Precision Spectroscopy of the Fine and Hyperfine Structures of High Molecular Rydberg-Stark States: Metrology of Molecular Hydrogen Ions.

The Stark effect in autoionizing high-n Rydberg states decouples the Rydberg electron from the ion core through ℓ mixing with core-nonpenetrating high-ℓ 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-H_{2} (total nuclear spin I=0,2) with a rotationally excited (N^{+}=2) H_{2}^{+} ion core and Rydberg states of ortho-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-H_{2} and the absence of such interactions in rotationless ortho-D_{2} Rydberg states. In ortho-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)  MHz of D_{2}^{+}(v^{+}=1,N^{+}=0), the spin-rotation coupling constant c_{e}=39.62(11)  MHz of H_{2}^{+}(v^{+}=1,N^{+}=2) and the fundamental vibrational interval of ortho-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.