Under the Thomas-Fermi approximation, a relatively much simpler analytical solutions of the coupled Gross-Pitaevskii equations for the two-species BEC have been derived. Additionally, a model for the asymmetric states has been proposed, and the competition between the symmetric and asymmetric states has been evaluated. The whole parameter-space is divided into zones, each supports a specific phase, namely, the symmetric miscible phase, the symmetric immiscible phase, or the asymmetric phase.

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... ed on the division the phase-diagrams against any set of parameters can be plotted. Thereby, the effects of these parameters can be visualized. There are three critical values in the inter-species interaction numbers N_A/N_B. They govern the transitions between the phases. Two cases, (i) the repulsive V_AB matches the repulsive (ii) the attractive V_AB nearly cancels the effect of the repulsive V_A+V_B have been particularly taken into account. The former leads to a complete separation of the two kinds of atoms , while the latter lead to a collapse. Finally, based on an equation derived in the paper, a convenient experimental approach is proposed to determine the ratio of particle numbers .