Experimental cross sections of Ho 165 ( α , n ) Tm 168 and Er 166 ( α , n ) Yb 169 for optical potential studies relevant for the astrophysical γ process

Background: Optical potentials are crucial ingredients for the prediction of nuclear reaction rates needed in simulations of the astrophysical $\\ensuremath{\\gamma}$ process. Associated uncertainties are particularly large for reactions involving $\\ensuremath{\\alpha}$ particles. This includes $(\\ensuremath{\\gamma},\\ensuremath{\\alpha})$ reactions which are of special importance in the $\\ensuremath{\\gamma}$ process.Purpose: The measurement of $(\\ensuremath{\\alpha},n)$ reactions allows for an optimization of currently used $\\ensuremath{\\alpha}$-nucleus potentials. The reactions $^{165}\\mathrm{Ho}$$(\\ensuremath{\\alpha},n)$ and $^{166}\\mathrm{Er}$$(\\ensuremath{\\alpha},n)$ probe the optical model in a mass region where $\\ensuremath{\\gamma}$ process calculations exhibit an underproduction of $p$ nuclei which is not yet understood.Method: To investigate the energy-dependent cross sections of the reactions $^{165}\\mathrm{Ho}$$(\\ensuremath{\\alpha},n)$ and $^{166}\\mathrm{Er}$$(\\ensuremath{\\alpha},n)$ close to the reaction threshold, self-supporting metallic foils were irradiated with $\\ensuremath{\\alpha}$ particles using the FN tandem Van de Graaff accelerator at the University of Notre Dame. The induced activity was determined afterwards by monitoring the specific $\\ensuremath{\\beta}$-decay channels.Results: Hauser-Feshbach predictions with a widely used global $\\ensuremath{\\alpha}$ potential describe the data well at energies where the cross sections are almost exclusively sensitive to the $\\ensuremath{\\alpha}$ widths. Increasing discrepancies appear towards the reaction threshold at lower energy.Conclusions: The tested global $\\ensuremath{\\alpha}$ potential is suitable at energies above 14 MeV, while a modification seems necessary close to the reaction threshold. Since the $\\ensuremath{\\gamma}$ and neutron widths show non-negligible impact on the predictions, complementary data are required to judge whether or not the discrepancies found can be solely assigned to the $\\ensuremath{\\alpha}$ width.