application/xmlStructure and decay of the s-hole state in 11B studied via the 12C(p,2p)11B[formula omitted] reactionM YosoiH AkimuneI DaitoH EjiriH FujimuraM FujiwaraT IshikawaM ItohT KawabataM NakamuraT NoroE ObayashiH SakaguchiH TakedaT TakiA TamiiH ToyokawaN TsukaharaM UchidaT YamadaH.P YoshidaPhysics Letters B 551 (2003) 255-261. doi:10.1016/S0370-2693(02)03062-9journalPhysics Letters BCopyright © 2002 Elsevier Science B.V. All rights reserved.Elsevier B.V.0370-26935513-49 January 20032003-01-09255-26125526110.1016/S0370-2693(02)03062-9http://dx.doi.org/10.1016/S0370-2693(02)03062-9doi:10.1016/S0370-2693(02)03062-9http://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/JournalsS300.3PLB19399S0370-2693(02)03062-910.1016/S0370-2693(02)03062-9Elsevier Science B.V.ExperimentsFig. 1(a) Energy spectrum of 11B of the 12C(p,2p)11B∗ reaction at Ep=392 MeV. Dashed and solid lines show the results of a least χ2 fit for the energy region between 11 MeV to 40 MeV (see text). The sum of all peaks (solid line) reproduces well the experimental data at energies below 40 MeV. The detection efficiency decreases gradually above this energy due to the finite momentum acceptance of the spectrometers. (b) Excitation energy spectra of 11B in coincidence with emitted charged particles. The contributions of p-, d-, t- and α-decays are separately shown.Fig. 2The left side panels show two-dimensional plots of the energies of the decay particles versus the excitation energy Ex in 11B for (a) p-, (b) d-, (c) t- and (d) α-decay channels. The locus lines for the ground states in the corresponding residual nuclei are shown. The right side panels display separation energy spectra for the final states of (e) 10Be, (f) 9Be, (g) 8Be and (h) 7Li obtained from projecting events in panels (a), (b), (c) and (d) onto the excitation energy axes of the residual nuclei, respectively. The threshold energies of the 3-body decay channels are indicated.Fig. 3Comparison of the measured branching ratios of the p-, d-, t- and α-decays from the s-hole state in 11B with those of the statistical model calculation using the code Cascade. The error bars shown include only statistical ones. The branching ratio of the n-decay with the energy above 3.1 MeV is also shown in the results of the statistical model calculation. The branching ratios of the decay onto the ‘2-body decay’ regions are indicated with dark areas (see text).Fig. 4(a) Experimental branching ratios of the p-, d-, t- and α-decays onto the ‘2-body decay’ regions from the three excitation energy regions of 16–20, 20–26 and 26–35 MeV in 11B. (b) Branching ratios of the n-, p-, d-, t- and α-decays from the doorway s-hole state in 11B calculated by the microscopic cluster model with SU(3) wave functions 4. Branching ratios for the states with [f](λμ)=[4421](04) and [f](λμ)=[443](04) and total branching ratios are shown.Table 1Measured differential cross sections of the s-hole state in 11B and the branching ratios of decay particles are listed. Only statistical errors are shown. The branching ratios of the decay onto the ‘2-body decay’ regions are given in parentheses (for further details see text)Ex(11B)d3σ/dΩ1dΩ2dEaBranching ratio (%)b(MeV)(μb/sr2 MeV)pdtα16–35128.7±0.211.7±0.66.5±0.418.6±0.616.8±0.6(8.5±0.5)(5.3±0.3)(16.4±0.6)(7.7±0.4)16–2036.3±0.113.6±1.10.0±0.049.1±0.811.3±1.0(13.6±1.1)(0.0±0.04)(9.1±0.8)(11.1±1.0)20–2648.9±0.19.7±0.97.4±0.623.3±1.115.5±1.0(8.2±0.8)(7.4±0.6)(22.6±1.1)(9.3±0.8)26–3543.5±0.112.3±1.011.0±0.921.4±1.123.1±1.3(4.4±0.6)(7.4±0.7)(15.6±1.0)(3.1±0.5)aThe normalization errors due to the uncertainties of the target thickness and the acceptances of angles and the charge collection are estimated to be about 10%.bLower limits of the detection energies are 3.1, 4.0, 4.6 and 4.5 MeV for p, d, t and α, respectively.Structure and decay of the s-hole state in 11B studied via the 12C(p,2p)11B∗ reactionMYosoiayosoi@ne.scphys.kyoto-u.ac.jpHAkimunebIDaitocHEjirideHFujimurafMFujiwarafgTIshikawaa1MItoha2TKawabataa3MNakamuraaTNorof4EObayashifHSakaguchiaHTakedaaTTakiaATamiihHToyokawadNTsukaharaaMUchidaaTYamadaiH.PYoshidafaDepartment of Physics, Kyoto University, Kyoto 606-8502, JapanbDepartment of Physics, Konan University, Kobe 658-8501, JapancCenter for Integrated Research in Science and Engineering, Nagoya University, Nagoya 464-8601, JapandJapan Synchrotron Radiation Research Institute, Hyogo 679-5198, JapaneInternational Institute for Advanced Studies, Soraku, Kyoto 619-0225, JapanfResearch Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, JapangAdvanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, JapanhDepartment