of adjacent particles overlap, causing the atoms to lose their identity, and the behavior of the system becomes strongly correlated. The system is now governed by quantum statistics. The density distribution of the condensate is represented by a single macroscopic wave function with a well-defined amplitude and phase, which are the order parameters of the system, and a Bose Einstein condensate is formed. Figure 1 shows illustrates this.

The Bose-Einstein condensation is associated with bosonic particles at low temperatures that condensate into a quantum state at a temperature $T_{BEC}$. At low temperatures, the density of bosons with mass $m$ may be expressed by the power law dependence equation within the BEC picture as

$$\rho=\zeta(3/2)\left(\frac{mk_{B}}{2\pi\hbar^{2}}\right)^{3/2}
  T_{BEC}^{3/2},$$

where $\zeta$ is the Riemann zeta function, and $\zeta(3/2) =
2.612$ [@1; @7; @9].

For diluted bosons with small interaction, meaning that the two-particle scattering length $x$ is much shorter than the interatomic distance, the observed $T_{BEC}$ agrees well with the theoretical expectation for free particles. For less diluted systems, the interaction between bosons gives rise to a small shift of $\ T_{BEC}$ [@4; @5]: $$\Delta(T_{BEC})/T_{BEC} = c \rho^{1/3}x.$$

Various authors have attempted to determine the value of $c$, which was found to be in 