Gamma spectroscopy of hypernuclei: a decade of Hyperball project and future plans at J-PARC

Nuclear Physics A 835 (2010) 3–10 www.elsevier.com/locate/nuclphysa

Gamma spectroscopy of hypernuclei: a decade of Hyperball project and future plans at J-PARC H. Tamura∗,a , Y. Maa , N. Chigaa , K. Hosomia , T. Koikea , M. Mimoria , K. Miwaa , M. Satoa , K. Shirotoria , M. Ukaib , T. O. Yamamotoa a Department

of Physics, Tohoku University, Aoba-ku, Sendai 980-8578, Japan Department, Gifu University, Gifu 501-1193, Japan

b Physics

Abstract Since 1998 we have conducted the project of precision hypernuclear γ-ray spectroscopy using the Ge detector array, Hyperball, and revealed precise level schemes of various p-shell hy12 pernuclei. In the latest experiment at KEK (E566), the ground-state spacing of 11 Λ C and Λ C 12 + + 11 12 hypernuclei have been obtained using the C(π ,K )Λ B,Λ C reaction. The accumulated data on the p-shell hypernuclear level energies allow us to establish all of the four strengths of the ΛN spin-dependent interactions and to discuss the ΛN-ΣN coupling force in a nucleus. Further experiments at J-PARC are being prepared, where we tackle new experimental challenges such as a precise measurement of the Λ-spin-flip B(M1) values and exploration of sd-shell hypernuclei. Key words: Hypernuclei, Gamma-ray spectroscopy, ΛN interaction, Hyperball, J-PARC 1. A Decade of Hyperball In 1998 we developed a germanium detector array (Hyperball) dedicated to hypernuclear experiments and started a project of precision γ-ray spectroscopy of Λ hypernuclei [1]. Within the same year 7Λ Li was studied via the 7 Li(π+ ,K + ) reaction at the KEK-PS K6 beam line (KEK E419), and four transitions in 7Λ Li were successfully observed. The strength of the ΛN spinspin interaction (Δ = 0.43 MeV) was derived from the ground-state spin doublet (3/2+ ,1/2+ ) spacing, and that of the nucleon-spin-dependent spin-orbit interaction (S N ∼ −0.4 MeV) was also extracted from the spacing of 7Λ Li(5/2+ ,1/2+ ). In addition, the shrinking effect of hypernuclei was first confirmed through a B(E2) measurement [2]. In the same year, Hyperball was shipped to BNL and employed for the E930 experiment at the AGS D6 beam line using the (K − ,π− ) reaction. We investigated 9Λ Be hypernucleus and the hypernuclear fine structure of the (3/2+ , 5/2+ ) doublet with a 43 keV spacing was observed, from which the strength of the Λ-spindependent spin-orbit interaction (S Λ = −0.01 MeV) was obtained [3, 4]. In the second run of 9 15 16 E930 in 2001, we studied 16 O(K − ,π− ) reaction [5, 6] as well as 10 Λ O and Λ N via the Λ B, Λ Be and 7Λ Li via the 10 B(K − ,π− ) reaction. From the 16 O ground-state doublet spacing of only 26 keV Λ indicated a small value of the ΛN tensor interaction (T ∼ 0.03 MeV) [7]. The ground-state ∗ The

authors thank all the members of KEK E566 and Hyperball-J collaborations.

0375-9474/$ – see front matter © 2010 Published by Elsevier B.V. doi:10.1016/j.nuclphysa.2010.01.168

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Figure 1: Level schemes of hypernuclei determined from recent γ-ray experiments. See Ref. [12] for references. Here, the level scheme of 13 Λ C was studied with an NaI counter array [13]. All the others were studied with Hyperball/Hyperball2. Level energies are given after recoil correction to the observed γ-ray energies.

