SummaryExperimental studies on the transmutation of some long-lived radioactive waste nuclei, such as129I,237Np, and239Pu, as well as on natural uranium and lanthanum were carried out at the Synchrophastron of the Laboratory for High Energies at the Joint Institute for Nuclear Research (JINR) in Dubna, Russia. The radioactive targets (I, Np and Pu) were contained in weld-sealed aluminium holders produced by the Institute of Physics and Power Engineering, Obninsk, Russia. Spallation neutrons were produced by relativistic protons with energies in the range of 0.5 GeV≤Ep≤1.5 GeV interacting with 20 cm long uranium or lead target stacks. The metallic targets were surrounded by 6 cm thick paraffin moderators. The uranium and lanthanum samples were positioned on the outside of the moderator surface and typically contained approximately 0.5 to 1.0 gram of uranium or lanthanum. The highest fluence of spallation neutrons was observed in the region of 5 to 10 cm downstream the entrance of the primary beam into the metallic target, rather independent of the target material or the proton energy. The results obtained by nuclear chemistry methods were supplemented by SSNTD (Solid State Nuclear Track Detector) studies. Consistent and systematic results ofB-values and spectral distributions for neutrons have been found. From the experimentally observed transmutation rates one can extrapolate that in a subcritical nuclear power assembly (or "energy amplifier") using a 10 mA proton beam of 1 GeV onto a Pb-target as used here, one can transmute within one month in one gram of sample about 3 mg129I, 21 mg237Np, 3.3 mg238U, and 200 mg239Pu. Rather similar results have been found by another group for129I and239Pu. Observations show that the transmutation rates increase almost linearly with the proton energy in the energy interval 0.5 GeV up to 7.4 GeV. These findings are largely confirmed by model calculations using the LAHET- and DCM/CEM-codes.