In experiments where ultraviolet light produces aerosols from trace amounts of ozone, sulphur dioxide, and water vapour, the number of additional small particles produced by ionization by gamma sources all grow up to diameters larger than 50 nm, appropriate for cloud condensation nuclei. This result contradicts both ion-free control experiments and also theoretical models that predict a decline in the response of larger particles due to an insufficiency of condensable gases (which leads to slower growth) and to larger losses by coagulation between the particles. This unpredicted experimental finding points to a process not included in current theoretical models, possibly an ion-induced formation of sulphuric acid in small clusters.