Helium nanodroplets are doped with SF6, C4F8, CCl4, C6H5Br, CH3I, and I2. Upon interaction with free electrons a variety of positively and negatively charged cluster ions X±Hen are observed where X±=F±, Cl±, Br±, I+, I2+, or CH3I+. The yield of these ions versus cluster size n drops at characteristic sizes ns that range from ns=10.2±0.6 for F+ to ns=22.2±0.2 for Br−. ns values for halide anions are about 70 % larger than for the corresponding cations. The steps in the ion yield suggest closure of the first solvation shell. We propose a simple classical model to estimate ionic radii from ns. Assuming the helium density in the first solvation shell equals the helium bulk density one finds that radii of halide anions in helium are nearly twice as large as in alkali halide crystals, indicating the formation of an anion bubble due to the repulsive forces that derive from the exchange interaction. In spite of the simplicity of our model, anion radii derived from it agree within approximately 10 % with values derived from the mobility of halide anions in superfluid bulk helium, and with values computed by quantum Monte Carlo methods for X−Hen cluster anions.