application/xml7ΛLi ground-state spin determined by the yield of γ-rays subsequent to weak decayJ SasaoD AbeH AkikawaK ArakiH BhangT EndoY FujiiT FukudaO HashimotoK ImaiH HotchiY KakiguchiJ.H KimY.D KimT MiyoshiT MurakamiT NagaeH NoumiH OutaK OzawaT SaitoY SatoS SatohR SawaftaM SekimotoT TakahashiH TamuraL TangK TanidaH.H XiaS.H ZhouL.H ZhuΛ hypernucleiMesonic decayγ spectroscopyΛN interactionPhysics Letters B 579 (2004) 258-264. doi:10.1016/j.physletb.2003.11.022journalPhysics Letters BCopyright © 2003 Elsevier B.V. All rights reserved.Elsevier B.V.0370-26935793-422 January 20042004-01-22258-26425826410.1016/j.physletb.2003.11.022http://dx.doi.org/10.1016/j.physletb.2003.11.022doi:10.1016/j.physletb.2003.11.022http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/JournalsS300.3PLB20461S0370-2693(03)01745-310.1016/j.physletb.2003.11.022Elsevier B.V.ExperimentsFig. 1Hypernuclear mass spectrum of 7ΛLi, in the scale of Λ binding energy BΛ, taken by the (π+,K+) reaction with a 25 cm thick 7Li target. The “bound region” of 7ΛLi is defined as −10<−BΛ<2 MeV. The spectrum was decomposed into four Gaussians, a quasi-free continuum, and a constant background (see text).Fig. 2γ-ray spectra measured in the 7Li(π+,K+) reaction (a) for the bound region (−10<−BΛ<2 MeV) and (b) for the unbound region (−BΛ>2 MeV) of 7ΛLi. The insets show the spectra expanded around 400–500 keV. The two peaks at 429 and 478 keV observed in (a) are attributed to the transitions from the first excited states of 7Be and 7Li, respectively. In (b), only the 478 keV peak was observed. The region around these peaks were fitted with three Gaussians and a linear background.Fig. 3Scheme of γ transitions and mesonic weak decays of 7ΛLi. The ground state of 7ΛLi decays into 7Be or 7Li through the π− or π0 mesonic weak decays, respectively. When 7ΛLi decays into the first excited states of 7Be or 7Li, γ-rays of 429 or 478 keV are emitted, respectively.7ΛLi ground-state spin determined by the yield of γ-rays subsequent to weak decayJSasaoaDAbeaHAkikawab1KArakiaHBhangcTEndoaYFujiiaTFukudad2OHashimotoaKImaibHHotchie1YKakiguchidJ.HKimcY.DKimfTMiyoshia3TMurakamibTNagaedHNoumidHOutad4KOzawaaTSaitogYSatoa5SSatohaRSawaftahMSekimotodTTakahashiaHTamuraatamura@lambda.phys.tohoku.ac.jpLTangiKTanidae4H.HXiajS.HZhoujL.HZhubjaDepartment of Physics, Tohoku University, Sendai 980-8578, JapanbDepartment of Physics, Kyoto University, Kyoto 606-8502, JapancDepartment of Physics, Seoul National University, Seoul 151-742, South KoreadInstitute of Particle and Nuclear Studies, KEK, Tsukuba 305-0801, JapaneDepartment of Physics, University of Tokyo, Tokyo 113-0033, JapanfDepartment of Physics, Sejong University, Seoul 143-747, South KoreagLaboratory of Nuclear Science, Tohoku University, Sendai 980-0826, JapanhPhysics Department, North Carolina A&T State University, Greensboro, NC 27411, USAiDepartment of Physics, Hampton University, Hampton, VA 23668, USAjDepartment of Nuclear Physics, China Institute of Atomic Energy, P.O. Box 275(80), Beijing 102413, China1Present address: Center for Proton Accelerator Facilities, Japan Atomic Energy Research Institute, Tokai 319-1195, Japan.2Present address: Laboratory of Physics, Osaka Electro-Communication University, Neyagawa 572-8530, Japan.3Present address: Department of Physics, University of Houston, Houston, TX 77204-5506, USA.4Present address: Institute of Physical and Chemical Research (RIKEN), Wako 351-0198, Japan.5Present address: Institute of Particle and Nuclear Studies, KEK, Tsukuba 305-0801, Japan.Editor: J.P. SchifferAbstractUsing a large-acceptance germanium detector array (Hyperball), we measured a γ-ray spectrum in coincidence with production of 7ΛLi bound states in the 7Li(π+,K+) reaction. We observed a γ-ray peak at 429 keV due to the transition from the first excited state of 7Be produced by the weak decay of 7ΛLi, 7ΛLi→7Be∗(1/2−,429 keV)+π−. From the yield of this γ-ray, the branching ratio of the 7ΛLi weak decay to 7Be∗(429) was obtained to be (6.0+1.3−1.6)×10−2. Compared with theoretically calculated values of the partial decay rates, the measurement indicates that the ground-state spin of 7ΛLi is 1/2 but not 3/2.PACS21.80.