A survey of hypernuclear physics

A SURVEY OF HYPERNUCLEAR

B.F. GIBSON”,

E.V. HUNGERFORD

PHYSICS

IIIb

a Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 8754.5, USA b Department of Physics, The University of Houston, Houston, TX 77004, USA

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Physics Reports 257 ( 1995) 349-388

A survey of hypernuclear physics B.F. Gibson a, E.V. Hungerford

III b

a Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA b Department of Physics, The Universi~ of Houston, Houston, TX 77004, USA Received November

1994; editor: W. Weise

Contents: 1. Introduction 2. Hyperon-nucleon interaction 2.1. Free AN interaction 2.2. YN potential models 2.3. Effective A-nuclear potentials 2.4. ZN interaction 2.5. BN and Ah interactions 2.6. Strange dibaryons 3. Few-body systems 3.1. Hypertriton 3.2. A = 4 isodoublet and charge symmetry breaking 3.3. A = 5 anomaly 3.4. B hypemuclei 3.5. S = -2 systems 4. p-shell hypemuclear systems 4.1. p-shell potential parameters 4.2. Hypemuclear y transitions

352 353 353 354 355 356 356 357 358 358 359 360 361 362 362 363 363

4.3. Collective states 4.4. Hypemuclear supersymmetry 4.5. I: systems 4.6 . 3 hypemuclei 5. Heavier hypemuclear systems 5.1. A single-particle potential 5.2. C hypemuclear systems 6. Weak decays of hypemuclei 6.1. Mesonic decay 6.2. Nonmesonic decay 7. Comparison of production mechanisms 7.1. Stopping and low momentum kaon induced reactions 7.2. (K, T) reactions 7.3. (7, K) reactions 7.4. Electromagnetic production 8. Conclusions and future prospects References

0370-1573/95/$29.00 @ 1995 Elsevier Science B.V. All rights reserved SSDIO370-1573(94)00114-6

366 366 367 368 369 369 372 372 372 374 376 376 376 378 378 379 383

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Abstract The present status of experimental and theoretical investigations of hypernuclear physics is reviewed. We emphasize the unique aspects of hadronic many-body systems containing nonzero strangeness and the opportunities that exist to exploit this physics. Our understanding of the elementary hyperon-nucleon interaction and its role in few-body systems is summarized. In particular, we examine the constraints that our knowledge of few-body systems place upon parameterizations of the realistic hyperon-nucleon force models. Also, issues involving the structure of p-shell hypernuclei as well as the weak decays of hypernuclei are summarized in some detail. Finally, the future prospects for strange-particle nuclear physics involving As, Zs, and Es at existing facilities are discussed.

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1. Introduction A hypemucleus is a many-body system composed of conventional (nonstrange) nucleons and one or more strange baryons or hyperons (the A, C, or 8) [ 1,2]. The presence of this strangeness degree of freedom (flavor) in a hypemucleus adds a new dimension to the evolving picture of nuclear physics. At the hadron level, hypemuclei provide a new many-body spectroscopy, where dynamical symmetries may appear that are forbidden in ordinary nuclei by the Pauli principle. To be more specific, let us focus on A hypemuclei. A hypemuclei provide a laboratory in which properties of the AN interaction in the nuclear medium may be explored. The decay A + N + N + N, a strangeness-changing weak interaction, provides a unique opportunity to investigate the four-fern-non weak vertex which occurs only in the nuclear medium. In addition, one can treat the A as an “impurity” in the condensed matter sense and employ it as a probe of nuclear structure [ 31. On the other hand, at the quark level, if one requires that the u and d quarks in the A be antisymmetrized with the nonstrange quarks in neighboring nucleons, then observable effects such as isospin mixing in hypemuclei or modifications of the A -+ N + 7r weak-decay rate in the nuclear medium may occur. The high momentum transfer arising in the nonmesonic A + N + N + N process implies that explicit quark/gluon effects, if observable at all in nuclei, might be especially evident in such weak decays of hypemuclei. Other hyperons may be added to the nuclear medium as well. Of the resulting systems, Z hypernuclei have received the most attention. Although the C interacts strongly with nucleons, converting into a A with the release of some 80 MeV, evidence has been reported of hypemuclear structure narrower than would be naively expected. These reports, however, are not without controversy. Still, the gross features of the X-nucleus interaction have been mapped, primarily with the help of model baryon-baryon potentials. Because the strangeness -1 hyperon masses differ markedly from those of the neutron and proton, SU(3) symmetry is broken. How it is broken is a question of importance to our fundamental understanding of the baryon-baryon interaction and the relation of hypemuclear properties to QCD. Although hadrons are composites of quarks and gluons, at large nucleon separations the quark/gluon degrees of freedom do not manifest themselves, so that a description in terms of baryon and meson variables works well. Thus, boson exchange models of the baryon-baryon interaction have proven quite successful. However, where the interquark separations become very small, a complete description of the baryon interaction may well involve explicit quark and gluon degrees of freedom. At very small interquark distances where asymptotic freedom prevails, one can use perturbation theory to describe a quark/gluon system. However, even with modem lattice gauge calculations, we appear to be some distance from understanding the baryon-baryon interaction in the nonperturbative intermediate region. The search for dibaryon states bears directly on this, because the structure of the quark-level hypertine interaction makes such configurations more likely in the strange rather than the nonstrange sector. Evidence for such low-lying 6-quark states is sought in Mv scattering. Several novel features of the hyperon-nucleon interaction play a significant role in hypemuclear physics. In the case of the AN interaction, the A (T = 0) and the N (T = i) cannot exchange a 7~ (T = 1)) so that there is no dominant OPE tensor force as exists in the nucleon-nucleon interaction. (The K and K* exchange tend to cancel more completely than do the v and p exchange in the NN force.) The two-pion-exchange interaction, which is overshadowed by OPE in the NN force, is the major long-range component of the AN interaction. The absence of a direct AN OPE force ensures that shorter range properties of the baryon-baryon interaction are important in A hypemuclei. On the

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other hand, while the CN interaction is not as well known, it appears to be strongly spin and isospin selective. It does exhibit a long range OPE component, but the central potential is expected to be somewhat weaker than that of the AN force. With regard to production mechanisms, hypemuclei were first observed in 1952 with the discovery of a hyperfragment by Danysz and Pniewski in a balloon-flown emulsion stack [ 41. The initial cosmicray observations of hypemuclei were followed by pion and proton beam production in emulsions and then 4He bubble chambers. The weak decay of the A into a rTT-+ p was used to identify the A hypemuclei and to determine binding energies, spins, and lifetimes for masses up to A = 15 [ 5,6]. Average properties of heavier systems were estimated from spallation experiments, and two double A hypemuclei were reported from B - capture [ 7,8]. More systematic investigation of hypemuclei began with the advent of separated K- beams, which permitted the use of counter techniques [ 91. The (K-, C) reaction at 700-800 MeV/c produced much information about substitutional states, particularly in the p shell [ 1,2]. The low intensity ( 104-105K-ls) and poor resolution of the beams and the strong distortion of the incident K- has hampered this work. The (K, r) reaction has also been used to study S hypemuclei, although the momentum transfer, being somewhat larger than that for A production, has a higher yield to the quasifree region, and the question of narrow structure in C hypemuclei has not been resolved. The (n-+, K+) associated production studies of hypemuclei began at Brookhaven [ lo] in 1983, and have been continued more recently at KEK [ 111. After the practicality of this reaction was established, an improved experiment [ 121 ran at BNL, which covered a range of A up to medium mass nuclei: 1 Be -+ “:Y. One result was a textbook example of shell-model single-particle states sk - fp in “:Y [ 13,141. The (GT,K) reaction at nonzero angles can also be used to produce polarized hypemuclei. [ 151 For a spin-zero target, this leads to a negligible polarization of unnatural parity states, and substantial polarization of natural parity states. Furthermore, the asymmetry of weak decay pions in coincidence measurements relates directly to the structure of the hypemucleus. Other reactions such as (r+,K’) and (K-, TO) have been proposed as a means to produce charge symmetric hypemuclear states to investigate directly violations of charge symmetry in hypemuclei [ 163. At present, single-arm counter experiments are limited in resolution. While major shell spacings are resolved, no spin splitting has been observed. Although (K, rry) coincidence studies can resolve individual transitions between levels with ? 10 keV resolution, such experiments collect only a few tens of events in a peak for a 5-6 week run. In addition weak decay measurements are statistics limited, providing only a slight improvement upon data from earlier emulsion studies. It is clear that a significant increase in beam flux and resolution is required to make major advances in hypemuclear research.

