Background: Low-mass neutron-rich isotopes between Fe and Ag are predicted to be synthesized in neutrino-driven winds emitted after the collapse of a massive star. The modeling of this nucleosynthesis scenario, called weak $r$-process or $\alpha$-process, requires large nuclear reaction network calculations. The necessary reaction cross sections are usually taken from the statistical model which uses global optical potentials. Several global $\alpha +$ nucleus optical potential ($\alpha$-OMP) parametrizations exist and deviations between their predicted cross sections exceed even an order of magnitude at astrophysical energies.

Purpose: In the relevant mass range of the weak $r$-process, cross-section calculations performed with the Atomki-V2 potential generally reproduce experimental data within $\pm 50\%$. However, recently the ${}^{88}\mathrm{Sr}$($\alpha ,n){}^{91}\mathrm{Zr}$ cross section was measured and it was found that, unlike other available cross section data, it is lower than the calculations performed with recent OMPs, including the Atomki-V2 calculations, by a factor of 3. Thus, to better understand the source of the discrepancy, the present work aims to determine the ${}^{88}\mathrm{Sr}$ total reaction cross section by measuring ${}^{88}\mathrm{Sr}$($\alpha ,\alpha ){}^{88}\mathrm{Sr}$ elastic scattering angular distributions.

Methods: Between ${\vartheta }_{\mathrm{lab}.}={20}^{\circ }–167.5^{\circ }$ complete elastic $\alpha$ scattering angular distributions were measured at $E_{\mathrm{lab}.}=13.50,16.21,\mathrm{and}19.47\mathrm{MeV}$ energies, with precision better than $7\%$ for each angle.

Results: The total reaction cross section (${\sigma }_{\mathrm{reac}}$) was determined from the experimental data using three independent methods. First, the standard approach of fitting the parameters of the complex $\alpha$-nucleus optical potential was applied. Second, a model-independent phase shift fit was used. Finally, ${\sigma }_{\mathrm{reac}}$ values were also derived using a Bayesian analysis. The excellent agreement of the derived ${\sigma }_{\mathrm{reac}}$ from the three fundamentally different methods shows that the measured angular distributions constrain the total reaction cross sections well.

Conclusions: There is serious tension between the very-well-constrained experimental ${\sigma }_{\mathrm{reac}}$ values from elastic scattering and those obtained from the measured ($\alpha ,n$) data. The present results from elastic scattering are robust, agree well with the prediction of recent $\alpha$-OMPs, and fit into the general systematics of cross sections. Thus, an independent verification of the ${}^{88}\mathrm{Sr}$($\alpha ,n){}^{91}\mathrm{Zr}$ cross section data is clearly needed.

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• Elastic scattering reactions
• H & He induced nuclear reactions
• Nuclear astrophysics
• Nucleosynthesis in explosive environments
• r process
• 59 ≤ A ≤ 89