[en] RF electron guns require an external magnetic focussing field to produce a low-emittance electron beam. A DC magnetic field focuses electrons already inside the cavity as they leave the photocathode. In superconducting RF guns (SRF) the possibility of external magnetic focussing is quite limited. In this paper we investigate the effect of RF focussing in the first half-cell of a n+((1)/(2)) cell SRF gun cavity without a focussing magnet. The shape of the first half-cell is optimized. The calculations were done to fulfill the beam requirements of the injector for the ELBE project (Gabriel (Ed.), Internal Design Report, Forschungszentrum Rossendorf, Dresden, 1995) as well as the one for the TESLA Test Facility (TTF) (Edwards, TESLA Test Facility - Design Report, Technical Report, DESY, Hamburg, 1995). Normalized transversal emittances of the order of 1π mm mrad for bunch charges up to 1 nC were obtained