band); see Sec. 6 for details. Uncertainties for the case of no known discrete levels are shown in yellow, whereas uncertainties achieved using the experimental discrete levels are shown in pink. All calculations were done using the same parameters in TALYS with the exception of the NLD model.