Hyperfine interaction splits each Stark state by the ion-core Fermi-contact splitting while molecular rotation induces Stark-state-specific splittings that differ from the core spin-rotation splitting.
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The Stark effect in molecular Rydberg states: Calculation of Rydberg-Stark manifolds of H$_2$ and D$_2$ including fine and hyperfine structures
Hyperfine interaction splits each Stark state by the ion-core Fermi-contact splitting while molecular rotation induces Stark-state-specific splittings that differ from the core spin-rotation splitting.