+a13.30.Eg13.75.Ev21.30.Fe23.20.LvKeywordsΛ hypernucleiMesonic decayγ spectroscopyΛN interaction1IntroductionGround-state spins have particular importance for hypernuclei, because they reflect strengths of spin-dependent interactions between a hyperon and a nucleon. Low-lying level structure of Λ hypernuclei can be understood from a weak coupling of a Λ particle in the s-orbit and a core nucleus; each level of the core nucleus (spin J (≠0)) is split into two levels (J+1/2 and J−1/2). The order and the spacing of these two levels are determined by the ΛN spin-dependent (spin–spin, spin–orbit, and tensor) interactions [1,2]. Experimental determinations of not only the energy spacing of the doublet but also their spins are necessary to obtain information on the ΛN spin-dependent interactions.Recently, we have developed a technique of high-resolution hypernuclear γ spectroscopy using a germanium detector array, Hyperball, and measured the energy spacing of the ground-state doublet of 7ΛLi (3/2+,1/2+) by observing the spin–flip M1 transition between the members of the doublet [3]. The yield of this γ-ray suggested that the lower state of the doublet (the ground state) is 1/2+, and the strength of the ΛN spin–spin interaction (the parameter Δ) was derived to be Δ=+0.5 MeV based on this spin assignment. Since the other assignment gives the opposite sign and a different magnitude of the spin–spin interaction strength, it is desirable to determine the spin with another independent method.The ground-state spins of hypernuclei can be experimentally determined using the property of π-mesonic weak decay of Λ that the s-wave (spin–non-flip) amplitude is three times larger than the p-wave (spin–flip) amplitude [4,5]. It has been used to determine the ground-state spins of 3ΛH, 4ΛH, 4ΛHe, 8ΛLi, 11ΛB, and 12ΛB [4,6–12]. The branching ratios of the mesonic decays, AΛZ→A[Z+1]∗+π− or AZ∗+π0, going to some specific states of the daughter nucleus, A[Z+1]∗ or AZ∗, are sensitive to the spin of the parent hypernucleus, AΛZ, if the specific decays are caused selectively by the spin–flip amplitude or by the spin–non-flip amplitude.In this Letter, we present the first result on determination of the ground-state spin of a hypernucleus using a new method, namely, measurement of a weak-decay branching ratio to a specific excited state of the daughter nucleus using γ-ray spectroscopy technique. We detected the 429 keV γ-ray which is emitted from the excited daughter nucleus 7Be∗(1/2−,429 keV) of the 7ΛLi mesonic decay, 7ΛLi→7Be∗(429)+π−, and measured its weak decay branching ratio from the γ-ray yield.2ExperimentThe experiment (KEK E419) was performed at the 12 GeV proton synchrotron (PS) in the High Energy Accelerator Research Organization (KEK). It aimed at high-resolution γ-ray spectroscopy of 7ΛLi using a large-acceptance germanium (Ge) detector array called Hyperball. The details of the experiment and the results on hypernuclear γ transitions in 7ΛLi have already been reported in Refs. [3,13].Employing the K6 beam line and the Superconducting Kaon Spectrometer (SKS) [14,15], we produced bound states of 7ΛLi by the 7Li(π+,K+) reaction with 1.05 GeV/c pions. Each incident pion was momentum-analyzed with the K6 beam spectrometer and hit a 7Li target (25 cm thick, 98% enriched), and the outgoing K+ meson was identified and analyzed by the SKS. The target was irradiated with 1.0×1012 pions in total.