($p,\gamma$) cross section measurements on Sn isotopes relevant to the $p$ process

Background: Calculations of $p$-nuclei abundances depend heavily on the Hauser-Feshbach (HF) theory to compute cross sections and, consequently, the reaction rates entering a huge reaction network encompassing nearly 2000 isotopes, the vast majority of which are unstable. Therefore, the successful reproduction of $p$-nuclei abundances relies on the reliability of the nuclear parameters entering the HF calculations, i.e., the optical model potential (OMP), the nuclear level density (NLD), and the $\gamma$-ray strength function ($\gamma \mathrm{SF}$).

Purpose: New cross sections, astrophysical $S$ factors, and reaction rates for ($p,\gamma$) reactions on ${}_{116}\mathrm{Sn}$ and ${}_{118}\mathrm{Sn}$ were measured at energies relevant to the $p$ process with the aim of validating OMP, NLD, and $\gamma \mathrm{SF}$ models and investigating their "global" character, with particular emphasis on the Lane-consistent semimicroscopic OMP developed by Bauge et al. [Bauge, Delaroche, and Girod, Phys. Rev. C 63, 024607 (2001)].

Method: Cross sections were determined from $\gamma$-angular distribution measurements, angle-integrated $\gamma$ spectra taken with the $4\pi \gamma$-summing technique, and off-beam $\gamma$ activities measured with the activation method. HF calculations were performed with the talys code (version 1.96).

Results: Total and partial cross sections were determined for the ${}_{116}\mathrm{Sn}(p,\gamma ){}_{117}\mathrm{Sb}$ and ${}_{118}\mathrm{Sn}(p,\gamma ){}_{119}\mathrm{Sb}$ reactions at energies ranging from 2.2 to 5.2 MeV. These energies cover almost entirely the Gamow window relevant to $p$-process nucleosynthesis. The experimentally determined cross sections and the resulting $S$ factors were corrected for electron screening effects and subsequently compared with HF calculations, which were performed using various combinations of phenomenological or semi-microscopic models describing the proton-nucleus OMP ($p$-OMP), alpha-particle–nucleus OMP ($\alpha$-OMP), NLD, and $\gamma \mathrm{SF}$.

Conclusions: Our screening-corrected data were found to be in very good agreement with the corresponding calculations performed using a combination of the $p$-OMP of Bauge et al. with semimicroscopic models for the $\alpha$-OMP, NLD, and $\gamma \mathrm{SF}$. This agreement resulted from adjusting the energy dependent isoscalar normalization factors ${\lambda }_V$ and ${\lambda }_W$ for the real and imaginary components of the OMP. The model combination used by default in talys 1.96, which includes only phenomenological models for the nuclear parameters entering the HF calculations, was less successful in reproducing our screening-corrected data. The NLDs used in our talys calculations were compared with the experimental cumulative numbers of low-lying levels observed in ${}_{117}\mathrm{Sb}$ and ${}_{119}\mathrm{Sb}$. Average radiative widths from the systematics were also used to validate the combination of NLD and $\gamma \mathrm{SF}$ models found to best reproduce our data. Finally, the stellar reaction rates obtained in the present work were compared with those provided in the REACLIB and BRUSLIB databases. In the temperature range relevant to the $p$ process, it was found that the REACLIB stellar rates are smaller by a factor of $\approx 2$, whereas the BRUSLIB rates exhibit deviations of no more than 20%.