Quasicontinuum $\gamma$-decay of ${}^{91,92}$Zr: benchmarking indirect ($n,\gamma$) cross section measurements for the $s$-process

Nuclear level densities (NLDs) and $\gamma$-ray strength functions ($\gamma$SFs) have been extracted from particle-$\gamma$ coincidences of the ${}^{92}$Zr($p,p^{\mathrm{\prime }}\gamma$)${}^{92}$Zr and ${}^{92}$Zr($p,d\gamma$)${}^{91}$Zr reactions using the Oslo method. The new ${}^{91,92}$Zr $\gamma$SF data, combined with photonuclear cross sections, cover the whole energy range from $E_{\gamma} \approx 1.5$MeVuptothegiantdipoleresonanceat$E_{\gamma} \approx 17$MeV\mathrm{.}Thewide-range$\gamma$SFdatadisplaystructuresat$E_{\gamma} \approx 9.5$MeV,compatiblewithasuperpositionofthespin-flip$M1$resonanceandapygmy$E1$resonance\mathrm{.}Furthermore,the$\gamma$SF shows a minimum at $E_{\gamma }\approx 2-3$~MeV and an increase at lower $\gamma$-ray energies. The experimentally constrained NLDs and $\gamma$SFs are shown to reproduce known ($n,\gamma$) and Maxwellian-averaged cross sections for ${}^{91,92}$Zr using the {\sf TALYS} reaction code, thus serving as a benchmark for this indirect method of estimating ($n,\gamma$) cross sections for Zr isotopes.