γ-rays emitted from the target were detected with Hyperball installed around the target. Hyperball consisted of fourteen N-type coaxial Ge detectors and had a photo-peak efficiency of about 2.5% at 1 MeV. Each Ge detector was surrounded by bismuth germanate (BGO) counters which provide veto signals to suppress backgrounds for the Ge detector due to Compton scattering, high-energy γ-rays from π0, and high-energy charged particles. Data from all the detectors in Hyperball and the K6/SKS system were recorded with a (π+,K+) trigger provided by the K6/SKS system alone. Energy calibration of the Ge detectors was made in the energy range of 0.1–1.8 MeV using a standard mixed source containing 241Am, 109Cd, 57Co, 139Ce, 51Cr, 113Sn, 85Sr, 137Cs, 60Co and 88Y.The in-beam performance of each Ge detector was continuously monitored through the whole beam time, by using triggered γ-rays from a weak (1 kBq) 60Co source embedded in a plastic scintillator and installed behind each Ge detector. The most important role of this monitoring system is to measure the in-beam dead time caused by pile-up and preamplifier reset. The dead time was obtained by comparing 60Co peak counts measured in the beam-on time gate and in the beam-off time gate for every synchrotron cycle. Since a peak shift of 1–2 keV was observed between the beam-on and beam-off periods, the energy scale of the in-beam γ-ray spectrum was corrected, using beam-induced γ-ray peaks from surrounding materials, in an accuracy less than 0.6 keV.3Derivation of branching ratioWith the K6/SKS spectrometer system, the excitation spectrum of 7ΛLi hypernucleus in 7ΛLi(π+,K+) reaction was obtained in the same manner as in previous SKS experiments [15–17]. Fig. 1 shows the excitation spectrum of 7ΛLi plotted in the Λ binding energy, BΛ, where the absolute energy scale was adjusted using the known BΛ of the 7ΛLi ground state (5.58 MeV [18]). The same 7ΛLi spectrum but with a thinner target was previously measured with 2.2 MeV FWHM resolution (KEK E336) [16]. In this thin-target spectrum, the bound state region of the observed 7ΛLi spectrum was decomposed into four Gaussian peaks, a quasi-free continuum, and a constant background, according to theoretical predictions [19,20] that the four states (1/2+ (T=0), 5/2+ (T=0), 1/2+ (T=1), and 5/2+ (T=1)) of 7ΛLi (see Fig. 3) are strongly populated. (Hereafter, the notation “(T=0)” is omitted.) The energies and relative intensities for the fitted four peaks agreed fairly well with the predictions. In the present spectrum, the energy resolution is worse due to the energy loss in the thick target. By folding these four peaks of the same energies and relative intensities with 4.2 MeV FWHM resolution, the present spectrum was reproduced well, as shown in Fig. 1. We set the gate for the “bound region” at −10<−BΛ<2 MeV, as shown in the figure.Fig. 2(a) is the γ-ray energy spectrum when the bound region (−10<−BΛ<2 MeV) of 7ΛLi is gated, while Fig. 2(b) is the spectrum when the unbound region (−BΛ>2 MeV) is gated. The peaks at 429, 692 and 2050 keV were observed only in the bound region spectrum, and the peak at 478 keV is more prominent in Fig. 2(a) than in Fig. 2(b). As described in Ref. [3], the peaks at 692 and 2050 keV are attributed to the M1 (3/2+→1/2+) and E2 (5/2+→1/2+) transitions in 7ΛLi, respectively. The energies of the 429 keV peak (429.7±0.8 keV) and the 478 keV peak (478.0±0.8 keV) agree with those of 7Be(1/2−→3/2−,429.1 keV) and 7Li(1/2−→3/2−,478.6 keV) transitions. Since the 429 and 478 keV γ-rays prominently appear in coincidence with 7ΛLi bound states, they are interpreted as transitions in the daughter nuclei resulting from the 7ΛLi weak decays, 7ΛLi→7Be∗(1/2−,429 keV)+π− and 7ΛLi→7Li∗(1/2−,478 keV)+π0, as shown in the decay scheme in Fig. 3. Since each of 7Be and 7Li has only one particle-bound excited state, the 429 and 478 keV γ-ray events correspond to the direct productions of these first excited states of 7Be and 7Li, respectively, in the mesonic weak decay of 7ΛLi.The γ-ray spectrum around the 429 keV peak was fitted with three Gaussians and a linear background as shown in the inset in Fig. 2(a), and the numbers of events in the 429 keV peak and the 478 keV peak were obtained as: Nγ(429)=78±16,Nγ(478)=121±19. In the unbound-region spectrum (Fig. 2(b)), the 7Be∗ (429) peak was not observed at all but the 7Li∗(478) peak was seen with a smaller S/N ratio. It is understood from the fact that the 7Li∗(478) state can be also excited through the (n,n′) reaction by secondary neutrons produced in the (π+,K+) reaction, while the production rate of 7Be∗(429) through