Precision millimetre-wave spectroscopy and calculation of the Stark manifolds in high Rydberg states of para-H$_2$

TL;DR

This study combines precision millimetre-wave spectroscopy and advanced calculations to accurately characterize Stark manifolds in high Rydberg states of para-H₂, enhancing understanding of molecular ionization energies.

Contribution

It introduces a matrix-diagonalisation approach integrating MQDT and long-range models for precise Stark manifold calculations in high Rydberg states.

Findings

Transition frequencies measured with sub-500 kHz linewidths.

Calculated energy levels agree with experiments within 50 kHz residuals.

Quantum defects and ionization energies determined with unprecedented accuracy.

Abstract

Precision measurements of transitions between singlet ($S=0$) Rydberg states of H$_2$ belonging to series converging on the $\mathrm{X}^+\,^2\Sigma_g^+(v^+=0,N^+=0)$ state of H$_2^+$ have been carried out by millimetre-wave spectroscopy under field-free conditions and in the presence of weak static electric fields. The Stark effect mixes states with different values of the orbital-angular-momentum quantum number $\ell$ and leads to quadratic Stark shifts of low-$\ell$ states and to linear Stark shifts of the nearly degenerate manifold of high-$\ell$ states. Transitions to the Stark manifold were observed for the principal numbers 50 and 70, at fields below 50 mV/cm, with linewidths below 500~kHz. The energy-level structure was calculated using a matrix-diagonalisation approach, in which the zero-field positions of the $\ell\leq 3$ Rydberg states were obtained either from multichannel-quantum-defect-theory calculations or experiment, and those of the $\ell\geq 4$ Rydberg states from a long-range core-polarisation model. This approach offers the advantage of including rovibronic channel interactions through the MQDT treatment while retaining the advantages of a spherical basis for the determination of the off-diagonal elements of the Stark operator. Comparison of experimental and calculated transition frequencies enabled the quantitative description of the Stark manifolds, with residuals typically below 50 kHz. We demonstrate how the procedure leads to quantum defects and binding energies of high Rydberg states with unprecedented accuracy, opening up new prospects for the determination of ionisation energies in molecules.