  Standard analytical construction of the many-body wave function of
interacting particles in one dimension, beyond mean-field theory, is based on
the Jastrow approach. The many-body interacting ground state is build up from
the ground state of the non-interacting system and the product of solutions of
the corresponding interacting two-body problem. However, this is possible only
if the center-of-mass motion is decoupled from the mutual interactions. In our
work, based on the general constraints given by contact nature of the atom-atom
interactions, we present an alternative approach to the standard construction
of the \textit{pair-correlation} wave-function. Within the proposed ansatz, we
study the many-body properties of trapped bosons as well as fermionic mixtures
and we compare these predictions with the exact diagonalization approach in a
wide range of particle numbers, interaction strengths, and different trapping
potentials.