2. Hyperon-nucleon

interaction

2.1. Free AN interaction Although the free hyperon-nucleon interaction can be directly measured [ 9,171, experiments are difficult due to low beam intensities and short lifetimes. Production and scattering in the same target is almost automatically required. Angular distributions and polarizations have been measured at a

354 Table 1 The scattering Model

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lengths and effective ranges in fm for the YN potential models listed Ref.

as

r:

a’

rh

[221

- 1.90 -2.29 -2.78 -1.56 -2.04

3.12 3.17 2.88

-1.96 -1.88 -1.41 - 1.59 -1.33

3.24 3.36 3.11 3.16 3.91

Nijmegen D Nijmegen F Nijmegen SC Jiilich A Jiilich .&

[221 ~231 ~251 [251

1.43 0.64

few energies, particularly for the AN system, but data are too sparse and imprecise for a phase-shift analysis. The experimental data on AN and XN scattering consist of some 600 scattering events in the low energy (momenta of 200-300 MeV/c) region [ l&20] and another 250 events in the momentum range 300-1500 MeV/c [ 21] . The low energy data fail to adequately define even the relative sizes of the dominant s-wave spin-triplet and spin-singlet scattering lengths and effective ranges. Table 1 lists the AN scattering lengths and effective ranges that result from a number of potential model representations [ 22-251 of the data. The diversity in values indicates how poorly determined are the parameters of the low energy effective range expansion. Nonetheless, it is obvious that no bound state exists for the 2-body AN system, because the scattering lengths are negative. A phase-shift analysis of the existing data is not a practical possibility. Furthermore, neither mesonexchange models nor QCD inspired quark-gluon models of the strong interaction have sufficient predictive power to enable one to model ab initio the AN force. To date the limited AN and C N cross section measurements have been grouped with the more plentiful NN scattering data in a combined analysis to constrain the OBE potential models, which have been successful in describing the NN interaction. Recall that the A (T = 0) cannot exchange a pion (T = 1) with a nucleon (T = i). Thus, the AN interaction is expected to have a short range, and OPE, which dominates the nucleon-nucleon interaction, enters only in second order through AN - 2 N coupling. The spin-singlet force must be stronger in the hypertriton, because the v-decay mode was shown to exhibit an angular distribution characteristic of the decay from a J” = 2’ ground state rather than from a J” = i’ state

[261. 2.2. YN potential models In lieu of reliable data on the A-nucleon interaction, the Nijmegen group has developed several one-boson exchange potentials, which are simultaneous fits to all NN and YN data using SU(3) constraints on the coupling constants [ 22,23,27]. These potentials have been the basis for extensive calculations of hypemuclear structure. In addition, the Jtilich group has also produced hyperonnucleon potential models with different character [ 24,251. In particular, assumptions about the F/D ratio (scalar-singlet/scalar-octet coupling) differ, which affects the relative strengths in the AN and XN channels. The Jiilich models show evidence for a CN resonance below the threshold cusp in the AN elastic scattering channel, whereas the Nijmegen models do not [ 28,291. Furthermore, the difference between OBE and quark-cluster models of the baryon-baryon interaction begin to appear at short range, because the model parameters, fixed in fitting to the precision nucleon-nucleon scattering

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q

.

Berkeley71 Berkeley74

800

900

1000

P,abww

Fig. 1. Comparison of the Ap total cross section data for pan/, from 0 to 1000 MeV/c Nijmegen SC model 1281.

with the predictions

from the

data, lead to qualitative differences in the S # 0 sector. The Nijmegen potential predicts strong attraction in specific XN channels where the quark-cluster approach predicts repulsion [28,30,31]. In the limit of zero quark mass, the neutron, proton, and hyperons satisfy SU(3) symmetry exactly. In fact, the s quark is much heavier than the u and d quarks. Consequently, the A is measurably heavier than the neutron and proton. This breaking of SU( 3) symmetry in the baryon-baryon force is not fully understood. Although the coupling constants can be related by SU( 3)) the SU( 3) symmetry in an OBE picture is broken by the form factors, where the ranges corresponding to the masses of exchanged mesons have different values. Even though broken SU(3) symmetry may be imposed, there remain parameters in the description of the exchange of the vector meson nonet and the scalar singlet and/or scalar octet which are not uniquely specified. For example, in the region of the cusp expected near the threshold for hp - Cop, C+n, (at pA = 635 MeVlc) [ 321, the various Nijmegen models predict such a structure (See Fig. 1 for a comparison of the Nijmegen SC model predictions with the available low energy AN cross section data.), but neither the position nor magnitude is uniquely defined. The model predictions for cross sections in this region exhibit differences of a factor of 2-4. More extensive data below threshold for 7r production (1 GeV/c) are demanded. 2.3. Effective A-nuclear The two-body [13]: V(r)

potentials

potential for the general hyperon-nucleon

= V,(r) + K.(SN. SY) + V&2 + ti,(L

interaction

x S+) + V,k(L

can be expressed

by the form

x S-1.

Here, Si2 is the usual spin-tensor operator, and S* = i ( SN f Sr) are the symmetric and antisymmetric combinations of the nucleon and hyperon spin operators. The new feature of the YN, as opposed to the NN, system is the antisymmetric spin-orbit term, V&. This vanishes for the NN system because of charge independence [ 331. The net spin-orbit potential, then, is determined by the interplay between

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V,,Yand L& [ 341. The SU( 3) -breaking property (the NN spin-orbit force is large, whereas the AN spin-orbit force is small) is present in the OBE models as well as the quark-cluster models of the AN force. The heavy mass of the strange quark leads one to predict a small AN spin-orbit interaction in a naive valence quark picture [ 351. That is, the ud diquark in the A has spin-O, so that the spin of the A is carried by the s quark and the resulting spin-orbit force is proportional to the inverse of the mass of that s quark. Both baryon-baryon potential models and resonating-group quark-cluster models yield a small spin-orbit interaction, although the details differ. The baryon-baryon mode1 produces symmetric and antisymmetric terms which are separately small, whereas the individual terms are large in the quark model calculations but interfere destructively [ 361. Short of A and proton polarization in Ap scattering, one should seek distinguishing effects for the two models in hypernuclear spectra.

2.4. CN interaction In the case of the ZN system, the potential is strongly isospin dependent [ 371. The data are consistent with a strong attraction in the ‘S0, T = i and 3Si, T = 4 CN channels, and a weak interaction in the “S,, T = 5, channel [ 381, but other interpretations are possible [39]. The data do not conclusively define the strength of the spin dependence, although the OBE model with SU(3) constraints [ 171 shows strong spin sensitivity. The spin-orbit strength as obtained from the OBE models is expected to be about l/2 the strength and of the same sign as that for the NN interaction; however, primitive quark models give substantially higher values [ 351. The tensor-force component is also expected to be significant. Most important for C hypemuclei is the fact that the C-p-An interaction is close to the s-wave unitarity limit at low energy. Thus it should be expected that a ‘c will convert on a nucleon, releasing 80 MeV to the recoiling AN system. The energy release seems too high for Pauli blocking to suppress this decay channel in nuclei, although arguments have been made to the contrary. Because the A-C mass difference is only some 80 MeV, the A (T = 0) and the C (T = 1) couple more strongly than do the N and A in the nonstrange sector. This strong coupling leads to a nonnegligible second order tensor force in the AN channel and to sizable ANN three-body forces [ 40,411. The existence of C hypemuclei, in the sense of having bound states of narrow width, depends critically upon suppression of the strong coupling between the C and A through the CN-AN channel. In fact, without suppression of this strong coupling by some mechanism [42,38], narrow C-nucleus structure should not exist. In summary, we might expect strong conversion in the ‘So, T = ; channel and less of an effect in the “Sr, T = i channel.

2.5. EN and AA interactions In the case of Z N interactions there are few data. Taken together with the Nijmegen models, one finds repulsion for the Z N and AA interaction in model F and attraction in mode1 D [ 221. The latter model is more consistent with the limited data [43], and with the existence of bound states in B hypemuclei [44]. Only indirect evidence based upon the three reported AA hypemuclei events [7,8,45] provides any measure of the AA interaction. Analysis of the these events requires an attractive matrix element from the AA potential of about 4 MeV [46], but insufficient to support a AA bound state.