of Physics, University of Tokyo, Hongo, Tokyo 113-0033, JapaniLaboratory of Physics, Kanto Gakuin University, Yokohama 236-8501, Japan1Present address: Laboratory of Nuclear Science, Tohoku University, Sendai 982-0826, Japan.2Present address: Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan.3Present address: Center for Nuclear Study, University of Tokyo, Hongo, Tokyo 113-0033, Japan.4Present address: Department of Physics, Kyushu University, Fukuoka 812-8581, Japan.Editor: V. MetagAbstractCharged particle decay of the s-hole state in 11B was measured in coincidence with the quasifree 12C(p,2p) reaction at 392 MeV incident energy. Triton-decay was found to be dominant despite its smaller Q-value than that of α-decay. The measured decay pattern is compared to the results of statistical model and microscopic SU(3)-cluster model calculations. The energy spectrum around the s-hole state exhibits three bump-like structures, which can be qualitatively explained by a recent shell-model calculation.PACS21.10.Pc24.10.-i25.40.-h27.20.+nExclusive knockout reactions provide a wealth of information on the structure of single-nucleon states of nuclei. Excitation energies (Ex) and widths (Γ) of proton–hole states were systematically measured with quasifree (p,2p) and (e,e′p) reactions 1–3, which revealed the existence of inner orbital shells in nuclei. However, the detailed structure and fragmentation of deep-hole states are still not well known. The 1s-hole states are observed as broad bumps in the highly excited energy region above 20 MeV 1. It is estimated that the ratio of the nuclear radius to the mean free path of a 1s-hole is about 1 or less than 1 in p-shell nuclei, and larger than 1 in heavy nuclei 4. This results indicate that the s-hole states in light nuclei may have large escape widths (Γ↑) and that the spreading widths (Γ↓) are dominant in heavy nuclei. It is expected that the character of the fragmentation of deep-hole states in light nuclei is considerably different from that in heavy nuclei, since the nuclear saturation property of the ground states largely deviates in light nuclei.Yamada et al. calculated spectroscopic factors and partial decay widths for two-body cluster decay processes from the doorway s-hole states of 11B and 15N in the framework of the microscopic cluster model with SU(3)[f](λμ) wave functions 4. The description of the s-hole state is based on the fact that the doorway s-hole state produced by the quasifree knockout reactions should have the same spatial symmetry as the ground state of the target nucleus, whose wave function is well described by the SU(3)-cluster model in light nuclei. The authors showed that a selection rule owing to a spatial symmetry is valid for fragmentations of s-hole states in light nuclei: n-, p-, d-, t- and 3He-fragments are allowed, while the fragments such as the α-particle and the heavier particles are forbidden. Since the Q-values for α-fragments in most light nuclei are larger than those for other cluster decay channels, α-decay is favored in the statistical decay process. Thus, the experimental study of the α-decay partial widths (Γα) is especially important to investigate if deep-hole states are statistically fragmented.Nuclear deep-hole states are closely related to hypernuclear physics 5. The production of hypernuclei with strangeness S=−2 via the Ξ− atomic capture reaction at rest is of particular interest because the Q-value of the elementary process (Ξ−p→ΛΛ+28 MeV) is almost the same as the separation energy of an s-state proton in light nuclei. According to recent hybrid emulsion-counter experiments with the (K−,K+) reaction 6–10, several double-Λ and twin-Λ hypernuclear production events were identified. Five events including an event with two interpretations were produced by Ξ− atomic captures into 12C. Only the following three processes were observed: Ξ−+12C→10ΛΛBe+t,6ΛΛHe+α+tand9ΛBe+4ΛH, where a triton or a 4ΛH(=t⊗Λ) was emitted in all cases. This high probability of the S=−2 formation with a triton-based fragment is hardly understood on the basis of the statistical decay model 11 and the microscopic transport model 12. The S=−2 hypernuclear production rates were also explored by Yamada et al. using a direct reaction model 13. Their calculation, however, does not explain the enhancement of t-based fragments if the Ξ− particle interacts mainly with a p-state proton in 12C. It is therefore important to better understand the fragmentation of the s-hole state in 11B.Decay properties of the s-hole states produced from the targets such as 12C and 16O are also interesting from a particle