In the present work we have reported comprehensive analysis of recently available experimental data [H.M. David et al., Phys. Lett. B {bf 726}, 665 (2013)] for high-spin states up to $17^+$ with $T=0$ in the odd-odd $N=Z$ nucleus $^{62}$Ga using shell model calculations within the full $f_{5/2}pg_{9/2}$ model space and deformed shell model based on Hartee-Fock intrinsic states in the same space. The calculations have been performed using jj44b effective interaction developed recently by B.A. Brown and A.F. Lisetskiy for this model space. The results obtained with the two models are similar and they are in reasonable agreement with experimental data. In addition to the $T=0$ and $T=1$ energy bands, band crossings and electromagnetic transition probabilities, we have also calculated the pairing energy in shell model and all these compare well with the available theoretical results.
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