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3.57

Strange dibaryons

Theoretical baryon-baryon models may be extended to include multiquark (more than 3 valence quarks) systems, although the ability to treat continuum states correctly becomes somewhat more complicated [ 471. It is not possible to uniquely extend color symmetry beyond baryon number B = 1; however, considerable experimental and theoretical effort has gone into studies of dibaryon, B = 2, systems [48]. Before proceeding further, a short discussion of the simple SU( 3) flavor symmetry multiplets for B = 2 will be helpful, not only for the following dibaryon discussion, but also for the few-body hyperon-nucleon interaction as well. The deuteron, which is the only unambiguous B = 2 state, resides in the SU( 3), B = 2 antidecuplet, {lo}. All states in the {lo} multiplet are s-wave spin triplets, “S, . There is no A-C mass splitting in this model, so that an isospin doublet exists in the AN, CN system at the CN mass. This doublet is identified as the S = - 1 analog of the deuteron, and should be understood as a conventional nuclear state describable in terms of meson exchange forces. ‘Experimentally a strong, narrow peak occurs in the AN scattering cross section essentially at the CN threshold mass [ 321. This peak is now interpreted as a cusp due to RN-CN coupling in the 3Si channel. There are still questions as to whether there also exists a resonance pole near the cusp [49]. As noted previously, the Jiilich models exhibit a peak below the cusp, whereas any pole in the Nijmegen models would likely fall above the C threshold. While this pole has implications for 2 hypemuclei, such a pole would not correspond to a dibaryon since, according to the above definitions, it would only be a reflection of a deuteron in the S = - 1 sector. Furthermore, one notes that the IS0 np system is strongly attractive, but unbound. This system would be placed in the same SU(3) multiplet as the AA, which suggests an attractive but nonbinding AA potential for the ‘S, configuration. The addition of two strange quarks to the six quark system allows the lowest dimensional representation for the flavor-spin wave function in the three-flavor bag models. Consequently the uu-dd-ss system has the greatest attraction because of the color-magnetic force, and all bag models predict a bound state or resonance for the B = 2, J” = O+, T = 0, S = -2 system [50]. In fact, a number of the models predict that such a state lies below the AA threshold, making it stable with respect to strong decay processes. This predicted dibaryon is unique in this respect and is given the identifying symbol H. To summarize the experimental situation, previous searches for doubly strange dibaryons taken collectively have yielded a null result [51]. On the other hand, there are three reported double lambda hypemuclear events. It is well known that if the H exists and is deeply bound, then the existence of AA hypemuclei presents a puzzle because the hypemucleus would decay into an H plus residual nucleons. Nonetheless, discovery of a bound S = -2, B = 2 system would provide strong confirmation that the bag model realizations of QCD are physically reasonable, and searches continue. It is also interesting to compare the relativistic bag model to the non-relativistic quark models in the case that the di-lambda system is unbound or just barely so. The difference between models is found to be due to the volume energy of the bag; i.e., it is intimately connected to the confinement problem [ 521. Within the three-flavor bag models, dibaryons other than the H lie above particle thresholds. In the case of the hypercharge 1 system the additional color-magnetic attraction derived from the more flavor symmetric wave function leads to a prediction of two p-wave dibaryons, among others, lying below meson production threshold near the CN mass. These states could be narrow since they lie below

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meson thresholds and require rearrangement of the quark sub-structure for decay [ 531. Because they are p-wave resonances, they cannot be associated with the threshold cusp or a possible 3S1 resonance which could lie in this mass region. Unfortunately, the dominant structure of the cusp masks the more delicate effects due to dibaryons. Still, while there have been several experimental searches for these resonances, there is no consistent evidence of structure which would require the introduction of 6-quark states [ 541.

3. Few-body

systems

Quarks and gluons are believed to be the fundamental degrees of freedom in terms of which one can describe hadronic systems. However, in the realm of nonperturbative QCD our picture of nuclear phenomena in terms of their collective modes defined by the physically observable baryons and mesons has enjoyed enormous success. The question remains whether one can successfully calculate the physical properties of few-body systems in terms of a phenomenological hyperon-nucleon interaction without the need to include explicit quark/gluon degrees of freedom. It is certainly expected that the investigation of few-body hypernuclear systems offers the best chance of pressing this question to a firm conclusion.

3.1. Hypertriton The deuteron plays an important role in the non-strange sector by constraining models of the NN force. Because neither the AN nor the CN interactions possess sufficient strength to support a bound state, the hypertriton plays this role in hypemuclear physics. It is the ground state of the ANN system that must be used to constrain models [22-251 of the YN force. Emulsion studies have specified the A-separation energy [ 5,6]. Analysis of its nTT-weak decay has determined its spin and parity [ 261 to be J” = (i)+, so that in ?H the spin-singlet interaction must be stronger than the spin-triplet. Because the hypertriton is loosely bound [ BA (;H) = B(iH) - B( 2H) N 130 f 50 keV] , one expects this system to be most sensitive to the long-range aspects of the YN interaction. As noted in the introduction, tensor-force effects are anticipated to be somewhat smaller than those found in the NN interaction, because of the lack of direct OPE in the AN channel. (The inclusion of tensor coupling in both the NN and AN channels produces a surprising dependence on the relative sign of the 3S1-3D1 mixing parameter el for the NN and AN interactions [ 411.) On the other hand, A N-XN coupling effects are expected to be much more important in hypemuclei than are NN-NA coupling effects in conventional, nonstrange nuclei. The mA - mp mass difference is only some 80 MeV and the 2 width is small compared to that of the A. Eliminating the C channel from the Mv force leads to an energy dependence in the resulting AN interaction and to ANN three-body forces. Both effects are the subject of current interest in the nonstrange sector. Separable-potential model calculations [41] indicate: 1. the dispersive energy dependence that results from embedding the coupled-channel AN-CN potential in a three-body system is repulsive and reduces the IH binding energy; and 2. the true three-body force due to coupling C NN states to the ANN state is attractive and increases the ;H binding.

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Given the small A separation energy, one is led to inquire whether the hypertriton is bound only because of the hypemuclear (ANN) three-body force. The Bochum group [55] has recently demonstrated that the hypertriton is not bound when the energy-independent Jtilich model A (See Ref. [ 251.) is used in a local-potential Faddeev calculation. It appears that there may be too much strength in the RN-CN transition potential of that model, which is less effective “in the medium” than in free space just as is the NN tensor force. This lack of ;H binding represents a puzzle, because the scattering lengths and effective ranges of that model, as listed in Table 1, are sufficiently attractive to predict significant binding in a simple separable potential calculation. This raises the question of why the short-range properties of the Jtilich model A should play such an important role in this loosely-bound system. In addition, the Erlangen group [56] has generated an RGM model of the YN interaction which produces approximately the correct :H binding. To take full advantage of the hypertriton as a laboratory for investigating the XW interaction, a more precise measurement of the :H binding energy is required. 3.2. A = 4 isodoublet and charge symmetry breaking The :H-ZHe isodoublet provides a strong test of models of the I7v interaction. A good model should reproduce both the binding energies of the O+ ground states [5,6] and the excitation of the l+ excited states [57,58]. This includes the charge-symmetry breaking (CSB) exhibited by the difference of the measured A-separation energies. For the ground states one finds: AB,, = B,,(4He)

- Ba(4H)

= 2.39(3)

- 2.04(4)

MeV.