doublet spacing of 10 Λ B was found to be less than 0.1 MeV [4], which corresponds to Δ < 0.29 MeV, being inconsistent with the Δ = 0.43 MeV from 7Λ Li. In addition, 7Λ Li and 9Λ Be hypernuclei + were produced as hyperfragments from 10 Λ B excited states, from which we observed the 7/2 → + 7 + + 5/2 transition in Λ Li by γ-γ coincidence with the 5/2 → 1/2 transition and also succeeded in the spin assignment of the 9Λ Be(3/2+ ,5/2+ ) doublet [4]. In 2002 Hyperball was shipped back to KEK and used for a (stopped K − , γ) experiment (KEK E509) [8], where some transitions from 12 + + 12 11 hyperfragments were detected. In 2002 and 2005, the 11 B(π+ ,K + )11 Λ B [9] and C(π ,K )Λ C,Λ B 11 [10, 11] experiments (E518 and E566) were performed and the level schemes of Λ B and 12 Λ C were reconstructed. In the latter experiment, the upgraded version of the Hyperball array (Hyperball2) with the efficiency twice as large as Hyperball was constructed and employed. Figure 1 shows all the γ transitions and the level schemes of hypernuclei identified and determined by γ-ray spectroscopy experiments performed since 1998. Most of the p-shell hypernuclei which can be produced via the (π+ ,K + ) and (K − ,π− ) reactions have been investigated. 2. Final results of E566 The KEK E566 experiment was carried out in 2005 as the last hypernuclear experiment at KEK-PS before its shutdown. The K6 beam line and the SKS spectrometer were employed together with the Ge detector array, Hyperball2. The 12 C(π+ ,K + ) reaction at 1.05 GeV/c produced 12 11 bounds states (sΛ states) of 12 Λ C as well as pΛ excited states of Λ C that decay to Λ B via proton emission. See Ref. [10, 11] for details. 11 Bound-states events of 12 Λ C and those of Λ B were selected by setting the corresponding gates 12 in the Λ C mass spectrum. In the γ-ray spectrum for the 12 Λ C bound-states events, we observed two peaks at 2670.2±2.6 keV and 2833.9±5.6 keV (see Fig. 2), the latter of which has a statistical

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1-2 B

8

C

Counts / 2 keV

60

C

50

10

A

21-1

6

Counts / 10 keV

12 C ȃ

Doppler shift uncorrected

40 30 20 10 0 100

150

Doppler shift uncorrected

12

200

250

300

EȚ (keV)

4 2 0 20 18 16 14 12 10 8 6 4 2 0

A

Doppler shift corrected B

2300 2400 2500 2600 2700 2800 2900 3000 3100 3200

EȚ (keV)

Figure 2: γ-ray spectra for 12 Λ C obtained in the KEK E566 experiment. Right: spectra around 2.8 MeV without and with Doppler shift correction. Left: spectrum lower than 300 keV without Doppler shift correction. The observed peaks (A,B,C) correspond to the transitions shown in the 12 Λ C level scheme (left top).

significance of only 2.6σ. However, we also observed another peak at 161.4±0.7 keV in the same mass gate, which coincides with the energy spacing of these two peaks. Thus, the level scheme of 12 Λ C was obtained as shown in Fig. 1 (e), where the spins were assigned from the yield ratio of the 2670 and 2834 keV γ rays. When the pΛ peak region in the 12 Λ C spectrum is gated, three γ-ray peaks were observed at 262.9±0.2 keV, 503.9±0.7 keV, and 1482.9±0.4 keV. These γ rays were also observed in the previous experiment (E518) via the 11 B(π+ ,K + )11 Λ B reaction, but the 262.9±0.2 keV and 503.9±0.7 keV γ rays were not able to be assigned [9]. In the E566 experiment, we successfully assigned the 263 keV transition to be the spin-flip M1 transition in the 11 Λ B ground state doublet (7/2+ → 5/2+ ) and the 504 keV transition to be the spin-flip M1 transition in the 11 ΛB first excited state doublet (3/2+ → 1/2+ ). 3. Spin-dependent ΛN interaction In the past decade our Hyperball project has investigated almost all the p-shell hypernuclei that can be populated in the (π+ ,K + ) and (K − ,π− ) reactions. As shown in Fig. 1, we have identified 19 hypernuclear γ transitions and measured spacing energies of nine hypernuclear doublets. All of those data provide valuable information on the ΛN interaction. The radial integrals for the four spin-dependent terms in the effective sΛ pN interaction, which are denoted by Δ, S Λ , S N and T , respectively [14, 15], have been determined to be [16] Δ = 0.33 or 0.43, S Λ = −0.015, S N = −0.4, T = 0.02 (MeV).

(1)

