Proposal for J-PARC 50 GeV Proton Synchrotron

Spectroscopic Study of Ξ-Hypernucleus, 12
Ξ Be,
12
−
+
via the C(K , K ) Reaction
K. Aoki, M. Ieiri, T. Maruta, T. Nagae (Spokesperson), H. Noumi, Y. Sato,S. Sawada, M. Sekimoto, H. Takahashi, T. Takahashi, A. Toyada
High Energy Accelerator Research Organization (KEK), JapanY. Fujii, O. Hashimoto, T. Ishikawa, H. Kanda, M. Kaneta, T. Koike, Y. Ma,
K. Maeda, K. Shirotori, S. N. Nakamura, H. Tamura, M. Ukai, H. Yamazaki
Tohoku University, JapanP. K. Saha
Japan Atomic Energy Agency (JAEA), Japan
H. Fujioka, D. Nakajima, T. N. Takahashi
University of Tokyo, JapanK. Nakazawa, T. Watanabe
Gifu University, Japan
K. Imai, K. Miwa, K. Tanida
Kyoto University, JapanS. Ajimura, T. Kishimoto, A. Sakaguchi
Osaka University, Japan
M. Yosoi
Research Center for Nuclear Physics (RCNP), Osaka University, JapanT. Fukuda
Osaka Electro-Communication University, Japan
P. Evtoukhovitch, V. Kalinnikov, W. Kallies, N. Kravchuk, A. Moiseenko,
D. Mzhavia, V. Samoilov, Z. Tsamalaidze, O. Zaimidoroga
Joint Institute for Nuclear Research (JINR), Russia
J. K. Ahn, B. H. Choi
Pusan National University, Korea
Y. Fu, C. Li, X. Li, C. Zhou, S. H. Zhou, L. H. Zhu
China Institute of Atomic Energy (CIAE), China
R. E. Chrien
Brookhaven National Laboratory (BNL), USA
B. Bassalleck
University of New Mexico, USA

J. Arvieux
IPN-O, Universite Paris-Sud, France
A. P. Krutenkova, V. V. Kulikov
Institute of Theoretical and Experimental Physics (ITEP), Russia
J. Reinhold
Florida International University, USA
B. Luigi, S. Marcello
Università di Torino, Italy
F. Diego
INFN, Sezione di Torino, Italy
M, Ombretta
INAF-IFSI, Sezione di Torino, Italy
L. Tang
Hampton University, USA

April, 28, 2006

Abstract
We propose to obtain the spectroscopic information of Ξ-hypernucleus, 12
Ξ Be,
12
−
+
−
through the C(K , K ) reaction by using the high-intensity K beam at JPARC. Ξ-hypernuclei, the existence of which is not well established so far, will
be observed for the first time with enough statistics and a good energy resolutionof ∼3 MeV. In order to perform such high-resolution spectroscopy, a new K +spectrometer will be constructed based on the existing SKS spectrometer. We
request two weeks for the tuning of the new spectrometer system, and four weeks−
6 −for the measurement of 12
Ξ Be with the K beam intensity of 1.6 × 10 K /spill.
The Ξ single-particle potential obtained from the observation of Ξ-hypernuclear
states gives us not only the information on ΞN interaction but also insight into
the high-density hadronic matter with strangeness. This experiment will be thefirst step to explore multi-strangeness hadronic systems which only J-PARC has
an access to.

1..  6SHFWURVFRS\

7KUHH'LPHQVLRQDO1XFOHDU&KDUW'RXEOH/+\SHUQXFOHL
8+\SHUQXFOHL

6 
,a
3

1
XP

EH

U

6 

VWDEOHaXQVWDEOH!

3U

RW

RQ

6 W UD Q J H Q H V V/6+\SHUQXFOHL2UGLQDU\QXFOHL
6 
1HXWURQ1XPEHU

Figure 1: A three-dimensional nuclear chart with strangeness, S, as the third axis. On
the S = 0 sheet, more than 3,000 nuclei including ∼300 stable ones are known, while
about 35 Λ-hypernuclei and 1 Σ-hypernucleus are observed in the S = −1 systems. In
the S = −2 systems, on the other hand, only a few double-Λ hypernuclei are known
to exist at this moment.

1

Introduction

In 2002, we submitted Letter of Intent (LoI) for “New Generation Spectroscopy of
Hadron Many-Body Systems with Strangeness S = −2 and −1”[1]. In the LoI, we
proposed the construction of two separated kaon beam lines, namely, K1.8 and K1.1,
to conduct three major research subjects; (1) spectroscopy of Ξ-hypernuclei, (2) studyof double-Λ-hypernuclei by sequential pionic decays for S = −2 systems, and (3) γ-ray
spectroscopy of Λ-hypernuclei for S = −1 systems. The LoI was classified as one of
the two “Day-1” experiments by the Nuclear and Particle Physics Facility Committee(NPFC) in 2003. The NPFC recommended to construct the K1.8 beam line with highpriority and encouraged us to consider the experimental plans in detail toward the full
proposal.
This is the proposal to perform spectroscopy of Ξ-hypernuclei; one of the major re−+searches mentioned in the LoI. We will observe 12
Ξ Be for the first time via the (K , K )reaction with a good energy resolution and enough statistics using high intensity K −2

-/.02143507698;:<1, '    
    !"#"$%&     !"

+'
g

[d ef

*'

bc
_a`
Y[\^]
Y XZ
W

)'
('
'
(

( ,

)
K
I
J

L
D
M
#
N
2
O
=?> @ A .#BDCFE<PFG#QS
HR#8 TVU

) ,

Figure 2: The incident momentum dependence of the forward angle laboratory crosssection for K − p → K + Ξ− taken from ref.[2].
beams at K1.8 beam line and newly constructed high-resolution spectrometers. This
will be the first but significant step toward future exploration to the multi-strangenesshadronic systems.
The high intensity K − beam at ∼1.8 GeV/c available at J-PARC Hadron Facility isquite unique to open a new frontier of strangeness nuclear physics in the spectroscopic
studies of strangeness S = −2 systems (Fig.1); here, the S = −2 systems include
Ξ-hypernuclei, double-Λ-hypernuclei, and possibly H-hypernuclei. This is not only
a step forward from S = −1 systems as a natural extension, but also a significant
step to explore the multi-strangeness hadronic systems; in the course of the limit,
strange hadronic matter (S = −∞) in the core of a neutron star is our concern. It isalso important to extract quantitative information on ΞN and ΛΛ interactions fromthe spectroscopic data, considering the fact that there exists almost no data on theseinteractions at this moment. Hence, we can explore the SU(3) character of the strong
forces of QCD.

1.1

Previous Studies on S = −2 Systems

The (K − , K + ) reaction is one of the best tools to implant the S = −2 through theelementary process, K − p → K + Ξ− , the cross section of which in the forward angle
has a broad maximum around the momentum of 1.8 GeV/c as shown in Fig.2. This3

( %1/( .(.

Figure 3: The missing mass spectra for 12 C(K − , K + ) reaction obtained in KEK-E224(left) and BNL-E884 (right) taken from ref.[9] and [10]. Curves in the figures arecalculated spectra using various potential depths taking the experimental resolutions
into account.
reaction has been used for studies of S = −2 systems so far.
As for the Ξ-hypernuclei, there exist some hints of emulsion events for the existence.
However it is still not conclusive. Some upper limits on the Ξ-nucleus potential havebeen obtained from the production rate and spectrum shape in the bound region of
Ξ-hypernucleus via 12 C(K − , K + ) reaction[9, 10]. In these experiments, Ξ-hypernuclear
states were not clearly observed because of the limited statistics and detector resolution(Fig.3). As shown in the figure, the potential depth, VΞ , is favored to be ∼ −14 MeV
for A = 12 when a Woods-Saxon type potential shape is assumed.
As for double-Λ-hypernuclei, several emulsion events were reported[3, 4, 5, 6, 7].
Among them, however, Nagara event recently found in a hybrid-emulsion experiment,
KEK-PS E373, was able to be cleanly identify the 6ΛΛ He. The mass of the 6ΛΛ He and thus
Λ-Λ interaction energy, ∆BΛΛ , has been measured for the first time. It demonstrated

4

that Λ-Λ interaction is weakly attractive; weaker than that estimated before. The
production of 4ΛΛ H was also reported in a counter experiment by detection of pairs ofpions in sequential mesonic weak decays[8]. However, ∆BΛΛ was not well determined
due to poor statistics and the insufficient resolution.
A lot of searches for H-dibaryon have been carried out from the late 1980s to 1990s.
No evidence has been observed so far. The observation of the weak decays from doubleΛ hypernuclei limits the allowed mass range of the H very close to twice of mass of Λ.
There are suggestions that H-particle may exist as a resonance and/or the “H”-type
configuration might be mixed in the S = −2 systems.

