The ${}^{111,112,113}\mathrm{Sn}$ isotopes have been studied with ($p,d\gamma$), ($p,p^{\prime }\gamma$), and ($d,p\gamma$) reactions to extract the nuclear level densities (NLDs) and $\gamma$-ray strength functions (GSFs) of these nuclei below the neutron separation energy by means of the Oslo method. The experimental NLDs for all three nuclei demonstrate a trend compatible with the constant-temperature model below the neutron separation energy while also being in good agreement with the NLDs of neighboring Sn isotopes, obtained previously with the Oslo-type and neutron evaporation experiments. The extracted microcanonical entropies yield $\approx 1.5 k_B$ entropy of a valence neutron in both ${}^{111}\mathrm{Sn}$ and ${}^{113}\mathrm{Sn}$. Moreover, the deduced microcanonical temperatures indeed suggest a clear constant-temperature behavior above $\approx 3$ MeV in ${}^{111,113}\mathrm{Sn}$ and above $\approx 4.5$ MeV in ${}^{112}\mathrm{Sn}$. We observe signatures for the first broken neutron pairs between 2 and 4 MeV in all three nuclei. The GSFs obtained with the Oslo method are found to be in good agreement below the neutron threshold with the strengths of ${}^{112,114}\mathrm{Sn}$ extracted in the ($p,p^{\prime }$) Coulomb excitation experiments.

• Received 7 March 2023
• Accepted 27 June 2023

DOI:https://doi.org/10.1103/PhysRevC.108.014315