To investigate the structural configuration of \(^6\textrm{He}\) and \(^6\textrm{Be}\) in a three-cluster system and to highlight dinucleon correlations, we performed a two-cluster overlap amplitude (TCOA) calculation, which is an extension of the RWA formalism. The total wave functions were obtained using the generator coordinate method with microscopic cluster wave functions. Based on these wave functions, we calculated the overlap amplitudes to extract the relative motion and spatial correlations between clusters. The computed energy spectra showed reasonable agreement with the experimental data, emphasizing the effectiveness of the present framework for investigating dinucleon correlations in light nuclei. Our results revealed the presence of both dinucleon-like and cigar-like configurations in the ground states of \(^6\textrm{He}\) and \(^6\textrm{Be}\) , indicating a coexistence of compact and extended cluster structures. Furthermore, the \(2_1^+\) state of \(^6\textrm{He}\) revealed a pronounced dineutron structure, with strong spatial correlations between the two valence neutrons. We also performed calculations for the higher-lying \(2_2^+\) state, which showed a more spatially extended structure and provided potential references for future experimental investigations. These findings demonstrated that the TCOA method served as a powerful tool to explore cluster dynamics and dinucleon features in light, weakly bound nuclear systems.
