Experiments with the High Resolution Kaon Spectrometer at JLab Hall C and the new spectroscopy of ${}_{\Lambda }^{12}\text{B}$ hypernuclei

Since the pioneering experiment E89-009 studying hypernuclear spectroscopy using the $(e,e^{\prime }{K}^{+})$ reaction was completed, two additional experiments, E01-011 and E05-115, were performed at Jefferson Lab. These later experiments used a modified experimental design, the “tilt method,” to dramatically suppress the large electromagnetic background, and allowed for a substantial increase in luminosity. Additionally, a new kaon spectrometer, HKS (E01-011), a new electron spectrometer, HES, and a new splitting magnet (E05-115) were added to produce new data sets of precision, high-resolution hypernuclear spectroscopy. All three experiments obtained a spectrum for ${}_{\Lambda }^{12}\mathrm{B}$, which is the most characteristic $p$-shell hypernucleus and is commonly used for calibration. Independent analyses of these different experiments demonstrate excellent consistency and provide the clearest level structure to date of this hypernucleus as produced by the $(e,e^{\prime }{K}^{+})$ reaction. This paper presents details of these experiments, and the extraction and analysis of the observed ${}_{\Lambda }^{12}\mathrm{B}$ spectrum.

Figure 1

Schematic illustration of the experimental setup, technique, and upgrades for the Hall C HKS hypernuclear spectroscopy experiments E01-011 (top) and E05-115 (bottom).

Figure 2

The coincidence time spectra with a sequence of the kaon identification cuts.

Figure 3

The two-dimensional correlation between the derived mass squared and the coincidence time without the AČ and WČ cuts. After the AČ and WČ cuts, the three rows of pulse trains were clearly separated.

Figure 4

The HKS focal plane $Y$ vs $X$ correlations for the events selected from the seventh column of the SS holes. Blue denotes simulated data and magenta denotes real data. (a) Before field correction and (b) after field correction.

Figure 5

The reconstructed real HES and HKS SS events at the SS plate in comparison to the actual geometry of the SS holes. (a),(c) Before field correction and (b),(d) after field correction.

Figure 6

The mass correlations of free $\Lambda$ and ${\Sigma }^0$ from protons, and the ground state of ${}_{\Lambda }^{12}\mathrm{B}$ from ${}^{12}\text{C}$, from the $(e,e^{\prime }{K}^{+})$ reaction.

Figure 7

Spectroscopy of free $\Lambda$ and ${\Sigma }^0$ by the $p(e,e^{\prime }{K}^{+})\Lambda$ reaction from the ${\text{CH}}_2$ target. The mass is presented in terms of $\Lambda$ binding energy.

Figure 8

Correlations of the reconstructed kinematics parameters ($P$, $X^{\prime }$, and $Y^{\prime }$ at the target) from both spectrometers to the calculated invariant masses of $\Lambda$ and ${\Sigma }^0$ from the E05-115 analysis. The E01-011 analysis shows similar features except with lower statistics.

Figure 9

Spectroscopy of ${}_{\Lambda }^{12}\mathrm{B}$ obtained by the ${}^{12}\text{C}(e,e^{\prime }{K}^{+})$ reaction from the ${\text{CH}}_2$ and ${}^{12}\text{C}$ targets from experiment E05-115. The same alignment procedure was followed for E01-011.

Figure 10

Spectroscopy of ${}_{\Lambda }^{12}\mathrm{B}$ from the E05-115 and E01-011 experiments. The area below the black line is the accidental background.

Figure 11

The level structures of ${}_{\Lambda }^{12}\mathrm{C}$ (a) and ${}_{\Lambda }^{12}\mathrm{B}$ (b) for the first four doublets (energies in keV). The levels of the core nuclei, ${}^{11}\text{C}$ (a) and ${}^{11}\text{B}$ (b), are also shown. The four observed $\gamma$ ray transitions for ${}_{\Lambda }^{12}\mathrm{C}$ [30] are shown together with the three deduced excitation energies. For comparison, the energies of the peaks No. 1-2, No. 2, and No. 3 are shown for ${}_{\Lambda }^{12}\mathrm{B}$ (Tables 3).