We investigate the clustering structure of ${}^{10}\mathrm{C}$ using a microscopic four-body $\alpha + \alpha + p + p$ cluster model. The calculated low-lying energy spectrum agrees well with the experimental data. Based on the analysis of reduced width amplitudes and spectroscopic factors for the two-body configurations (${}^9\mathrm{B} + p, {}^6\mathrm{Be} + \alpha$, and ${}^8\mathrm{Be} + {}^{2}p$), as well as the three-body configuration (${}^8\mathrm{Be} + p + p$), several cluster structures are suggested. The analysis reveals that the $0_1^{+}$ state corresponds to a compact structure, while the $0_2^{+}$ and $2_3^{+}$ states show nonnegligible diproton clustering components. In particular, the $0_2^{+}$ state is found to exhibit a mixed structure, involving both the ${}^6\mathrm{Be} + \alpha$ and ${}^8\mathrm{Be} + p + p$ configurations, consistent with previous theoretical predictions and experimental observations. It is also indicated that the $2_1^{+}$ and $2_2^{+}$ states are dominated by the ${}^9\mathrm{B}+p$ configuration, while the $0_3^{+}$ state features a more spatially extended configuration.

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• Cluster models
• Nuclear many-body theory
• Nuclear structure & decays
• 6 ≤ A ≤ 19