A nucleator nozzle (20) for producing ice nuclei is designed as convergent-divergent nozzle. The nozzle channel (25) has a section (27) that is widening. The ratio of the cross-sectional area of the outlet opening (23) to the cross-sectional area of the nozzle channel (25) in the region of the nucleus diameter (26) is at least approximately 4:1. A snow lance (1) having at least one nucleator nozzle (20) and having at least one water nozzle (30; 30′) is designed such that water droplets (32) produced by the water nozzle (30; 30′) pass through a droplet path (31; 31′) of at least 20 cm until they reach ice nuclei (28) from the nucleator nozzle (20) in a germination zone E.