the 7Li(p,n)7Be∗(429) reaction by secondary protons is expected to be much smaller than that of 7Li∗(478). This is because the 7Li(p,n)7Be∗(429) cross section is by a factor of 3–5 smaller than the 7Li(n,n′)7Li∗(478) (and 7Li(p,p′)7Li∗(478)) cross sections [21,22], and the effective 7Li target thickness for most protons is smaller than that for neutrons due to the proton ranges (<2 cm for <30 MeV protons) shorter than the target size (5.6×4×25 cm).Here we estimate possible contamination of the 7Li(p,n)7Be∗(429) events in Nγ(429). Since 7Be and 7Li are mirror nuclei, the branching ratio of 7ΛLi→7Li∗(478)+π0 to 7ΛLi→7Be∗(429)+π− should be almost 1 to 2 due to the ΔI=1/2 rule, while the observed ratio of Nγ(478) to Nγ(429) is 1.6 to 1. This difference is ascribed to a contribution of the 7Li(n,n′)7Li∗(478) reaction in the 7Li∗(478) γ-ray yield in the bound region spectrum. If all the 7Be∗(429) γ-rays stem from the 7ΛLi weak decay, 85±20 counts out of Nγ(478)=121±19 counts are attributed to the 7Li(n,n′) reaction, considering the energy dependence of the Hyperball efficiency. From the similar fit for the unbound region spectrum (Fig. 2(b) inset), the upper limit of the 429 keV γ-ray yield, which could be attributed to the 7Li(p,n)7Be∗(429) reaction, was obtained to be 12% of the 478 keV γ-ray yield by the 7Li(n,n′)7Li∗(478) reaction. Therefore, by applying the same upper limit to the bound region spectrum, the upper limit of the contamination of the 7Li(p,n)7Be∗(429) reaction events in Nγ(429) was estimated to be (85+20)×0.12=13 counts. Thus, the yield of the 429 keV γ-rays due to the 7ΛLi weak decay is: Nγweak(429)=78±16(stat)+0−13(contamination). It is to be mentioned that the 429 keV peak has a width of σ=5.1±1.2 keV in the Gaussian fit, which is consistent with the expected Doppler broadening width of ±7 keV (σ=4 keV) for the recoil velocity of 7Be∗ in the 7ΛLi→π−+7Be∗(429) decay and the prompt γ-ray emission (the half life of 7Be∗(429) is 0.13 ps) before slowing-down of the recoil hypernucleus (stopping time is about 5 ps). The observed larger width of the 7Li∗(478) γ-ray peak (σ=6.6±1.0 keV) is understood by the larger recoil motion in the (n,n′) reaction.In order to extract the branching ratio of 7ΛLi→7Be∗(429)+π− decay, we need to know the total number of events of all the populated 7ΛLi bound states which undergo weak decay from the 7ΛLi ground state. As described in Ref. [3], we also observed two γ-ray peaks at 3877±7 keV and at 3186±6 keV in the Doppler-shift corrected spectrum. Since their energy difference (691±6 keV) coincides with the energy (692 keV) of the M1 transition between the ground-state doublet members (3/2+,1/2+), they are assigned as M1 transitions from the 1/2+(T=1) state to the ground-state doublet members. The observation of these transitions, as well as the 3877±7 keV excitation energy of the 1/2+(T=1) state slightly lower than the 5ΛHe+d decay threshold (3.94±0.04 MeV), indicates that the 1/2+(T=1) state is bound and contributes to the weak decay of the 7ΛLi ground state. On the other hand, the 5/2+(T=1) state, of which energy is expected to be much higher than the 5ΛHe+d threshold [20], does not contribute to the 7ΛLi weak decay. The total number of events of all the 7ΛLi bound states, Nbs, was thus obtained to be: Nbs=(8.3±0.3)×104, as the sum of the peak counts for the 1/2+, 5/2+, and 1/2+(T=1) states integrated in the bound region gate in Fig. 1.In order to obtain the branching ratio from the γ-ray yield, the absolute photo-peak efficiency of all the Ge detectors should be precisely determined. When the beam was off, we carried out calibration measurements of the photo-peak efficiency with the standard mixed source, which was located at several points in the target region along the beam axis. A simulation with the GEANT code was also carried out in the same setup as the calibration measurements, and the calculated efficiency agreed with the measured one. Then the simulation was made again with the target material and with the realistic source point distribution taken into