1.2

Spectroscopy of Ξ-Hypernuclei and S = −2 Systems

The Ξ-hypernuclei will play an important role in the investigations of S = −2 systems
as the entrance channel to the S = −2 world. In Fig.4, typical energy spectrum anddecay threshold for Ξ- and double-Λ hypernuclear configurations are shown. Produced
Ξ-hypernuclear states eventually decay into several forms of double-Λ systems througha strong conversion process, Ξ− p → ΛΛ. Moreover, Ξ-hypernuclei give valuable information on the S = −2 baryon-baryon interactions such as ΞN , and ΞN → ΛΛ. At
this moment, we still even don’t know whether the ΞN interaction is attractive or not,thus nor if Ξ-hypernuclei really exists or not. Although, the BNL E885 claims theevidence[10].
While single-Λ and double-Λ hypernuclear ground states decay via weak interaction and therefore they are long-lived, Ξ-hypernuclei decay via the strong interaction
through a conversion process Ξ− p → ΛΛ (Q=28.3 MeV). This situation is very similarto Σ-hypernuclei in which the strong conversion process ΣN → ΛN (Q ∼75 MeV) also
exists and broadens the width of the states. However, Ξ− p → ΛΛ conversion occurs
in the 1 S0 (T =0) state, a weight of which is only 1/16 even in the nuclear matter. Although it depends on the interaction models, the width for finite nuclei may be reduced
to ≤1 MeV due to the reduction of the phase space and the reduction of an overlap of
the wave functions. The calculated widths in several interaction models are listed inTable 1 for the nuclear matter and Table 2 for finite nuclei.
Therefore, it is expected that the spectroscopy of the Ξ-hypernuclei is promising.
Here we use the (K − , K + ) reaction in which we can use the same method as in the(π + , K + ) reaction succeeded for the Λ-hypernuclear spectroscopy. The (K − , K + ) reaction has the following characteristics in comparison with the (π + , K + ) reaction.
1. A Ξ− is produced with a large recoil momentum similar to a Λ for the (π + , K + )reaction; pΞ ∼500 MeV/c and pΛ ∼350 MeV/c. Due to the large momentum
transfer of the reaction, spin-stretched states can be selectively populated as in
the case of Λ-hypernuclei by the (π + , K + ) reaction. This selectivity helps us
to observe well-separated peak structures even for heavy targets among many
possible excitations.

5

°²±7³£´µ·¶¹¸»º·³½¼<¾ ´¿ÁÀÂ·ÃÄ¸ÆÅ£ÇÈÊÉS¶É<¾³DÀËÉK?;& mx&y z{o|<} ~VS{5¦} ~V Ù­Ú Û"Ú Ü ÞS{5¦} ~V Ù­Ú Û"Ú ÜvÝx&yÓ×{o|<}   Ì7ØÎÌxy; z {o|<}   Ì  ÍåæÏÒÑ nÓsl#kFq"np Ô Ñ < K^& S&{5¦Ö}  Ù­Ú Û"Ú ÜvÝ ÖÞx&y 
z  {o|<}   ÑÖ&

{5¦}   Ù­Ú Û"Ú ÜvÝ  ×Õ ¢£¤  ¡£¢D¤ÌÌßáàãâ Î ßD } 

Ì·ÍÎÌÐÏÒÑ nÓsl#k­qnp Ô Ñßáàãä  ßD } &h¥{5¦}  hjiFkmlonp qFr sutvkFww§¨s/k/©«ª¬s­q®k¯®w

Figure 4: Typical energy spectrum and decay threshold for S = −2 system; Ξ- anddouble-Λ hypernuclear configurations.
2. The large momentum transfer of the reaction, however, means small nuclear
form factors. The transition form factors (c.f. overlap of the wave functions )are smaller than those for the (π + , K + ) reaction. Therefore smaller production
cross section is expected.
3. The (K − , K + ) reaction converts a proton to a Ξ− with double charge exchange,
while the (π + , K + ) reaction converts a neutron to a hyperon. Therefore theproduced hypernuclei are neutron-rich in general.
4. In other word, the isospin transfer of the reaction is 1. Therefore only the statesof ∆T = 1 transition can be excited.
5. There could be a possibility to have some strengths for unnatural-parity (spin6

F .(.(D %1/$*6

0H9

E .(.(D0H90H9

12Figure 5: 12
C(π + , K + ) reaction at BNL (a)[14], KEKΛ C spectra measured in the
E140a (b)[15], and KEK E369 (c)[16]. Missing mass resolutions are 3, 2, and 1.45
MeV (FWHM), respectively.

flip) transitions, while no reliable prediction exists. The data on the elementary
production [11, 12] are too uncertain to conclude whether spin-flip amplitude issizable[13].
6. The cross section of the elementary p(K − , K + )Ξ− process is considerably smaller
than that of the n(π + , K + )Λ reaction; 35 µb/sr for the (K − , K + ), while ∼500
µb/sr for the (π + , K + ).
In spite of several demerits such as a small cross section, the (K − , K + ) reactionis the best tool for the reaction spectroscopy of Ξ-hypernuclei. The previous studies
were not able to clearly conclude the existence of the Ξ-hypernuclear states. This isbecause that their detector resolution was not so good to identify the states and thestatistics was not enough to detect the states with such small cross sections.
The good resolution is crucial for the spectroscopy as demonstrated in Fig.5 for Λ12C(π + , K + )hypernuclear spectroscopy. The figure shows 12
Λ C spectra obtained in thereaction at BNL[14], KEK E140a[15], and KEK E369[16], the resolutions of which were3, 2, and 1.45 MeV (FWHM), respectively. Thanks to the best energy resolution of7

Table 1: Ξ potentials UΞ and partial wave contributions in nuclear matter at normal
density, calculated with NHC-D, Ehime and ESC04d∗ . Conversion widths in nuclear
matter, ΓΞ , is also listed. Unit is MeV.
Model
NHC-D
Ehime
ESC04d

∗

T
0
1
0
1
0
1

1

S0
−2.6
−3.2
−0.9
−1.3
6.3
7.2

3

S1
0.1
−2.3
−0.5
−8.6
−18.4
−1.7

1

P1
−2.1
−3.0
−1.0
−0.8
1.2
−0.8

3

3
3
UΞ
P0
P1
P2
−0.2 −0.7 −1.9
−0.0 −3.1 −6.3 −25.2
0.3 −2.4 −0.7
−0.4 −1.7 −4.2 −22.3
1.5 −1.3 −1.9
−0.5 −1.2 −2.8 −12.1

ΓΞ
0.9
0.5
12.7

1.45 MeV, several core-excited states were clearly resolved in KEK E369.
Therefore it is important to perform the reaction spectroscopy again by using thehigh-intensity K − beams at J-PARC and the spectrometers with a much improved
energy resolution. Convincing evidence for Ξ single-particle states would yield information on Ξ single-particle potential and the effective ΞN interaction. Several topics
are described bellow.
1.2.1

