Spectroscopy of $A=9$ hyperlithium with the $(e,e^{\prime }{K}^{+})$ reaction

Missing mass spectroscopy with the ($e,e^{\prime }{K}^{+}$) reaction was performed at Jefferson Laboratory's Hall C for the neutron-rich $\mathrm{\Lambda }$ hypernucleus ${}_{\mathrm{\Lambda }}{}^9\mathrm{Li}$. The ground-state (g.s.) energy was obtained to be $B_{\mathrm{\Lambda }}^{\mathrm{g}.\mathrm{s}.}=8.84\pm 0.{17}^{\mathrm{stat}.}\pm 0.{15}^{\mathrm{sys}.}\mathrm{MeV}$ by using shell-model calculations of a cross-section ratio and an energy separation of the spin doublet states ($3/2_1^{+}$ and $5/2_1^{+}$). In addition, peaks that are considered to be states of $[{}^8\mathrm{Li}\left(3^{+}\right)\otimes s_{\mathrm{\Lambda }}=3/2_2^{+},1/2^{+}]$ and $[{}^8\mathrm{Li}\left(1^{+}\right)\otimes s_{\mathrm{\Lambda }}=5/2_2^{+},7/2^{+}]$ were observed at $E_{\mathrm{\Lambda }}\left(\mathrm{no}.2\right)=1.74\pm 0.{27}^{\mathrm{stat}.}\pm 0.{11}^{\mathrm{sys}.}$ and $E_{\mathrm{\Lambda }}\left(\mathrm{no}.3\right)=3.30\pm 0.{24}^{\mathrm{stat}.}\pm 0.{11}^{\mathrm{sys}.}\mathrm{MeV}$, respectively. The $E_{\mathrm{\Lambda }}\left(\mathrm{no}.3\right)$ is larger than shell-model predictions by a few hundred keV, and the difference would indicate that a ${}^5\mathrm{He}+t$ structure is more developed for the $3^{+}$ state than those for the $2^{+}$ and $1^{+}$ states in a core nucleus ${}^8\mathrm{Li}$ as a cluster model calculation suggests.

Figure 1

Differential cross section of the ${}^9\mathrm{Be}(e,e^{\prime }{K}^{+}){}_{\mathrm{\Lambda }}{}^9\mathrm{Li}$ reaction as a function of $-B_{\mathrm{\Lambda }}$. Events exceeding over the accidental coincidence background in the bound region ($-B_{\mathrm{\Lambda }}<0$) were analyzed in the present Letter.

Figure 2

Fit of the ${}^9\mathrm{Be}(e,e^{\prime }{K}^{+}){}_{\mathrm{\Lambda }}{}^9\mathrm{Li}$ spectrum by three Voigt functions after the accidental coincidence events obtained by the mixed event analysis (Fig. 1) was subtracted.

Figure 3

Comparison of the obtained excitation energy $E_{\mathrm{\Lambda }}$ of ${}_{\mathrm{\Lambda }}{}^9\mathrm{Li}$ with theoretical calculations [9, 34, 38] and experimental data taken at JLab Hall A [36, 37]. $E_{\mathrm{\Lambda }}$ was obtained with the assumption that the cross-section ratio of the $5/2^{+}$ state to that of the ground state $3/2^{+}$ is 5–7 and the doublet separation is 0.5–0.7 MeV [9, 31, 34].