Determination of the ${}^{60}\mathrm{Zn}$ level density from neutron evaporation spectra

Nuclear reactions of interest for astrophysics and applications often rely on statistical model calculations for nuclear reaction rates, particularly for nuclei far from $\beta$ stability. However, statistical model parameters are often poorly constrained, where experimental constraints are particularly sparse for exotic nuclides. For example, our understanding of the breakout from the NiCu cycle in the astrophysical $rp$-process is currently limited by uncertainties in the statistical properties of the proton-rich nucleus ${}^{60}\mathrm{Zn}$. We have determined the nuclear level density of ${}^{60}\mathrm{Zn}$ using neutron evaporation spectra from ${}^{58}\mathrm{Ni}{(}^3\mathrm{He},n)$ measured at the Edwards Accelerator Laboratory. We compare our results to a number of theoretical predictions, including phenomenological, microscopic, and shell-model-based approaches. Notably, we find the ${}^{60}\mathrm{Zn}$ level density is somewhat lower than expected for excitation energies populated in the ${}^{59}\mathrm{Cu}(p,\gamma ){}^{60}\mathrm{Zn}$ reaction under $rp$-process conditions. This includes a level density plateau from roughly 5 to 6 MeV excitation energy, which is counter to the usual expectation of exponential growth and all theoretical predictions that we explore. A determination of the spin distribution at the relevant excitation energies in ${}^{60}\mathrm{Zn}$ is needed to confirm that the Hauser-Feshbach formalism is appropriate for the ${}^{59}\mathrm{Cu}(p,\gamma ){}^{60}\mathrm{Zn}$ reaction rate at x-ray burst temperatures.

Figure 1

Intrinsic NE213 neutron detection efficiency determined using ${}^{27}\mathrm{Al}(d,n)$.

Figure 2

Measured (points) $d\sigma /dE$ for ${}^{58}\mathrm{Ni}({}^3\mathrm{He},n)$ at ${105}^{\circ }$ compared to default TALYSV1.8 calculations, including a breakdown of the total $d\sigma /dE$ by reaction mechanism. Asterisks indicate contamination from $({}^3\mathrm{He},n)$ on carbon and oxygen.

Figure 3

${}^3\mathrm{He}+{}^{58}\mathrm{Ni}$ proton (a) and neutron (b) spectra compared to results from model calculations we describe as Mod-1, Mod-2, and Mod-3 in the text. Solid and long-dashed lines show the total $d\sigma /dE$, while the short-dashed and dot-dashed lines show the contribution from the statistical reaction mechanism to the long-dashed and solid lines, respectively.

Figure 4

Measured ${}^{58}\mathrm{Ni}({}^3\mathrm{He},n)$ differential cross section before (open triangles) and after (solid triangles) subtracting calculation results for nonstatistical contributions. Calculation results for the total differential cross section using ${\rho }_{\mathrm{expt}}$ (solid gray line) are shown, along with the contributions to the total from the direct (dotted line), pre-equilibrium (dot-dot-dashed line), and statistical (dot-dashed line) components. For comparison, the statistical component of the differential cross section calculated using ${\rho }_{\mathrm{CT}}$ is also shown.

Figure 5

The extracted ${\rho }_{\mathrm{expt}}$ for ${}^{60}\mathrm{Zn}$ (markers) compared to global theoretical $\rho$ models discussed in the text. The gray-dashed histogram is $\rho$ from known levels up to $E^{*}$, where all levels are thought to be known, where our experimental energy resolution has been applied.

Figure 6

Extracted ${}^{60}\mathrm{Zn}\rho$ (markers) compared to microscopic theoretical $\rho$ models discussed in the text.

Figure 7

Extracted ${}^{60}\mathrm{Zn}\rho$ (markers) compared to the shell-model-based theoretical $\rho$ model discussed in the text (ELM). Lines are $\rho$ summed up to a maximum $J$ from $J=0$ (lowest line) up through $J=12$ (red, upper bold line), where the sum up through $J=3$ is the lower bold line, indicated in blue.

Figure 8

Calculated $P\left(J\right)$ of ${}^{60}\mathrm{Zn}$ at $E^{*}=5$ MeV using the nominal ${\sigma }_{\mathrm{FG}}^2$ (“Rigid Body”), ${\sigma }_{\mathrm{FG}}^2$ increased or decreased by a factor of 2, or ${\sigma }^2$ from Ref. [9] (“von Egidy”), compared to ELM $P\left(J\right)$ and microscopic $P\left(J\right)$ available in talysv1.8. The green band indicates the relevant $J$ for ${}^{59}\mathrm{Cu}{(p,\gamma )}^{}60\mathrm{Zn}$ in a type-I x-ray burst (XRB) environment.