The hyperfine structures of the $2{}^{3}S_1$ and $2{}^{3}P_J$ states of ${}^7\mathrm{Be}^{2+}$ and ${}^9\mathrm{Be}^{2+}$ are investigated within the framework of the nonrelativistic quantum electrodynamics, including relativistic and radiative corrections up to order $m{\alpha }^6$. The uncertainties of the calculated hyperfine splittings are on the order of tens of ppm, and for ${}^9\mathrm{Be}^{2+}$ our results improve the previous theoretical and experimental values by at least two orders of magnitude. The improved sensitivity of the hyperfine splittings of ${}^{7,9}\mathrm{Be}^{2+}$ to the nuclear Zemach radius and electric quadrupole moment opens the way to future measurements to extract the atomic physics values of these two nuclear properties to an accuracy of 5% or better.

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• Fine & hyperfine structure
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions
• First-principles calculations
• Perturbative methods
• Schroedinger equation