γ-ray spectroscopy of ${}_{\Lambda }^{16}$O and ${}_{\Lambda }^{15}$N hypernuclei via the ${}^{16}\mathrm{O}$($K^{-},{\pi }^{-}\gamma$) reaction

The bound-state level structures of the ${}_{\Lambda }^{16}$O and ${}_{\Lambda }^{15}$N hypernuclei were studied by γ-ray spectroscopy using a germanium detector array (Hyperball) via the ${}^{16}\mathrm{O}$ ($K^{-},{\pi }^{-}\gamma$) reaction. A level scheme for ${}_{\Lambda }^{16}$O was determined from the observation of three γ-ray transitions from the doublet of states ($2^{-},1^{-}$) at $~6.7$ MeV to the ground-state doublet ($1^{-},0^{-}$). The ${}_{\Lambda }^{15}$N hypernuclei were produced via proton emission from unbound states in ${}_{\Lambda }^{16}$O. Three γ rays were observed, and the lifetime of the $1/2^{+};1$ state in ${}_{\Lambda }^{15}$N was measured by the Doppler shift attenuation method. By comparing the experimental results with shell-model calculations, the spin dependence of the $\Lambda N$ interaction is discussed. In particular, the measured ${}_{\Lambda }^{16}$O ground-state doublet spacing of $26.4\pm 1.6\pm 0.5$ keV determines a small but nonzero strength of the $\Lambda N$ tensor interaction.

Figure 1

Expected level schemes and γ-ray transitions of ${}_{\Lambda }^{16}$O and ${}_{\Lambda }^{15}$N from the ${}^{16}\mathrm{O}$($K^{-},{\pi }^{-}$) reaction. The $1^{-}$ states and $0^{+}$ states of ${}_{\Lambda }^{16}$O (thick lines) are most strongly populated by this reaction. The superscript $a$ shows excitation energies from the present experiment, $b$ from Ref. [19], and $c$ from Ref. [27]. The particle-decay thresholds, except for ${}_{\Lambda }^{15}$N$+p$ and ${}_{\Lambda }^{15}$O$+n$ (see text), are determined from emulsion data [30] assuming $B_{\Lambda }=13.21$ MeV for ${}_{\Lambda }^{16}$O. The $0^{+}$ and $2^{+}$ states in ${}_{\Lambda }^{16}$O can decay to all the low-lying $3/2^{+}$ and $1/2^{+}$ states in ${}_{\Lambda }^{15}$N via $s$- and $d$-wave proton emission.

Figure 2

Angular distributions, calculated in the DWIA [25], for the ${}^{16}\mathrm{O}$$(K^{-},{\pi }^{-}){}_{\Lambda }^{16}$O reaction at $p_K=900$ MeV/$c$ as a function of the laboratory reaction angle ${\theta }_{K\pi }$. The cross sections are for the (i) $0_1^{+}$, (ii) $0_3^{+}$, (iii) $1_2^{-}$, and (iv) $2_2^{+}+2_3^{+}$ states shown in Fig. 1. For the $0_2^{+},1_1^{-}$, and $2_1^{+}$ states, the cross sections for (i), (iii), and (iv) should be multiplied by 1.65, 0.61, and 0.60, respectively. These different angular distribution patterns will be used later in Secs. 5a2 and 5b2 for the assignment of observed γ transitions.

Figure 3

Schematic view of the experimental setup (side view). The 48D48 is a dipole magnet; ID's, FD's, and BD's are drift chambers; IT, FV, and BT are plastic scintillation counter hodoscopes with IT and BT used to measure time of flight; and IC1, IC2, and FC are aerogel Čerenkov counters with $n=1.03$. The Hyperball consisted of 14 sets of Ge detectors, each surrounded by six BGO counters. A ${}^{60}\mathrm{Co}$ pulser was used to monitor the Ge detector live time between the beam-on and beam-off periods and consisted of a 1 kBq ${}^{60}\mathrm{Co}$ source encapsulated together with a plastic scintillation counter. γ-ray events were selected by hits in a Ge detector without hits in the BGO counters. The 20 g/cm${}^2$ H${}_2$O target was irradiated with $4\times {10}^{10}$ kaons.

Figure 4

Missing-mass spectrum for the ${}^{16}\mathrm{O}$($K^{-},{\pi }^{-}$) reaction plotted against the Λ binding energy ($B_{\Lambda }$) for those events accompanying γ rays with energies of 1.5–7.0 MeV. The indicated regions show the definitions of the $1_2^{-}$ state region ($-17<-B_{\Lambda }<3$ MeV), the $p_n^{-1}{p}_{\Lambda }$ states region ($-12<-B_{\Lambda }<14$ MeV), and the highly unbound region ($-B_{\Lambda }>50$ MeV).