The CSB differs between the ground and excited states of this isodoublet. Charge-symmetry breaking is expected in mirror A hypemuclei, because of the significant AN-ZiV coupling. For example, the C+ and C- masses differ by some 8 MeV, and Ap couples to Z+n, whereas An couples to C-p. The size of the effect is important. The nominal 350-keV CSB binding energy difference in this hypemuclear system is much larger than the =:I 00-keV CSB effect seen in the nuclear 3H-3He binding energy difference after correcting for the pp Coulomb energy in 3He. A key question is whether models can account for the measured CSB using as input the free YN interaction [ 59-611. Significant improvement in the precision of both the YN scattering data and the A = 4 A-separation energies are required before detailed conclusions can be drawn from such investigations. As with conventional isobaric mirror nuclear pairs, mass differences are attributed primarily to Coulomb effects, with some small contribution from CSB [62]. Although CSB in hypemuclei is expected to be larger, the dominant contribution to the total binding energy is still from Coulomb effects. Table 2 lists the A-separation energies for several hypemuclear mirror pairs. Because the A is uncharged and resides in the 1s shell for the ground state, the main contribution to the mass difference is due to the change in Coulomb energy as the radius of the hypemucleus changes when the A is added [ 631. Thus, for a decrease in radius, the Coulomb energy for the T = i component of the isospin doublet increases. The table clearly shows this effect is a function of the nuclear charge. In principle, it should be possible to measure the change in radius of the nuclear core due to the addition of a A by measuring this change in the Coulomb energy. As previously noted, the A = 4 isodoublet have particle-stable excited states [ 57,581. These provide a further constraint on models of the YN interaction. The Ml transitions are:

B.F

360 Table 2 A-separation

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energies for mirror pairs

A

Z

4

AA

2

B,\

ABA

2.39 f 0.03 2.04 i 0.04 0.35 zt 0.06

6

8

3

:Li

2

h,He

4.18 + 0.10

4

:Be RLi

6.80 IIZ0.03

3

6.84 i 0.05 0.04 + 0.06

IO

12

E,(iH)

5

8.89 * 0.12

4

9.11 f 0.22

6

10.76 I!Z0.19

5

11.37f 0.06

= 1.04 f 0.04 MeV,

E,(iHe)

-0.22

xt 0.25

-0.61

f 0.20

= 1.15 f 0.04 MeV.

Fitting both the 0+ ground state and the 1+ spin-flip excited state within the same model is not a trivial exercise [64,65], because the spin structure of these states is more complex than one might naively expect. A simple AN effective interaction picture would lead one to predict the l+ excited state is bound more than the actual O+ ground state. Here, AN-EN coupling plays an important role in addition to the composite nature of the trinucleon core states. A more precise understanding of the Mv force and greater precision in the measurement of the excited-state energies are needed before a complete understanding of the A = 4 spectra can be claimed. 3.3. A = 5 anomaly Finally, the anomalously small binding [5,6] of IHe [B*(iHe) N 3.12 MeV] remains an enigma. Simple model calculations based upon AN potentials, parameterized to account for the low-energy AN scattering data and the binding energy of the A = 3,4 hypernuclei, overbind ;He by 2-3 MeV [ 661, That is, the calculated A = 5 A-separation energy is about a factor of 2 too large. In the baryon picture, the A is distinguishable. All five baryons can coexist in 1s states to form the :He bound state. (This is in contrast to ‘He, where only four of the five nucleons can reside in the 1s shell, and consequently a bound “He nucleus does not exist.) An explanation of the model overbinding has been sought in terms of: ( 1) tensor forces that bind the triton and alpha particle less than do central force models. and (2) the strong AN-ZN coupling that is weakened when the nucleon is part of a composite nuclear core state [64]. However, the question arises as to whether the hadron picture can account for the :He binding anomaly [ 671. That is, one can ask whether the ;He binding anomaly results in part because of the

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quark/gluon substructure of the baryons. In a simple valence-quark picture only the s quark of the A, which is a uds composite, is distinguishable. When combined with the 12 u and d quarks of the 4He core, the u and d quarks of the A may be Pauli blocked from 1s states. Thus, one would predict that the binding of ;He should be smaller than would be estimated based upon knowledge AN scattering or the binding of IH and :H, where the u and d quarks of the A are not Pauli blocked [68]. To distinguish between these two different pictures of ;He would require higher precision KN scattering data and a correct model of the hypemuclear systems. 3.4. 2 hypernuclei Turning to 2 hypemuclei, theoretical analyses using the SU(3) symmetric potentials generated by the Nijmegen group [ 221 have been used to investigate the properties of Cs in the nucleus [ 38,69,70]. The result is that the C-nucleus potential is strongly spin and isospin dependent, being attractive in the (S = I, T = i), and (S = 0, T = i) channels but weak or repulsive in the other two s-wave cases, so that there are possible spin-isospin states in light nuclei where the CN -+ AN strong decay mode would be suppressed and could produce narrower than expected structure. This process has been labeled “selectivity”. The authors of Ref. [ 381 calculate conversion widths (note that this width is only that due to the process CN --+ AN) for various spin-isospin states in the A = 3 and 4 Z-nuclear systems which show a range of conversion width suppression from 0 to 3. (Here a number greater than 1 means an increased decay width). However, the states with total (0) width suppression are those having weakly attractive or even repulsive interactions. The interaction in the A = 3 system (S = i, T = 1) state is predicted to be attractive, perhaps enough to bind, and the width suppression is estimated to be l/3. According to selectivity, at least, this state provides the best candidate for narrow structure below threshold. On the other hand, the experimental stopped K- spectra has been interpreted as evidence for a bound (S = 0, T = i) state in the A = 4 system [ 7 11. Selectivity predicts this state to have an enhanced conversion width, but in another model calculation this is suppressed by adding a repulsive core to the X-nucleus potential [ 721. Interestingly, the existence of an A = 4 C-nucleus bound state was predicted using such a model before the stopped K- data were reported [731. The same data can be interpreted with a somewhat different perspective, if both particle breakup thresholds and the isospin structure of the nuclear core are considered. In fact, the 4He bubble chamber data [ 741, which measure the branching ratio into all C and A channels may provide the information needed to understand all the data [ 7.51. These data exhibit an apparent cusp behavior in the A-nucleus channels, due to the coupling of the A-dp and C-dn channels. In fact, while the C’/Z:- ratio is 0.46 for stopping K- on hydrogen, it is 1.2 for the 4He target, because a X+ interacting with the neutrons in the 3H core can convert to a A-dp system, while the C- must convert on the one core proton to produce three unbound neutrons. In addition, the C+ spectrum shows a strong peak, 10 MeV in width, about the C threshold [74]. In contrast to this, the C- spectrum exhibits an enhancement at threshold, but it is not nearly as large or as narrow as that in the Cf spectrum. The data are interpreted to show that 67% of the A production strength in the cusp region comes from C conversion. This large percentage means that it is crucial to properly include the isospin and threshold dependence of the nuclear core when determining the spectrum shape. One thus infers that the dominant spectrum shape is due to the A N-C N coupling involving nucleons embedded in the nuclear core. A A (T = 0) converts to a C (T = 1) which can lead to a change

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in the isospin of the nuclear core. Then, as the bubble chamber data show, the (K-, n--) reaction on 4He can produce a A with an isospin l/2 core (R-3He for example) which can couple directly to a C with a simple isospin reflection of the core (either C”-3He or Ec’-3H). However a (K-, T’) reaction on the same target must couple to a T = i core (A-nnn), which is unbound and nonresonant in the A=3 system. Therefore, the structure seen in the A = 4 ZZ hypernuclei can be interpreted in terms of the spin and isospin dependence of the Mv interaction, but in a way in which the selectivity mechanism does not play an observable role. Other examples of this threshold dependence are present in the data base and are discussed in the next section. Afnan et al. [49] have investigated the isospin zero, A-d scattering amplitude near the X-nn threshold in a Faddeev type separable-potential model calculation. The A-d elastic scattering and total cross section exhibit a resonance-like peak just below the CNN threshold for several different AN-CN potentials. The structure exists whether the actual pole lies above (a resonance) or below (a bound state in the continuum) the threshold, because the position of the pole in the resonance situation is shielded from the physical sheet by the threshold cut. Thus, one cannot necessarily determine from the existence of a peak in the cross section below the threshold that there is a pole in the complex plane that corresponds to a bound (SH) system. In the ‘He( K- , T+) reaction, there is evidence for enhancement in the cross section below the Cd threshold but just above Cnn [ 761.

3.5. S = -2 systems With regard to the S = -2 sector, we have previously noted that there are three reported AA hypernuclei events [ 7,8,45]. The ,6,He event is controversial. However, its analysis is consistent with that for the other two. The AA-separation energy [B,,*(*tHe) = B(,,6,He) - B(4He) N 10.6 MeV] can be combined with the value of B,(;He) = 3.1 MeV to estimate (VA*) = B,,* (,6,He) 2B,,(:He) r” 4.4 MeV. It has previously been established that a AA potential similar in character to that which accounts for A = 4 isodoublet ground state energies will also account for i,,He in a Hartree-Fock, mean-field calculation [77]. That is, the AN and AA potentials are comparable. However, because AA-5 N conversion in the 1s shell of the A = 6 system would require excitation of the 4He core, one is likely looking at a measure of the V Ai\ component of the AA-EN potential and not that corresponding to the free space interaction. Thus, the free interaction is probably stronger than that acting in ,,6,He. To examine the full AA-8 N interaction, one must investigate a lighter system such as ,,‘!,H or ,iHe to avoid the EN Pauli blocking.