ΞN Interaction Model and Ξ-Hypernuclei

Since little is known for S = −2 baryon-baryon systems, especially ΞN system, there
is no established interaction model in S = −2 channels. This is mainly due to the lackof experimental data such as ΞN elastic and inelastic scattering. As a consequence,the derived one-body Ξ potentials, UΞ , are remarkably different among the available
interaction models. In some cases, they are even repulsive. Therefore the experimental
determination of UΞ is decisively important in order to obtain a reasonable interaction
model.
Here, we briefly show the calculation results[17] in three different interaction models;• Nijmegen Hard-Core model D (NHC-D)[18]• Ehime model[19]• Extended Soft-Core model 04d∗ (ESC04d∗ )[20]These models give attractive (negative) value of UΞ . The details of the interaction
models are described in Appendix.A.
Table 1 shows the calculated values of Ξ potential (UΞ ), conversion width (ΓΞ ) andpartial wave contribution in nuclear matter obtained in the G-matrix calculations withthree interaction models. In Table 2, the energies and widths for the Ξ− bound states
produced via the (K − , K + ) reaction on 12 C, 27 Al, 40 Ca, 89 Y are listed for four different
8√Table 2: Energies, widths and mean radii, r = < r 2 >, predicted by NHC-D, Ehime
and ESC04d∗ . The Ξ− -nucleus potentials are obtained by folding the ΞN G-matrix
interactions. The results for the Woods-Saxon potential with VΞ0 = −14 MeV are also
listed.
Target

E

NHC-D
Γ

E

Ehime
Γ

r

[MeV]

[MeV]

[fm]

−4.4
−1.9

0.5
0.5

−14.9
−8.4
−7.1
−2.0

ESC04d∗
E
Γ

r

r

W.S.
E

[MeV]

[MeV]

[fm]

[MeV]

[MeV]

[fm]

[MeV]

3.2
3.7

−4.5
−1.9

0.3
0.2

3.1
3.7

−4.6
−2.1

4.6
3.9

3.3
3.7

0.7
0.7
0.4
0.3

2.0
2.2
3.4
4.0

−13.4
−7.3
−5.9
−1.1

0.2
0.2
0.2
0.1

2.3
2.6
3.6
4.5

−10.1
−4.7
−5.2
−0.8

5.7
4.7
2.8
1.9

3.0
3.4
4.1
5.1

−5.1

−19.7
−10.8
−13.7
−5.7

0.6
0.6
0.5
0.4

2.2
2.4
3.0
3.3

−18.7
−9.9
−11.5
−3.9

0.2
0.2
0.2
0.2

2.4
2.6
3.3
3.7

−14.1
−6.2
−9.3
−2.4

5.9
4.9
3.3
2.5

3.0
3.4
3.9
4.5

−6.5

−31.4
−16.4
−26.2
−12.0
−20.6
−7.3
−14.8

0.6
0.6
0.5
0.4
0.4
0.3
0.3

2.3
2.5
3.0
3.2
3.5
3.9
4.1

−29.8
−15.0
−23.6
−9.8
−17.3
−4.6
−11.0

0.2
0.2
0.2
0.2
0.2
0.1
0.1

2.5
2.8
3.3
3.6
3.9
4.4
4.6

−22.4
−8.5
−17.8
−5.3
−13.3
−2.0
−8.7

6.5
5.2
3.9
2.8
2.4
1.7
1.6

3.0
3.7
4.0
4.6
4.7
5.5
5.4

12 C [12 Be]
Ξsw/o Coulomb
27 Al [27 Na]Ξsw/o Coulombp
w/o Coulomb
40 Ca [40 Ar]Ξs
w/o Coulombp
w/o Coulomb
89 Y [89 Rb]Ξs
w/o Coulombp
w/o Coulombdw/o Coulomb

f

−2.2

−1.2
−9.0
−4.6
−0.2

potentials; three Ξ-nucleus potentials obtained from the ΞN G-matrix interaction and asimple Woods-Saxon type potential with the depth of −14 MeV. It should be noted that
NHC-D and Ehime models predict deep UΞ and strong mass-number (A) dependencefor Ξ energies. This is owing to the strong odd-state attractions which come from thelack of space-exchange terms in one-boson-exchange potential picture. On the other
hand, ESC04d∗ model predicts the energies very close to those with the Woods-Saxon
potential, when the Coulomb interactions are switched off. Therefore, the experimental
data on not only the Ξ-binding energies but also the their A-dependence have valuable
information to probe the ΞN interaction. It should be also noted that the conversion
widths for ESC04d∗ and NHC-D/Ehime are very different from each other.
For s- and light p-shell systems, NHC-D and Ehime give rise to almost no Ξ boundstate because of their weak even-state attractions, when the Coulomb interactions are9

switched off. In the case of ESC04d∗ , however, interesting Ξ bound states such as4+3Ξ H(0 ) are produced owing to the strong attraction in the S1 (T = 0) state. Unfortunately, most of them cannot be produced through the (K − , K + ) reaction. One
interesting possibility is to use a proton-rich target such as 3 He.
1.2.2

Ξ Potential and Hadronic Matters

Knowledge of the depth of the Ξ-nucleus potential is also important for estimating theexistence of strange hadronic matter with Ξ. For a long time, it was believed thatΣ− hyperons would appear in neutron stars earlier (i.e. at lower density) than evenlighter Λ hyperons due to their negative charge. However, recent data[21], strongly
suggest that the interaction of the Σ− with neutron-rich nuclear systems is strongly
repulsive, which means Σ− hyperons can no longer appear in neutron stars. It wasargued that the disappearance of Σ− does not necessarily leads to crucial changes ofneutron star features if they were substituted effectively by Ξ− hyperons. Furthermore,
it is also argued quite recently that even K − mesons may appear in neutron stars after
the discovery of deeply-bound kaonic nuclear systems[22, 23, 24]. However better
understanding of ΞN interaction is necessary for a definite conclusion. With respect
to the structure of the neutron star, it becomes much more important to investigate
the Ξ dynamics than it was considered previously because the Σ-nucleus repulsion has
been established.
1.2.3

Mixing of Other S = −2 States

It has been discussed the possibilities of the mixing between Λ- and Σ-hypernuclear
states in S = −1 system through the ΣN -ΛN couping. For example, the admixtureof Σ states is estimated approximately 1% at A = 4 hypernuclei[25]. This couplinginteraction also produces 3-body force via (N -Λ)-N → N -Σ-N → N -(Λ-N ). The
mixing and the 3-body force are important to reproduce the energy levels for few bodyΛ-hypernuclear systems. In the case of S = −2 systems, on the other hand, the massdifference between ΞN and ΛΛ is much smaller (∼28 MeV) than the one between ΣNand ΛN (∼75 MeV) for S = −1 systems. Therefore the state-mixing and the mixing
process are expected to play more important roles in S = −2 systems than in S = −1
systems.
The existence of 4ΛΛ H is brought in question by many authors[26, 27]. The ΛΛinteraction deduced from 6ΛΛ He is so weak that pnΛΛ system is not bound in simple
calculations. However, it is argued recently that this contradiction can be resolved if
one takes the ΞN -ΛΛ couping into account when the ΞN interaction is attractive[28].
Therefore the nature of the ΞN interaction affects the existence of light double Λhypernuclei and thus the ΛΛ interaction deduced from them.

101.2.4

Observation of Double-Λ Hypernuclei

Through the (K − , K + ) reaction, double-Λ hypernuclei could be produced directly
through a two-step process, K − p → Λ(π 0 , ρ0 , ω), (π 0 , ρ0 , ω)p → K + Λ or K − p →K + Ξ− , Ξ− p → ΛΛ. Since these double-Λ hypernuclear states are kinematically separated from the Ξ-hypernuclear states, we can easily identify these states with good energy resolution of ∼3 MeV. However, a theoretical estimation for 16 O(K − , K + )16ΛΛ C[29]
suggests a very small cross section for the ground state but a few nb/sr for the excitedstates at 1.1 GeV/c. If there were large mixing between Ξ hypernuclear states andthe excited levels of double-Λ hypernuclei, some enhancements would be expected forthe excitation. This method has a unique advantage to allow us direct access to theexcited states of double-Λ hypernuclei.
There are a lot of interesting and important physics in the study of the Ξ-hypernucleusof new S = −2 world. It is emphasized here that the J-PARC is the only facility inthe world which can explore the S = −2 world.