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The spin-spin strength, which was determined to be Δ = 0.43 MeV for 7Λ Li from both of (3/2+ , 1/2+ ) and (7/2+ , 5/2+ ) doublet spacing [1, 7], has been found to be smaller (Δ ∼ 0.33 MeV) in the heavier p-shell hypernuclei. By using recent shell-model calculations by Millener 12 which include effects of ΛN-ΣN coupling, the measured doublet spacing energies in 16 Λ O, Λ C, 11 and Λ B lead to the Δ value of 0.33 MeV, where S Λ = −0.015 MeV and T = 0.024 MeV derived − − from the 9Λ Be (3/2+ , 5/2+ ) doublet spacing and the 16 Λ O (0 , 1 ) doublet spacing are used. The good agreement of the Δ values among several different hypernuclei seems to suggest that the theoretically estimated effect of the ΛΣ coupling is correct. It is thus found that the Δ value is significantly large only in 7Λ Li. This is opposite to the binding energy effect, in which the Δ value in 7Λ Li is expected to be smaller than those in other p-shell hypernuclei because of more spread Λ and N wavefunctions in 7Λ Li [17]. The reason is not understood yet. The S N value is determined from the change of the excitation energy in the core nucleus by a presence of a Λ. The difference between the 3+ and 1+ (g.s.) energy spacing in 6 Li and the (7/2+ , 5/2+ ) and (3/2+ , 1/2+ ) energy spacing (taking a center-of-gravity energy for the doublet) 16 in 7Λ Li gives S N = −0.4 MeV. Other excitation energy changes in 9Λ Be, 15 Λ N and Λ O also lead + + to S N ∼ −0.4 MeV. However, the difference between the 1 and 3 (g.s.) energy spacing in 10 B and the (3/2+ , 1/2+ ) and (7/2+ , 5/2+ ) energy spacing in 11 Λ B corresponds to S N = −0.9 MeV, and the difference between the 1/2+ and 3/2+ (g.s.) energy spacing in 11 C and the 1+2 and the (2+ , 1+1 ) energy spacing in 12 Λ C gives S N = −0.6 MeV. This inconsistency is presumably ascribed to an incomplete wavefunction of the core nucleus in the p-shell model space. In other words, inaccuracy in wavefunctions of ordinary nuclei is revealed by examining the response of nuclear level energies by a Λ. 4. Experiments at J-PARC The high-intensity proton accelerator facility, J-PARC, has started delivering 30 GeV proton beams. In the hadron hall, two sets of experimental apparatus at the K1.8BR line and the K1.8 line are under commissioning as of December, 2009. Various type of hypernuclear γ-ray spectroscopy experiments are planned [18]. The first experiment E13 has been approved as one of the Day-1 experiments. In this experiment, we will use the 1.5 GeV/c (K − ,π− ) reaction at the K1.8 line using a new setup with the SKS spectrometer, which enables us to populate both spin-flip and non-spin-flip hypernuclear states simultaneously. 4.1. Further study of ΛN interaction As described above, several p-shell hypernuclear levels are well explained by the Δ = 0.33 MeV value and the Λ-Σ coupling effect estimated by Millener. Since the effect of the Λ-Σ coupling generally augments the doublet spacing in p-shell hypernuclei, however, it is difficult to clearly separate the Λ-Σ effect from that of the spin-spin interaction (the Δ value) which has a dominant contribution in the doublet spacing. Therefore, the measurement of the transition (2− → 1− ) in the 10 Λ B ground-state doublet is still crucial, because it is predicted to be almost the only doublet in which the Λ-Σ coupling decrease the spacing [19]. In J-PARC the 10 Λ B measurement will be attempted again by pushing down the sensitive energy window, and in future the mirror hypernucleus, 10 Λ Be, will be also investigated. Another important subject in the study of ΛN interaction is charge symmetry breaking (CSB). The Λp and Λn interactions should be identical if the charge symmetry holds exactly, but the Λ