4. p-shell hypernuclear

systems

In the nuclear medium the many-body shell model has been used to successfully describe hypemuclear spectra. This mean field approach requires the diagonalization of a many-body Hamiltonian that includes the residual YN interaction [ 33,78-811. After rearrangement of the spin-orbit terms in the potential expression given in Section 2.2, the effective A-nucleus potential can be expressed in terms of: V, D, S,,, SN, and T. Here V is the central potential parameter, D is the spin-spin parameter, S, is the A spin-orbit parameter, SN is the induced spin-orbit parameter, and T is the tensor parameter.

B.E Gibson, E.V Hungerford Ill/Physics Reports 257 (1995) 349-388 Table 3 The historical

sequence of A-nucleus

A Sh SN

T

effective interaction

parameters

363

in the p-shell

Ref. [33]

Ref. [78]

Ref. [81]

0.15 0.57 -0.21 0

0.50 -0.04 -0.08 0.04

0.30 -0.02 -0.10 0.02

4.1. p-shell potential parameters The p-shell A hypemuclei have been extensively investigated. There is one radial integral for each component of the transition potential, and the set of parameters characterizing the p-shell can be optimized for the binding energies and level structure as presently measured [ 811. However, there are both experimental and theoretical concerns that such a parameter set cannot be consistently defined. Theoretically, it is expected that the ANN three-body force will be important, because of the AN-CN conversion [82]. This naturally introduces a three-body force by coupling the AN system with an intermediate C hyperon. Because the rnx - m,, mass difference is only 80 MeV, this coupling can be significant, especially since long range OPE is not excluded in the A-C conversion potential. It is known, for example, that a repulsive three-body force is needed to fit the s-shell hypemuclei when modeled using an effective AN potential [ 661. Although exact values of the parameter set described above are somewhat uncertain, it is known that the spin-orbit term S,, is small, perhaps zero, and its measurement or at least an upper limit has been one of the rnore important results from hypemuclear studies to date [ 83,841. The historical sequence of the measurement of the above parameter set is presented in Table 3. Set 2 was used to predict the spin-spin splitting in loi\ B [79] which resulted in a null search for the y-ray from the ground-state doublet transition [ 851. The negative result of this search for the Ml spin-flip transition remains a puzzle. It has been interpreted as establishing a limit on the size of the spin-spin splitting, and the last parameter set in the table is a result of that assumption [ 8 1 I. However, this assumption conflicts with the 1 .l MeV measurement of the spin-spin splitting in A = 4 [42], and it gives the wrong binding energy for the mass difference of the A = 7 isodoublet ground states. In general, generating a consistent set of A-nucleus interaction parameters would be an important step in testing any candidate AN potential. 4.2. Hypernuclear

y transitions

In lieu of high resolution spectrometer systems, several attempts have been made to use y-ray spectroscopy to determine the position of excited hypemuclear levels with greater precision, as was discussed in Section 3 for the A = 4 system. The selection of y-coincidence experiments in the p-shell has been motivated by a desire to define the effective spin-orbit strength parameter for the A-nucleus potential. This parameter is small, consistent with zero. An upper limit was obtained by observing the centroid shift of states excited in ”,C at different angles in the (K-, r-) reaction and the 2-3 MeV resolution of existing spectrometer systems [ 861. A good example [ 871 of the experimental difficulties involved with the use of hypemuclear y

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1.0

2.0

3.0

4.0

5.0

E,,(MeV) (a>

Fig. 2. The y spectra in coincidence with pions from the (K, a) reaction on a 7Li target is shown for several cuts in the excitation spectrum of the excited hypernucleus. (a) Cut intervals applied to the (K-, n-) spectrum and the level diagrams. (b) Summary of the y spectra and a y identified with the de-excitation of the A = 4 hypernuclei produced by fission. spectroscopy is illustrated in Fig. 2. Rates in these experiments are so low that thick targets are required, preventing all but a very crude determination of the excitation region in which one seeks a coincident gamma. Fig. 2a. shows y spectra obtained by placing cuts on energy bands in the excitation spectrum of :Li produced via the (K-, W) reaction. The ys were detected in NaI crystals. As expected, no y transitions are seen in the region below the ground state. As the band is moved upward in excitation, several coincident ys are seen, albeit with poor statistics. The y at 2.08 MeV is identified as a hypernuclear y from the i’ level to the ground state, as indicated in the level diagram. Note that the energy is very near the energy of the core excitation. Also seen is a purely nuclear y which occurs in true coincidence with the region above the A emission threshold. Fig. 2b. summarizes the spectra for excitation intervals of (a) -2 to 6 MeV, (b) 6 to 22 MeV, and (c) 22 to 39 MeV. In spectrum 2c which is above the threshold for fission into iHe-3H and iH-3He, ys from the two A = 4 excited states at 1.l MeV are seen but are not resolved. It is only because of some knowledge of the spectrum and because a limited number of ys are seen that these identifications can be made with some certainty. To decipher a more complex level scheme containing a mix of nuclear and hypemuclear ys would be difficult.

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IO2

I

‘Lif K-,r;y) PK_= 820 MeV/C

0.511 MeV

n

! IO

I ll C-8

I

MeV

I

-20

1 I

P

nrl II’

B,(MeV)

IH +3tie

I

I

1.00

2.00

’ 3.00

14

-

12

-

IO

*He+‘H

IO

-2 --+4

MeV

i 3 -8

IV A 4-10

MeV

4

4.00 Ey (MeV)

-

h

1

Y

40

20

0

IO

IO

-6

5.00

II

-4

% =

_

2

-2

-0 ,/UNBOUND

’ He+“H A

- -2

--4

(b) Fig. 2. Continued.

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366

Using the same apparatus, ys from the :Be levels at 3.09 MeV were also observed to be unsplit. Theory predicts that these levels should be equally excited in a (K, n) reaction and have equal decay strengths to the ground state. The fact that no splitting was seen places an upper limit upon the nuclear spin-orbit parameter of 40 keV.

4.3. Collective states Most discussions in the literature treat the A hypemuclear spectrum using a single-particle basis. However, one expects that some hypemuclear degrees of freedom are best interpreted in terms of collective modes, as they are in ordinary nuclei. Perhaps the most interesting example is the development of a purely hypemuclear rotational band [ 881. That is, one finds a series of rotational states built on a nuclear structure, which is only possible because the A can be treated as a distinguishable baryon. Thus, the A can be placed in a symmetric orbit with respect to the other nucleons or nuclear clusters. The :Be nucleus is a good case in point. When treated as an LX+ (Y+ A cluster, it forms: 1. a *Be analog band (rotational band similar to the structure of 8Be modified by the A in the 1s level) ; 2. a 9Be analog band (rotational band similar to the structure of 9Be with the A in an antisymmetric lp shell orbit); and 3. a genuine hypemuclear band with the A in the lp orbit but symmetric with respect to nuclear exchange. Shell-model calculations can also reproduce this band structure.

4.4. Hypernuclear

supersymmetry

The XBe hypemuclear spectrum produced by means of the (K, V) and (7~, K) reactions [ 89,13,70] is shown in Fig. 3. As noted above, a series of rotational bands of different structure is expected. Comparison of the experimental and theoretical spectra is also shown. Experimentally one can see the Of and l- band heads for the *Be analog and 9Be analog states. In addition, the supersymmetric 3- state near BA = 4 MeV can be identified in the experimental spectrum, although it is not resolved [ 88,901. It is obvious that the complementarity of the different probes is necessary to interpret the structure, although higher resolution is certainly required. The above discussion can be generalized to include all states which use strangeness to develop a higher degree of spatial symmetry than would be found in conventional nuclei [ 911. This is labeled strangeness supersymmetry (not to be confused with particle supersymmetry). Such states arise from a coherent response of the nucleons in a given shell to their interchange with a A. Thus, the symmetry is comparable to isobaric symmetry in ordinary nuclei. Nature appears to tend toward the supersymmetric configuration but generally does not reach this limit. However, this tendency does manifest itself in observable effects [92]. In the case of ‘IC the (K, n-) substitutional reaction with angular momentum transfer equal to zero cannot reach all excited hypemuclear states composed of the 4.44 MeV ‘*C excited core with the A in the 1s shell. This is because the 13C target symmetry of (441) does not overlap well with the resulting (54) symmetry of the hypemucleus. Experimentally these states are observed to be suppressed in the (K, 7~) spectrum.