2

Purpose of the Proposed Experiment

Main physics goal of the experiment proposed here is to obtain the conclusive resultson the existence of Ξ-hypernuclei by observing bound states of Ξ hypernuclei via the(K − , K + ) reaction with the best energy resolution of a few MeV so far achieved and inlarge statistics. For this purpose, we will construct two high-resolution spectrometersfor K − beam and scattered K + ’s.
We will measure the 12 C(K − , K + ) reaction as a first step of a series of measurements on various targets. This is because the previous BNL measurement with thesame reaction claimed a substantial number of events in the bound region of 12
Ξ Be,
and the production cross section was estimated already although the statistical error
was large. Thus, a rather reliable design of the experiment is possible for this reaction. An unambiguous experimental observation of Ξ-hypernuclear bound states isvery significant progress even in a single target.
Further, in the previous measurement, the potential depth of ∼14 MeV was extracted from the shape analysis near the Ξ binding threshold with a help of theoretical
calculations. It suggests that we could definitely observe a bound state peak distinguished from the quasi-free continuum as shown in Fig.6. This figure shows the−potential
calculated spectra for the 12 C(K − , K + )12
Ξ Be reaction for Woods-Saxon Ξwith the depths of −14 MeV and −20 MeV without smearing the experimental resolution [10]. The figure demonstrates the importance of the good resolution of themeasurements when one compares it with the right-top of Fig.3. A peak position will
give us more direct information of the depth of Ξ-nucleus potential than the previous
shape analysis.
The width of the bound state peak also has information on the imaginary part ofthe Ξ-nucleus potential, or the ΞN inelastic channel. Thus, even no observation of
11

Figure 6: The calculated spectrum for 12 C(K − , K + )12
Ξ Be reaction for Ξ potential depthsof −14 MeV (solid) and −20 MeV (dotted) taken from ref.[10]. The cross section has
been averaged over the kaon angular range from 0◦ to 14◦ .
clear peaks is also informative because it may be due to a large spreading width. Onthat account, a well experimental control of the energy resolution in the measurement
is very important. Fortunately, we can use the elementary process of K − p → K + Ξ−
for this calibration with a CH2 target.
Anyway, nobody has ever succeeded to observe any peaks for Ξ-hypernuclei or
double-Λ hypernuclei in the (K − , K + ) spectroscopy. Therefore, at this moment, we
think it is important to establish the methodology of the (K − , K + ) spectroscopy like
we did it for the (π + , K + ) spectroscopy. Here the methodology means not only the
hardware devices such as a beam line spectrometer, a high-resolution K + spectrometer,
etc. but also know-hows to operate the new devices keeping good performances, tounderstand the production rate and backgrounds, and to even establish the analysis
method. Once the methodology is well established, it is relatively easy to plan further
measurements on other targets or other objects such as double-Λ hypernuclei withsome modifications and/or upgrade of the detectors. In this regard, we think the12C(K − , K + ) reaction is the best choice to start with.

12

Table 3: Design parameters of K1.8 beam line

Max. Mom.
Length
AcceptanceElectro-static Separator
K − Intensity[GeV/c][m][msr·%][/spill]
1.8 GeV/c
1.1 GeV/c−−
K /π @ FF@ 1.8 GeV/c
X / Y(rms) size @ FF[mm]
Singles-rate @ MS2@ 1.8 GeV/c

3

Phase-II
Phase-I(50GeV-15µA) (30GeV-9µA)
2.045.853
1.4
750 kV/10 cm, 6 m × 2
6.6 × 106
3.8 × 1058
19.8 / 3.2>3.3 × 107

1.4 × 106
8.0 × 104
6.9
>8 × 106

Experimental Methods and Apparatus

Ξ hypernuclei are produced via the (K − , K + ) reaction. As described in ref.[2], theforward-angle laboratory (differential) cross section of the elementary process, K − p →K + Ξ− , peaks at around the incident momentum of 1.8 GeV/c. In the case of nuclear targets, the momentum dependence is somewhat smeared out by Fermi motion.
However, the optimal beam momentum is also around 1.8 GeV/c. In this case, theoutgoing K + momenta range from 1.3 to 1.4 GeV/c. Produced hypernuclear states aremeasured as a missing mass of the reaction. Therefore, we need spectrometers with agood resolution both for the incident beam and the outgoing particles.

3.1

K1.8 Beam Line and Beam Analyzer

Design work of the K1.8 beam line was already finished by the J-PARC hadron beamline construction group after NPFC meeting held in 2004. Figure 7 shows a beam line
layout together with the K + spectrometer in the K1.8 experimental area. In Table
3, design parameters are listed. Figure 8 shows beam envelope of the K1.8 beam line
calculated by TRANSPORT. The beam line has two characteristic features; (1) highintensity and high-purity K − beams are obtained. (2) a high resolution beam analyzer
is located at the end of the beam line. These features are required and optimized toperform the spectroscopic studies on Ξ-hypernuclei.
The beam line has two stages of electro-static separators (ES1 and ES2) with two
mass slits (MS1 and MS2) in order to separate kaons from pions and other particles atthe level of K − /π − ratio greater than 5. Optimization study of the shape of the mass
slits is still in progress in order to further improve the K − /π − ratio and decrease theunwanted particle rate at the upstream of the beam analyzer.
13

4
4
'
4
4
4
4
(6
&0
4 &0'
4
6 06
4
2 6
&0
7WDUJHW
06
&0 (6
6
))
' 4
' 4 4
4
26
%HDP
$QDO\]HU

Figure 7: The layout of K1.8 beam line and K1.8 area.
The beam analyzer located after MS2 comprises QQDQQ magnets and four sets oftracking detectors. The QQDQQ optics is tuned to point-to-point focus condition and< X|θ >= 0 in order to minimize the multiple scattering effect on the resolution. The
expected momentum resolution ∆p/p is 1.4 × 10−4 in rms when a position resolutionof 200 µm is realized in the tracking detectors placed before and after the QQDQQ
system.
The tracking detectors are one of the most important detectors in the beam line.
They should be as thin as possible to keep good energy or momentum resolutionof the beam analyzer. They should also work with good enough resolutions and goodefficiencies under high-rate environment. When we use flat top of 0.7 seconds operation
at the Phase-I full intensity ( 30GeV-9µA ), the charged particle rate at downstreamof the QQDQQ magnet is expected to be 1.4×106 ×(7.9/6.9) / 0.6 = 2.67 × 106 /sec..
Higher rate of one order of magnitude is expected at the upstream of the QQDQQ,
due to the kaons not decayed yet and other background particles scattered at MS2 etc.
A wire chamber is one of such detectors with thin materials and high-rate capability.
At KEK-PS K6 beam line, we could operate drift chambers with the anode-spacingof 5 mm under 3 – 4 ×106 pions/spill on the target with the flat-top length of 2.0
seconds. The particle rate at the upstream of the beam spectrometer was estimated
14

(cm)
25

K1.8 Beam Line Optics
D
1

Q
1

Q
2

D
2

W C
N O
D L
W

Q
3

IF
I
F

Q S
4 1
O
1

F:5.656m
M:0.6@MS1
S Q
2 5

C
M
1

Q
6

C
M
2

D
3

M
S
1

(Beam envelope to the 1st Order)
F:5.038m
M:-0.8@MS2

Q S
7 3

S Q
4 8

O C
2 M
3

C
M
4

Q
9

O
3

Q
1
0

M
S
2

Q
1
1

D
4
A

D
4
B

D D
4 4
C D

Q Q
1 1
2 3

V
I

V
O

(%/cm)-25

FWCIOCCMOCCOMVFNOF1MMS2MM3SI
DL 121 34 2
W

Vertical

QQDQQ
ES1

ES2

Horizontal

0

25
(cm)

