Structure of multielectron bubbles in liquid helium

We present a detailed density-functional calculation for multielectron bubbles with charges {ital z}{le}50. The calculation is similar to that for metal clusters, but we found no obvious shell structure in the charged bubbles. The exchange-correlation interaction has the important effect of reducing the bubble radius and, hence, enhances its stability. A simple but useful analysis is introduced, which explains the calculated results and could also work for large-{ital z} bubbles. The calculated mobilities of bubbles agree well with the measured values but, quite surprisingly, the results indicate that the {ital z}=3 bubbles have not been observed experimentally.