We apply the optimized-basis generator coordinate method (OptGCM) to $\mathit{sd}$-shell nuclei, ${}^{20}\mathrm{Ne}, {}^{24}\mathrm{Mg}$, and ${}^{28}\mathrm{Si}$. This method variationally optimizes both the basis Slater determinants in the generator coordinate method (GCM) and the corresponding weight coefficients. To analyze the low-lying excited states of those nuclei, we implement the angular momentum projection. With the Skyrme interaction, we show that the simultaneous optimzation of the basis functions and the weight factors lowers the energy of the excited states and at the same time leads to an appreciable effect on transition probabilities. These results highlight the effectiveness of the OptGCM method.

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• Collective levels
• Electromagnetic transitions
• Nuclear many-body theory
• Nuclear shapes and moments
• Nuclear structure & decays
• 20 ≤ A ≤ 38
• Nuclear density functional theory