High-resolution millimeter wave spectroscopy and multichannel quantum defect theory of the hyperfine structure in high Rydberg states of molecular hydrogen H2.

Abstract

This study developed experimental and theoretical approaches combining high-resolution millimeter-wave spectroscopy with multichannel quantum defect theory (MQDT) to characterize the hyperfine structure of molecular hydrogen H2 in high Rydberg states. Measurements were performed for l=0–3 Rydberg states in the principal quantum number range n=50–65 at sub-MHz resolution. The np1(1), nd1(1), and nf1(0–3) series exhibited metastable lifetimes exceeding 5 µs beyond n=50. Hyperfine structure was found to depend strongly on orbital angular momentum l: exchange interaction dominates in penetrating s and p states, while hyperfine coupling prevails in d and f states, producing mixed singlet-triplet character. MQDT was extended to incorporate hyperfine interactions via a frame transformation between Born-Oppenheimer and asymptotic coupling schemes. Agreement between theory and experiment was achieved to within 600 kHz after adjustment of quantum defect functions. The extrapolated ionic hyperfine structure was consistent with prior ab initio predictions within experimental error.