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350

0.25

II

0.20

9Be(K-,n-)9ABe 720MeVk

>

z250 150

F z z

0.10

100

f s!

0.05

1

50

g

150

E

100

.

s 0

II

I

I

8=0"

E

200

II

0.15

‘;; 200

>

I,.1 I

300

2 0

II

367

-

'Be(n+, K+)9ABe 1.05GeVk

0

2 z Q) > '5 0 5Q)

1+1II

”

s b

1

9Be(n+,K+):Be 0.008

_

1.04 GeVlc 8=0"

0.006

0.004

50

0.002

-10 A

0

10

20

30

Binding Energy Bh (MeV) (a>

-B,, (MeV) (b)

Fig. 3. (a) Experimental spectra of “Be as produced by the (K, T) and (T, K) reactions to be compared with (b) the theoretical predictions. Note that the (T, K) spectrum, while certainly compatible with the theory, provides very little discrimination due to the poor resolution.

4.5. C systems C-nucleus interactions are not well understood despite ten years of experimental and theoretical effort [ 381. In fact much of this work has tended to cloud the issues rather than illuminate them. On the experimental side the data suffer from poor statistics, with spectra taken for different targets, at different momenta, and under different conditions [ 93-981. On the theoretical side considerable effort has been invested to essentially force narrow structure in the calculated results, although experimental evidence for such structure is ambiguous [ 99-1041. Except for 4He, no X-nucleus bound states are reported [ 71,751, and while continuum structure exists, much of it is consistent with phase space plus the addition of some amount of final-state interactions [ 105-1081. With regard to the C continuum structure, the original 9Be target spectra [94,95] show two peaks of perhaps 10 MeV width separated by about 12 MeV. This structure is very similar to the A hypernuclear spectra also seen in the (K, s--) reaction, and was the first evidence reported for 2 hypemuclear states. On the other hand, no structure is evident in the (K-, ,rr+) spectra on the same target. A narrow peak (3 MeV) was reported in the 6Li target spectra [96] about 22 MeV above

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threshold. Although structure is clearly evident, the width could be much larger than deduced due to uncertainties in the shape of the spectrometer acceptance near cut-off, the statistics, and the size and shape of the background. Other continuum spectra can be explained by a generic phase space with final-state interaction curve [ 105--1081, perhaps because the data have very limited statistics. Finally, a recent high statistics experiment has retaken data using the (K-, S-*) reaction on both 9Be and 6Li targets. Although broad enhancements are observed, there is no indication of any of the states reported in the earlier spectra [ 1091. There have been two attempts to extract the X-nucleus spin-orbit splitting with widely different results [94,97]. The analysis of these experiments was based on misinterpretations of the experimental spectrum, so that no conclusions can be drawn about the E spin-orbit splitting from the present experimental spectra. However, structure in both (‘He + C-) and (‘Be + C ’ , ‘Li + X+) X-nuclear systems may be explained by C-h conversion. In the case of a 6Li target, a (K-, 7~.+) reaction on the p-shell proton leads to a C- plus “He core. The core has broad ground and excited states which can decay into 4He + R, a narrow excited state at an excitation of 16.8 MeV corresponding to the threshold of the core break-up into “H + d, and a broad level at 19.8 MeV excitation with core decay into 3He + (nn) having isospin 3/2. Because of isospin, a C- cannot couple to a A through 4He or ‘H nuclei, and coupling through a “H nucleus leads to a 5-body final state as discussed above. The He bubble chamber data show that a cusp is expected at the C--“He threshold and this is produced through the T = i state of “He. The X--5He*(T = i) threshold lies at an excitation energy of approximately 20 MeV. On the other hand, the (K-, r-) reaction at 400 MeV/c shows only one peak of about 12 MeV width. In this case the A can directly couple to the C through the ground state of the core nucleus, so that this then dominates the cross section. The ratio of C+ to C- production from hydrogen in the (K, rr) reaction is about 0.1 at 715 MeVlc incident momentum, and the ratio of Co production from a neutron to C- production from a proton is about 0.6. These ratios could be modified significantly by C-A conversion through coupling to the appropriate core isospin states. In the case of the (K-, F) on a 9Be target, 8Be core states have isospin zero and are broad up to the several T = 1 states located between 16 and 18 MeV. This is in contrast to the A = 5 isospin-doublet core discussed above. Here the Co can couple only through the T=l excited states to produce a A-nucleus system. Presumably this gives rise to the structure in the data at approximately this position. The lower portion of the spectrum would be due mainly to Co production. In the case of the (K, r+) reaction on the same target, the core has isospin 1 but cannot couple with a X- to form a A except through the narrow T = 2 state at 10.8 MeV. One notes there is a break in the observed spectrum at approximately this location. The 2 spectrum above threshold, as produced from C targets, has been studied using the continuum shell model [ 381. These calculations also show the gross features of the data can be reproduced using threshold effects. 4.6. E hypernuclei Regardless of whether narrow, bound C hypemuclear states exist, it still would be possible that B hypemuclei could be formed. As pointed out in Ref. [ 431, the E is much more massive and carries less kinetic energy. Thus, it would be more tightly bound in a given potential well. A few emulsion events [ 110-l 151 have been interpreted as E hypemuclear states, and they have been analyzed to indicate an attractive well depth of about 20 MeV. However, of more importance is the conversion

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369

width: EN -+ AA. Recall that the conversion width for the ‘C in nuclear matter, CN -+ AN, is probably the main reason why C hypemuclei have not been observed. In the 2 conversion, however, only 26 MeV is released, and within a nucleus the decay phase space is severly restricted. In addition, the H conversion is suppressed by the mismatch in the overlap of the E and nucleon wave functions. This reduces the free space conversion estimate of E states from some 13 MeV to less than 2 MeV [44]. Production of B hypemuclei is proposed as a method of producing double-h hypemuclei, either through atomic orbits, or nuclear states. The E and AA hypemuclear states couple, so that direct formation of a AA hypemucleus can occur through nucleon emission. In fact, in the case of ‘;B, neutron emission leading to &B is estimated to represent 60% of the total width and is thus an important production channel for AA hypemuclear formation [ 441.

5. Heavier hypernuclear

systems

We begin the discussion with a consideration of a A hyperon implanted in a medium to heavy nucleus. A few remarks will be added at the end of Section 5 regarding heavier C hypemuclei. In the simple valence quark model, baryons are composed of three quarks symmetrized in spin-flavor, and anti-symmetrized in color. The proton, neutron and A are the lightest three baryons in the ground state baryon octet, and they were chosen by Sakata in his prequark triplet model to represent the fundamental particle system from which all other baryons would be constructed [ 1161. It is simplest to discuss hypemuclei, in particular heavier hypemuclei, using the Sakata triplet concept, which provides a useful way of interpreting the spectra, even though it is not correct in detail. Thus, the triplet set of particles (p, ~1,A) are considered identical to first order under the strong interaction [ 11. Therefore, the concept of strangeness exchange is introduced in analogy with the familiar concept of charge exchange. The most naive model would then treat the A as a distinguishable nucleon. Of course, this strangeness symmetry is broken as is reflected in the significantly larger mass of the A, mh = 1115 MeV in contrast to 939 MeV for the nucleon, and the weaker AN potential. 5. I. A single-particle

potential

In large measure the A is expected to maintain its identity within the nuclear medium. This reflects conventional understanding that nucleons retain their identity in nuclei due to the strong quark hyperfine interaction [ 1171. Thus, the structure of hypemuclei can be described using a simple single-particle model basis [33,118]. In fact, because the A-nucleus interaction is weak, the weakcoupling model works quite well. The A, as a distinguishable baryon, resides in the 1s shell for the hypemuclear ground state. Excited states are obtained by coupling an excited core to the ground-state A, or by promoting the A into a higher orbital. The best evidence that single-particle A hypemuclear states exist in heavier nuclei comes from analysis of the structure observed in the (n, K) reaction on heavier nuclear targets [ 79,891. This reaction populates a series of levels associated with the conversion of a valence neutron into a A residing in one of the many available shells within the nucleus [ 119,120]. An example is 89Y where a g7/2 neutron is removed and the A is placed in orbitals ranging from the 1s to the lg shell. (See Fig. 4.) Fine structure within these levels cannot be seen with current resolution; however, the centroid of the various A-shell orbitals as a function of the atomic mass can be fit with a spin-independent

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6

-

n BNL data

-30

-20 -

Fig. 4. Experimental obvious.

