Rare information on photodisintegration reactions of nuclei with mass numbers $A \approx 160$ at astrophysical conditions impedes our understanding of the origin of $p$-nuclei. Experimental determination of the key ($p,\gamma$) cross sections has been playing an important role to verify nuclear reaction models and to provide rates of relevant ($\gamma,p$) reactions in $\gamma$-process. In this paper we report the first cross section measurements of $^{ 160}$Dy($p,\gamma$)$^{ 161}$Ho and $^{ 161}$Dy($p,n$)$^{ 161}$Ho in the beam energy range of 3.4 - 7.0 MeV, partially covering the Gamow window. Such determinations are possible by using two targets with various isotopic fractions. The cross section data can put a strong constraint on the nuclear level densities and gamma strength functions for $A \approx$ 160 in the Hauser-Feshbach statistical model. Furthermore, we find the best parameters for TALYS that reproduce the A $\thicksim$ 160 data available, $^{ 160}$Dy($p,\gamma$)$^{ 161}$Ho and $^{ 162}$Er($p,\gamma$)$^{ 163}$Tm, and recommend the constrained $^{ 161}$Ho($\gamma,p$)$^{ 160}$Dy reaction rates over a wide temperature range for $\gamma$-process network calculations. Although the determined $^{ 161}$Ho($\gamma$, p) stellar reaction rates at the temperature of 1 to 2 GK can differ by up to one order of magnitude from the NON-SMOKER predictions, it has a minor effect on the yields of $^{ 160}$Dy and accordingly the $p$-nuclei, $^{ 156,158}$Dy. A sensitivity study confirms that the cross section of $^{ 160}$Dy($p$, $\gamma$)$^{ 161}$Ho is measured precisely enough to predict yields of $p$-nuclei in the $\gamma$-process.
Categories: nucl-ex astro-ph.SR nucl-th