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First, the creation of a free neutron spinless pairs is predicted in asuperfluid liquid $^4$He and a neutron gas mixture. For solving the givenproblem, it is presented an exact solution to the model of dilute Bose gas asan extension of the Bogoliubov model, at quantity of the condensate fractionvarying in the state $0\leq\frac{N_0}{N}\leq 1$, which in turn might be usefulfor a description of the superfluid liquid $^4$He. Due to an application ofpresented new model of dilute Bose gas, we prove that an appearance of atoms inthe condensate is a suppressor for the collective modes as well as a creatorfor single-particle excitations On other hand, it is shown that the terms ofthe interaction between the Bogoliubov excitations (Bogoliubov phonon-rotonmodes) and the density modes of the neutron meditate an attractive interactionvia the neutron modes, which in turn leads to a bound state on a spinlessneutron pair.

Creation of neutron spinless pairs in a superfluid liquid $^4$He and a neutron gas mixture