Lambda transition and Bose-Einstein condensation in liquid ^{4}He.

We present the theory describing Bose-Einstein condensation (BEC) and superfluidity in a liquid ^{4}He based on the concept that for some temperature interval, there exist metastable diatomic clusters or diatomic quasiparticles which are the bound states of two atoms of ^{4}He. It is shown that in liquid ^{4}He for the temperature region 1K≤T≤T_{λ} diatomic quasiparticles macroscopically populate the ground state which leads to BEC in liquid ^{4}He. The approach yields the lambda temperature as T_{λ}=2.16K, which is in excellent agreement with the experimental lambda transition temperature T_{λ}=2.17K. The concept of diatomic quasiparticles also leads to superfluid and BEC fractions which are in good agreement with experimental data and Monte Carlo simulations for liquid ^{4}He. It is also shown that the condensate fraction for low temperature (T≤0.5K) at saturated vapor pressure is ρ_{0}/ρ=7.22%, which is very close to the value 7.25±0.75% obtained in recent measurements.