Zero-Quantum-Defect Method and the Fundamental Vibrational Interval of H_{2}^{+}.

Area of Science:

• Molecular Spectroscopy
• Quantum Chemistry
• Atomic and Molecular Physics

Background:

• Accurate determination of molecular properties is crucial for understanding chemical bonding and physical interactions.
• The hydrogen molecular ion (H_{2}^{+}) is a fundamental system in quantum mechanics, serving as a benchmark for theoretical calculations.

Purpose of the Study:

• To precisely measure the fundamental vibrational interval of H_{2}^{+} using continuous-wave laser spectroscopy.
• To achieve a significant improvement in measurement accuracy compared to previous experimental values.
• To validate theoretical predictions from nonrelativistic quantum electrodynamic calculations.

Main Methods:

• Employed continuous-wave laser spectroscopy to probe Rydberg states of H_{2}.
• Investigated Stark manifolds of H_{2} with H_{2}^{+} ion cores in ground and vibrationally excited states.
• Extrapolated Stark shifts to zero field to determine zero-quantum-defect positions and ionization energies.

Main Results:

• Determined the fundamental vibrational interval of H_{2}^{+} to be ΔG_{1/2}=2191.126 614(17) cm⁻¹.
• Achieved a four-orders-of-magnitude improvement in measurement precision.
• Experimental results show excellent agreement with theoretical values from nonrelativistic quantum electrodynamics calculations.

Conclusions:

• The study provides a highly accurate experimental value for the fundamental vibrational interval of H_{2}^{+}.
• The agreement with theoretical calculations validates both the experimental method and the underlying quantum electrodynamic theory.
• This precise measurement advances our understanding of fundamental molecular physics and provides a benchmark for future studies.