physics point of view. In fact, C and O are typical nuclei used as detectors for studies of proton decay and neutrinos. Both the decay of an s-proton and the neutrino knockout of an s-proton leaves an s-hole. Thus, proton decay and neutrino interactions can be studied by observing the decay from the s-hole states as well.In the present Letter, charged particle decay from the quasifree proton-knockout reaction on 12C is studied to understand the structure and the fragmentation mechanism of the s-hole state in 11B. The (p,2p) reaction at intermediate energies is well described by the direct reaction picture and is flexible enough to choose the proper kinematics to enhance the s-hole state.The experiment was carried out at the Research Center for Nuclear Physics (RCNP), Osaka University, by using a 392 MeV proton beam accelerated by the AVF and Ring cyclotrons. The quasifree (p,2p) reaction was measured with the dual spectrometer system consisting of the high resolution spectrometer Grand Raiden (GR) 14 and the large acceptance spectrometer (LAS) 15. GR was set at 25.5° and detected protons with higher energies, taking into account the difference of the momentum acceptance of GR (5%) and LAS (30%). The laboratory angle of LAS (−51.6°) and the magnetic fields of the spectrometers were determined to satisfy the zero-recoil momentum condition at the central energy of the 1s1/2-knockout bump, where the cross section leading to the s-hole state is maximum. The entrance slits of both spectrometers were fully opened for maximum acceptance. Absolute values of cross sections were determined by normalizing results obtained in a separate measurement with slits defining the solid angles of GR and LAS to 2.4 mrad and 12.0 mrad, respectively. Two multi-wire drift chambers in each focal plane of both spectrometers determined the positions and the incidence angles of particles. Particle identification was provided by the ΔE signals from plastic scintillation counters, that were also used for trigger signals. We used a natural carbon target with a thickness of 0.5 mg/cm2, rotated through 45° towards LAS. The beam was transported to a Faraday cup in a well shielded beam dump about 25 m downstream of the target.Charged particles decaying from the highly excited states in 11B were measured in sixteen telescopes of ΔE–E Si solid-state detectors (SSD) in coincidence with the two protons of the (p,2p) reaction. Each telescope consisted of a thin (20 μm, 50 μm or 100 μm) ΔE SSD and a thick (5000 μm) E Si(Li) detector. The active area of a ΔE is 300 mm2 or 450 mm2 and that of an E is 450 mm2. Eight 20 μm ΔE detectors were used for the identification of α-particles with Eα⩾4.5 MeV. The 50 μm and 100 μm ΔE detectors were used for identification of protons, deuterons and tritons. The SSD telescopes were mounted on a copper frame of a hemisphere shape and placed in the scattering chamber at backward angles around 135°. The total solid angle of the SSD array was 3.5% of 4π. In order to reduce the leakage current, the SSD system was cooled to about −20°C with four Peltier elements. The beam intensity was limited to about 70 nA by the maximum counting rate of the SSD closest to the beam. The lowest detectable energy of particles was given by the thickness of the ΔE SSD and therefore different for each particle (see Table 1). In the analysis, the same energy threshold was set for the 50 μm ΔE SSD as for the 100 μm ΔE SSD.An excitation energy spectrum of 11B calculated by summing up the energies of both emitted protons is shown in Fig. 1(a). Several discrete states, such as the ground state (3/2−) and the first excited state (2.125 MeV, 1/2−), are observed with a energy resolution of 450 keV (FWHM). The s-hole state is strongly excited in the higher excitation energy region. The bump corresponding to the s-hole state in 11B obviously splits into several components. A similar structure could be seen in the spectrum of the 12C(e,e′p)11B experiment at Ee=0.5 GeV 16, although the statistics was not enough to discuss the splitting of the s-hole state.In order to investigate the sub-structure of the s-hole state, we fitted the excitation energy spectra between 11 and 40 MeV with several peaks and a non-quasifree background. An asymmetric Lorentz formula 18 folded with an experimental energy resolution function was assumed for the shape of each peak. We fixed the integrated value of the background function to 10% of the total yields, since Noro et al. 17 concluded that the inclusion of non-quasifree processes around the s-hole state in the 12C(p,2p) reaction was less than 10% in the present