Experimental constraints on the ${}^{73}\mathrm{Zn}(n,\gamma ){}^{74}\mathrm{Zn}$ reaction rate

Background: The recent observation of a neutron-star merger finally confirmed one astrophysical location of the rapid neutron-capture process (r-process). Evidence of the production of $A<140$ nuclei was seen, but there is still little detailed information about how those lighter elements are produced in such an environment. Many of the questions surrounding the $A\approx 80$ nuclei are likely to be answered only when the nuclear physics involved in the production of r-process nuclei is well understood. Neutron-capture reactions are an important component of the r-process, and neutron-capture cross sections of r-process nuclei, which are very neutron rich, have large uncertainties.

Purpose: Indirectly determine the neutron-capture cross section and reaction rate of ${}^{73}\mathrm{Zn}(n,\gamma ){}^{74}\mathrm{Zn}$.

Methods: The nuclear level density (NLD) and $\gamma$-ray strength function ($\gamma \mathrm{SF}$) of ${}^{74}\mathrm{Zn}$ were determined following a total absorption spectroscopy (TAS) experiment focused on the $\beta$ decay of ${}^{74}\mathrm{Cu}$ into ${}^{74}\mathrm{Zn}$ performed at the National Superconducting Cyclotron Laboratory. The NLD and $\gamma \mathrm{SF}$ were used as inputs in a Hauser-Feshbach statistical model to calculate the neutron-capture cross section and reaction rate.

Results: The NLD and $\gamma \mathrm{SF}$ of ${}^{74}\mathrm{Zn}$ were experimentally constrained for the first time using $\beta$-delayed $\gamma$ rays measured with TAS and the $\beta$-Oslo method. The NLD and $\gamma \mathrm{SF}$ were then used to constrain the neutron-capture cross section and reaction rate for the ${}^{73}\mathrm{Zn}(n,\gamma ){}^{74}\mathrm{Zn}$ reaction.

Conclusions: The uncertainty in the neutron-capture cross section and reaction rate of ${}^{73}\mathrm{Zn}(n,\gamma ){}^{74}\mathrm{Zn}$ calculated in TALYS was reduced to under a factor of 2 from a factor of 5 in the cross section and a factor of 11 in the reaction rate using the experimentally obtained NLD and $\gamma \mathrm{SF}$.

Figure 1

(a) Raw $E_x$ vs. $E_{\gamma }$ matrix from the $\beta$ decay of ${}^{74}\mathrm{Cu}$, with 20 keV/channel binning. (b) Unfolded matrix with 40 keV/channel binning. (c) Primary matrix with 200 keV/channel binning. The black box outlines the $E_x$, $E_{\gamma }$ ranges used in the NLD and $\gamma \mathrm{SF}$ extraction.

Figure 2

Distribution of spins for the levels in ${}^{74}\mathrm{Zn}$ around the neutron separation energy based on tabulated spin-dependent level densities from Ref. [33]. Spins highlighted in blue are populated following the $\beta$ decay of ${}^{74}\mathrm{Cu}$ and one dipole photon transition. The ground state of ${}^{74}\mathrm{Cu}$ is $2^{-}$ [36].

Figure 3

(a) Nuclear level density for ${}^{74}\mathrm{Zn}$ showing the experimental data (black circles), known levels from NNDC (solid black line), and level density calculated in Ref. [33] using the Hartree-Fock-Bogoliubov plus combinatorial method (solid blue line, see text for details). Dashed blue lines indicate uncertainties on the shift of the calculated level density. (b) Gamma strength function for ${}^{74}\mathrm{Zn}$ showing the experimental data (black circles), experimental data for ${}^{70}\mathrm{Zn}$ and ${}^{74,76}\mathrm{Ge}$ from Ref. [37] (blue squares, triangles, and diamonds), and the GLO fit to that data and extrapolation to lower energies (blue solid, dashed, and dot-dashed lines). The last 15 points of the experimental $\gamma \mathrm{SF}$ were used to minimize the distance between the experimental $\gamma \mathrm{SF}$ and the extrapolations of the ($\gamma ,n$) data sets. The green band indicates the combined statistical and systematic uncertainty.

Figure 4

(a) Cross section for the ${}^{73}\mathrm{Zn}(n,\gamma ){}^{74}\mathrm{Zn}$ reaction calculated in TALYS. The lighter band shows the variation in the cross section resulting from combinations of the available NLD and $\gamma \mathrm{SF}$ options in TALYS. The darker band shows the uncertainty in the cross section when using the experimental NLD and $\gamma \mathrm{SF}$. (b) Astrophysical reaction rate calculated by TALYS. The lighter and darker bands are the same as for the cross-section calculation.