Figure 5

Simulated reaction angle (${\theta }_{K\pi }$) dependent acceptance of the scattered-particle spectrometer. Differences in acceptance for the $1_2^{-}$ ($E_x=6.6$ MeV) and $0_2^{+}$ ($E_x=17.1$ MeV) states of ${}_{\Lambda }^{16}$O are negligibly small. Momentum transfers $q$ (MeV/$c$) for these states corresponding to the reaction angles are also shown. Events with reaction angles less than $2^{°}$ were rejected in the off-line analysis.

Figure 6

(a) TDC spectrum for a typical Ge detector plotted for γ-ray energies over 1.5 MeV. (b) and (c) are the γ-ray energy spectra plotted for the highly-unbound region in ${}_{\Lambda }^{16}$O with the prompt and delayed timing cuts shown in (a), respectively.

Figure 7

Simulated peak shapes of γ rays emitted from recoiling ${}_{\Lambda }^{16}$O, produced by the ${}^{16}\mathrm{O}$ ($K^{-},{\pi }^{-}$) reaction, assuming a γ-ray energy of 6.55 MeV. The figure shows (i) not broadened (original response function), (ii) fully Doppler-broadened (before correction), and (iii) Doppler-shift-corrected peak shapes.

Figure 8

Simulated peak shapes for 2-MeV γ rays from ${}_{\Lambda }^{15}$N following proton emission from the ${}_{\Lambda }^{16}$O($0_2^{+}$) state produced via the ${}^{16}\mathrm{O}$ ($K^{-},{\pi }^{-}$) reaction. Figure (a) shows the (i) fully Doppler-broadened and (ii) Doppler-shift-corrected peak shapes. Figure (b) shows the lifetime dependence of the peak shape, (iii) $\tau \gg$ stopping time (no broadening, original response function), (iv) $\tau =1.5$ ps, and (v) $\tau =0.5$ ps.

Figure 9

Mass-gated γ-ray spectra measured in the ${}^{16}\mathrm{O}$($K^{-},{\pi }^{-}$) reaction at ${\theta }_{K\pi }>2^{°}$ for (a) the highly unbound region ($-B_{\Lambda }>50$ MeV), (b) the $1_2^{-}$ state region ($-17<-B_{\Lambda }<3$ MeV), and (c) the same spectrum as in (b) but with event-by-event Doppler-shift corrections applied. A structure around 6.5–6.6 MeV in (b) becomes two narrow peaks after Doppler-shift correction. The two peaks are assigned as $M1(1_2^{-}\to 1_1^{-},0^{-})$ transitions. Single-escape (SE) peaks from these $M1$ transitions can also be seen in (c), and likewise SE γ-ray peaks from ${}^{15}\mathrm{O}$(6175 keV) and ${}^{16}\mathrm{O}$(6129 keV) in (a). Inset in (c) shows the Doppler-corrected spectrum for a narrower mass cut ($-13<-B_{\Lambda }<-1$ MeV) which is set to maximize the signal-to-noise ratio for the 6534- and 6560-keV γ-ray peaks. A gathering of events with a statistical significance $3\sigma$ from background appears at 6758 keV.

Figure 10

Reaction angle (${\theta }_{K\pi }$) dependence of the ${}_{\Lambda }^{16}$O $\gamma$-ray intensities (sum of the 6534- and 6560-keV γ rays) from the $1_2^{-}$ state in ${}_{\Lambda }^{16}$O measured in the ${}^{16}\mathrm{O}$($K^{-},{\pi }^{-}$) reaction for the $1_2^{-}$ state region ($-17<-B_{\Lambda }<3$ MeV) defined in Fig. 4. Shown are the γ-ray counts divided by the solid angle taking into account the spectrometer acceptance (Fig. 5).

Figure 11

Missing-mass spectra measured in the ${}^{16}\mathrm{O}$($K^{-},{\pi }^{-}$) reaction plotted against the Λ binding energy ($B_{\Lambda }$) for events accompanying a γ ray with $E_{\gamma }$(cor.) = 6500–6600 keV for (a) $2^{°}<{\theta }_{K\pi }<{16}^{°}$, (b) $2^{°}<{\theta }_{K\pi }<8^{°}$, and (c) $8^{°}<{\theta }_{K\pi }<{16}^{°}$. The dotted lines show the expected background shapes plotted for events accompanying γ rays with $E_{\gamma }$(cor.) = 6600–7000 keV and scaled to fit the background region ($-90<-B_{\Lambda }<-40$ MeV).

