High-Precision Quantum Dynamics of He${}_2$ over the b ${}^3{\mathrm{\Pi }}_{\mathrm{g}}$-c ${}^3{\mathrm{\Sigma }}_{\mathrm{g}}^{+}$ Electronic Subspace by including Non-adiabatic, Relativistic and QED Corrections and Couplings

Relativistic, quantum electrodynamics, as well as non-adiabatic corrections and couplings, are computed for the b ${}^3{\mathrm{\Pi }}_{\mathrm{g}}$ and c ${}^3{\mathrm{\Sigma }}_{\mathrm{g}}^{+}$ electronic states of the helium dimer. The underlying Born-Oppenheimer potential energy curves are converged to 1 ppm ($1:{10}^6$) relative precision using a variational explicitly correlated Gaussian approach. The quantum nuclear motion is computed over the b ${}^3{\mathrm{\Pi }}_{\mathrm{g}}$-c ${}^3{\mathrm{\Sigma }}_{\mathrm{g}}^{+}$ (and B ${}^1{\mathrm{\Pi }}_{\mathrm{g}}$-C ${}^1{\mathrm{\Sigma }}_{\mathrm{g}}^{+}$) 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 ${}^3{\mathrm{\Pi }}_{\mathrm{g}}$-state fine structure. Fine-structure splittings are also predicted for the c ${}^3{\mathrm{\Sigma }}_{\mathrm{g}}^{+}$ levels, which have not been fully resolved experimentally, yet.