Indivisibility of electron bubbles in helium
A recent proposal by Maris[1], that single electron bubbles in helium might fission into separate, particle-like entities, does not properly take into account the failure of the adiabatic approximation when, due to tunneling, there is a long electronic time scale. The point along the fission pathway of a photoexcited p-state bubble, where the adiabatic approximation first breaks down, occurs well before the bubble waist has pinched down forming two cavities. In the connected two-lobed geometry, the p- and s-states are strongly mixed by an antisymmetric vibrational mode, and the excitation decays by the mechanism where one lobe collapses while the other expands into the spherical s-state geometry. The extreme pressure jump in a photoexcited bubble leads to shock formation that may halt the elongation even before adiabaticity is compromised. In this case, the photoexcited bubble decays radiatively from the relaxed p-state geometry. [1] H.J. Maris, On the fission of elementary particles and the evidence for fractional electrons in liquid helium, J. Low Temp. Phys. 120, 173 (2000)