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The cross sections of the nuclear reactions induced by neutrons at $E_n$= 14.6 MeV on the isotopes of Dy, Er, Yb with emission of neutrons, proton and alpha-particle are studied by the use of new experimental data and different theoretical approaches . New and improved experimental data are measured by the neutron-activation technique. The experimental and evaluated data from EXFOR, TENDL, ENDF libraries are compared with different systematics and calculations by codes of EMPIRE~3.0 and TALYS~1.2. Contribution of pre-equilibrium decay is discussed. Different systematics for estimations of the cross-sections of considered nuclear reactions are tested.
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