Resonant states of the neutron-richΛhypernucleusHeΛ7

Abstract

The structure of the neutron-rich $\mathrm{\ensuremath{\Lambda}}$ hypernucleus, $_{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{He}$ is studied within the framework of an $\ensuremath{\alpha}+\mathrm{\ensuremath{\Lambda}}+n+n$ four-body cluster model. We predict second $3/{2}^{+}$ and $5/{2}^{+}$ states, corresponding to a $0s\phantom{\rule{4pt}{0ex}}\mathrm{\ensuremath{\Lambda}}$ coupled to the second ${2}^{+}$ state of $^{6}\mathrm{He}$, as narrow resonant states with widths of $\mathrm{\ensuremath{\Gamma}}\ensuremath{\sim}1$ MeV to be at 0.03 and 0.07 MeV with respect to the $\ensuremath{\alpha}+\mathrm{\ensuremath{\Lambda}}+n+n$ threshold. From a separate estimate of the differential cross section for the ${}^{7}\mathrm{Li}(\ensuremath{\gamma},{K}^{+})_{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{He}$ reaction, we suggest a possibility to observe these states at the Thomas Jefferson National Accelerator Facility (JLab) in the future. We also calculate the second ${2}^{+}$ state of $^{6}\mathrm{He}$ as a resonant state within the framework of an $\ensuremath{\alpha}+n+n$ three-body cluster model. Our result is $2.81$ MeV with $\mathrm{\ensuremath{\Gamma}}=4.63$ MeV with respect to the $\ensuremath{\alpha}+n+n$ threshold. This energy position is $\ensuremath{\sim}1$ MeV higher, and with a much broader decay width, than the recent SPIRAL data. We suggest that an experiment at JLab to search for the second $3/{2}^{+}$ and $5/{2}^{+}$ states of $_{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{He}$ would provide an opportunity to confirm the second ${2}^{+}$ state of the core nucleus $^{6}\mathrm{He}$.