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In the framework of Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function approach, the 0$^+_2$ state at 7.65MeV in $^{12}$C (Hoyle state) is recognized as featuring the Bose-Einstein Condensation (BEC)state [1]. When one α-particles in $^{12}$C is replaced with $^{6}$He, a system of three bosons can also be formed. And if all clusters are moving in relative s-wave, it represents a possible Hoyle-like configuration for $^{14}$C[2].
Based on the above-mentioned anticipation, we conducted an experiment using $^{14}$C as the projectile which was excited to very high lying states followed by three-cluster decay. This experiment was carried out at the Radioactive Ion Beam Line at the Heavy Ion Research Facility in Lanzhou (HIRFL-RIBLL1). Special efforts were devoted to coincidently measure and identify three helium clusters at forward angles.
A prominent resonance above the $^6$He + 2$\alpha$ threshold were firmly identified after selecting the $^8$Be(g.s.) + $^6$He decay channel. Analysis of angular correlation and decay suggests a spin-parity assignment of $J^\pi = 0^+$. Our finding is further supported by the microscopic 3α+2n GCM model and Control neural network calculations, which provides a valuable insight into the structural and dynamic behavior of unstable nuclei.
[1]. FREER M, FYNBO H. Progress in Particle and Nuclear Physics, 2014, 78: 1. DOI: 10.1016/j.ppnp.2014.06.001.https://doi.org/10.1007/s41365-024-01588-x
[2]K. Wei, Y. Ye and Z. Yang, "Clustering in nuclei: progress and perspectives", Nucl. Sci. Tech. 35, 216(2024), https://doi.org/10.1007/s41365-024-01588-x