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[en] We consider ultracold neutron (UCN) sources based on a new method of UCN production in superfluid helium ("4He). The PIK reactor is chosen as a perspective example of application of this idea, which consists of installing "4He UCN source in the beam of thermal or cold neutrons and surrounding the source with moderator-reflector, which plays the role of cold neutron (CN) source feeding the UCN source. CN flux in the source can be several times larger than the incident flux, due to multiple neutron reflections from the moderator–reflector. We show that such a source at the PIK reactor would provide an order of magnitude larger density and production rate than an analogous source at the ILL reactor. We estimate parameters of "4He source with solid methane (CH_4) or/and liquid deuterium (D_2) moderator–reflector. We show that such a source with CH_4 moderator–reflector at the PIK reactor would provide the UCN density of ~1·10"5 cm"−"3, and the UCN production rate of ~2·10"7 s"−"1. These values are respectively 1000 and 20 times larger than those for the most intense UCN user source. The UCN density in a source with D_2 moderator-reflector would reach the value of ~2·10"5 cm"−"3, and the UCN production rate would be equal ~8·10"7 s"−"1. Installation of such a source in a beam of CNs would slightly increase the density and production rate.