account. Then the off-beam absolute efficiency was obtained as (3.27±0.11)×10−2 at 429 keV.Using the 60Co monitoring system, the dead times of the Ge detectors were continuously measured. They ranged from 30 to 50%, being small for the detectors located upstream of the target and large for those located downstream. They were almost stable through the beam time of one month. The dead time averaged for all the Ge detectors and through the whole beam time was 46.6±0.5%. Namely, the in-beam/off-beam efficiency ratio was 0.534±0.005. The inefficiency due to accidental veto by the BGO counters was 6±2%, and the inefficiency due to a timing cut with the Ge detector TDC's was 5±3%. Thus, the γ-ray detection efficiency at 429 keV was obtained to be: εγ(429)=(1.56±0.08)×10−2, as a product of the off-beam absolute efficiency at 429 keV, the in-beam/off-beam efficiency ratio, and the analysis efficiency for the BGO veto and the Ge timing cut.Then the branching ratio of the 7ΛLi weak decay going to the first excited state of 7Be was obtained as: BR7ΛLi→7Be∗(429)+π−=NγweakNbsϵγ(429)=6.0+1.3−1.6×10−2, where the error is given from a quadratic sum of all the errors.4Determination of the spinThe mesonic weak-decay rates of p-shell Λ hypernuclei were theoretically calculated by Motoba et al. with a shell model and with pion distortion taken into account [23]. For each case of the 7ΛLi spin of 1/2+ and 3/2+, the calculated decay rate of 7ΛLi to the first excited state of 7Be is Γ7ΛLi(1/2+)→7Be∗+π−=0.070ΓΛ (0.052 ΓΛ),Γ7ΛLi(3/2+)→7Be∗+π−=0.007ΓΛ, where ΓΛ denotes the total decay rate of a free Λ. The value in the square parenthesis is the result calculated with a cluster model. The 1/2+ and 3/2+ members of the ground-state doublet of 7ΛLi dominantly have L=0 with S=1/2 and S=3/2, respectively, while the first excited state 7Be∗(1/2−) has L=1 and S=1/2. Therefore, the weak decay of 7ΛLi(3/2+) to 7Be∗(1/2−)+π− requires spin–flip and is consequently an order of magnitude weaker than that of 7ΛLi(1/2+) due to the property of the π-mesonic weak decay of Λ.In order to compare these theoretical decay rates with the measured branching ratio, the decay rates were converted to branching ratios by dividing by an expected total decay rate, Γtot(7ΛLi)≈(1.2±0.4)ΓΛ. Here, as there are neither measurements nor calculations of Γtot(7ΛLi), it was assumed to be within the range of measured total decay rates of A=4–12 hypernuclei, namely, 4ΛH (1.36+0.21−0.15[24]), 4ΛHe (1.03+0.12−0.10[25], 1.07±0.11 [26]), 5ΛHe (1.03±0.08 [27]), 11ΛB (1.37±0.16 [28], 1.25±0.08 [29]), and 12ΛC (1.25±0.18 [28], 1.14±0.07 [30]) in the unit of ΓΛ. The theoretical branching ratios to the first excited state of 7Be are derived to be (5.8±1.9)×10−2 (or (4.3±1.4)×10−2 for the cluster model) for the 1/2+ case, and (0.6±0.2)×10−2 for the 3/2+ case. The measured branching ratio agrees with the value for the 1/2+ case, but obviously disagrees with the value for 3/2+. Therefore, the ground state spin of 7ΛLi was determined to be 1/2. It is noted that the calculation of Ref. [23] well reproduces experimental π− and π0 mesonic weak decay rates of 11ΛB and 12ΛC [31,32]. Furthermore, it is to be stressed that the present determination of the spin is based on the large difference of the spin–flip/spin–non-flip amplitudes and not affected by details of the theoretical calculations.As mentioned in Ref. [3], the measured yields of hypernuclear γ-rays of 7ΛLi suggested the ground-state spin of 1/2, and the effective interaction parameter of the ΛN spin–spin force was derived to be Δ=+0.5 MeV based on this assignment. The present result independently supports this spin assignment.5SummaryIn summary, we observed a 429 keV γ-ray peak from 7Be∗(1/2−,429 keV) produced by the weak decay of 7ΛLi, 7ΛLi→7Be∗(429)+π−. From the yield of this γ-ray, the branching ratio of the 7ΛLi weak decay to 7Be∗(429) was obtained as (6.0+1.3−1.6)×10−2. By comparing this value with theoretically calculated ones, the 7ΛLi ground-state spin was determined to be 1/2. 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