1
3
.
0
9
9

7
.
6
0
0

7
.
4
0
9

1
7
.
4
6
5

7
.
9
0
0

8 0
. .
8 5
0 7
0 1

- 1 6
. .
4 5
3 1
6 5

7
.
6
3
9

1
4
.
1
1
6

- 5 1
. .
3 5
0 8
0 5

0 8
. .
2 6
5 6
0 0

1
0
.
6
2
7

9
.
7
8
9

7
.
9
9
5

1
5
.
0
1
0

1
5
.
0
1
0

1
5
.
0
1
0

1
5
.
0
1
0

Total Length:45.853 m

8
.
5
0
0

6
.
7
0
1

25

(%/cm)
3 Vertical Slits: IF and 2 Mass Slits (MS1,MS2)
5
to purify kaon beam with 2 Electrostatic Separators

Figure 8: Beam envelope of the K1.8 beam line calculated by TRANSPORT.
to be twice as high as that at the downstream. Thus, these chambers should be able
to be operated under the rates of 4 ×106 / 2 × 2 = 4 ×106 /second. Taking accountof the beam size, we will use MWPCs with 1 mm anode pitch and drift chambers withanode pitch of 3 mm at the upstream and downstream parts of the QQDQQ magnets,
respectively.
Segmented plastic scintillator hodoscopes will be located at the upstream and downstream of the beam analyzer for trigger and offline particle identification. Aerogel
Cerenkov counter located just upstream of the target (BAC) will be also used in thetrigger level. Time of flight measurement between two beam hodoscopes whose distanceis ∼8 m can separate kaons from pions at 1.8 GeV/c in offline analysis.

15

6.6

6'&

1HZ
'0DJQHW

6'&
72)
$&
*H9F
*H9F

6'&
6'&

6'&
6'&

*H9F

Figure 9: SksPlus Spectrometer in consideration.

3.2

Spectrometer for Scattered Particles

For the K + spectrometer, we will use the existing SKS spectrometer with some modifications. The K + momentum corresponding to the production of Ξ-hypernuclei isaround 1.3 GeV/c. The SKS maximum magnetic field of ∼2.7 T does not allow us
to put the central ray at 1.3 GeV/c. Therefore, the central ray is shifted outer side
and a dipole magnet with ∼1.5 T will be added at the entrance of the SKS magnet
as shown in Fig.9. Although a detailed design is still in progress, a simulation showsthat the spectrometer, ( called as SksPlus ), has a solid angle of ∼30 msr with theangular range up to 10◦ , and momentum resolution ∆p/p = 0.17% (FWHM) when
the position resolution of 300 µm in rms is achieved. (Fig.10)
We will use 6 sets of drift chambers (SDC1–6) as tracking detectors of the SksPlus
spectrometer. The SDC1 and SDC2 located after the target should be high-rate chambers, since the beam particles will directly pass through. These chambers are similar
to the beam line chambers except for the size. Other chambers do not require highrate capability, because the beam does not pass through these detectors thanks to the
double-charge-exchange reaction. The SDC3 will be installed between the newly installed dipole magnet and the SKS magnet in order to tune up the spectrometer optics
16

Figure 10: Momentum acceptance (left) and resolution (right) of the SksPlus spectrometer from simulation.
etc. Once we understand the optics and establish the analysis method, this detector
may be removed in order to avoid multiple scattering.
For trigger and particle identification, the following detectors will be used; TOF
wall, Aerogel Cerenkov counters (AC), Lucite Cerenkov counter (LC), and possibly
water Cerenkov counter. These detectors as well as SDC4–6 are reused ones in theexisting SKS detectors.

3.3

Missing Mass Resolution

The energy resolution is a key point in the experimental point of view for the spectroscopy. The resolution should be better than the spacing of the hypernuclear levels
and comparable to or better than the widths of the states. Here the energy resolution
is estimated.
Missing mass, M , is expressed as,
M 2 = (EB + mT − ES )2 − (~pB − p~S )2= m2B + m2S + m2T + 2 (mT EB − mT ES − EB ES + pB pS cos θ) ,(1)

where θ is scattering angle, m, E, p~ and p are mass, energy, three-momentum andmagnitude of the momentum, respectively. Suffixes B, S and T mean beam andscattered particles, and target, respectively. By differentiating above equation, missing
mass resolution, ∆M is expressed as follows,
∆M

2

∂M
∂pB

!2

!2

∂M
∂M
∂M
∆p2B +∆p2S +
=
∂pB
∂pS
∂θ
1
=
[βB (mT − ES ) + pS cos θ],
M
17

!2

2
∆θ 2 + ∆Estrag.
,

(2)
(3)

Table 4: Estimated energy resolution from individual terms in MeV.
+

H(K , K )ΞC(K − , K + )12
Ξ Be
−

12

∂M
∂pS
∂M
∂θ

−

∆pB ∆pS∆θ
0.39 1.56 0.30 1.64
0.56 2.26 0.04 2.33

1
[βS (mT + EB ) − pB cos θ],M1= − pB pS sin θ,M= −∆Estrag.
<2.0
<2.0

∆M
<2.6
<3.1

(4)
(5)

where βB and βS are velocities of the beam and scattered particles, respectively. ∆pB ,∆pS and ∆θ are resolution of the measurements of momenta of the beam and scatteredparticles and scattering angle, respectively.
Momentum resolution of the beam analyzer at 1.8 GeV/c is 1.4×10−4 × 2.355 ×1800 = 0.6 MeV/c(FWHM), while that of the K + spectrometer is assumed to be
2.5 MeV/c(FWHM). In Table 4, the expected energy resolution for each reaction at
scattering angle of 5◦ are listed assuming spectrometer resolution above and angle
resolution of 2 mrad. The contribution of the individual terms are also listed. Energy
resolution is mainly determined by the K + spectrometer as well as the energy loss
straggling in the target. In order to keep the resolution within the acceptable level,
c.f. 3 MeV, the energy loss straggling should be less than 2 MeV. Thus, maximum
thickness of a target is 5 – 6 g/cm2 .

3.4

Backgrounds and Trigger Rate

There is no physical background in the region of our interest except for the productionof double-Λ hypernuclei and a continuum component producing a single-Λ fragmentwith one Λ escaping. However, these states are of our another interest and can beeasily separated from the Ξ-hypernuclear states with a good energy resolution. The
quasi-free Ξ− production is a main contribution in the (K − , K + ) reaction. Thus misidentification of the beam and/or scattered particles as well as a wrong reconstructionof the momentum are possible background sources. However they seems to be within
our acceptable level.
Because of the double-charge-exchange reaction, the beam particles and negatively
charged particles are swept out by the first dipole. Therefore, negatively charged
particles such as K − from an elastic scattering, π − and µ− from K-decay, cannot reachthe trigger counters. The rate of K + is determined by the quasi-free Ξ production.
The cross section on carbon target was measured to be 99±4 µb/sr at 1.65 GeV/c[30].
On the other hand, momentum of the K + associated with Ξ∗− production is out of thespectrometer acceptance. Assuming the beam intensity of 2 MHz and neglecting the18decay factor, true K + trigger rate is estimated as,
dσ
× ∆Ω
(6)
dΩ
= 2 × 106 [Hz] × {5.4 × 6.02 × 10−7 /12}[/µb] × 100[µb/sr] × 0.030[sr]= 1.63[Hz].
(7)

R(K + ) = Rbeam × Ntarget ×

Three order of magnitude higher rates are expected for π + and protons than thatfor K + . The pions, however, can be easily suppressed by the existing AC in thetrigger level. Suppression more than 99% has been achived in the SKS experiments at
KEK-PS, although the momentum region is different; ∼0.7 GeV/c for KEK-PS, while∼1.3 GeV/c for J-PARC. Thus protons are main trigger backgrounds and have to be
suppressed by at least 10% level. The existing LC ( n = 1.49 ) is not efficient for p/K +discrimination in this momentum region, although they can be somewhat separated by
the light outputs. Therefore, we are going to prepare a water ( n = 1.33 ) Cerenkov
counter. Another choice is to use an aerogel counter with the index of ∼1.2, which
has been recently available. A counter of small-size can be installed downstream of thetarget, though it may affects the energy resolution.
Anyway, trigger rate of several hundreds Hz can be handled by the existing frontend modules such as TKO and VME as well as a new DAQ system.

