Cross sections of the ${}^{83}\mathrm{Rb}(p,\gamma ){}^{84}\mathrm{Sr}$ and ${}^{84}\mathrm{Kr}(p,\gamma ){}^{85}\mathrm{Rb}$ reactions at energies characteristic of the astrophysical $\gamma$ process

We have measured the cross section of the ${}^{83}\mathrm{Rb}(p,\gamma ){}^{84}\mathrm{Sr}$ radiative capture reaction in inverse kinematics using a radioactive beam of ${}^{83}\mathrm{Rb}$ at incident energies of 2.4 and $2.7A$ MeV. Prior to the radioactive beam measurement, the ${}^{84}\mathrm{Kr}(p,\gamma ){}^{85}\mathrm{Rb}$ radiative capture reaction was measured in inverse kinematics using a stable beam of ${}^{84}\mathrm{Kr}$ at an incident energy of $2.7A$ MeV. The effective relative kinetic energies of these measurements lie within the relevant energy window for the $\gamma$ process in supernovae. The central values of the measured partial cross sections of both reactions were found to be $0.17–0.42$ times the predictions of statistical model calculations. Assuming the predicted cross section at other energies is reduced by the same factor leads to a slightly higher calculated abundance of the $p$ nucleus ${}^{84}\mathrm{Sr}$, caused by the reduced rate of the ${}^{84}\mathrm{Sr}(\gamma ,p){}^{83}\mathrm{Rb}$ reaction derived from the present measurement.

Figure 1

Typical energy spectrum from one of the SSB detectors. The proton and carbon scattering peaks are labeled; the target constituents scattered by the ${}^{83}\mathrm{Rb}$ and ${}^{83}\mathrm{Sr}$ beam components are indistinguishable on the basis of energy and contribute to both of these peaks. The inset shows the same plot zoomed in on the proton scattering peak with selection cuts indicated by the vertical dashed lines.

Figure 2

Measured charge state distribution of ${}^{84}\mathrm{Kr}$ incident at $2.7A$ MeV emerging from the $727\mu \mathrm{g}{\mathrm{cm}}^{-2}$ polyethylene target. EMMA was set for a kinetic energy of 166 MeV during all of the yield measurements. The error bars represent systematic beam current uncertainties estimated to be $\pm 10\%$. Also shown are the results of a Gaussian fit.

Figure 3

Energies of $\gamma$ rays detected in the TIGRESS array during a measurement of the ${}^{84}\mathrm{Kr}(p,\gamma ){}^{85}\mathrm{Rb}$ reaction as a function of TIGRESS-EMMA correlation time. A vertical cluster of counts indicates the observation of correlated primary and secondary $\gamma$ rays, with energies approaching the $p$ emission threshold in ${}^{85}\mathrm{Rb}$ of 7 MeV, corresponding to ${}^{84}\mathrm{Kr}(p,\gamma )$ events.

Figure 4

Simplified energy level diagram of ${}^{85}\mathrm{Rb}$ showing only levels relevant to this measurement of the ${}^{84}\mathrm{Kr}(p,\gamma ){}^{85}\mathrm{Rb}$ reaction. The states initially populated via $s$-wave capture are shown schematically about 2.4 MeV above the proton separation energy $S_p$.

Figure 5

$\gamma$ rays observed in the eight TIGRESS detectors centered at ${90}^{\circ }$ with respect to the beam axis in coincidence with $A=84$ recoils, following the ${}^{83}\mathrm{Rb}(p,\gamma ){}^{84}\mathrm{Sr}$ reaction. The inset shows a zoomed-in view of the same spectrum centered about the energy of the 793 keV transition.

Figure 6

Simplified energy level diagram of ${}^{84}\mathrm{Sr}$ showing only levels relevant to this measurement of the ${}^{83}\mathrm{Rb}(p,\gamma ){}^{84}\mathrm{Sr}$ reaction. The states initially populated via $s$-wave capture are shown schematically about 2.4 MeV above the proton separation energy $S_p$.

Figure 7

Cross section of the ${}^{83}\mathrm{Rb}(p,\gamma ){}^{84}\mathrm{Sr}$ reaction from experiment (shown are the partial cross section for populating the $2_1^{+}$ state and the inferred total cross section with 90% CL error bars) compared to statistical model predictions of the total cross sections with the non-smoker [15] and smaragd [34] codes. The wider, lightly shaded region indicates the approximate location of the relevant energy window [16] for the ${}^{83}\mathrm{Rb}(p,\gamma ){}^{84}\mathrm{Sr}$ reaction in ccSNe $(2\mathrm{GK}<T<3.5\mathrm{GK})$. The narrower, darkly shaded region indicates the range of relative kinetic energies covered in the measurement of the $E_{\mathrm{c}.\mathrm{m}.}=2.386$ MeV data point. The measured and inferred points at $E_{\mathrm{c}.\mathrm{m}.}=2.26$ MeV are 90% CL upper limits. Also shown are smaragd calculations with the default proton width divided by two and four, respectively.

Figure 8

Same as Fig. 7 but comparing the experimental data to smaragd calculations using various $p+{}^{83}\mathrm{Rb}$ optical potentials (smaragd default [36, 37], ppot1 [38], ppot2 [39], ppot5 [40], ppot6 [41], ppot7 [42]).

Figure 9

Same as Fig. 7 but for the ${}^{84}\mathrm{Kr}(p,\gamma ){}^{85}\mathrm{Rb}$ reaction.

Figure 10

Same as Fig. 8 but for the ${}^{84}\mathrm{Kr}(p,\gamma ){}^{85}\mathrm{Rb}$ reaction.

Figure 11

Relative change in the abundance of ${}^{84}\mathrm{Sr}$ in a 15 (cc15) and 25 (cc25) $M_{\odot }$ star with solar metallicity exploding as a core-collapse supernova, and in a thermonuclear supernova (snIa), when using the new rates for ${}^{83}\mathrm{Rb}(p,\gamma ){}^{84}\mathrm{Sr}$ and its inverse reaction. The error bars illustrate the remaining uncertainties due to the combined effect of all reaction rates (see text for details).