Observation of a BEC-like state in $^{14}$C

Bose-Einstein condensation (BEC) is a novel state of matter initially discovered in atomic systems where many bosonic particles are distributed in the same lowest-energy quantum state. In recent years, the BEC concept has also been adopted in nuclear physics to account for the specially structured system in which a number of bosonic clusters are condensed onto the same relative $s$-wave, as can be represented by the famous Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave function (WF). The 0$_2^+$ state of $^{12}$C, known as the Hoyle state, was first evidenced as an excellent example of the BEC-like state, which has triggered strong interest in the search for other candidates with a similar structural configuration.Here we report the observation of a new BEC-like state in $^{14}$C, having two more neutrons in comparison to $^{12}$C. The state was reconstructed from the sequential decay channel, $^{14}$C $\rightarrow$ $^8$Be(g.s.) + $^6$He followed by $^8$Be(g.s.) $\rightarrow$ 2$\alpha$, which depends essentially on the precise detection of the three decaying helium fragments. This finding is supported by the present state-of-the-art theoretical calculations, comprising the microscopic Brink WF combined with the generator coordinate method (GCM) and the control neural network (Ctrl.NN) tools.