4

Yield Estimation

The production cross sections of the Ξ-hypernuclei in the (K − , K + ) reaction havebeen calculated by several theorists within the framework of distorted-wave impulse
approximation (DWIA)[31, 32]. In the calculation using the Kapur-Peiers method
assuming Woods-Saxon type potential for Ξ− in the nuclei,
V0Ξ,
1 + exp((r − R)/a)
R = r0 (A − 1)1/3

V (r) =

(8)
(9)

with r0 = 1.1 fm and a = 0.65 fm, the forward angle laboratory cross section forC(K − , K + )12
Ξ Be(s-state) at p = 1.6 GeV/c is estimated to be from 215 to 81 nb/sr
for the potential depth of V0Ξ = −24 to −12 MeV[31]. Another calculation using Greenfunction method and the complex Woods-Saxon potential[32] gives similar results; 250
nb/sr for V0Ξ = −24 MeV. Table 5 summarizes the calculation results.
On the other hand, experimental studies reported cross sections, although they
could not observe the bound states clearly due to the insufficient experimental resolution and statistics[9, 10]. The BNL AGS-E885 reported that the cross section for
12
C(K − , K + )12
Ξ Be reaction at p=1.8 GeV/c is 89±14 and 42±5 nb/sr for the angularaverage from 0◦ to 8◦ and from 0◦ to 14◦ , respectively[10], while KEK-PS-E224 reported 0.21±0.07 µb/sr for the region of EΞ ≤ 7 MeV, which is angular averaged from

12

19

Table 5: The calculated cross sections at 0◦ for 12 C(K − , K + )12
Ξ Be reaction at p = 1.6
GeV/c for various potential depths from [31].

statess-state
0p3/2 → 0s1/2
p-states
0p3/2 → 0p3/2
0p3/2 → 0p1/2
sum

−24
1−

215

0+
2+
2+

29
164
152
345

V0Ξ [MeV]−20 −16 −12[nb/sr]168 12381[nb/sr]
20
—
—
103
—
—
93
—
—
216
—
—

0◦ to 12◦ at p=1.65 GeV/c[9]1 . Here we take 60 nb/sr for carbon target, taking into
our angular acceptance of from 0◦ to 10◦ .
For the number of K − , we can expect 3.7×1010 /day for 1.4×106 [/spill] when wechoose flat-top length of 0.8 second, which corresponds to the singles-rate of 2.0 MHz
at the target as shown in Fig.11.
Thus the yield of 12
Ξ Be is estimated as follows,dσ
× ∆Ω × fdecay × fanalysisdΩ
3.7 × 1010 [/day] × {5.4 × 6.02 × 10−7 /12}[/µb]×0.06[µb/sr] × 0.030[sr] × 0.5 × 0.7
6.3[/day]45[/week]
190[/month].

Y (12 C) = Nbeam × Ntarget ×
=
=
∼
∼

(10)

(11)

Therefore, we need ∼1 month data-taking for 12 C(K − , K + )12
Ξ Be reaction. For heavier
targets, production cross sections are not reliably calculated since Ξ− potential depth,
especially the A-dependence, is not known at all. Even if the cross section is as large
as that for the carbon target, the yield is proportional to 1/A from the target thickness
due to the energy resolution.
On the other hand, the cross section for H(K − , K + )Ξ− which is used for tuning
and calibration of the beam and K + spectrometers, was measured to be 35±4 µb/sr
at 1.65 GeV/c[30]. The yield for the elementary Ξ− production using CH2 target with
5 g/cm2 is estimated as,
Y (elem) = 3.7 × 1010 [/day] × {5 × 6.02 × 10−7 × 2/(2 + 12)}[/µb]1

In ref.[10], cross section for E224 is cited to be 60±45 nb/sr for the bound region.

20

Figure 11: The instantaneous beam intensity and total number of K − per day against
flat-top length of the accelerator operation.
×35[µb/sr] × 0.030[sr] × 0.5 × 0.7= 5.8 × 103 [/day].

(12)

This number is large enough for performance study of spectrometers, tuning, andcalibration.

5

Requested Beam Time

Here we summarize the requested beam time.
• Stage.0
K1.8 beam line study and tuning for K − beams
3 – 4 weeks• Stage.1
Detector tuning, trigger tuning etc. Spectrometer performance check such as
optics, resolution, and acceptance using CH2 target.
2 weeks• Stage.2
Measurement of 12 C(K − , K + )12
Ξ Be reaction.
4 weeks• Stage.3 ( future extension )Measurement on a heavy target, for example, 89 Y.
3 months
21

9 0H9: 0H99 0H9: 0H9

Figure 12: The calculated spectra for 208 Pb(K − , K + ) reaction taken from ref[32]. Realpart of the Woods-Saxon potential is taken to −24 MeV, while imaginary part is taken
to −1 MeV (left) or −3 MeV (right).
Studies at Stage.1 can be performed with lower beam intensity, c.f. 10% of thefull beam intensity, because the production yield for the elementary process is large
enough for the spectrometer optics study, etc. The operation and performance studies
for the beam line counters under high-rate circumstance can be done shortly by using
π − beams instead of K − .
At Stage.2, however, full intensity or at least half of the full intensity beam at Phase
1 is needed. Here, the full intensity means so-called 30 GeV-9 µA primary beam whichcorresponds to 1.4×106 K − [/spill].
At Stage.3, although we have no intention to request the beam time at this moment,
we will require higher beam power, by means of 15 µA operation or beam energy
upgrade, etc.

6

Future Extension

Although the measurement on 12 C target proposed here is a significant and essential
step to investigate Ξ-hypernuclei, it is necessary to extend the measurements for avariety of targets to fully explore plentiful physics in the S = −2 and multi-strangenesssystems.
Two directions are considered to extend our studies on Ξ-hypernuclei and ΞNinteraction.
One is to go on heavier targets to measure the A-dependence of the single-particle
potential of Ξ by using a few targets in a wide mass number range. As described22

in ”Introduction”, the A-dependence of Ξ-binding energies has a key information for
discriminating the underlying ΞN interaction models. The measurement with heavy
targets is also essential to obtain the Ξ-potential in nuclear matter at normal density,
which is necessary in the study of high-density hadronic matters such as a core ofneutron star.
Furthermore, for heavy nuclei, the Coulomb force becomes more attractive to bind−
Ξ more deeply (so-called Coulomb-assisted states). It is also argued that very narrow peaks with a large orbital angular momentum can be observed in the heavy Ξhypernuclei as shown in Fig.12. In such states, a Ξ− stays at the surface region of low
nucleon density due to strong centrifugal barrier. Therefore, the ΞN → ΛΛ conversion
is suppressed, and the conversion width is reduced. Since large production cross sections can be expected for such peculiar states, it may be possible to observe such states
within a reasonable beam time, if we could increase the primary beam intensity with
15-bunch operation. For example,in the 89 Y case, the number of events is expected as
15
12(thickness) × (intensity) × 2.4(time) × f
89
9= 0.54f N (12 C) ≥ 100(f ≥ 1),

N (89 Y) = N (12 C) ×

(13)

where f is the cross section ratio between 12 C and 89 Y targets.
The other direction is a search for p-n-Ξ− (n-n-Ξ0 ) state via the 3 He(K − , K + ) reaction. The existence of this bound state strongly depends on the spin-isospin structureof the ΞN interaction. At present, there is no reliable theoretical prediction whether
this three-body system is bound or not. If it is bound, however, this system might play
an important role in the study of ΞN interaction like a deuteron in the N N interaction.

