Spectroscopy of ${}_{\Lambda }{}^9\mathrm{Li}$ by electroproduction

Background: In the absence of accurate data on the free two-body hyperon-nucleon interaction, the spectra of hypernuclei provides information on the details of the effective hyperon-nucleon interaction.

Purpose: To obtain a high-resolution binding-energy spectrum for the ${}^9\mathrm{Be}(e,e^{\prime }{K}^{+}){}_{\Lambda }{}^9\mathrm{Li}$ reaction.

Method: Electroproduction of the hypernucleus ${}_{\Lambda }{}^9\mathrm{Li}$ has been studied for the first time with sub-MeV energy resolution in Hall A at Jefferson Lab on a ${}^9\mathrm{Be}$ target. In order to increase the counting rate and to provide unambiguous kaon identification, two superconducting septum magnets and a ring imaging Cherenkov detector were added to the Hall A standard equipment.

Results: The cross section to low-lying states of ${}_{\Lambda }{}^9\mathrm{Li}$ is concentrated within 3 MeV of the ground state and can be fit with four peaks. The positions of the doublets agree with theory while a disagreement could exist with respect to the relative strengths of the peaks in the doublets. The $\Lambda$ separation energy, $B_{\Lambda }$, of $8.36\pm 0.08$ (stat.) $\pm 0.08$ (syst.) MeV was measured, in agreement with an earlier experiment.

Figure 1

The calculated spectrum of ${}_{\Lambda }{}^9\mathrm{Li}$. The ${}^8\mathrm{Li}$ core states are shown on the left along with the spectroscopic factors for proton removal from ${}^9\mathrm{Be}.$ All excitation energies are in keV. On the right, the factors giving the relative population of levels in purely non-spin-flip $(\Delta S=0)$ and purely spin-flip $(\Delta S=1)$ production reactions on ${}^9\mathrm{Be}$ are given.

Figure 2

The binding-energy spectrum obtained after kaon selection with aerogel detectors and RICH in (a) the whole energy range and (b) restricted to the region of interest.

Figure 3

The ${}_{\Lambda }{}^9\mathrm{Li}$ differential cross section as a function of the binding energy. Experimental points vs Monte Carlo results (red curve) and vs Monte Carlo results with radiative effects turned off (blue histogram).

Figure 4

The radiatively unfolded experimental spectrum compared to a theoretical prediction (thin green line). The solid black line represents a fit to the data with four Gaussians of a common width. The theoretical curve was calculated with the width extracted from the fit (FWHM = 730 keV).

Figure 5

One peak of the excitation energy spectrum of the hypernucleus ${}_{\Lambda }{}^9\mathrm{Li}$ obtained through the reaction ${}^9\mathrm{Be}{(e,e^{\prime }{K}^{+})}_{\Lambda }^9\text{Li}$ as predicted by the Monte Carlo SIMC when including all effects (red curve) and “turning off” the radiative effects (blue curve). Arbitrary units. The position of the peak has been made coincident with the ground state.

Figure 6

${}_{\Lambda }{}^9\mathrm{Li}$ excitation energy spectra as predicted by the Monte Carlo SIMC for the peak configurations $\alpha ,\beta ,\gamma ,\delta$, and $\epsilon$ quoted in Table 4 [panels (a)–(e), respectively].

Figure 7

${}_{\Lambda }{}^9\mathrm{Li}$ excitation energy spectra as predicted by the Monte Carlo SIMC for the peak configurations $\alpha ,\beta ,\gamma ,\delta$, and $\epsilon$ quoted in Table 4, when the radiative effects are “turned off” [panels (a)–(e), respectively].

Figure 8

(a) The spectrum of the configuration $\alpha$ (dashed line) and of the configuration $\gamma$ (continuous line) as predicted by the Monte Carlo SIMC when the radiative effects are turned off. (b) The statistical errors (error bars) and the systematic errors (full band) as a function of the excitation energy. The systematic error was defined as the difference between the dashed line and the continuous line of panel (a); see text for details.