Single vs. double electron emission following the beta decay of He-6

When a helium atom containing a $^6$He halo nucleus undergoes beta decay, the two atomic electrons become redistributed over all possible states of the daughter $^6$Li nucleus, including single- and double-electron emission (shake-off). The present study focuses on the probability for double electron emission to form Li$^{3+}$, where there is a substantial disagreement between theory [1] and experiment [2]. We use pseudospectral representations together with Stieltjes imaging to separate the ${\rm Li}^{3+} + 2e^-$ channel from the energetically overlapping ${\rm Li}^{2+} + e^-$ single ionization channel. We find that the formation of Li$^{3+}$ is strongly suppressed near threshold relative to Li$^{2+}$, thereby accounting for part of the disagreement with experiment. However, there still remains a substantial disagreement in the total probability. \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 {\bf96}, 053411 (2017).