Precision measurement of the ionisation energy of the 3dσ GK state of H₂

Abstract

The frequency of the transition between the 3dσ GK ¹Σ⁺ _g (v=1, N=1) state of H₂ and the Rydberg state belonging to a series converging to the X ⁺²Σ⁺ _g (v ⁺=0, N ⁺=1) ground state of ortho H⁺ ₂ has been measured with an accuracy of 1.2 MHz using a narrow-band pulsed near-infrared (NIR) laser. Systematic errors originating from ac and dc Stark shifts, from pressure shifts and from the frequency shift and chirp accompanying the generation of the NIR laser pulses were quantified. By combining this frequency with the binding energy of the 56p (N = 1, S = 0) Rydberg state, the ionisation energy of the GK ¹Σ⁺ _g (v=1, N=1) state of ortho H₂ was determined to be 379855188.3(12) MHz [12670.60522(4) cm⁻¹]. This new result represents the first step towards the determination of the ionisation and dissociation energies of molecular hydrogen at a ν/Δν level of accuracy beyond 10¹⁰. Using the current value of the ionisation energy of ortho H₂ [124357.23797(36) cm⁻¹, from Liu et al. [J. Chem. Phys. 130, 174306 (11)] and the frequency interval between the N = 1 and N = 0 rotational levels of the X (υ = 0) ground state of H₂ [118.48684(10) cm⁻¹, from Jennings et al. [J. Mol. Spectrosc. 126, 19 (28)], the term value of the GK ¹Σ⁺ _g (υ=1, N=1) state was determined to be 111805.1196(4) cm⁻¹.

Keywords:

• molecular hydrogen
• precision measurement
• GK state
• Rydberg states
• ionisation energy
• dissociation energy

Acknowledgements

This article is dedicated to Professor Martin Quack whom we thank for his interest in our work, for his stimulating influence and for fruitful scientific exchanges over many years. We thank Professor Horst Knöckel (University of Hannover) for his advice concerning pressure shifts of the I₂ calibration lines and Professor Wim Ubachs (Free University of Amsterdam) for a useful discussion concerning possible origins of the discrepancy between the term value of the GK (υ = 1, N = 1) state reported in this article and that reported in Ref. [29]. We also thank Josef A. Agner, Guido Grassi, Urs Hollenstein, and Hansjürg Schmutz for their help in the construction of the new setup for the iodine spectroscopy. This work is supported financially by the Swiss National Science Foundation under project 200020-135342 and by the European Research Council advanced grant program under project 228286.

Notes

¹Ionisation energy of the GK (υ = 1, N = 1) state, determined as (1) + (2). ²Determined as (3) − (4). ³Term value of the GK (υ = 1, N = 1) state, determined as (6) + (7) − (3).