Semiconductor photon detectors combined with radioactive sources are becoming increasingly used for energy-dispersive X-ray fluorescence analysis* -lo. The increased application of the non-dispersive technique is mainly due to its multielement capability and the simplicity and stability of the excitation provided by a radioactive source compared to a high-voltage X-ray generator. The analytical sensitivity at energies well below the primary radiation is however limited, owing to the relatively large background activity arising from : 1. multiple Compton interactions in the sample and in supporting and shielding material for the source, the sample and the detector; 2. Compton scattering in the detector; 3. background caused by incomplete charge collection of interactions in parts of the detector, especially the edges ; 4. the direct measurement of y-rays or bremsstrahlung of the radioactive source, background isotopes and the X-rays arising from fluorescence in materials in the vicinity of the detector. Until now applications have been described for the determination of gram amounts to submicrogram amounts of a few elements. The latter sensitivity can be obtained only with long counting periods and for pure samples evaporated on thin backing foils such as mylar. The continuum resulting from scattering in the sample is thus reduced considerably and practically only effect (4) remains as a factor limiting the sensitivity. On the other hand the sensitivity is limited to about 10 p.p.m. for samples such as rocks, ores or liquids where effects (1) and (2) contribute significantly to the background continuum. It may be expected that the geometrical arrangement of sample, source and detector rather critically influences the sensitivity. The purpose of this investigation was to develop a suitable arrangement for the simultaneous, sensitive and precise analysis of elements from 2 = 30 to 2 = 78 with a radioactive y-emitter. The detection of higher 2 elements is hindered by the coherently and incoherently scattered radiation with the 24'Am and ' 'OTrn sources. This difficulty could have been circumvented of course by the use of a y-emitter of higher energy such as "'Cd, 153Gd or 57Co. EXPERIMENTAL Instrumentation An Ortec germanium detector, model 8113-10 was used. The detector was * Research associate I.I.K.W. '4naI. Chim. Acta, 59 (1972)