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First, a condition for the Bose-Einstein transition in the superfluid liquidhelium is presented due to the creation of a free neutron spinless pairs in aliquid helium and a dilute neutron gas mixture. We proposed a new model ofdilute Bose gas, where presence atoms in the condensate is a suppressor for thecollective modes as well as a creator for single-particle excitations On otherhand, it is shown that the terms, of the interaction between the excitations ofthe Bose gas and the density modes of the neutron, meditate an attractiveinteraction via the neutron modes, which in turn leads to a bound state on aspinless neutron pair. The lambda transition is defined by a condition for theBose-Einstein transition, which transforms reflected neutron pair modes tosingle neutron modes.

A condition for the Bose-Einstein transition in the superfluid liquid helium