Spin assignment and statistical properties of neutron resonances from Dy161,163(n,γ) and Er167(n,γ) measured at the DANCE facility

Background: Average resonance spacing ${D}_{0}$ and spin dependence of nuclear level density (NLD) are essential quantities in nuclear physics, especially important for calculations of nuclear reactions and the normalization of NLD models.Purpose: Neutron resonances with different spins in odd-mass targets can form close doublets that are often difficult to resolve. These doublets are not corrected for when accounting for subthreshold resonances during ${D}_{0}$ determination. Moreover, different literature sources disagree on the isotopic assignment of some resonances.Methods: The $\ensuremath{\gamma}$ rays following radiative neutron capture on $^{161,163}\mathrm{Dy}$ and $^{167}\mathrm{Er}$ were measured with the highly segmented $\ensuremath{\gamma}$-ray calorimeter Detector for Advanced Neutron Capture Experiments (DANCE) at the Los Alamos Neutron Science Center. The analysis of spectra using the $\ensuremath{\gamma}$-multiplicity-based spin assignment method allows checking for the presence of the above-mentioned doublets. The calorimetric sensitivity provides unambiguous isotopic assignment.Results: We were able to assign spin to tens of resonances as well as to identify new ones in all three isotopes. Some isotope assignments from the literature were corrected. Detailed analysis of the number of unobserved resonances, assuming that the resonance positions obey predictions of the Gaussian orthogonal ensemble and reduced neutron widths Porter-Thomas fluctuations, allowed determination of ${D}_{0}$ with an uncertainty of a few percent, ${D}_{0}=2.15(5)$, 6.39(24), and 3.86(12) eV for $^{161,163}\mathrm{Dy}$ and $^{167}\mathrm{Er}$, respectively. Thanks to the spin assignment, the spacings for the resonances with the two spins formed in $s$-wave neutron capture, ${D}_{0}^{\ensuremath{-}}$ and ${D}_{0}^{+}$, were determined. Their ratio was compared to different NLD models.Conclusions: Our deduced ${D}_{0}$ for $^{163}\mathrm{Dy}$ is lower than any $^{163}\mathrm{Dy}$ value found in the literature. Good consistency was found with some literature values for $^{161}\mathrm{Dy}$ and $^{167}\mathrm{Er}$. The ratios ${D}_{0}^{\ensuremath{-}}/{D}_{0}^{+}$ are consistent with several models available in the literature, but in a clear contradiction with a few microscopic NLD models.