Photo-nuclear reaction rates of $^{157,159}$Ho and $^{163,165}$Tm and their impact in the $γ$--process

Reliable photo-nuclear reaction rates at the stellar conditions are essential to understand the origin of the heavy stable neutron-deficient isotopes between $^{74}$Se and $^{196}$Hg-p-nuclei, however, many reaction rates of relevance still have to rely on the Hauser-Feshbach model due to rare experimental progress. One such case is in the mass range of 160 for Dy, Er, Ho and Tm isotopes. In this work we attempt to constrain the Hauser-Feshbach model in the TALYS package by reproducing the available experimental data of $^{160}$Dy($p,\gamma$)$^{161}$Ho and $^{162}$Er($p,\gamma$)$^{163}$Tm in the $A\sim 160$ mass region, and examine the effects of level density, gamma strength function and the optical model potential. The constrained model then allows us to calculate the reaction rates of $^{157, 159}$Ho($\gamma$, $p$) and $^{163,165}$Tm($\gamma$, $p$) for the $\gamma$-process nucleosynthesis in carbon-deflagration SNe Ia model. Our recommended rates differ from the JINA REACLIB by more than 1 order of magnitude in the temperature range of 2-3 GK. This results in the changes of final abundance of $p$-nuclei in the $A\sim 160$ mass range by -5.5-3\% from those with JINA, which means that the ($\gamma$, $p$) reactions uncertainty is not predominant for the synthesis of these nuclei.