Speaker
Description
The Bethe–Salpeter (BS) QED wave equation and its equal-time variant $[1, 2, 3]$ are considered for numerical precision computations. If only single-photon instantaneous Coulomb(–Breit) interactions are considered in the interaction kernel, then the equal-time BS equation simplifies to the with-pair Dirac–Coulomb(–Breit) wave equation. Mathematical properties and numerical results are discussed for this linear wave equation and its non-Hermitian Hamiltonian. A numerical basis set approach is presented which is used to converge the with-pair (and no-pair) DC(B) energies to 1:10$^9$ to 1:10$^{12}$ relative precision for the He atom (& isolectronic ions), H$_2$, HeH$^+$, and H$^+_3$ with clamped nuclei $[4-10]$ and for the two-spin-1/2 fermion systems, Ps, Mu, H, and $\mu$H $[10, 11]$. The $\alpha$ fine-structure dependence of the variational energy is in excellent agreement with the relevant non-relativistic QED (nrQED) values up to $\alpha^4E_\mathrm{h}$ ($m\alpha^6$) and $\alpha^4 \ln \alpha \ E_\mathrm{h}$ ($m\alpha^6 \ln \alpha$) orders. Ongoing work targets a perturbative account for higher-order interaction kernels, retardation and self-energy effects through the equal-time BS equation using the no-pair or the with-pair state as a high-precision reference $[12, 13]$ as a replacement to the non-relativistic reference of nrQED.
References
$[1]$ E. E. Salpeter and H. A. Bethe, Phys. Rev. A 84, 1232 (1951).
$[2]$ E. E. Salpeter, Phys. Rev. A 87, 328 (1952).
$[3]$ J. Sucher, Ph. D. Thesis (1958), Columbia University.
$[4]$ P. Jeszenszki, D. Ferenc, E. Mátyus, J. Chem. Phys. 154, 224110 (2021).
$[5]$ P. Jeszenszki, D. Ferenc, E. Mátyus, J. Chem. Phys. 156, 084111 (2022).
$[6]$ D. Ferenc, P. Jeszenszki, E. Mátyus, J. Chem. Phys. 156, 084110 (2022).
$[7]$ D. Ferenc, P. Jeszenszki, E. Mátyus, J. Chem. Phys. 157, 094113 (2022).
$[8]$ P. Jeszenszki and E. Mátyus, J. Chem. Phys. 158, 054104 (2023).
$[9]$ P. Hollósy, P. Jeszenszki, E. Mátyus, under review (2024).
$[10]$ P. Jeszenszki and E. Mátyus, in preparation (2024).
$[11]$ D. Ferenc and E. Mátyus, Phys. Rev. A. 107, 052803 (2023).
$[12]$ E. Mátyus, D. Ferenc, P. Jeszenszki, Á. Margócsy, ACS Phys. Chem. Au 3, 222 (2023).
$[13]$ Á. Margócsy and E. Mátyus, arXiv:2312.13887 (2024).
