Prediction for a Four-Neutron Resonance

We utilize various ab initio approaches to search for a low-lying resonance in the four-neutron ($4n$) system using the JISP16 realistic $NN$ interaction. Our most accurate prediction is obtained using a $J$-matrix extension of the no-core shell model and suggests a $4n$ resonant state at an energy near $E_r=0.8\mathrm{MeV}$ with a width of approximately $\mathrm{\Gamma }=1.4\mathrm{MeV}$.

Figure 1

NCSM results for the tetraneutron ground state energy obtained with various $N_{\max }$ (symbols) plotted as functions of $\hslash \mathrm{\Omega }$ (upper panel). The shaded area shows the NCSM result selection for the $S$-matrix parametrization; the solid curves are obtained from the phase shifts parametrized with a single resonance pole by solving Eq. (2) for the eigenenergies at given $N_{\max }$ and $\hslash \mathrm{\Omega }$ values. The $4\to 4$ phase shifts obtained directly from the NCSM results using Eq. (2) are shown in the lower panel.

Figure 2

The $4\to 4$ scattering phase shifts: parametrization with a single resonance pole (solid line) and obtained directly from the selected NCSM results using Eq. (2) (symbols). The dashed line shows the contribution of the resonance term.

Figure 3

The same as Fig. 2 but for the parametrization with resonance and false state poles. The dashed-dotted line shows the contribution of the false state pole term.