High accuracy measurements in Mössbauer transitions open up the possibility to use them in the search for temporal and spatial variations of the fine structure constant $\alpha$, quark mass $m_q$, and dark matter field which may lead to the variations of $\alpha$ and $m_q$. We calculate the sensitivity of nuclear transitions to variations of $\alpha$ and $m_q$. Mössbauer transitions have high sensitivity to variation of quark mass $m_q$ and the strong interaction scale ${\mathrm{\Lambda }}_{\mathrm{QCD}}$ to which atomic optical clocks are not sensitive. The enhancement factors $K$, defined by $\frac{\delta f}{f}=K_{\alpha }\frac{\delta \alpha }{\alpha }$ and $\frac{\delta f}{f}=K_q\frac{\delta m_q}{m_q}$ where $f$ is the transition energy, may be large in some transitions. The 8-eV nuclear clock transition in ${}^{229}\mathrm{Th}$ $(K_q\approx {10}^4)$ and 76-eV transition in ${}^{235}\mathrm{U}$ $(K_{\alpha }\approx K_q\approx {10}^3)$ may be investigated using laser spectroscopy methods.

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• Nuclear tests of fundamental interactions
• Particle dark matter
• Mössbauer spectroscopy
• Optical spectroscopy