The interaction of the quadrupole electric moment of the muonic molecules with the Coulomb field of the embedding ${\mathrm{D}}_{2}$ molecule gives rise to corrections to the energy levels that depend on the spin and significantly modify the muonic molecule fine structure. We present the first-order calculation of the fine and hyperfine structure of the energy levels of the weakly bound states $(dt\ensuremath{\mu}{)}_{11}$ and $(dd\ensuremath{\mu}{)}_{11}$ that accounts for the quadrupole finite-size corrections as well. The reported results are of interest for the upcoming high-precision measurement of the energy levels and the formation rate of the muonic molecules $\mathrm{dt}\ensuremath{\mu}$ and $\mathrm{dd}\ensuremath{\mu}$.The interaction of the quadrupole electric moment of the muonic molecules with the Coulomb field of the embedding ${\mathrm{D}}_{2}$ molecule gives rise to corrections to the energy levels that depend on the spin and significantly modify the muonic molecule fine structure. We present the first-order calculation of the fine and hyperfine structure of the energy levels of the weakly bound states $(dt\ensuremath{\mu}{)}_{11}$ and $(dd\ensuremath{\mu}{)}_{11}$ that accounts for the quadrupole finite-size corrections as well. The reported results are of interest for the upcoming high-precision measurement of the energy levels and the formation rate of the muonic molecules $\mathrm{dt}\ensuremath{\mu}$ and $\mathrm{dd}\ensuremath{\mu}$.

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The interaction of the quadrupole electric moment of the muonic molecules with the Coulomb field of the embedding

{\mathrm{D}}_{2}

molecule gives rise to corrections to the energy levels that depend on the spin and significantly modify the muonic molecule fine structure. We present the first-order calculation of the fine and hyperfine structure of the energy levels of the weakly bound states $(dt\ensuremath{\mu}{)}_{11}$ and $(dd\ensuremath{\mu}{)}_{11}$ that accounts for the quadrupole finite-size corrections as well. The reported results are of interest for the upcoming high-precision measurement of the energy levels and the formation rate of the muonic molecules $\mathrm{dt}\ensuremath{\mu}$ and $\mathrm{dd}\ensuremath{\mu}$.