kinematical condition. Here we adopted an almost flat background multiplied by a function gradually decreasing to zero at the threshold energy of the three-particle emission. At least three broad peaks except for two small sharp peaks at 11.7 and 13.2 MeV were needed to obtain a good χ2 value. The fitting results are shown in Fig. 1(a). The central energies (widths) of three broad peaks are 16.6±0.1 MeV (5.3±0.3 MeV), 21.9±0.2 MeV (8.1±0.2 MeV) and 28.7±0.7 MeV (9.7±2.5 MeV), respectively.The coincidence spectra with decay particles are shown in Fig. 1(b). Accidental coincidence events were subtracted. The threshold energies of 2-body decay from 11B to the channels 10B+n, 10Be+p, 9Be+d, 8Be+t, 8Li+3He and 7Li+α are 11.5, 11.2, 15.8, 11.2, 27.2 and 8.7 MeV, respectively. The 3He-decay events, which are hardly expected due to its large threshold energy, are included in the α-decay portion. It is apparent in Fig. 1(b) that the triton contribution is the largest, although the Q-value is smaller than that of α-decay.The panels (a), (b), (c) and (d) in Fig. 2 show four two-dimensional spectra of the energies of p-, d-, t- and α-decay particles versus the excitation energy Ex of 11B. The loci corresponding to the ground states in the residual nuclei are clearly observed in all spectra. The projection spectra onto the excitation energy axes of the residual daughter nuclei are shown in Fig. 2(e), (f), (g) and (h). The peaks populating low-lying states up to the excitation energy of about 5 MeV in each nucleus indicate that those events occur mainly through a binary decay process, while events in the higher excited region include the 3-body decay and sequential decay processes.The experimental differential cross sections and the branching ratios of decay particles are listed in Table 1. The excitation energy region is restricted to the range between 16 MeV and 35 MeV, because high energy protons above 35 MeV decaying to the ground state of 10Be were not detected due to the small energy losses in the ΔE SSD. The branching ratios are calculated on the assumption that the decay from the s-hole state is isotropic: Bri=∫ni(4π/ΔΩSSD)dEx∫NdEx,i=p,d,tandα, where N is the number of events of the 12C(p,2p) reaction, ni is the number of particles detected for i-decay and Ex is the excitation energy of 11B. The sum of the branching ratios including that of neutron-decay can exceed 100% if the decay multiplicity is more than 1. Thus, the n-decay probability cannot be estimated unambiguously from the present experimental results. The branching ratios of the decay to the low-lying states of the residual nuclei are also calculated. The ‘2-body decay’ region in each decay channel is defined as Ex(res)⩽Max(5 MeV,Eth(3-body)), where Ex(res) indicates the excitation energy relative to the ground state and Eth(3-body) denotes the threshold energy of particle decay in the residual nucleus. It should be noted that, for particles with small Eth(3-body), the 3-body decay and sequential decay processes are partially included in the ‘2-body decay’ region defined above. Taking the sub-structures around the s-hole state into consideration, we separately evaluated the branching ratios for three excitation energy regions of 16–20, 20–26 and 26–35 MeV in 11B (see Table 1).In Fig. 3, the experimental branching ratios of decay particles from the excitation energy region of 16–35 MeV are shown together with the results of a statistical-model calculation with the code Cascade19. The transmission coefficients were calculated with the global optical potential parameters of Ref. 20–24, which are well suited for light nuclei. Energy levels known below 12 MeV excitation energy were explicitly included for all nuclei (6⩽A⩽12) necessary for the calculation, while the levels of higher excitation energies were calculated using level-density parameters given in the code. In the Cascade calculations, decay particles above the experimental detection thresholds were only employed to obtain the branching ratios.The measured branching ratios of both t-decay and α-decay are much larger than those of the statistical model calculations. The experimental α-decay in the ‘2-body decay’ region is about one half of the total α-decay, suggesting that contributions of the sequential decay and 3-body decay processes are large in this channel. It should be noted that the α+α+t 3-body decay channel has a very low threshold energy of 11.2 MeV and may compete against the 2-body decay process, while the statistical model calculations include only the 2-body decay and sequential decay processes. This suggests that the 3-body decay