Measurement of the electron shake-off in the $\beta$-decay of laser-trapped $^{6}$He atoms

Electron shake-off is an important process in many high precision nuclear $\beta$-decay measurements searching for physics beyond the standard model. $^{6}$He being one of the lightest $\beta$-decaying isotopes, has a simple atomic structure. Thus, it is well suited for testing calculations of shake-off effects. Shake-off probabilities from the $2^3S_1$ and $2^3P_2$ initial states of laser trapped $^{6}$He matter for the on-going beta-neutrino correlation study at the University of Washington. These probabilities are obtained by analyzing the time-of-flight distribution of the recoil ions detected in coincidence with the beta particles. A $\beta$-neutrino correlation independent analysis approach was developed. The measured upper limit of the double shake-off probability is $2\times10^{-4}$ at 90\% confidence level. This result is $\sim$100 times lower than the most recent calculation by Schulhoff and Drake\footnote{Eva E. Schulhoff and G. W. F. Drake, Phys. Rev. A {\bf 92} 05070 (2015)}.