High-Precision Quantum Dynamics of He₂ over the b ³Π_g-c ³Σ_g⁺ Electronic Subspace by including Non-adiabatic, Relativistic and QED Corrections and Couplings

2025/06/30 by Rácsai, Balázs, Jeszenszki, Péter, Margócsy, Ádám +1
#Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2506.23879

Abstract

Relativistic, quantum electrodynamics, as well as non-adiabatic corrections and couplings, are computed for the b ³Π_g and c ³Σ_g⁺ electronic states of the helium dimer. The underlying Born-Oppenheimer potential energy curves are converged to 1 ppm (1:10⁶) relative precision using a variational explicitly correlated Gaussian approach. The quantum nuclear motion is computed over the b ³Π_g-c ³Σ_g⁺ (and B ¹Π_g-C ¹Σ_g⁺) 9-(12-)dimensional electronic-spin subspace coupled by non-adiabatic and relativistic (magnetic) interactions. The electron's anomalous magnetic moment is also included; its effect is expected to be visible in high-resolution experiments. The computed rovibronic energy intervals are in excellent agreement with available high-resolution spectroscopy data, including the rovibronic b ³Π_g-state fine structure. Fine-structure splittings are also predicted for the c ³Σ_g⁺ levels, which have not been fully resolved experimentally, yet.

Citations

• Rovibrational computations for He₂⁺ X~Σ_u⁺ including non-adiabatic, relativistic and QED corrections
• Spin-dependent terms of the Breit-Pauli Hamiltonian evaluated with an explicitly correlated Gaussian basis set for molecular computations
• Laser cooling Rydberg molecules -- a detailed study of the helium dimer
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• Lamb dip of a Quadrupole Transition in H₂
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• On the inclusion of cusp effects in expectation values with explicitly correlated Gaussians

Cited by

• Rovibrational computations for the He₂ a ³Σ_u⁺ state including non-adiabatic, relativistic, and QED corrections
• Spin-dependent terms of the Breit-Pauli Hamiltonian evaluated with an explicitly correlated Gaussian basis set for molecular computations

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• Theory for the Rydberg states of helium: Results for 2 ≤ n ≤ 35 and comparison with experiment for the singlet and triplet P-states