Structure of neutron-rich He $\mathrm{\Lambda }$ hypernuclei using the cluster orbital shell model

We calculated the energy spectra of the neutron-rich He $\mathrm{\Lambda }$ hypernuclei with $A$ = 6 to 9 within the framework of an $\alpha +\mathrm{\Lambda }+Xn$ ($X$ = 1–4) cluster model using the cluster orbital shell model. The employed constituent particles reproduce their observed properties. For resonant states of core nuclei such as ${}^5\mathrm{He}$, ${}^6\mathrm{He}$, and ${}^7\mathrm{He}$, the complex scaling method is employed to obtain energies and decay widths. The calculated ground states of ${}_{\mathrm{\Lambda }}{}^6\mathrm{He}$ and ${}_{\mathrm{\Lambda }}{}^7\mathrm{He}$ are in good agreement with published data. The energy levels of ${}_{\mathrm{\Lambda }}{}^8\mathrm{He}$ and ${}_{\mathrm{\Lambda }}{}^9\mathrm{He}$ are predicted. In ${}_{\mathrm{\Lambda }}{}^9\mathrm{He}$, we find one deeply bound state and two excited resonant states, which are proposed to be produced at the Japan proton accelerator research complex (J-PARC) by the double-charge-exchange reaction $({\pi }^{-},K^{+})$ using a ${}^9\mathrm{Be}$ target.

Figure 1

Coordinate system of $\alpha +n+n+n+n+\mathrm{\Lambda }$ in the COSM.

Figure 2

The calculated energy spectra of the He isotope nuclei together with experimental data. Black lines are experimental data and red line are calculated values. The experimental data are taken in Refs. [30, 31, 32, 33, 34]. Numbers above the red lines are values of decay widths. The energies are measured with respect to $\alpha +Xn$ ($X$ = 1–4) threshold.

Figure 3

The calculated rms radii of ${}^6\mathrm{He}$ and ${}^8\mathrm{He}$ for matter ($R_{\mathrm{m}}$, circle) and charge ($R_{\mathrm{ch}}$, triangle) with red solid symbols together with experimental data. The data are taken from Refs. [35, 36, 37, 38, 39].

Figure 4

The calculated energy spectra of the He isotope hypenuclei. The energies are measured with respect to the ${}^A\mathrm{He}+\mathrm{\Lambda }$ ($A$ = 4,5,6,7,8) thresholds.