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Effects of variation of the fine structure constant $α$ and quark mass $m_q$ in Mössbauer nuclear transitions

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