Conduct investigations into the feasibility of treating tumors in the major anatomic sites (brain, head and neck, lung, mediastinum, upper abdomen, pelvis, trunk, extremities, superficial and deep lymph nodes) with neutrons, protons, heliumions, pions, and heavy ions (12C, 20Ne, etc.) by: carrying out sophisticated treatment planning utilizing precise tissue density inhomogeneity corrections; and confirming the ability to deliver the radiation treatment (biologically equivalent dose where appropriate) in accordance with the treatment plans by measurements both in patients and in phantoms.