Recent high-precision ($e,e^{\prime }{K}^{+}$) experiments have observed two prominent bump structures in the ${}_{\mathrm{\Lambda }}^{10}\mathrm{Be}$ spectrum, challenging our understanding of hypernuclear structure and hyperon-nucleon ($YN$) interactions. Motivated by this, we perform a systematic study of ${}_{\mathrm{\Lambda }}^{10}\mathrm{Be}$ using a microscopic cluster model with a state-of-the-art $YN$ interaction, guided via a control neural network (Ctrl.NN). Our calculations reveal several theoretically significant states within the energy domains of the experimental bumps. In the bump $a$ region ($\approx 8.5\mathrm{MeV}$), we find states corresponding to a $p$-wave $\mathrm{\Lambda }$ hyperon coupled to the ${}^9\mathrm{Be}(3/2_1^{-})$ ground state. Their density distributions show the $p$-wave $\mathrm{\Lambda }$ orbit oriented parallel to the two-$\alpha$ cluster axis, indicating a genuine hypernuclear excitation. In the bump $b$ region, a peculiar $0^{+}$ state is identified, featuring an $s$-wave $\mathrm{\Lambda }$ coupled to a contracted ${}^9\mathrm{Be}$ core (in its $1/2_1^{+}$ state). The density analysis confirms a distinct $\sigma$-orbit structure for the ${}^9\mathrm{Be}$ core. This work provides a detailed structural investigation of candidate states for the observed bumps and underscores the need for higher-resolution experiments to resolve these states and further refine our knowledge of $YN$ interactions.

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• Hypernuclei & mesic nuclei
• 6 ≤ A ≤ 19
• Artificial neural networks
• Cluster methods