4 . PA J\i -10

0

Binding Energy (MeV)

spectra from the (s-, K) reaction on “‘Y at P,, = 1.05 GeV/c

and 0~ = IO’. The A shell structure is

A Single Particle States

0.00

0.05

-’

0.10

0.15

0.20

0.25

Fig. 5. Comparison of binding energies of A single-particle states with those calculated Woods-Saxon potential. The A appears as an identifiable particle within the nuclear medium.

from a density

dependent

A-nucleus optical potential of Wood-Saxon form. (See Fig. 5.) The level spacings vary smoothly as a function of A, signifying the A single-particle behavior. However, it is not possible to simultaneously fit the spectra of both light and heavy hypernuclei with a potential linear in the nuclear density [ 791. A density dependence, producing repulsion, is needed to ameliorate the overbinding problem in nuclear matter. Such terms are consistent with a repulsive three-body ANN interaction, and similar terms are needed in light hypemuclear systems. Subject to this caveat, the observed deeply bound A states are well defined. Spectra from some targets (shown in Fig. 6) are featureless. This is attributed to the spread in spectroscopic factors for neutron pick-up from a particular nuclear target. That is, in these cases the reaction strength is fractionated among many levels which are not resolved within the present experimental resolution. Although the de-excitation of the hypemucleus was not observed in the

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371

5

&l z

&3 i5 J2 c: 31 UO -30

-20

-10 0 -BE (MeV)

10

-20

-10

0 10 -BE (MeV)

20

-10

0 10 -BE (MeV)

20

-BE (MeV)

F

$3 ;ij B2 J

-20

-10

10 -BE &eV)

G!l B uO 20 -20

Fig. 6. A survey of spectra produced by the (r, K) reaction on a series of light to medium A nuclear targets. Note that while some nuclei show well resolved structure, some have many overlapping states. This is attributed to the fractional single-neutron pick-up strength in a particular target.

(71, K) experiment, a highly excited hypernucleus will decay by the emission of electromagnetic radiation or nucleons to reach an energy minimum [ 1191. In fact, above particle emission threshold the emission of nucleons, the so-called nuclear “Auger” effect, predominates for all but the lowest energy levels [ 1211. This, of course, presupposes that single-particle A states in nuclear matter provide a reasonable representation of the structure. As the A makes transitions to the hypernuclear ground state via nucleon emission, a series of particle-hole states are formed. These are broadened by the residual interaction, which is expected to be less than an MeV [ 119,121]. It is intriguing that the A single-particle states are so narrow. In comparison to similar particle-hole nuclear excitations, the spreading width is reduced by as much as a factor of two orders in magnitude. This has been investigated by several authors and attributed to the weak spin dependence of the A-nucleus potential, as well as the distinguishability of the A. Therefore, an identifiable A (i.e., a lambda in a particular single-particle state which resides deeply within the nuclear medium) appears to be a well defined concept.

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5.2. C hypemuclear

systems

As has been previously discussed, there are theoretical predictions for narrow, bound Z hypernuclear levels in heavy hypernuclei [ 38 J . These calculations were motivated by reports that narrow structure was observed in p-shell hypemuclei. However, further experiments have not confirmed such structure, so the rationale for narrow, bound states in heavier systems is weakened considerably. The essence of the basis for these theoretical predictions is the Pauli suppression of the 2.N + AN conversion. By extrapolating the observed binding energies of p-shell hypemuclei, the binding energy of a A in infinite nuclear matter was estimated to be about 30 MeV [ 1221. This is only half the estimated well depth of a nucleon in nuclear matter, confirming that the AN interaction is much weaker than the NN interaction. Numerous attempts have been made to calculate the binding of a A in nuclear matter, but only a few have been carried out simultaneously for the A and Z which are inexorably coupled by the AN ++ XN transition potential [ 123,124]. In fact, one should anticipate from such coupling that the value of the A well depth would increase while that for the C. would decrease as the transition potential strength is increased [ 1251. Using all of the available A hypemucleus binding energy data, Millener et al. [ 79] have determined that the empirical well depth for the A-nucleus single-particle potential should be 28 MeV, rather than 30 MeV. Based upon this number, Kimura and Satoh [ 1251 have estimated that the corresponding Z$nucleus well depth should be only about 1 MeV smaller. Interestingly, the widths for Z hypemuclei in such calculations are estimated to be only some 6 MeV.

6. Weak decays of hypernuclei The weak decay of A hypemuclei, first cousin to the P-decay of conventional (S = 0) nuclei, was first observed in the 1950’s. The mesonic rates are still not well understood in terms of the underlying weak Hamiltonian. We do not yet know whether the pionic decay rates are consistent with our parameterization of the free A -+ N + 7;~amplitude and microscopic models of the nuclear-wave functions. This is in part because nonmesonic decay is the dominant decay mode for all but the lightest A hypemuclei. The nonmesonic decay process provides our primary means of exploring the four-Fermion, strangeness-changing A + N =+ N + N weak interaction. The ANp weak vertex can be investigated by no other means. The large momentum transfer in the nonmesonic decay process implies that it probes short distances and might, therefore, expose the role of explicit quark/gluon substructure of the baryons. Furthermore, in investigating the nonmesonic decay of hypemuclei, we can explore the question of whether the AI = i rule that governs pionic decay applies to the nonmesonic decays. This fertile field of medium-energy physics requires systematic investigation. Only the first steps toward understanding the AS = 1 weak decay processes have been taken. 6.1. Mesonic decay The free A decays principally

via the pionic decay modes

A + p + T- + 38 MeV (64%) + n+r”

+41

MeV (36%)

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(7l”J

d

,’

u(d)

A

A

N

IJ

”

d

,,iv d

u(d)

N

u(d) Pm)

Ll

*s

’ p(n)

,’

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N

373

d

p(n) u(d’

Iis

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u,

d

A

N

Fig. 7. Quark and meson exchange diagrams for weak decay of a A hypemucleus.

with a lifetime of rA = Ii/&

= 2.63 x lo-”

s.

Such a decay can occur with an isospin change (AZ) of l/2 or 3/2. An s quark converts to a u (or d) quark through the exchange of a W boson (see Fig. 7). A V-A Hamiltonian description of this transition implies equal AZ = i and AZ = i strength. However, it was observed experimentally that the AZ = i amplitude is enhanced by an order of magnitude over the AZ = 5 amplitude, just as in mesonic K decay. The practical result is that the ratio of pionic decay widths is:

which is given approximately by the ratio of the square of the Clebsch-Gordan coefficients in the AZ = i amplitude. This implies an enhancement of the AZ = i component relative to the AZ = i component of approximately a factor of 20 [ 1261. The complex nature of the AZ = i rule is not understood [ 127- 1291. A factor of 4 in the relative amplitude enhancement in K --+ 7i-v may be attributable to long distance, final-state interaction effects. Penguin graphs produce nontrivial contributions to the AZ = i rule, and their structure differs significantly from the conventional meson and W-exchange graphs as shown schematically in Fig. 7 [ 1301. Furthermore, it is not at all clear whether the AZ = i rule, which governs the pionic decay of the A, should play any role in the nonmesonic decay process discussed below. The energy release in the pionic decay produces a nucleon having a momentum of only some 100 MeVlc. This is much less than the nucleon Fermi momentum kF N 280 MeV/c. Thus, the pionic decay modes are severely inhibited by Pauli blocking of the final-state nucleons in all but the lightest hypernuclei. Furthermore, in s-shell hypemuclei the variety of open channels has a dramatic effect upon the r-/r0 ratio. Given our developing ability to generate few-body wave functions with high precision from realistic NN and YiV forces, a significant test of our understanding will be a calculation of the decay of A 5 5 hypemuclei. The early work in this field was pioneered by Dalitz and collaborators [ 131,132 ] ; it was recently reviewed by Dover [ 1331 and by Schumacher [ 1341. The question remains whether we can predict correctly the Trr- /Zi\ and r,o/Z’, partial rates, as have been reported for :He and IHe [ 135,136] . Clearly, we are now in a position to do better theoretically, and one would hope for increased experimental precision.

