The condition of existence of the Bose–Einstein condensation in the superfluid liquid helium

The condition for the Bose–Einstein transition in the superfluid liquid helium is presented due to the formation of a free neutron spinless pairs in a liquid helium-dilute neutron gas mixture. We show that the term, of the interaction between the excitations of the Bose gas and the density modes of the neutron, meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair. The lambda transition point is defined by a condition for the Bose–Einstein transition, which transforms reflected neutron pair modes to single neutron modes.