In the present work recently available experimental data for high-spin states of four nuclei, $^{124}_{ 52}$Te, $^{125}_{ 52}$Te, $^{126}_{ 52}$Te, and $^{127}_{ 52}$Te have been interpreted using state-of-the-art shell model calculations. The calculations have been performed in the $50-82$ valence shell composed of $1g_{7/2}$, $2d_{5/2}$, $1h_{11/2}$, $3s_{1/2}$, and $2d_{3/2}$ orbitals. We have compared our results with the available experimental data for excitation energies and transition probabilities, including high-spin states. The results are in reasonable agreement with the available experimental data. The wave functions, particularly, the specific proton and neutron configurations which are involved to generate the angular momentum along the yrast lines are discussed. We have also estimated overall contribution of three-body forces in the energy level shifting. Finally, results with modified effective interaction are also reported.
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