Speaker
Description
The equal-time Bethe–Salpeter (Salpeter–Sucher) relativistic QED wave equation is used to describe two-spin-1/2-fermion systems, e.g., positronium-like systems or two-electron atoms and molecules. The equation containing only the instantaneous part of the interaction is the with-pair Dirac–Coulomb(–Breit) equation (wpDC(B)), which includes the double-pair correction to the no-pair DC(B) Hamiltonian (npDC(B)). The npDC(B) energy can be converged within ppb to ppt relative precision using an explicitly correlated Gaussian basis set approach$^{1,2}$. While the DC(B) equations are eigenvalue equations, the non-instantaneous retardation and further QED corrections to the interaction are accounted for within a complicated, total-energy-dependent operator in the Salpeter–Sucher equation$^3$. Including, e.g., the single-transverse-photon exchange (T), irreducible crossed-Coulomb ($\text{C}\times\text{C}$), or radiative irreducible interaction kernels through this term renders the wave equation non-linear in energy.
Therefore, a novel perturbative approach$^{4,5}$ is under development for treating these contributions, using the npDC(B) results as high-precision correlated relativistic reference energies and wave functions. Our results are not limited to the lowest $Z$ nuclear charge number values and include a partial resummation in $Z\alpha$. The numerical results are extensively tested (wherever possible) with respect to the known fine-structure constant orders, $\alpha^n$, of the non-relativistic QED (nrQED) scheme (and related precision spectroscopy experiments). The newest result is the contribution of the retardation effect ($\text{T}-\text{B}$) in the single-photon exchange interaction to the BO electronic energy of the 1 $^1S_0$ (ground) and 2 $^1S_0$ states of the helium atom.
$^1$Jeszenszki, P., Ferenc, D. and Mátyus, E. 2022 J. Chem. Phys., 156, 084111
$^2$Ferenc, D., Jeszenszki, P. and Mátyus, E. 2022 J. Chem. Phys., 157, 094113
$^3$Mátyus, E., Ferenc, D., Jeszenszki, P. and Margócsy, Á. 2023 ACS Phys. Chem. Au, 3, 222
$^4$Nonn, Á., Margócsy, Á. and Mátyus, E. 2024 J. Chem. Theory Comput., 20, 4385
$^5$Margócsy, Á. and Mátyus, E. 2024 J. Chem. Phys., 160, 204103