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pair correlation function. 

The paper is organized as follows. In the next section, we briefly review our theoretical approach. In Section III, we present the results of our calculation of one-body density, pair distribution function and their momentum distributions. Finally, in Section IV we draw our conclusions. 

## II. POTENTIAL HARMONIC EXPANSION METHOD 

We adopt the potential harmonics expansion method together with a short range cor- relation function (CPHEM), which has already been established as a successful and useful technique for investigating BEC with realistic two-body interactions. In the following, we briefly describe the technique. Interested readers can find the details in Refs. $^{17–19}$. 

We start with the many-body Schr¨ odinger equation of A spinless bosons trapped in an isotropic harmonic oscillator potential of frequency ω at zero temperature. The center of mass motion can be separated by introducing the center of mass vector ( ⃗ R ) and N = A − 1 Jacobi vectors { ζ$_{1}$, ..., ζ$_{N}$ } defined as 20 

<img src='content_image/366816.jpg'>

where ⃗ x$_{i}$ is the position vector of the i -th particle. The relative motion of the system is described by 

where V$_{trap}$ and V$_{int}$ are respectively the trapping and pair-wise interaction potentials, ex- pressed in terms of the Jacobi vectors. The energy of the relative motion is E$_{R}$ . Next hyperspherical variables are introduced by defining a ‘hyperradius’ 

<img src='content_image/366818.jpg'>

<img src='content_image/366815.jpg'>

