Fundamental vibration frequency and rotational structure of the first excited vibrational level of the molecular helium ion ( He 2 + )

Ionization Energy of the Metastable 2 ^{1}S_{0} State of ^{4}He from Rydberg-Series Extrapolation

In a recent breakthrough in first-principles calculations of two-electron systems, Patkóś, Yerokhin, and Pachucki [Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] have performed the first complete calculation of the Lamb shift of the helium 2 ^{3}S_{1} and 2 ^{3}P_{J} triplet states up to the term in α^{7}m. Whereas their theoretical result of the frequency of the 2 ^{3}P←2 ^{3}S transition perfectly agrees with the experimental value, a more than 10σ discrepancy was identified for the 3 ^{3}D←2 ^{3}S and 3 ^{3}D←2 ^{3}P transitions, which hinders the determination of the He^{2+} charge radius from atomic spectroscopy. We present here a new measurement of the ionization energy of the 2 ^{1}S_{0} state of He [960 332 040.491(32) MHz] which we use in combination with the 2 ^{3}S_{1}←2 ^{1}S_{0} interval measured by Rengelink et al. [Nat. Phys. 14, 1132 (2018).NPAHAX1745-247310.1038/s41567-018-0242-5] and the 2 ^{3}P←2 ^{3}S_{1} interval measured by Zheng et al. [Phys. Rev. Lett. 119, 263002 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.263002] and Cancio Pastor et al. [Phys. Rev. Lett. 92, 023001 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.023001] to derive experimental ionization energies of the 2 ^{3}S_{1} state [1152 842 742.640(32) MHz] and the 2 ^{3}P centroid energy [876 106 247.025(39) MHz]. These values reveal disagreements with the α^{7}m Lamb shift prediction by 6.5σ and 10σ, respectively, and support the suggestion by Patkóš et al. of an unknown theoretical contribution to the Lamb shifts of the 2 ^{3}S and 2 ^{3}P states of He.

Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of ^{4}He_{2}^{+} (X ^{2}Σ_{u}^{+})

The rovibrational intervals of the ^{4}He_{2}^{+} molecular ion in its X ^{2}Σ_{u}^{+} ground electronic state are computed by including the nonadiabatic, relativistic, and leading-order quantum-electrodynamics corrections. Good agreement of theory and experiment is observed for the rotational excitation series of the vibrational ground state and the fundamental vibration. The lowest-energy rotational interval is computed to be 70.937 69(10)  cm^{-1} in agreement with the most recently reported experimental value, 70.937 589(23)(60)_{sys}  cm^{-1} [L. Semeria et al., Phys. Rev. Lett. 124, 213001 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.213001].

H3 + as a five-body problem described with explicitly correlated Gaussian basis sets

Various explicitly correlated Gaussian (ECG) basis sets are considered for the solution of the molecular Schrödinger equation with particular attention to the simplest polyatomic system, H₃ ⁺. Shortcomings and advantages are discussed for plain ECGs, ECGs with the global vector representation, floating ECGs and their numerical projection, and ECGs with complex parameters. The discussion is accompanied with particle density plots to visualize the observations. In order to be able to use large complex ECG basis sets in molecular calculations, a numerically stable algorithm is developed, the efficiency of which is demonstrated for the lowest rotationally and vibrationally excited states of H₂ and H₃ ⁺.

Non-adiabatic mass-correction functions and rovibrational states of 4 He 2 + ( X 2 Σ u + )

The mass-correction functions in the second-order non-adiabatic Hamiltonian are computed for the ⁴ He 2 + molecular ion using the variational method, floating explicitly correlated Gaussian functions, and a general coordinate-transformation formalism. When non-adiabatic rovibrational energy levels are computed using these (coordinate-dependent) mass-correction functions and a highly accurate potential energy and diagonal Born-Oppenheimer correction curve, significantly improved theoretical results are obtained for the nine rotational and two rovibrational intervals known from high-resolution spectroscopy experiments.