Quantum-defect analysis of $np$ and $nd$ $\rm{H_3}$ Rydberg energy levels

TL;DR

This paper employs multichannel quantum-defect theory and ab initio calculations to analyze Rydberg energy levels of the triatomic hydrogen molecule, providing detailed quantum defect data and energy level predictions.

Contribution

It introduces a comprehensive method combining ab initio data and multipole models to compute Rydberg energy levels of H3, including laboratory-frame quantum defects.

Findings

Quantum defects for np and nd states of H3 are extracted.

Calculated Rydberg energy levels match experimental data.

Method enables precise predictions of Rydberg states in triatomic molecules.

Abstract

In this work, Rydberg energy levels of the triatomic hydrogen molecule ($\rm{H_3}$) are studied with multichannel quantum-defect theory. We extract the body-frame p-wave quantum defects from highly accurate \emph{ab initio} electronic potential surfaces and calculate the quantum defects of higher momentum states by using the long-range multipole potential model. To obtain laboratory-frame quantum defects, we perform a rovibrational-frame transformation with accurate rovibrational states of $\rm{H_3^+}$. Finally, we use the laboratory-frame quantum defects to calculate Rydberg energy levels for the fundamental neutral triatomic molecule $\rm{H_3}$.