The Zero-Quantum-Defect Method and the Fundamental Vibrational Interval of H${}_2^{+}$

Abstract

The fundamental vibrational interval of H${}_2^{+}$ has been determined to be $\Delta G_{1/2}=2191.126614(17)$ cm${}^{-1}$ by continuous-wave laser spectroscopy of Stark manifolds of Rydberg states of H${}_2$ with the H${}_2^{+}$ ion core in the ground and first vibrationally excited states. Extrapolation of the Stark shifts to zero field yields the zero-quantum-defect positions $-R_{{\text{H}}_2}$/$n^2$, from which ionization energies can be determined. Our new result represents a four-order-of-magnitude improvement compared to earlier measurements. It agrees, within the experimental uncertainty, with the value of 2191.126\,626\,344(17)(100) cm${}^{-1}$ determined in non-relativistic quantum electrodynamic calculations V. Korobov, L. Hilico and J.-Ph. Karr, Phys. Rev. Lett. 118, 233001 (2017) http://doi.org/10.1103/PhysRevLett.118.233001.