7

Schedule and Cost Estimate

We are going to recycle or reuse the detectors in the existing SKS spectrometer system as many as possible when they fit for the (K − , K + ) spectroscopy, including thereadout and front-end electronics. However, several components should be newly constructed dedicated for the J-PARC experiment, such as beam line detectors including
their readout and an additional dipole magnet, by using the budget (Kakenhi) of
the Grant-In-Aid for Priority Areas, “Multi-quark systems with strangeness” (2005 –2009). These items are listed in Table 6.
Figure 13 shows the time schedule of the preparation for the proposed experiment.
The beam line detectors and their readout will be fabricated first with the highest
priority by the Kakenhi budget.
In addition to those instruments prepare by the experimental group, K1.8 beam line
including the beam analyzer system, and the SKS spectrometer without the additional
dipole magnet should be prepared by the J-PARC construction team as planned. Of
course, the experimental group is willing to work together from the installation. As
for the superconducting magnet of the SKS, the present large refrigerator system will23

FY2006

Beam Analyzer

magnet
MWPC, DCMWPC Readout
Counters

SksPlus Spectrometer
SKS
DipoleSDC1-3SDC4-6Counters (existing)Water Cerenkov

Design, R&D
R&D Test

FY2007Fabrication
Fabrication

FY2008Installation

Test
Production

FY2009Installation
Installation
Installation
Beam Tuning

DesignDisassemble Modification
Assemble & Test
Fabrication
Intallation & Field Meas.
DesignFabrication
Test
Installation
Test
Installation
Installation
DesignProduction
Installation

Area Construction
Electronics Hat
Ladder, piping, etc

Constructiuon
Construction
Beam time

Figure 13: Schedule of the preparation for the proposed experiment
be replaced by several small-sized GM-JT refrigerators with some modifications of thecoil and helium vessels. It will allow us for easy operation and maintenance with theestimated cost of ∼200M JYen in total.

24

Table 6: A list of items needed for this experiment
Item
Beam Analyzer
1mm MWPC ×2
3mm DC ×2
Readout Amp.& Discri.
MWPC Encoder
DC MultiHit TDC
Beam Hodoscope
Beam Aerogel Counters
Support Frame etc.
SksPlus Spectrometer
Dipole Magnet
Power Supply
DC (SDC1–3)
DC (SDC4–6)
TOF
AC ×2
LC
Water Cerenkov Counters
Readout Amp.& Discri.
DC M.H.Tdc and DrT-II
Support Frame etc.
Area Construction etc.
Electronics Hat
SKS Ref. Control Hat
AVR etc.
Cable Ladder
Gas piping, alarm system
Gas mixer system
CablesElectronics etc.
PMT P.S.’s
Racks, Bins, Crates etc
NIM, CAMAC, TKO modules
Discriminators
Trigger Logic (FPGA)DAQ System
Analysis Computer System
Data Storage
VME Crates and P.S.’s

Cost [kJY]
New
New
New
New
Existing
New
New
New

4,000
3,000
9,000
20,000
0
3,000
1,000
2,000

Kakenhi
Kakenhi
Kakenhi
Kakenhi

N/R
N/R
New
Existing
Existing
Existing
Existing
New
New
Existing
New

30,000Kakenhi

25,000Kakenhi

1,000
2,000
1,000
10,000
6,000
0
5,000

Kakenhi
Kakenhi
Kakenhi
Kakenhi
KakenhiReuse
RecycleNew
New
Existing
N/R
Existing
Existing
Existing
New
New
New
New
New
New

25

Kakenhi
Kakenhi

5,000
8,000
4,000
5,000
7,000
10,000Kakenhi

3,000
2,000
2,000
6,000
6,000
2,000

Electronics Pool
Electronics Pool
Electronics Pool
Kakenhi
Kakenhi
Kakenhi
Kakenhi
Kakenhi
KakenhiAΞN Interaction Models and Ξ-Potentials

Since little is known for S = −2 baryon-baryon systems, there is no established interaction model in S = −2 channels. SU(3)-invariant interaction models give usefulpredictions for unknown S = −2 sectors. The derived one-body Ξ potentials UΞ ,however, are remarkably different among interaction models. Here, we pick up thefollowing three interaction models, which give attractive (negative) values of U Ξ :• Nijmegen Hard-Core model D (NHC-D)[18]• Ehime model[19]• Extended Soft-Core model 04d∗ (ESC04d∗ )[20]
NHC-D and Ehime are One-Boson-Exchange (OBE) potentials. In these models,there appear the following important features:
1. When the scalar-meson nonet (octet+singlet) are taken into account straightforwardly, the derived ΞN interactions are not attractive enough to give attractive
values of UΞ . In the cases of NHC-D and Ehime, the attractive UΞ ’s are owing to
the following peculiar modeling: In the NHC-D case, only the unitary-singlet σmeson is included with neglect of octet scalar mesons, which gives universal attractions in all baryon-baryon (BB) channels. In the Ehime case, the additional
σ meson is included together with the nonet mesons.
2. In ΞN channels, strangeness −2 cannot be carried by a single boson, which leads
to no space-exchange term. Namely, the OBE parts of odd-state interactions are
the same as those of the even-state ones. Thus, the attractive values of UΞ are oflarge contributions from odd-state attractions, which brings about a strong mass
number (A) dependence of UΞ ; even if the UΞ ’s are shallow in light systems, thedeep values are expected in heavy systems.
3. In the case of NHC-D (Ehime), the hard-core radii (the coupling constant gΞΞσ )can be adjusted so as to reproduce the appropriate value of UΞ . In the present
calculations, they are adjusted so that the derived Ξ-11 B potentials are similar
to the Woods-Saxon potential with the depth of −14 MeV.
On the other hand, the features of the recent model ESC04d∗ are very different
from those of the above OBE models.
1. All exchange mesons and their coupling constants are of physical meaning, namely
no effective boson is included. The interaction parameters in S = −2 channels
are derived uniquely from those in S = 0 and −1 channels.
2. Even in ΞN channels, strangeness −2 can be carried by meson pairs, which leadto space-exchange terms. Then, the odd-state interactions in ESC04d∗ are far
26

less attractive than those in the above OBE models. An attractive value of UΞ isowing to the strong attraction in the 3 S1 (T = 0) state. This attraction produces
peculiar Ξ bound states in s- and light p-shell systems, differently from the casesof NHC-D and Ehime.
3. The ΞN -ΛΛ coupling interaction in ESC04d∗ is far stronger than those in NHC-D
and Ehime. This feature is due to the meson-pair exchange terms in ESC04d∗ .
The deep values of Ξ potential in nuclear matter at normal density, UΞ , for NHC-D
and Ehime in Table 1 are owing to the strong odd-state attractions, whose contributions are not so large in light systems. In the case of ESC04d∗ , the large attractive
contribution in the 3 S1 (T = 0) state turns out to be decisive role for the negative valueof UΞ . Another important difference between ESC04d∗ and NHC-D/Ehime is that theconversion width for the former is far larger than those for the latters.
The energies and widths, which is listed in Table 2, for Ξ− bound states are calculated by the spin- and isospin-averaged Ξ-nucleus potentials derived by folding theΞN G-matrix interactions into Skyrme-Hartree-Fock nuclear-core wave functions[17].
Calculations are performed with and without Coulomb interactions. Here, it should be
noted that the Ξ− s-state energies in 12
Ξ Be are more or less similar to each other. The
differences turn out to become substantial with increase of mass numbers A. Therefore,
the experimental information on the A-dependence of Ξ-binding energies is indispensable for discriminating the underlying ΞN interaction models. It is also important that
calculated conversion widths for ESC04d∗ and NHC-D/Ehime are very different fromeach other.
In order to obtain more realistic energies for Ξ bound states, one should add interaction energies between Ξ-particle and nucleon-hole (N −1 ) on the above Ξ binding−1
energies. For instance, the estimated values for h(s1/2 )Ξ (p3/2 )−1
p |VΞN |(s1/2 )Ξ (p3/2 )p iT J
12in Ξ− B are as follows (in MeV):T J NHC-D Ehime ESC04d∗
01
+0.7
+0.9
–1.2
02
+0.5
+0.4
–0.5
11
+0.3
+0.6
+2.2
12
+1.0
+0.6
+0.2
These values indicate that the Lane potentials for NHC-D and Ehime are weak, andthe one for ESC04d∗ is strongly repulsive. It should be noted that only T = 1 Ξ− p−1
states are produced by (K − , K + ) reaction. In addition, due to a large momentum
transfer in this reaction, the J = 2 state is expected to be more strongly excited thanthe J = 1 state.

