Lightest neutral hypernuclei with strangeness $-1$ and $-2$

Our current knowledge of the baryon-baryon interaction suggests that the dineutron $(n,n)$ and its strange analog $(n,\Lambda )$ are unstable. In contrast, the situation is more favorable for the strange three-body system $(n,n,\Lambda )$, and even better for the four-body system $T\equiv (n,n,\Lambda ,\Lambda )$ with strangeness $-2$, which is likely to be stable under spontaneous dissociation. The recent models of the hyperon-nucleon and hyperon-hyperon interactions suggest that the stability of the $(n,n,\Lambda )$ and $T$ is possible within the uncertainties of our knowledge of the baryon-baryon interactions. This new nucleus $T$ could be produced and identified in central deuteron-deuteron collisions viathe reaction $d+d\to T+K^{+}+K^{+}$, and the tetrabaryon $T$ could play an important role in catalyzing the formation of a strange core in neutron stars.

Figure 1

Domain in which binding is forbidden for a $(m,m,M)$ (a) or $(m,m,M,M)$ (b) system. The scale is set such that the pair $(m_i,m_j)$ is bound for $g_{ij}>1$. This drawing corresponds to $M/m=1.2$.

Figure 2

Three-body energy $E_3$ as a function of the two-body effective range parameter $r_{\mathrm{eff}}$, for the exponential, Yukawa and Morse (with $R=0.6$) potentials, where $g$ and $\mu$ are linked to reproduced a two-body scattering length $a=-10$.

Figure 3

Mechanism for $T$ production in $dd$ collisions.

Figure 4

Total cross section for $d+d\to K^{+}+K^{+}+(n,n,\Lambda ,\Lambda$). From upper to lower the curves stand for the total cross sections of the full calculations, exclusive process from the nucleon Born terms, exclusive process from the double $S_{11}\left(1535\right)$ excitations, and exclusive process from the one Born transition and one $S_{11}\left(1535\right)$ excitation.

Figure 5

The missing mass spectra for the recoiled $(n,n,\Lambda ,\Lambda )$ at different energies above the production threshold in $d+d\to K^{+}+K^{+}+(n,n,\Lambda ,\Lambda )$.