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binding energies of the lightest mirror pair of hypernuclei, 4Λ H and 4Λ He, are reported to have a large difference, suggesting that the Λp interaction is more attractive than the Λn interaction. An accurate few-body calculation on 4Λ H and 4Λ He from various Nijmegen Y N interaction models, together with the effect of the mass difference of Σ+ , Σ0 and Σ− in ΛN-ΣN coupling, failed to reproduce the reported energies [20]. Systematic study of various pairs of mirror hypernuclei as well as confirmation of the 4Λ H/4Λ He data is indispensable to confirm the spin-dependence in CSB interaction and to clarify the origin of the CSB interaction. 4.2. Impurity effect in nuclear structure Addition of a Λ hyperon into a nucleus may give rise to various changes of the nuclear structure, such as changes of the size, shape and cluster structure, emergence of new symmetries, changes of collective motions, etc. Level schemes and B(E2) values of Λ hypernuclei obtained by γ spectroscopy will reveal such “impurity effects”. In a previous Hyperball experiment (KEK E419), the lifetime of the 7Λ Li(5/2+ ) state was determined by analyzing the E2(5/2+ →1/2+ ) γ-ray peak shape (Doppler-shift attenuation method, DSAM). Then a very small +0.5 B(E2; 5/2+ →1/2+ ) value of 3.6±0.5(stat)−0.4 (syst) e2 fm4 was derived [2], indicating a significant 7 6 shrinkage of the Λ Li nucleus compared to Li. This result confirmed the hypernuclear shrinking effect which was predicted by Motoba et al. [21]. The measured reduction of the B(E2) value agreed with results of cluster model calculations [22]. Such a nuclear structure change induced by a Λ may appear in various hypernuclei [23]. In general, presence of a Λ results in a shrinkage of the nucleus, of which effect is expected to be sensitive to the spatial structure of the nucleus, such as clustering structure, halo structure, and deformation. In particular, drastic changes of nuclear structure are expected when a Λ is implanted into a neutron-rich hypernucleus having a neutron skin or halo. We are planning to investigate 7Λ He by using the 7 Li(K − ,π0 ) reaction and measuring the B(E2) value, which is expected to be reduced by one order of magnitude from the B(E2) value in 6 He due to disappearance of neutron halos [23]. In addition, we plan to examine change of deformation and collective motion in sd-shell hypernuclei. A relativistic mean field calculation implies a disappearance of nuclear deformation induced by a Λ in Si isotopes [24]. Such effects can be studied by measuring excitation energies in the rotational band. If B(E2) values are measured, the change of deformation will be better determined. Possibilities of such experiments are being discussed [25]. 4.3. Magnetic moment of Λ in a nucleus The most important subject in the J-PARC E13 is to measure a B(M1) value of a Λ-spin-flip M1 transition and to investigate the Λ’s g-factor in a nucleus, of which direct measurement from the magnetic moment of a hypernucleus is extremely difficult at present. Since hyperons are free from the Pauli effect in a nucleus, they are sensitive to a possible modification of baryons deeply embedded in nuclear matter. In the weak-coupling limit between the Λ and the core nucleus, the B(M1) value can be expressed as [14] B(M1) =

(2Jup + 1)−1 | < φlow | μ||φup > |2 =

3 2Jlow + 1 (gc − gΛ )2 μ2N . 8π 2Jc + 1

(2)

Here gc and gΛ denote effective g-factors of the core nucleus (with spin Jc ) and the Λ hyperon, and the spatial components of the wave functions for the lower and upper states of the doublet (φlow and φup , with spins Jlow and Jup ) are assumed to be identical.

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In the last several years, we have attempted to measure B(M1) values of hypernuclear spinflip transitions, but have not succeeded in measurement accurate enough to discuss a possible change of the gΛ value in a nucleus. In the BNL E930 experiment, 7Λ Li hypernuclei were pro∗ 10 ∗ 7 + 3 duced as hyperfragment in the reaction 10 B(K − ,π− )10 Λ B , Λ B → Λ Li(3/2 ) + He, and the B(M1) 7 + + value for the Λ Li(3/2 → 1/2 ) transition was obtained by DSAM, and the gΛ value was derived to be gΛ = −1.1+0.6 −0.4 μN (the error is statistical only). The large error is caused by a large background which results from the production mechanism and a limited hypernuclear mass resolution in the E930 apparatus. + + Recently, in the E566 experiment [11], the 263 keV 11 Λ B(7/2 → 5/2 ) peak shape was analyzed and the lifetime of the transition was obtained via DSAM. The result corresponds to gΛ > −1.76 μN . The density of the 12 C target (polyethylene, 0.93 g/cm3 ) was found to be too large to obtain a finite value of the lifetime by DSAM. − − − − In the 12 Λ C data, the yield ratio for the 2 → 1 (162 keV) and the 2 → 1 (2670 keV) − − transitions provides information on the B(M1) value of the 2 → 1 transition. The branching ratio of the 2− → 1− decay was obtained to be BR = 0.19 ± 0.12. The weak decay lifetime of 12 Λ C was measured to be τ = 231 ± 15 ps [26]. By assuming that the weak decay rates Γw of both 2− and 1− states are the same as 1/τ, the M1(2− → 1− ) transition rate was obtained from Γ M1 = BR/(1 − BR)Γw and gΛ = −1.04 ± 0.41 μN was derived. All these three results are consistent with the free space value of gΛ = −1.226 μN but with large errors. In the J-PARC E13 experiment, we plan to take high-statistics data for 7Λ Li γ rays and to measure the B(M1) value for the M1(3/2+ → 1/2+ ) transition, which will determine the gΛ value in 5% accuracy. In future we hope to extend our study to heavier hypernuclei to investigate nuclear density dependence and isospin dependence of the gΛ change. The B(M1) values as well as level energies in heavy hypernuclei will provide new means to explore baryon properties in nuclear matter. 5. Experimental apparatus at J-PARC The K1.8 beam line and the SKS magnet, together with the detector systems for the two spectrometers, have been installed and their commissioning with the beam has started in October, 2009. The details are described in Ref. [27]. In the E13 experiment, the K − beam of 1.5 GeV/c will be used and the π− around 1.4 GeV/c should be analyzed by the SKS system. For this purpose, we will use the SKS magnet with the highest excitation (2.7 T). In order to accept high momentum particles up to 1.4 GeV/c with a large acceptance using the SKS magnet, we prepared two sets of large-area (effective area of 2.1 m × 1.1 m) planer drift chambers and a large area of a plastic counter wall at the exit of the SKS magnet, which significantly increase the SKS spectrometer acceptance to 130 msr even for 1.4 GeV/c particles. In order to reject backgrounds of muons and pions from the beam K − decays (mainly K − → μ− ν¯ and K − → π− π0 ) in the trigger level, a “muon filter”, thick iron blocks with timing counters behind them, will be installed to identify muons, and a “π0 veto counter”, multilayered lead-sandwiched plastic scintillators, will be constructed and installed at the downstream of the target in order to reject π0 accompanying background events. 5.1. Present status of Hyperball-J We have also developed a new type of a Ge detector array, Hyperball-J, for the purpose of the E13 and subsequent γ spectroscopy experiments at J-PARC. The new Ge detector array should

