High resolution spectroscopic study of ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}$

Spectroscopy of a ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}$ hypernucleus was carried out at JLab Hall C using the $(e,e^{\prime }{K}^{+})$ reaction. A new magnetic spectrometer system (SPL+HES+HKS), specifically designed for high resolution hypernuclear spectroscopy, was used to obtain an energy spectrum with a resolution of $\sim 0.78$ MeV (FWHM). The well-calibrated spectrometer system of the present experiment using $p(e,e^{\prime }{K}^{+})\mathrm{\Lambda },{\mathrm{\Sigma }}^0$ reactions allowed us to determine the energy levels; and the binding energy of the ground-state peak (mixture of $1^{-}$ and $2^{-}$ states) was found to be $B_{\mathrm{\Lambda }}=8.55\pm 0.07\left(\mathrm{stat}.\right)\pm 0.11\left(\mathrm{sys}.\right)$ MeV. The result indicates that the ground-state energy is shallower than that of an emulsion study by about 0.5 MeV which provides valuable experimental information on the charge symmetry breaking effect in the $\mathrm{\Lambda }N$ interaction.

Figure 1

A schematic drawing of the JLab E05-115 experimental geometry. The setup consists of SPL, HKS, and HES spectrometers. An electron beam with the energy of 2.344 GeV is incident on the target located at the entrance of SPL. A $K^{+}$ and an $e^{\prime }$ with the momenta of $\sim 1$ GeV/$c$ are observed by HKS and HES, respectively.

Figure 2

Binding energy spectrum of ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}$. A distribution of an accidental coincidence between an $e^{\prime }$ and a $K^{+}$ was obtained by the mixed event analysis as described in the text.

Figure 3

Binding energy $\left(B_{\mathrm{\Lambda }}\right)$ and excitation energy $[E_{\mathrm{\Lambda }}\equiv -(B_{\mathrm{\Lambda }}-B_{\mathrm{\Lambda }}(\#1))]$ spectra for the ${}^{10}\mathrm{B}(e,e^{\prime }{K}^{+}){}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}$ reaction with a fitting result of Fit I. The ordinate axis is $\left(\overline{d\sigma /d{\mathrm{\Omega }}_K}\right)$ per 0.3 MeV.

Figure 4

Obtained energy levels of ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}$ (Fit I) compared to those of the theoretical calculations [23, 32, 33, 34]. The energy levels of ${}^9\mathrm{Be}$ [35] and ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{B}$ [31] are shown for comparison as well.

Figure 5

Binding energy $\left(B_{\mathrm{\Lambda }}\right)$ and excitation energy $[E_{\mathrm{\Lambda }}\equiv -(B_{\mathrm{\Lambda }}-B_{\mathrm{\Lambda }}(\#1))]$ spectra for the ${}^{10}\mathrm{B}(e,e^{\prime }{K}^{+}){}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}$ reaction with a fitting result of Fit II. The ordinate axis is $\left(\overline{d\sigma /d{\mathrm{\Omega }}_K}\right)$ per 0.3 MeV.

Figure 6

Binding energy differences of ${}_{\mathrm{\Lambda }}{}^7\mathrm{Li},{}_{\mathrm{\Lambda }}{}^9\mathrm{Be},{}_{\mathrm{\Lambda }}{}^{10}\mathrm{B}$, and ${}_{\mathrm{\Lambda }}{}^{13}\mathrm{C}$ between the emulsion experiments [16] and the $({\pi }^{+},K^{+})$ experiments [2] with the statistical errors. The values of $({\pi }^{+},K^{+})$ experiments were subtracted from those of the emulsion experiments. The obtained weighted mean was $+0.54\pm 0.05$ MeV as represented by a solid line. The plots should be on a line of zero (dashed line) if the binding energies measured in the $({\pi }^{+},K^{+})$ and emulsion experiments are consistent.