Prompt gamma ray spectrometry has been used as an analytical tool for many years. The high level of background noise does, however, remain a major problem with this technique. From simple theoretical consideration, conditions (particle, energy) were determined to reduce significantly the background noise under irradiation. Alpha particles of 3.5 MeV were chosen. Some fifty elements were studied, of which 24 gave interesting results. The detection limits obtained for a sample of niobium were as follows: approximately 1 ppm (10/sup -6/g/g) for the light elements Li, B, F and Na, and between 50 ppm and 1% for the others. Numerous applications may be envisaged in the geo- and cosmo-sciences.