The discharge tube is 60 cm long and has a diameter of 2.2 cm. The experiments are carried out at pressures of around 0.7 Torr and at currents below 0.2 mA. External waves are excited by means of a double probe or an external ring electrode placed 7 cm from the anode. For simplicity, it is assumed that the discharge plasma consists of three species of particles, namely electrons and positive and negative ions. In general, quasi-neutrality is assumed, and a one-dimensional treatment is used. This makes it possible to use practically the same basic equations as used by Matsumoto et al. (1981), the only exception being that the radial terms are rewritten in terms of the ambipolar diffusion rate. Half-integer harmonics are observed in ionization waves in SF6 gas. The interpretation provided is in terms of parametric excitation owing to an interaction between externally excited waves and spontaneous ionization waves.