  The Bose-Einstein condensation of correlated atoms in a trap is studied by
examining the effect of inter-particle correlations to one-body properties of
atomic systems at zero temperature using a simplified formula for the
correlated two body density distribution. Analytical expressions for the
density distribution and rms radius of the atomic systems are derived using
four different expressions of Jastrow type correlation function. In one case,
in addition, the one-body density matrix, momentum distribution and kinetic
energy are calculated analytically, while the natural orbitals and natural
occupation numbers are also predicted in this case. Simple approximate
expressions for the mean square radius and kinetic energy are also given.
