Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ (

Dávid Ferenc

¹

,

V. I. Korobov

²

,

Edit Mátyus

³

Abstract

The rovibrational intervals of the 4 He + 2 molecular ion in its X 2 Σ + u ground electronic state are computed by including the non-adiabatic, relativistic, and leading-order quantumelectrodynamics 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

On the Breit interaction in an explicitly correlated variational Dirac-Coulomb framework

“…The most common route for the theoretical determination of energy levels of low-Z atoms and molecules is provided by the non-relativistic quantum electrodynamics (nrQED) framework, in which the leading-order relativistic corrections are the well-known Breit-Pauli Hamiltonian terms. The nrQED approach gives excellent agreement with high-resolution spectroscopy measurements for several atomic and molecular systems [1][2][3]. At the same time, the derivation of the correction operators is tedious, and one has to deal with (cancellation of) divergent terms at higher orders [4][5][6].…”

Vibronic mass computation for the $EF$-$GK$-$H\bar{H}$ $^1Σ_\text{g}^+$ manifold of molecular hydrogen

“…The single-state mass correction, Eq. ( 8), has been formulated several times [13][14][15][16] and was successfully used in spectroscopic applications [15,[17][18][19][20][21][22]. We are not aware of any computation with the multi-state expression, Eqs.…”

“…III has been implemented in the in-house developed computer program named QUANTEN (QUANTum mechanical description of Electrons and atomic Nuclei). QUANTEN has recent applications including non-relativistic energy upper and lower bounds, non-adiabatic, pre-Born-Oppenheimer, perturbative and variational relativistic computations [21][22][23][24][25][26][27][28][29][30][31][32]. The program contains a (stochastic and deterministic) non-linear variational engine and an integral library for variants of explicitly correlated Gaussian (ECG) functions.…”

Variational Dirac-Coulomb explicitly correlated computations for atoms and molecules

“…( 59), is implemented in the QUANTEN computer program [57] (for recent applications of the program see Refs. [7,10,19,[58][59][60][61][62]). QUANTEN was written using the Fortan90 programming language and contains several analytic ECG integrals.…”

“…For a quantitative description of the high-resolution spectroscopic measurements of atoms [1,2] and molecules [3,4], calculations of highly accurate energies are required corresponding to an at least parts-per-billion (ppb) relative precision [5][6][7]. To ensure a ppb-level of convergence for atomic and molecular energies, it is necessary to use explicitly correlated basis functions [6,[8][9][10].…”