Electron Emission and Angular Anisotropy following the Beta Decay of Helium-6

Probabilities for atomic electron excitation (shake-up) and ionization (shake-off) are studied following the beta-decay process $^6{\rm He} \rightarrow \,^6{\rm Li}^+ + {\rm e}^- + \bar{\nu}_e$, and in particular, recoil corrections to the shake-off probability are calculated within the sudden approximation. A pseudostate expansion method together with Stieltjes imaging is used to represent the complete two-electron spectrum of final $^6$Li$^+$, $^6$Li$^{++}$, and $^6$Li$^{3+}$ states. Previous results [1] for the $1s2s\;^3S_1$ state of $^6$He as the initial state are extended to include the $1s2p\;^3P$ state, and rotational anisotropies in the electron emission spectrum are discussed. A variety of sum rules, including a newly derived TRK oscillator strength sum rule for dipole recoil terms, provides tight constraints on the accuracy of the results. The results are compared with recent experiments [2].\newline [1] E. E. Schulhoff and G. W. F. Drake, Phys.\ Rev.\ A {\bf 92}, R050701 (2015).\newline [2] R. Hong et al., Phys.\ Rev.\ A {\bf 96}, 053411 (2017).