The Broad Applicability of Pseudospectra in Atomic Physics

Atomic systems have infinitely many bound and continuum states, posing a computational challenge for calculations involving perturbation sums over intermediate states. In this talk, I will discuss my dissertation (completed under the supervision of Prof. Gordon Drake at the University of Windsor), which employed variationally constructed two-electron pseudospectra to treat three such distinct atomic processes.

We first consider the beta decay of helium-6, a process that is interrogated in some low-energy tests of the Standard Model. The change in nuclear charge induced by beta decay results in electronic shake-up and shake-off processes within the atom, which must be carefully accounted for in searches for new physics. We partition the single- and double-ionization channels, reducing a previously reported discrepancy between theory and experiment [Atoms 11, 41 (2023)].

The second process treated is spontaneous two-photon decay in heliumlike ions, including finite-nuclear-mass effects [Phys. Rev. A 102, 052807 (2020)]. This critical process serves as a temperature and pressure probe in low-particle-density regimes such as planetary nebulae. Mass polarization is treated within a gauge-dependent expansion, leading to new algebraic relations that serve as a powerful way to test the accuracy of calculations involving approximate wave functions [Phys. Rev. A 108, 022807 (2023)].

Lastly, the tune-out frequency of metastable helium is calculated via a reformulation of the problem as a zero in Rayleigh scattering cross section (rather than the frequency-dependent polarizability), leading to the inclusion of retardation effects. This joint theoretical-experimental effort with the Baldwin group at the Australian National University provides a novel QED test independent of traditional energy level measurements such as the Lamb shift [Science 376, 199 (2022)].