Observation of the Exotic $0_2^{+}$ Cluster State in ${}^8\mathrm{He}$

We report here the first observation of the $0_2^{+}$ state of ${}^8\mathrm{He}$, which has been predicted to feature the condensatelike $\alpha +{}^{2}n+{}^{2}n$ cluster structure. We show that this state is characterized by a spin parity of $0^{+}$, a large isoscalar monopole transition strength, and the emission of a strongly correlated neutron pair, in line with theoretical predictions. Our finding is further supported by the state-of-the-art microscopic $\alpha +4n$ model calculations. The present results may lead to new insights into clustering in neutron-rich nuclear systems and the pair correlation and condensation in quantum many-body systems under strong interactions.

Figure 1

(a) Correlated plot between $\cos ({\theta }_{nn})$ and $|\cos ({\psi }_{nn})|$, exhibiting distinct behaviors in the small- and large-$|\cos ({\psi }_{nn})|$ regions. (b) $|\cos ({\psi }_{nn})|$ spectrum compared to simulations of different $2n$-emission processes (details in text).

Figure 2

(a) $E_r$ spectra for $({\mathrm{CH}}_2{)}_n$ and carbon targets (c.m. scattering angle ${\theta }_{\mathrm{c}.\mathrm{m}.}<2°$), fitted using a Gaussian peak and a second-order polynomial background, modified by the acceptance. Error bars are statistical only (1 s.d.). Negligible contribution from the target frame was checked with the empty target data. (b) Angular distribution of the 4.5-MeV state for the $({\mathrm{CH}}_2{)}_n$ target. Horizontal error bars stand for the bin size and vertical ones for the combined statistical and systematic uncertainties. The curves show the least-square fitting with DWBA calculations convoluted with the resolution ($\sigma =0.2°$). A spin parity of $0^{+}$ is clearly supported due to the much smaller ${\chi }^2$ (0.9) compared to $1^{-}$ (11.4) and $2^{+}$ (13.6).

Figure 3

$\cos ({\theta }_{nn})$ spectrum of ${}^8\mathrm{He}(0_2^{+})$, compared to simulations of different decay models (details in text). The gates $|\cos ({\psi }_{nn})|<0.65$ and ${\theta }_{\mathrm{c}.\mathrm{m}.}<2°$ are applied to reduce the background. Error bars are statistical only (1 s.d.).

Figure 4

(a) Overlap of the ${}^8\mathrm{He}(0_2^{+})$ wave function with the ${}^{2}n$-condensate THSR wave functions $\mathrm{\Phi }(\mathit{B},b_n)$ specified by $B$ and $b_n$ (illustration in the inset). The cutoff in the upper left corner originates from the forbidden states of $\mathrm{\Phi }(\mathit{B},b_n)$. (b) $M(\mathrm{IS}0)$ of ${}^8\mathrm{He}(0_2^{+})$). Our data are presented as the blue-solid line with a shaded band showing the combined statistical and systematic uncertainty, and compared to calculations of COSM [62], AMD [9], the ${}^{2}n$ cluster model [10], and our microscopic $\alpha +4n$ model.