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The status of neutron-capture therapy of malignant tumors and its problems -damage to healthy tissue as a result of neutron transport to the irradiation location and presence in the therapeutic beam of a background consisting of γ rays and fast neutrons -are presented. To solve these problems, the authors have proposed using ultracold neutrons with energy less than 10 -7 eV, whose unique capability is to undergo total reflection from the surface of a condensed substance at any angle of incidence. Numerous works have demonstrated that such neutrons can be transported along neutron guides. The cross section for inelastic scattering of neutrons by hydrogen-containing substances -water, ethyl alcohol, and biological tissue -has been measured in an IR-8 beam of ultracold and very cold neutrons. At temperature 200-300 K, the experimental data are in very good agreement with calculations, but as temperature decreases further a discrepancy appears, which could be due to the inaccuracy of the model spectra of the oscillations hydrogen-containing substances used in the calculations. The use of ultracold neutrons opens up new possibilities of neutron-capture therapy for treating malignant tumors localized in body cavities or organs.Radiation therapy is one of the main methods of treating cancer. Up to 70% of cancer patients need radiation therapy in one form or another.The methods of radiation therapy are developing along the lines of optimizing and creating new technologies characterized by selective destruction of tumor tissues and sparing radiation exposure of normal tissues in the body. A promising therapy meeting these requirements is neutron-capture therapy, characterized by high linear transfer of energy of heavy particles and, correspondingly, higher relative biological effectiveness than conventionally used forms of radiation.Neutron-capture therapy of malignant tumors is based on the absorption of neutrons by the stable boron isotope 10 B or gadolinium 157 Gd and release of substantial energy by the reaction products [1,2]. At the first stage a preparation containing, for example, 10 B, is introduced into the tumor. Then the tumor is irradiated with neutrons. When a 10 B nucleus absorbs a neutron, an α particle and a 7 Li ion, whose ranges in biological tissue are ~10 μm, are formed as a result of the reaction 10 B(n, α) 7 Li. An amount of energy equal to 2.3 MeV is released in a cancer cell; this destroys the cell. In a reaction with 157 Gd, high-energy photon and electron radiation (conversion and Auger electrons), are formed; this radiation is localized within 1-40 μm from the point of the reaction.Today nuclear reactors, accelerators, and generators are used in radiation therapy as sources of neutrons. In addition, the possibility of using sources based on 252 Cf is being investigated for contact neutron therapy. These sources of neutrons can be ranked on the basis of different grounds but only nuclear reactors and accelerators are the real competitors for mass use. They will make it possible to perform most o...