Determination of 170,172Yb(α,n)173,175Hf reaction cross sections in a stacked-target experiment

Abstract

Background: For understanding the synthesis of elements in the universe, precise knowledge of reaction rates and cross sections is paramount. This is especially true for the $p$ process because its study requires large network calculations including thousands of nuclei and nuclear reactions with little room for simplification. Therefore, robust theoretical methods for predicting cross sections are needed which are usually based on Hauser-Feshbach calculations. These calculations use physics input in the form of $\ensuremath{\gamma}$-ray strength functions, nuclear level densities, and particle $+$ nucleus optical-model potentials. These have to be constrained using experimental results.Purpose: To constrain the $\ensuremath{\alpha}$ optical-model potential $\ensuremath{\alpha}$-induced reactions are well suited. The ytterbium isotopic chain not only offers multiple stable isotopes on which cross sections can be measured and insights into the evolution of the $\ensuremath{\alpha}$ optical-model potential with the neutron-to-proton ratio can be gained but also includes the $p$ nucleus $^{168}\mathrm{Yb}$. Its abundance is significantly impacted by the $^{164,166}\mathrm{Yb}(\ensuremath{\alpha},\ensuremath{\gamma})$ reactions and is, therefore, also affected by the constraints resulting from the experiment presented in this paper.Method: To study the $^{170,172}\mathrm{Yb}(\ensuremath{\alpha},n)^{173,175}\mathrm{Hf}$ reaction cross sections the activation method was used. During irradiation the targets were arranged in stacks of four to reduce the required irradiation time. Aluminum degrader foils served as backings. The average interaction energy inside each ytterbium layer was determined via geant4 simulations. A third layer, consisting of manganese, was used to verify the simulations by comparing the measured $^{55}\mathrm{Mn}(\ensuremath{\alpha},(2)n)^{57,58}\mathrm{Co}$ reaction cross sections to previous results. For irradiation the 10 MV FN tandem accelerator located at the University of Cologne was used and the activation measurement was performed utilizing the Cologne Clover Counting setup consisting of two clover-type high-purity germanium detectors in a face-to-face geometry.Results: For the $^{170}\mathrm{Yb}(\ensuremath{\alpha},n)$ reaction seven cross sections at center-of-mass energies between 12.7 and 16.5 MeV were measured. For the $^{172}\mathrm{Yb}(\ensuremath{\alpha},n)$ reaction six cross sections for center-of-mass energies of 13.1 to 16.5 MeV could be determined with an additional upper limit at ${E}_{\mathrm{c}.\mathrm{m}.}=12.3$ MeV.Conclusion: Comparisons to theoretical models show that state-of-the-art $\ensuremath{\alpha}$-optical model potentials reproduce the measured cross sections very well. The ratios of $(\ensuremath{\alpha},n)$ reaction cross sections in the ytterbium isotopic chain can be accurately reproduced as well.