First measurement of the ${}^{96}\mathrm{Ru}\left(p,\gamma \right){}^{97}\mathrm{Rh}$ cross section for the $p$ process with a storage ring

This work presents a direct measurement of the ${}^{96}\mathrm{Ru}(p,\gamma ){}^{97}\mathrm{Rh}$ cross section via a novel technique using a storage ring, which opens opportunities for reaction measurements on unstable nuclei. A proof-of-principle experiment was performed at the storage ring ESR at GSI in Darmstadt, where circulating ${}^{96}\mathrm{Ru}$ ions interacted repeatedly with a hydrogen target. The ${}^{96}\mathrm{Ru}(p,\gamma ){}^{97}\mathrm{Rh}$ cross section between 9 and 11 MeV has been determined using two independent normalization methods. As key ingredients in Hauser-Feshbach calculations, the $\gamma$-ray strength function as well as the level density model can be pinned down with the measured ($p,\gamma$) cross section. Furthermore, the proton optical potential can be optimized after the uncertainties from the $\gamma$-ray strength function and the level density have been removed. As a result, a constrained ${}^{96}\mathrm{Ru}(p,\gamma ){}^{97}\mathrm{Rh}$ reaction rate over a wide temperature range is recommended for $p$-process network calculations.

Figure 1

Experimental setup for proton capture reactions in inverse kinematics at the ESR. The ${\mathrm{H}}_2$ target and the detectors used in this experiment are labeled. Both the multiwire proportional chamber (MWPC) and the double-sided silicon strip detectors (DSSSDs) were placed in pockets with 25-$\mu \mathrm{m}$-thick windows. A schematic of the DSSSDs is also shown. Unreacted ${}^{96}{\mathrm{Ru}}^{44+}$ ions [solid (magenta) line after the target] were recycled and focused on the ${\mathrm{H}}_2$ target repeatedly during the measurement phase.

Figure 2

The experimental $x$ position distribution of nuclear reaction products (filled black circles) registered by the DSSSDs at 11 $\mathrm{MeV}/u$ is compared with the simulated $x$ position distribution (red line). Events from different reaction channels, i.e., ($p,p$), ($p,\alpha$), ($p,\gamma$), and ($p,n$) reactions, can be disentangled based on the Geant4 simulation. The ($p,\gamma$) reaction products have a narrower distribution than other nuclear reaction products due to their smaller momentum spread.

Figure 3

(a) Position spectra of EC events measured by the MWPC at 11 $\mathrm{MeV}/u$. Black and gray (red) lines refer to the spectrum with and without the hydrogen target, respectively. Spectra have been downscaled by a factor of about 300. (b) X-ray spectrum (black line) at 11 $\mathrm{MeV}/u$ registered by the ${90}^{\circ }$ Ge detector. The spectrum is not corrected for the detection efficiency. The background is fitted with a linear function.

Figure 4

A comparison of the measured ($p,\gamma$) cross sections with the predictions by the standard non-smoker code [3] (dash-dotted line) as well as the talys-1.4 code [4] using different $\gamma$-ray strength functions, i.e., HFB (solid line) [24], Brink-Axel Lorentzian (dotted line) [25, 26], and Kopecky-Uhl generalized Lorentzian (dashed line) [27]. Filled (red) circles and filled (purple) squares represent the measured ($p,\gamma$) cross sections normalized to the K-REC cross sections and the single EC cross sections, respectively. The latter (squares) have been slightly offset in energy for clarity. Inset: A zoom around our measured data. Note that all energies are in the CM system.

Figure 5

Comparison of the measured ($p,\gamma$) cross sections with the predictions by the talys-1.4 code [4] using different level density models, i.e., the constant temperature (CT) [36], BSFG [34, 35], generalized superfluid (GS) [37], and Hartree-Fock-Bogolyubov (HFB) plus combinatorial [38] models. The BAL $\gamma$-ray strength function is applied in the talys calculations. Filled (purple) squares have been slightly offset in energy.

Figure 6

Our experimental results [filled (red) circles] and the experimental results of Bork et al. (small black circles) [39] in different energy regions are compared with predictions by non-smoker [3] [dashed (blue) line] and talys using the KD proton potential (dash-dotted black line) as well as talys using the modified KD proton potential [solid (magenta) line]. The staggering structure in the low-energy experimental data [39] is due to the low level density. Note that both the cross section and the energy are plotted on a logarithmic scale.

Figure 7

Stellar reaction rates over a large temperature region calculated by the talys code using the modified KD proton potential [solid (red) line]. They are compared to rates from the experimental data of Bork et al. [39] (filled black triangles in the shaded region) as well as the theoretical extrapolation (black triangles outside the shaded region), non-smoker calculations [3] [dashed (blue) line], and BRUSLIB [43] [dash-dotted (magenta) line]. Both the rate and the temperature are illustrated on a logarithmic scale.