27



D



0HDQ 
506 
6XP 

&RXQWV


























0HDQ 
506 
6XP 







E



&RXQWV    













F

.[


&RXQWV



\ FP

[ FP




06










\ FP





Figure 14: The horizontal (a) and vertical (b) images at the final focus (F.F.) of theK1.8 beam line. Beam image for kaons and pions at MS2 is drawn in figure (c).

B

K1.8 Beam LineHere, we briefly summarize the details of the design status of the K1.8 beam line tobe constructed.
In the current design, one of the most serious problems which should be consideredis the high radiation levels surrounding the production target. There, about 30% of the
primary proton power will be lost and distributed around the target. Thus, radiation
hardness of the materials to be used in the equipment near the production target
is required. Also, we should consider the cooling to remove the heat load in thesematerials. Therefore, new magnets with mineral-insulation coils will be constructedin the front end of the beam line, while most of the downstream magnets are existing
ordinary magnets. The first electro-static separator in the upstream has been also28

Table 7: Characteristics of the magnets and other elements of the K1.8 beam line
Name

D1
Q1
Q2
D2

Gap/Bore
[mm]
80
160
200
120

Width
[mm]
T1
200

Length
[mm]

Field
[kG]

350

800
600
800
900

13.10
7.60
−7.41
17.47

200

500
150
500
200
200

7.90
1.00
−8.80
0.57
3.76
6.20
3.76
−1.44
8.20
9.17

IF
Q3
O1
Q4
S1
CM1
ES1
CM2
S2
Q5
Q6

200
250
200
250
250

D3
Q7
O2
S3
CM3
ES2
CM4
S4
Q8
O3
Q9

170
200
300
300
300

Q10
Q11
D4
Q12
Q13

200
200
200
200
200

250
250
250
300

300
300
250
300
250

200

MS1
1000

300
300

200
200
500
500
1500
400
150
200
200
200
200
600
150
900

14.12
8.20
1.75
−1.59
3.76
6.50
3.76
0.25
−8.90
1.25
10.35

900
600
4468
600
600

9.79
9.79
15.01
8.50
-6.70

MS2

660

FF

29

Tot. Len.
[m]
0.000
1.200
2.400
3.600
4.800
5.900
7.000
7.675
8.000
8.800
9.300
9.600
16.10016.60017.10018.20019.30020.20022.28422.8347
23.1347
23.6347
24.0347
30.4347
30.9347
31.4347
32.1847
32.4847
33.8348
35.5848
36.784837.884842.852843.752845.8530

New
New
RecycleNewin vacuumin vacuum15◦ bend

RecycleNew
Recycle
New
New
New
New
RecycleRecycleRecycleRecycleRecycleNew
New
RecycleRecycleRecycleNew
RecycleNew
RecycleRecycleRecycleRecycleRecycleRecycle20 ◦ bend

PS-K6

64 ◦ bend*0-75HIULJHUDWRUV
:#.[5HIULJHUDWRUIRUVKHLOGV:#.
:#.
+HOLXP9HVVHO&RLO9HVVHO/+H

.6KLHOG

.6KLHOG

Figure 15: A conceptual design of the new cryogenic system for the SKS magnet. The
liquid state of the helium coolant is always kept by 3 GM-JT refrigerators.
newly constructed with several improvements against high radiation level, and tested
showing a good performance. In Table 7, we show which equipment is going to be
newly constructed for the K1.8.
The tuning of the beam optics to obtain a good K − /π − ratio has been carried out
by H. Noumi et al., already. Higher order corrections up to the 3rd order was taken
into account with four secta-pole magnets and three octa-pole magnets. Figures 14shows an example of the tuning simulation of the beam profile at the final focus point
and of the K − /π − separation at the second mass slit.

C

New Cryogenic System for SKS

The SKS superconducting magnet was designed to minimize the heat load at 4 K.
Although we have been using a large cryogenic system to cool down the magnet, it wassuggested that several small refrigerators could be used for the SKS magnet because of
the recent refrigeration power improvements in this type of small refrigerator system.
It will reduce the costs to transfer the SKS spectrometer system with the cryogenic
system from Tsukuba to Tokai. Also the operation of the cryogenic system will be
simplified and become easier. Since the system is not controlled under the regulation
for high-pressure gas system, the maintenance is also much easier.
In Fig.15, we show a conceptual design of the new cryogenic system for the SKS
magnet.

30

References[1] K. Imai, et al., Letter of Intent for Nuclear and Particle Physics Experiments at the
J-PARC, KEK, L06 (2003), http://www-ps.kek.jp/jhf-np/LOIlist/pdf/L06.pdf.
[2] C. B. Dover and A. Gal, Ann. of Phys. 146, 309 (1983).
[3] M. Danysz, et al., Nucl. Phys. 49, 121 (1963).
[4] R. H. Dalitz, et al., Proc. Roy. Soc. Lond. A426, 1 (1989).
[5] D. J. Prowse, Phys. Rev. Lett. 17, 782 (1966).
[6] S. Aoki, et al., Prog. Theor. Phys. 85, 1287 (1991).
[7] H. Takahashi, et al., Phys. Rev. Lett. 87, 212502 (2001).
[8] J. K. Ahn, et al., Phys. Rev. Lett. 87, 132504 (2001).
[9] T. Fukuda, et al., Phys. Rev. C 58, 1306 (1998).
[10] P. Khaustov, et al., Phys. Rev. C 61, 054603 (2000).
[11] G. Burgen, et al., Nucl. Phys. B8, 447 (1968).
[12] P. M. Dauber, et al., Phys. Rev. 179, 1262 (1969).
[13] D. E. Lanskoy, private communication.
[14] P. H. Pile, et al., Phys. Rev. Lett. 66, 2585 (1991).
[15] T. Hasegawa, et al., Phys. Rev. Lett. 74, 224 (1995).
[16] H. Hotchi, et al., Phys. Rev. C 64, 044302 (2001).
[17] Y. Yamamoto, private communication.
[18] M. M. Nagels, Th. A. Rijken and J. J. de Swart, Phys. Rev. D 15, 2547 (1977).
[19] M. Yamaguchi, K. Tominaga, Y. Yamamoto and T. Ueda, Prog. Thoer. Phys.
105, 627 (2001).
[20] Th. A. Rijken and Y. Yamamoto, Phys. Rev. C, to be published; arXiv:nuclth/0603042.
[21] T. Nagae, et al., Phys. Rev. Lett. 80, 1605 (1998).
[22] T. Suzuki, et al., Phys. Lett. B 597, 263 (2004).
[23] M. Agnello, et al., Phys. Rev. Lett. 94, 212303 (2005).
31

[24] T. Kishimoto, et al., Nucl. Phys. A 754, 383c (2005).
[25] E. Hiyama, Nucl. Phys. A670, 273c (2000).
[26] I. N. Filikhim and A. Gal, Phys. Rev. Lett. 89, 172502 (2002).
[27] H. Nemura, Y. Akaishi and Khin Swe Myint, Phys. Rev. C 67, 051001(R) (2003).
[28] E. Hiyama, et al., Nucl. Phys. A737, 138 (2004).
[29] A. J. Baltz, C. B. Dover, D. J. Millener, Phys. Lett. B123, 9 (1983).
[30] T. Iijima, et al., Nucl. Phys. A546, 588 (1992).
[31] K. Ikeda, T. Fukuda, T. Motoba, M. Takahashi and Y. Yamamoto, Prog. Theor.
Phys. 91, 747 (1994); Y. Yamamoto, T. Motoba, T. Fukuda, M. Takahashi andK. Ikeda, Prog. Theor. Phys. Suppl. 117, 281 (1994).
[32] S. Tadokoro, H. Kobayashi, and Y. Akaishi, Phys. Rev. C 51, 2656 (1995).

32