abstract: We consider a rubidium gas of few atoms confined in two dimensions and interacting via a logarithmic potential. A self-consistent calculation of the ground state wave function is implanted using the Hartree-Fock approximation to solve the time-independent Schrödinger equation.The system is transformed into a crystalline phase from Bose-Einstein Condensate if the strength of their interatomic repulsive interaction is increased. Although the repulsive potential is proper for the two dimensional system, we have only observed the Wigner crystallization for two particles in contrast to previous studies on the same subject. The potential appears to be not providing Wigner crystallization for the particle number more than two.