Abstract
We study the shape evolution of $N=Z$ nuclei $^{24}\mathrm{Mg},^{28}\mathrm{Si}$, and $^{32}\mathrm{S}$ in the axially symmetric deformed Woods-Saxon model, taking into account both $T=0$ and $T=1$ pairing interactions. We find the coexistence of $T=0$ and $T=1$ superfluidity phases in the large deformation region $|{\ensuremath{\beta}}_{2}|>0.3$ in these three nuclei. The interplay between the two pairing interactions has an important effect on determining the deformation of the ground states in these nuclei. The self-energy contributions from the pairing correlations to the single particle (s.p.) energies are also examined.
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