Investigating the beta decay of helium-6 has yielded significant physical insights. It helped clarify the V-A character of the weak interaction [1] and continues to be pivotal in probing for physics beyond the Standard Model by examining potential deviations [2]. During the beta decay of helium-6, the emitted beta particle corresponds to an expanding spherical shell of charge or Coulomb pulse that can eject one or both electrons. This shake-off must be accounted for in balancing energy and momentum to determine the critical electron antineutrino angular correlations. The principal challenge lies in separating the overlapping single and double ionization channels. Calculations have consistently overestimated double ionization compared with observations [3]. Our new theoretical method addresses this by partitioning the overlapping states into distinct charge states using projection operators [4]. This results in closer alignment with experiment; however, discrepancies persist. I will outline our continuing efforts to refine this approach, highlighting the use of delta function matrix elements to assess the fidelity of the daughter ion's charge state.

The one-electron pseudostates used to form the aforementioned projection operators are interesting in their own right. These pseudospectra are useful in several atomic physics problems requiring a complete set of states, especially those with important contributions from very-high-energy intermediate states. An example of this is the Bethe logarithm component of the Lamb shift, a leading order QED correction [5]. Our current activities on this problem will also be discussed.

Furthermore, I will touch on recent work concerning the theory of radiative transitions, where the usual gauge equivalence of the length and velocity forms applies only in the limit of infinite nuclear mass. We have extended this to the case of finite nuclear mass [6], developing a formalism which imposes strict constraints on calculations of atomic properties involving n-photon transitions, such as absorption and spontaneous decay.

[1] T. A. Carlson, F. Pleasonton, C.H. Johnson Phys. Rev. 129, 2220 (1963).
[2] R. Hong et al., Phys. Rev. A 96, 053411 (2017).
[3] E. E. Schulhoff and G. W. F. Drake, Phys. Rev. A 92, 050701 (2015).
[4] A. T. Bondy and G. W. F. Drake, Atoms 3, 41 (2023).
[5] S. P. Goldman and G. W. F. Drake, Phys. Rev. Lett. 68, 1683 (1992).
[6] A. T. Bondy and G. W. F. Drake, Phys. Rev. A 108, 032807 (2023).