Strong dineutron correlation in ${}^8\mathrm{He}$ and ${}^{18}\mathrm{C}$

We study the spatial structure of four valence neutrons in the ground state of ${}^8\mathrm{He}$ and ${}^{18}\mathrm{C}$ nuclei using a core$+4n$ model. For this purpose, we employ a density-dependent contact interaction among the valence neutrons, and solve the five-body Hamiltonian in the Hartree-Fock-Bogoliubov (HFB) approximation. We show that two neutrons with the coupled spin of $S=0$ exhibit a strong dineutron correlation around the surface of these nuclei, whereas the correlation between the two dineutrons is much weaker. Our calculation indicates that the probability of the ($1p_{3/2}){}^4$ and [$(1p_{3/2}){}^2(p_{1/2}){}^2$] configurations in the ground state wave function of ${}^8\mathrm{He}$ nucleus is 34.9% and 23.7%, respectively. This is consistent with the recent experimental finding with the ${}^8\mathrm{He}$($p,t){}^6\mathrm{He}$ reaction, that is, the ground state wave function of ${}^8\mathrm{He}$ deviates significantly from the pure ($1p_{3/2}){}^4$ structure.

Figure 1

The $S=0$ component of the two-particle density for ${}^6\mathrm{He}$ as a function of $r_1=r_2=r$ and the angle between the valence neutrons, θ. The top panel shows the exact solution of the three-body model, while the middle panel is obtained with the HFB method. The bottom panel shows the result of the HFB+particle number projection.

Figure 2

Same as Fig. 1, but with a multiplicative factor of $8{\pi }^2{r}^4\sin \theta$.

Figure 3

The mean-field potential for ${}^8\mathrm{He}$ (the upper panel) and for ${}^{18}\mathrm{C}$ (the lower panel). The dashed line shows the neutron-core potential, $V_{\mathit{nC}}$, while the solid line is for the total mean-field potential in the solution of the HFB equations.

Figure 4

The two-particle density, ${\rho }_2(r,\hat{\mathit{r}}=0,\uparrow ;r,\hat{\mathit{r}},\downarrow )$, for the ${}^8\mathrm{He}$ nucleus as a function of $r_1=r_2=r$ and the relative angle θ between a spin-up and a spin-down neutrons (the top panel). The middle panel shows the same two-particle density multiplied by a factor $8{\pi }^2{r}^4\sin \theta$, while the bottom panel is for the four-particle density for the dineutron-dineutron configuration.

Figure 5

Same as Fig. 4, but for ${}^{18}\mathrm{C}$.

Figure 6

Same as Fig. 4, but for the uncorrelated [($1p_{3/2}){}^4$] configuration for the ${}^8\mathrm{He}$ nucleus.

Figure 7

Same as Fig. 5, but for the uncorrelated [($1d_{5/2}){}^4$] configuration for the ${}^{18}\mathrm{C}$ nucleus.

Figure 8

The four-particle density of ${}^8\mathrm{He}$ for the dineutron-dineutron configuration when the first dineutron is on the $z$-axis. The top, middle, and bottom panels correspond to the cases where the first dineutron is at $z=1.5,2.5$, and 3.5 fm, respectively.

Figure 9

Same as Fig. 8, but for ${}^{18}\mathrm{C}$.