Measurements of proton capture in the $A=100\text{–}110$ mass region: Constraints on the ${}^{111}\mathrm{In}(\gamma ,p)/(\gamma ,n)$ branching point relevant to the $\gamma$ process

The $\gamma$ process is an explosive astrophysical scenario, which is thought to be the primary source of the rare proton-rich stable $p$ nuclei. However, current $\gamma$-process models remain insufficient in describing the observed $p$-nuclei abundances, with disagreements up to two orders of magnitude. A sensitivity study has identified ${}^{111}\mathrm{In}$ as a model-sensitive $(\gamma ,p)/(\gamma ,n)$ branching point within the $\gamma$ process. Constraining the involved reaction rates may have a significant impact on the predicted $p$-nuclei abundances. Here we report on measurements of the cross sections for ${}^{102}\mathrm{Pd}(p,\gamma ){}^{103}\mathrm{Ag},{}^{108}\mathrm{Cd}(p,\gamma ){}^{109}\mathrm{In}$, and ${}^{110}\mathrm{Cd}(p,\gamma ){}^{111}\mathrm{In}$ reactions for proton laboratory energies 3–8 MeV using the high efficiency total absorption spectrometer and the $\gamma$-summing technique. These measurements were used to constrain Hauser-Feshbach parameters used in talys 1.9, which constrains the ${}^{111}\mathrm{In}(\gamma ,p){}^{110}\mathrm{Cd}$ and ${}^{111}\mathrm{In}(\gamma ,n){}^{110}\mathrm{Ag}$ reaction rates. The newly constrained reaction rates indicate that the ${}^{111}\mathrm{In}(\gamma ,p)/(\gamma ,n)$ branching point occurs at a temperature of $2.71\pm 0.05\mathrm{GK}$, well within the temperature range relevant to the $\gamma$ process. These findings differ significantly from previous studies and may impact the calculated abundances.

Figure 1

The $\gamma$-process reaction flow for the $A=100\text{–}110$ mass region where photodisintegration reactions on seed nuclei can produce the $p$ nuclei (shown here ${}^{102}\mathrm{Pd},{}^{106}\mathrm{Cd},{}^{108}\mathrm{Cd}$, and ${}^{112}\mathrm{Sn}$). Colored arrows indicate the dominant photodisintegration reaction. Isotopes with two outgoing arrows are branching points; at a critical temperature, one reaction rate will become stronger than the other.

Figure 2

Stellar photodisintegration reaction rates for ${}^{111}\mathrm{In}$. The light shaded bands are $(\gamma ,p)$ rates taken from the jina reaclib database [13]. The labels refer to the version of non-smoker used. The uncertainty of the reaction rates makes it unclear at what temperature $(\gamma ,n)$ begins to dominate $(\gamma ,p)$, which can have a significant impact on $\gamma$-process model predictions of $p$-nuclei abundances.

Figure 3

Sum spectra (before background subtraction) for proton capture reactions on (a) ${}^{102}\mathrm{Pd}$, (b) ${}^{108}\mathrm{Cd}$, and (c) ${}^{110}\mathrm{Cd}$. Note that for the cadmium reactions due to the long-lived metastable (m.s.) state for the compound nuclei ${}^{109}\mathrm{In}$ and ${}^{111}\mathrm{In}$, there are two resolvable sum peaks.

Figure 4

Fitting of the ${}^{102}\mathrm{Pd}(p,\gamma ){}^{103}\mathrm{Ag}$ [panels (a) and (b)] and ${}^{108}\mathrm{Cd}(p,\gamma ){}^{109}\mathrm{In}$ [panels (c) and (d)] sum peaks. For panels (a) and (c), the purple curves highlight the Gaussian fits to the sum peak whereas the dashed black curve is the background to be subtracted. For ${}^{108}\mathrm{Cd}$ and ${}^{110}\mathrm{Cd}$, the two sum peaks are fitted simultaneously, but whereas determining the counts of one sum peak, the other is treated as background. The subtracted sum peak to be integrated is shown in orange whereas the three standard deviation windows are marked with vertical black dashes. Panels (b) and (d) show the segment-multiplicity distributions from events within the integrated region of the sum peak. These are adjusted by background subtracting segment multiplicities sampled from energies 25–100 keV below and above the gate windows (vertical dashed lines).

Figure 5

Experimentally measured cross sections for the ${}^{102}\mathrm{Pd}(p,\gamma ){}^{103}\mathrm{Ag}$, ${}^{108}\mathrm{Cd}(p,\gamma ){}^{109}\mathrm{In}$, and ${}^{110}\mathrm{Cd}(p,\gamma ){}^{111}\mathrm{In}$ reactions. Theoretical predictions from the non-smoker code are shown for comparison. The dashed line marks the Gamow window for each reaction.

Figure 6

Constraining of Hauser-Feshbach statistical parameters used to predict cross sections. The left panels show the MCMC-fitted result based off constrained parameters within the $\mathrm{KU}\text{−}\gamma \mathrm{SF}$ and GC-NLD models. The solid blue line is the median prediction whereas the band represents a 68% confidence interval. For the panels on the right-hand side, predictions based off different combinations of microscopic NLD and $\gamma \mathrm{SF}$ are shown. The shaded band represents the total range of predictions from all microscopic model combinations available in talys 1.9. The combination that best fits all three reactions from this work is labeled “Global” whereas the combination that best fits a single reaction is labeled as “Local.” The number notation represents NLD and $\gamma \mathrm{SF}$ model number consistent with the notation used in the talys 1.9 manual [31].

Figure 7

Relatives differences in cross sections between the experimental values and the microscopic-model predictions for each of the three reactions. Error bars are propagated from the experimental uncertainties.

Figure 8

Comparison of the MCMC-fitted GC-NLD, $\mathrm{KU}\text{−}\gamma \mathrm{SF}$, and microscopic models to the experimentally measured partial cross sections of (a) ${}^{108}\mathrm{Cd}$ and (b) ${}^{110}\mathrm{Cd}$.

Figure 9

(a) shows predicted stellar photodissociation decay rates for ${}^{111}\mathrm{In}$ based off MCMC-fitted and microscopic $\gamma \mathrm{SF}$ and NLD models. The previous rates based off of reaclib-v6 are plotted for comparison. (b) plots the ratio of the $(\gamma ,p)$/$(\gamma ,n)$ stellar decay rates. Band thickness of the MCMC-fitted ($\mathrm{KU}\text{−}\gamma \mathrm{SF}$ and GC-NLD) reflects a 68% confidence interval band.