The Stark effect in autoionizing high-$n$ Rydberg states decouples the Rydberg electron from the ion core through $\ell$ mixing with core-nonpenetrating high-$\ell$ states. The Rydberg states become long-lived, which is ideal for precision spectroscopy, and their structures reflect the fine and hyperfine structures of the ion-core levels. We report on precision measurements, in weak electric fields, of the fine and hyperfine structures of two distinct categories of high autoionizing molecular Rydberg-Stark states differing by the nature of the ion-core angular momentum: Rydberg states of para-${\mathrm{H}}_2$ (total nuclear spin $I=0\mathrm{,}2$) with a rotationally excited ($N^{+}=2$) ${\mathrm{H}}_2^{+}$ ion core and Rydberg states of ortho-${\mathrm{D}}_2$ ($I=0,2$) with a rotationless ($N^{+}=0$) ion core. The spectra reveal striking differences which are interpreted as arising from the dominance of anisotropic charge-quadrupole interactions between the rotating quadrupolar ion core and the Rydberg electron in para-${\mathrm{H}}_2$ and the absence of such interactions in rotationless ortho-${\mathrm{D}}_2$ Rydberg states. In ortho-${\mathrm{D}}_2$, the dominant interaction, the magnetic Fermi-contact hyperfine interaction in the ion core, does not significantly affect the motion of the Rydberg electron. By analyzing these spectra based on a treatment combining multichannel quantum-defect theory and matrix diagonalization, we derive new experimental values of the hyperfine coupling constant $b_F=139.84(5)\mathrm{MHz}$ of ${\mathrm{D}}_2^{+}(v^{+}=1,N^{+}=0)$, the spin-rotation coupling constant $c_e=39.62(11)\mathrm{MHz}$ of ${\mathrm{H}}_2^{+}(v^{+}=1,N^{+}=2)$ and the fundamental vibrational interval of ortho-${{\mathrm{D}}_2}^{+}$ [47 279 980.8(1.9) MHz]. The approach followed here in the study of molecular Rydberg-Stark states is general and broadly applicable to measurements of the fine and hyperfine structures of molecular cations.

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• Atomic & molecular structure
• Electronic excitation & ionization
• Electronic structure of atoms & molecules
• Electronic transitions
• Fine & hyperfine structure
• Molecular spectra
• Stark effect
• Atomic & molecular beams
• Rydberg atoms & molecules
• Optical spectroscopy
• Photoexcitation
• Photoionization