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Rovibrational computations for the He$_2$ a $^3Σ_\mathrm{u}^+$ state including non-adiabatic, relativistic, and QED corrections

Ádám Margócsy, Balázs Rácsai, Péter Jeszenszki, Edit Mátyus

Abstract

A potential energy curve (PEC) accurate to a fraction of 1 ppm ($1:10^6$) is computed for the $^3Σ_\mathrm{u}^+$ state of He$_2$ endowed with relativistic and QED corrections. The nuclear Schrödinger equation is solved on this PEC with diagonal Born-Oppenheimer and non-adiabatic mass corrections to obtain highly accurate rotational-vibrational levels. The computed rovibrational intervals and fine-structure splittings, spanning over several orders of magnitude in energy, are found to be in remarkable agreement with available high-resolution spectroscopy data.

Rovibrational computations for the He$_2$ a $^3Σ_\mathrm{u}^+$ state including non-adiabatic, relativistic, and QED corrections

Abstract

A potential energy curve (PEC) accurate to a fraction of 1 ppm () is computed for the state of He endowed with relativistic and QED corrections. The nuclear Schrödinger equation is solved on this PEC with diagonal Born-Oppenheimer and non-adiabatic mass corrections to obtain highly accurate rotational-vibrational levels. The computed rovibrational intervals and fine-structure splittings, spanning over several orders of magnitude in energy, are found to be in remarkable agreement with available high-resolution spectroscopy data.

Paper Structure

This paper contains 19 sections, 44 equations, 2 figures, 11 tables.

Table of Contents

  1. Introduction
  2. The rovibronic problem
  3. Solving the electronic problem
  4. Correcting the electronic energy
  5. Finite nuclear mass corrections
  6. Spin-independent relativistic & QED and finite nuclear size corrections
  7. Spin-dependent relativistic & QED corrections
  8. Computations, numerical results
  9. Solving the rovibronic problem and comparison with experimental data
  10. Ionization energy
  11. Vibrational intervals
  12. Rotational intervals
  13. Fine-structure splittings
  14. Summary, conclusion, outlook
  15. Acknowledgement
  16. ...and 4 more sections

Figures (2)

  • Figure 1: Top panel: corrected PEC of $\text{a}\ ^3\Sigma_\text{u}^+$ (with energy around the minimum $W(\rho \approx 1.98 \, a_0)\approx-5.150\ 662\ 7 \, E_\text{h}$ subtracted). The dashed line represents the dissociation limit $W(\rho\rightarrow \infty)= W[1 \, ^1S] + W[2 \, ^3S]\approx -5.078\ 414\ 1\ E_\text{h}$. Middle panel: spin-dependent correction to the PEC. Bottom panel: non-adiabatic vibrational and rotational mass corrections. All data used to prepare these figures (up to 100 $a_0$) are provided as SI.
  • Figure 2: A schematic depiction of the different energy scales accounted for in the ab initio He$_2$$\text{a}\ ^3\Sigma_\text{u}^+$ model developed in this work (not to scale). The typical absolute deviations from experimental values are shown as $\delta$ (the corresponding relative errors given in parentheses).