Verification of detailed balance for $γ$ absorption and emission in Dy isotopes

The photo-neutron cross sections of $^{162,163}\rm{Dy}$ have been measured for the first time in an energy region from the neutron threshold ($S_n$) up to $\approx$ $13$~MeV. The ($γ$,n) reaction was induced with quasi-monochromatic laser Compton-scattered $γ$ rays, produced at the NewSUBARU laboratory. The corresponding $γ$-ray strength functions ($γ$SF) have been calculated from the photo-neutron cross sections. The data are compared to reanalyzed $γ$SFs of $^{160-164}\rm{Dy}$, which are measured below $S_n$. The excellent agreement with the photo-neutron data at $S_n$ confirms the principle of detailed balance. Thus, a complete $γ$SF is established covering in total the energy region of 1 MeV $\leq$ E$_γ$ $\leq$ 13 MeV. These mid-shell well-deformed dysprosium isotopes all show scissors resonances with very similar structures. We find that our data predict the same integrated scissors strength as ($γ,γ^\prime$) data when integrated over the same energy range, which shows that the scissors mode very likely is consistent with the generalized Brink hypothesis. Finally, using the $γ$SFs as input in the reaction code TALYS, we have deduced radiative neutron-capture cross sections and compared them to direct measurements. We find a very good agreement within the uncertainties, which gives further support to the experimentally determined $γ$SFs.