process could contribute significantly to the branching ratios of α-decay. However, even in the ‘2-body decay’ regions, the t-decay strength is still dominant. Furthermore, the relative ratio of the t-decay to the α-decay in the experiment is opposite to that of the statistical calculations as well as the ratio of the p-decay to the d-decay. It is difficult to determine the proportion of the statistical process to the fragmentation obtained in the present experiment.Fig. 4(a) shows the branching ratios of p-, d-, t- and α-decays in the ‘2-body decay’ regions from the three excitation energy regions of 16–20, 20–26 and 26–35 MeV in 11B. The decay patterns from the respective regions suggested by the sub-structures are very different, indicating that the s-hole state in 11B splits into some components with different microscopic structures. Owing to the detection threshold, the measured deuteron branching ratio is zero in the low energy region. Predictions from the microscopic cluster model 4 are shown in Fig. 4(b), where the 11B(s-hole) state has the same spatial symmetry as the ground state of 12C, SU(3)(λμ)=(04), and has two degenerated partition symmetries [f]=[443] and [4421]. The calculations in Ref. 4 were made for an assumed centroid excitation energy of Ex=20 MeV. The energy dependence of the calculated branching ratios is not so much large as the qualitative change is caused in Fig. 4(b), although the calculated partial widths depend significantly on the energy. When the branching ratios of α-decay is neglected, the experimental decay pattern of the 26–35 MeV region is similar to that of the SU(3)[f](λμ)=[443](04) component. The first and second regions may have both the SU(3)[f](λμ)=[4421](04) and [443](04) components, whereas the mixing of [4421](04) component seems to decrease with increase of the excitation energy. The suppression of α-decay predicted by the SU(3)-model, however, is not clearly supported in the present experiment.Yamada has recently made new calculations within the framework of the 1ℏω shell model 25. The excitation spectrum of the 12C(p,2p) reaction was formulated within the impulse approximation, where calculated energy-dependent spectroscopic factors for the 12C(g.s.)→p+11B(s-hole) process were folded by a Lorentzian function. The result of the shell model calculation shows that the s-hole state in 11B splits into three parts. Although the calculated strength ratios of the three regions are different from the experimental results, the sub-structure of the s-hole state is reasonably explained by the shell model calculation. The energy dependence of the branching ratios for n-, p-, d-, t-, and α-decays from the 11B(s-hole) state were also calculated using the separation energy method 26, where the partial decay width is defined as the product of the penetration factor and reduced width. The calculated branching ratio of the t-decay is larger than that of the α-decay, reflecting the selection rule as mentioned above. The enhancement of the t-decay observed in the present experiment, however, is not reproduced by the shell-model calculation. Calculations including the direct 3-body decay process will be needed to explain the experimental decay pattern.In summary, we presented the first measurements of the p-, d-, t- and α-decays from the s-hole state in 11B excited by the 12C(p,2p)11B∗ reaction at Ep=392 MeV. The measured excitation energy spectrum shows that the s-hole state split into three sub-structures. This splitting agrees qualitatively with the result of recent shell-model calculations 25. The triton decay probability was found to be larger compared to any other decay, although the Q-value of the α-decay channel is larger. This provides useful information on the studies of the S=−2 hypernuclear production via the Ξ− capture at rest. The present results for the decay branching ratios cannot be reproduced by statistical model calculations. Microscopic cluster model calculations with SU(3)(λμ) wave functions 4 explains the experimental decay character qualitatively. However, a quantitative comparison between the experimental results and both calculations is not sufficient to deduce the ratio of the escape width Γ↑ to the spreading width Γ↓ of the s-hole state.AcknowledgementsWe are grateful to the RCNP cyclotron crew for preparing a stable and clean beam. We thank T. Baba, T. Inomata, K. Ishibashi, M. Kawabata, T. Kinashi, H. Kohri, and M. Tanaka for their helpful cooperation in the early stage of the experiment, and K. Ikeda for fruitful discussions and encouragement. 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