A new method utilizing alpha particles to treat solid tumors is presented. Tumors are treated with interstitial radioactive sources which continually release short-lived alpha emitting atoms from their surface. The atoms disperse inside the tumor, delivering a high dose through their alpha decays. We implement this scheme using thin wire sources impregnated with 224Ra, which release by recoil 220Rn, 216Po and 212Pb atoms. This work aims to demonstrate the feasibility of our method by measuring the activity patterns of the released radionuclides in experimental tumors. Sources carrying 224Ra activities in the range 10-130 kBq were used in experiments on murine squamous cell carcinoma tumors. These included gamma spectroscopy of the dissected tumors and major organs, Fuji-plate autoradiography of histological tumor sections and tissue damage detection by Hematoxylin-Eosin staining. The measurements focused on 212Pb and 212Bi. The 220Rn/216Po distribution was treated theoretically using a simple diffusion model. A simplified scheme was used to convert measured 212Pb activities to absorbed dose estimates. Both physical and histological measurements confirmed the formation of a 5-7 mm diameter necrotic region receiving a therapeutic alpha-particle dose around the source. The necrotic regions shape closely corresponded to the measured activity patterns. 212Pb was found to leave the tumor through the blood at a rate which decreased with tumor mass. Our results suggest that the proposed method, termed DART (diffusing alpha-emitters radiation therapy), may potentially be useful for the treatment of human patients.