Figure 12

Mass-gated γ-ray spectra from the ($K^{-},{\pi }^{-}$) reaction on the 20 g/cm${}^2$ H${}_2$O target. (a) and (c) are plotted for the highly unbound region ($-B_{\Lambda }>50$ MeV); (b), (d), and (e), for the $p_n^{-1}{p}_{\Lambda }$-states region. (e) is the spectrum with event-by-event Doppler-shift corrections applied to (d). Three γ-ray peaks, a narrow peak at 2268 keV in (d) and Doppler-broadened peaks at 1961 and 2442 keV in (d), which become narrower peaks in (e), are assigned as γ rays from ${}_{\Lambda }^{15}$N. (f) is a γ-γ coincidence spectrum plotted for $-6<-B_{\Lambda }<50$ MeV. The solid line is the spectrum of γ rays accompanied by another γ ray with $E_{\gamma }$(cor.) = $2442\pm 25$ keV, as shown in the inset. The shaded region in (f), which shows the background level, is the spectrum of γ rays accompanied by another γ ray with $E_{\gamma }$(cor.) = 2600–4000 keV, and with the counts scaled to the γ-ray counts at $2442\pm 25$ keV.

Figure 13

Reaction angle (${\theta }_{K\pi }$) dependence of the ${}_{\Lambda }^{15}$N $\gamma$ ray intensities measured in the ${}^{16}\mathrm{O}$($K^{-},{\pi }^{-}$) reaction for the $p_n^{-1}{p}_{\Lambda }$-states mass region ($-12<B_{\Lambda }<14$ MeV) in ${}_{\Lambda }^{16}$O. The panels show the relative intensities of (a) 2268-keV, (b) 2442-keV, and (c) 1961-keV γ rays. Relative intensities were obtained by dividing the measured γ-ray counts by the spectrometer acceptance (Fig. 5). The relative γ-ray efficiencies are normalized to that of the 6550-keV γ ray.

Figure 14

Missing-mass spectra for the ${}^{16}\mathrm{O}$($K^{-},{\pi }^{-}$) reaction as a function of Λ binding energy ($B_{\Lambda }$). The solid lines are plotted for those events accompanying γ rays in the energy range $E_{\gamma }=2268\pm$ 8 keV for (a), (b), and (c), $E_{\gamma }$(cor.) $=2442\pm 16$ keV for (d), (e), and (f), and $E_{\gamma }$(cor.) $=1961\pm 16$ keV for (g), (f), and (i). The reaction angles covered are $2^{°}<{\theta }_{K\pi }<{16}^{°}$ for (a), (d), and (g), $2^{°}<{\theta }_{K\pi }<8^{°}$ for (b), (e), and (f), and $8^{°}<{\theta }_{K\pi }<{16}^{°}$ for (c), (f), and (i). The dashed lines show the expected background shapes for the corresponding reaction angles, determined from the events accompanying γ rays with energies from 2500 to 3000 keV after scaling to fit the background region ($-90<-B_{\Lambda }<-30$ MeV).

Figure 15

Upper limit for the $B(M1)$ ratio between the $1/2^{+};1\to 1/2_1^{+}$ and $1/2^{+};1\to 3/2_1^{+}$ transitions as a function of the ground-state doublet spacing, $E(3/2_1^{+})-E(1/2_1^{+})$, and the $1/2^{+};1\to 1/2_1^{+}$ transition energy. The thick line is the result of a peak search for the $1/2^{+};1\to 1/2_1^{+}$ transition obtained by fitting the spectrum from 2000 to 2370 keV [Fig. 12]. The dashed line is from the same procedure but with the “prompt” TDC cut. The thin line is the result of a peak search for the $1/2_1^{+}\to 3/2_1^{+}$ transition obtained by fitting the spectrum from 100 to 270 keV [Fig. 12].

Figure 16

Experimentally determined level scheme of ${}_{\Lambda }^{16}$O and observed γ-ray transitions. The corresponding level scheme of ${}^{15}\mathrm{O}$ is also shown.

Figure 17

Experimentally determined level scheme of ${}_{\Lambda }^{15}$N and observed γ-ray transitions (solid arrows). The corresponding level scheme of the ${}^{14}\mathrm{N}$ core nucleus is also shown. Since the spin ordering of the ground-state doublet is not determined, the excitation energies of ${}_{\Lambda }^{15}$N are given as level spacings from the $3/2_1^{+}$ state. The existence of the 4229-keV excited state was not experimentally determined, but the 1961-keV γ ray is likely a transition to the $1/2^{+};1$ state.