High-Precision Calculation of the Hyperfine Structure of theHD+Ion

High-precision laser spectroscopy of ultracold hydrogen molecular ions has the potential of improving the precision of the electron-to-proton mass ratio. An accurate knowledge of the spin structure of the transition is required in order to permit precise comparison with experimental transition frequencies. We calculate with a relative accuracy of the order of $O({\alpha }^2)$ the hyperfine splitting of the rovibrational states of ${\mathrm{HD}}^{+}$ with orbital momentum $L\le 4$ and vibrational quantum numbers up to $v=17$, using the Breit-Pauli spin interaction Hamiltonian. These are the first complete ab initio calculations at this order of accuracy. A discrepancy between experiment and previous theory is resolved.