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A method of using a gravitational UCN spectrometer to search for long-rangeforces between neutrons and atoms is proposed. The constraints on the strengthof long-range forces within the range of 10-10 - 10-4 cm can be obtained fromthe experiments on measurements of the total cross section of interaction ofUCN with atoms of the noble gases (He, Ne, Ar, Kr) and the data on the coherentneutron scattering length of the nucleus. The first result of such an analysisis presented. Further prospect of UCN method is discussed.

Search for long-range forces of a neutron and atoms with a trap of ultracold neutrons