In this work, we have extracted the nuclear level density (NLD) and $\gamma$-ray strength function ($\gamma \mathrm{SF}$) using the Oslo method on particle-$\gamma$ coincidence data from the ${}^{90}\mathrm{Zr}(p,p^{\prime }\gamma ){}^{90}\mathrm{Zr}$ reaction. We have applied the shape method to the same data set, providing a model-independent $\gamma \mathrm{SF}$ and a cross-check on the slope of the Oslo-method NLD and $\gamma \mathrm{SF}$. Further, we have combined the $\gamma \mathrm{SF}$ from this work with photonuclear data, thus covering the $2.5<E_{\gamma }<18\mathrm{MeV}$ energy range. We see an increase in strength in the region around $E_{\gamma }\approx 9\mathrm{MeV}$, consistent with previous $(\gamma ,{\gamma }^{\prime })$ and $(\gamma ,n)$ data. On the other hand, surprisingly, we do not observe a strong low-energy increase at low transition energies. The resulting NLD and $\gamma \mathrm{SF}$ were used as inputs to the nuclear reaction code talys to estimate the cross sections and astrophysical reaction rates for the ${}^{89}\mathrm{Zr}(n,\gamma ){}^{90}\mathrm{Zr}$ and ${}^{89}\mathrm{Y}(p,\gamma ){}^{90}\mathrm{Zr}$ reactions. We find good agreement with available experimental cross sections and JINA calculations for the ${}^{89}\mathrm{Y}(p,\gamma )$ results, but not for the ${}^{89}\mathrm{Zr}(n,\gamma )$ reaction rate for stellar temperatures above 0.7 GK. Based on our data, we provide a much more narrow uncertainty band for the ${}^{89}\mathrm{Zr}(n,\gamma )$ cross section and reaction rate.

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• Gamma-ray strength functions
• H & He induced nuclear reactions
• Inelastic scattering reactions
• Level densities
• Nuclear astrophysics
• Nuclear reaction rates
• Nuclear structure & decays
• 90 ≤ A ≤ 149