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Figure 3: A new-generation Ge detector array, Hyperball-J. Left: one unit of the Ge detector with a pulse-tube regrigerator. Center: a lower half of the Hyperball-J detectors. Right: View of the whole system including the support frame.

be resistant against much higher counting and energy-deposit rates. The Hyperball-J array is illustrated in Fig. 3. It is characterized by the following two new techniques. 1) Mechanical cooling with a refrigerator instead of liquid nitrogen cooling. A compact pulse-tube refrigerator is directly connected to each Ge crystal and allows us to cool the Ge crystal down to 70 K, being lower by 20–25 K than the conventional liquid nitrogen method. Use of Ge detectors in such a low temperature greatly suppresses serious effects of radiation damage. After some R&D works the energy resolution less than 3 keV (FWHM) has been achieved even with our low-gain preamplifiers. 2) PWO counters instead of BGO counters for background suppression. In the previous detectors, Hyperball and Hyperball2, BGO counters surrounded each Ge detector and were used to veto background events such as Compton scattering, high energy electromagnetic showers from π0 , and penetration of high energy charged pions and muons. In J-PARC, however, the higher counting rate of the BGO counters due to much more intense beams causes serious accidental oversuppression. Therefore, we decided to use PWO counters having much shorter time for light emission (∼ 20 ns) than BGO (∼ 1 μs). Since PWO scintillator has extremely small light yields, we use doped PWO crystals at a low temperature (∼ −20◦ ) to increase the light yield. The PWO crystals were already produced and the counters are under fabrication. In addition, we are developing a new readout and analysis method; a waveform digitizer reads out waveform data of each Ge detector and off-line analysis for baseline restoration and pile-up decomposition will be carried out. This method will greatly improve the performance under higher counting rates that are expected when the full intensity beam is delivered in future at J-PARC. The support frame (Fig. 3 right), which incorporates a mechanism to modify the geometrical arrangement of the Ge detectors according to experimental requirement, was fabricated in the machine shop at Faculty of Science in Tohoku University. The control system for all the

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detectors in Hyperball-J has been also developed. The whole system of Hyperball-J will be ready soon and the first experiment E13 will be able to run in the later half of 2010. 6. Summary A series of experiments on precision hypernuclear γ-ray spectroscopy using the Ge detector array, Hyperball and Hyperball2, have revealed precise level schemes of various p-shell hyper12 nuclei. In particular, a recent experiment using the 12 C(π+ ,K + )11 Λ B,Λ C reaction successfully 11 observed the ground-state spacings of 12 C hypernuclei and B hypernuclei. The accumulated Λ Λ data for the p-shell hypernuclear level energies allow us to establish all of the four strengths of the ΛN spin-dependent interactions and to discuss the ΛN-ΣN coupling force in a nucleus. It is found that most of the hypernuclear data lead to the spin-spin interaction strength of Δ = 0.33 MeV, although deviations are found in 7Λ Li (Δ = 0.43 MeV) and 10 Λ B (Δ < 0.29 MeV). Further experiments at J-PARC are planned, where we will measure the Λ-spin-flip B(M1) values precisely and explore sd-shell hypernuclei and their impurity effects, as well as investigate further the ΛN interaction. A new-generation Ge detector array, Hyperball-J, has been developed and the whole apparatus is being prepared for J-PARC beams. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

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