The Rotational and Spin-Rotational Level Structure of para-H$_{2}^+$ from High-Resolution MQDT-Assisted Rydberg-State Spectroscopy

TL;DR

This study precisely determined the rotational and spin-rotational structure of para-H₂⁺ using high-resolution spectroscopy combined with MQDT, achieving sub-MHz accuracy and validating results with advanced ab initio calculations.

Contribution

It introduces a novel combination of frequency-comb spectroscopy and MQDT with ab initio quantum-defect parameters to accurately determine H₂⁺ rotational levels and spin-rotational constants.

Findings

Achieved sub-MHz accuracy in rotational level measurements.

Validated experimental results with high-order relativistic and QED corrections.

Corrected for artificial level shifts in MQDT calculations.

Abstract

The structure of the low-lying rotational levels of the X$^+$ $ ^2 \Sigma_g ^+$ ($v^+=0$) vibronic ground state of para-H$_2^+$ has been determined by combining frequency-comb calibrated continuous-wave high-resolution laser spectroscopy of $n$f Rydberg series in the range of principal quantum number $n$ between 28 and 115 and Rydberg-series extrapolation using multichannel-quantum-defect theory (MQDT). The use of accurate quantum-defect parameters obtained from new ab initio calculations enabled the experimental determination of the pure rotational term values of the $N^+= 2$, 4 and 6 rotational levels of H$_2^+$ with sub-MHz accuracy (174.236\,744\,6(77), 575.455\,632\,5(86) and 1191.385\,571(240) cm$^{-1}$, respectively), and of the corresponding spin-rotational coupling constants with an accuracy of better than 100 kHz (42.21(4), 41.26(8) and 40.04(8) MHz, respectively). These values are in agreement with the results of first-principles calculations that include high-order relativistic and quantum-electrodynamics corrections to the level energies. To reach the reported accuracy in the Rydberg series extrapolation, it was necessary to correct for artificial level shifts arising in the MQDT calculations in the vicinity of local perturbations of high-$n$ Rydberg states with a $v^+=0$ H$_2^+$ ion core caused by low-$n$ core-excited Rydberg states, and resulting from approximations in the treatment of the Rydberg-electron energy in the interacting channels.