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Emulsion data information about the ratio of nonmesonic decay rates to that for 7~~ decay confirms that the pionic decay mode is strongly suppressed as the mass number of the decaying hypemucleus increases [ 1371. For 40 < A < 100, the factor lies in the range 120-l 80. That is, pionic decay is less than 1% of the weak decay transition [ 1381. Nevertheless, this is a factor of 100 greater than simple estimates [ 1391. Pion distortion due to the T-nucleus interaction as well as modifications of the mean-field picture of the hypemucleus from short-range and tensor force correlations could produce vacancies in “occupied” orbits and modify the naive picture in which pionic decay is almost completely suppressed [ 1401. For ‘:C, Motoba et al. [ 1411 obtained T,.-/r,, N 0.066 in reasonable agreement with the experimental value [ 1361 of O.O6_,j,,. +Oo8 Estimates for a range of hypemuclei [ 1421 r,-

IL

- O.O6(*iSi);

O.O15(‘iZr);

0.010(20f:Pb)

are certainly within reach of experimental capability today. Such a comparison would probe our understanding of hypemuclear structure and pion propagation in the nuclear medium, although this simple picture has been called into question [ 1431. A further interesting prediction for pionic decays relates to the selective character of w and ?r” decay due to nuclear-shell effects [ 144,145]. That is, the nucleus acts as a filter to produce large oscillations in the r,-/Tfl ratio about the AZ = i rule value of N 2 found in the case of the A decay in free space. The ratio is predicted [ 140,141] to vary through the p shell from a minimum of N 0.1 to a maximum of - 1.5. Further experimental data are needed to confirm or refute this sharp variation predicted for the pionic decay mode. Finally, the angular distribution of pions from a polarized hypemucleus exhibits an asymmetry that depends crucially upon the structure of the parent hypemuclear and the daughter nuclear states. Generally, cross sections for natural parity states will drop with increasing angle while the polarization increases. Thus, the pion decay of a polarized hypemucleus can be used as a spectroscopic tool [ 15,146,147]. 6.2. Nonmesonic decay The nonmesonic

decay modes of the A

R+n-+n+n+176MeV,

A+p-+n+p+176MeV

can occur only within the nuclear medium. The 176 MeV energy release in the neutron-stimulated and proton-stimulated decay corresponds to a final-state nucleon momentum of the order of 400 MeV/c. Because this is well above the nuclear Fermi momentum, the nonmesonic decay modes dominate in all but the very lightest hypemuclei. The nonmesonic decay process is, in fact, already quite important for iHe. As noted above, the large momentum transfer involved implies that the decay probes short distances associated with explicit subnucleonic degrees of freedom. It is here that one might test such aspects as the microscopic nature of the AZ = i rule enhancements from the penguin and box graphs. Investigation of the weak baryon-baryon interaction via A + N + N + N scattering utilizing a hyperon beam would prove difficult, if not impossible. Thus, A hypemuclei provide the most practical laboratory in which to investigate the fundamental four-fermion weak interaction. A measurement of the proton, neutron, and r- weak-decay yields allows one to infer the ?r” weak decay width, when these are combined with a direct measurement of the mean lifetime of the hypemucleus [ 1481:

B.E Gibson, E.V Hungerford III/Physics Reports 257 (1995) 349-388 Table 4 Allowed transitions AN 31

+

SC, -+

3’s,, --f “s,

in (2’+‘)(2S+‘)LJ notation

NN

INN

SNN

“‘so

1 1 1 0 0 0

0

3”po

-+ 33P, ‘3s,

“s, + ‘-‘s, + 13Sl +

l3D, “P,

7

375

1 1 1 0

1

-l = r,, + r,,,,+ r,- + rd.

However, direct measurement of the no rate is also desirable. The total nonmesonic (nm) decay + r,,,,, appears to be relatively insensitive to details of the weak interaction models rate, rnn, = r,lp employed. In contrast, the r,,/rn,, ratio appears to be directly related to specific meson exchange components (r, p, K, . . .) of the weak Hamiltonian and sensitive to the question of whether the AZ = i rule holds for nonmesonic decay. Given the importance of r,, and r,,,, a coincidence measurement (energy and angular distributions) should be considered. The nonmesonic weak decay process conserves neither parity, isospin, nor strangeness. In the NN weak interaction, which governs parity mixing in conventional nuclei it is impossible to see the parityconserving component. In contrast, the A + N + N + N transition exposes both parity-conserving and parity-nonconserving components of the interaction. If one considers the case in which the initial AN pair resides in relative s-states, then there are six allowed transitions as listed in Table 4. Only decay, A + it * 12+ rz. Thus, the the INN = 1 amplitudes can contribute to the neutron-stimulated respective decay rates are given by:

r,,= 2u-(31so) +rc33po)+rWvi, r,,) = [r(31sO) +r(33po)+ r(33z5)+ zT3s,) + N30,) + rW,)i. The factor of 2 on the right-hand-side of the r,,, expression comes from the assumed AZ = i rule. Simple model calculations (e.g., Hamiltonians based upon only r and p exchange) exhibit a dominance of the 13S1 transition over the 3’So transition. Therefore, the A + it + n + IZbranch of the nonmesonic decay is predicted to be vanishingly small. Experimentally, one finds from early emulsion data [ 1381 for the mass range 40 < A < 100:

0.65 rn,/rnn, F 0.9. (Recent counter experiments have been performed at BNL for lighter systems [ 1361.) This implies that the neutron-stimulated decay dominates the process. Hence, the simple-model calculations appear to face a problem. Dubach et al. [ 1491 have suggested that, if one includes the Z = i meson exchanges (i.e., the K and K”) in addition to the isovector (n- and p) mesons, as shown in Fig. 7, then the rnn/Tnp ratio can be altered drastically. McKellar has produced a simple schematic model to elucidate this point [ 1371. Additional calculations of nonmesonic decays in terms of meson exchange mechanisms have been published [ 150,151]. While the meson exchange models have not been ruled out by the data, new interaction mechanisms have been proposed to account for larger r,,/r,, ratios

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[ 152,153]. Alternatively, it has been argued [ 1541 that quark effects exposed by the high momentum transfer nature of the reaction may come into play (see Fig. 7). Reliable quark model calculations are needed, and explicit measurement of parity conserving and parity violating transitions would provide valuable insight. In summary, precision measurements of the nonmesonic decay partial rates are needed to determine (1) the structure of the meson exchange description of the weak Hamiltonian, and (2) whether the AZ = i rule, which characterizes the pionic decay process and CP violation, also applies to the A + N + N + N decay of hyperons.

7. Comparison

of production

mechanisms

7.1. Stopping and low momentum

kaon induced reactions

The earliest hypemuclear studies used emulsions for detection. These experiments were forced to use stopping K- beams, with the hypemucleus formed via the (K, v) reaction. The hypemucleus was identified by reconstruction of the decay tracks in the emulsion [ 51. A stopping (K, T) reaction takes advantage of the large branching ratio for K-p --+ TR and thus effectively uses a large fraction of the beam kaons. However, the momenutm transfer to the A is greater than the Fermi momentum of the A in the nucleus, so that the probability of the A binding to the nucleus is small. Still, for low intensity beams this remains the most suitable reaction, and it has the advantage that the resolution is independent of the momentum resolution in the incident K- beam. A stopping K- reaction has recently been used to investigate C hypemuclear systems, again because of low K- beam intensity. Hyperon production can, of course, occur through many reaction channels [ 1551. To be useful, however, the recoiling hyperon should have a momentum which is matched to the momentum of the A in the bound nuclear state. That is, the recoil momentum should be comparable to the Fermi momentum [ 1201. In addition, the reaction should be easily detected and measured. Thus, as is illustrated by the stopping (K, n) reaction, for emulsion detection the capture of a K should lead to nuclear fission and eventual weak decay of a hypemuclear species. In non-mesonic decay the energetics of the hypemuclear decay cannot be uniquely determined, so that mesonic decay must be utilized for detection [ 51. As was pointed out in the previous section, this limits the detection scheme because mesonic decay is suppressed in heavier systems. In addition, this type of detection scheme is not practical for counter experiments. Bubble chambers were used with the first, low intensity separated K- beams for in-flight studies. These detectors with the (K, v) reaction made possible binding energy and lifetime studies. This is a task for which such detectors are well suited, having complete solid angle coverage of the decay products, and very good low-momentum energy resolution. However, as with emulsion experiments, the accumulated statistics are severely limited, and the range of hypemuclei studied is restricted to products from bubble chamber gas mixtures. 7.2. (K, z-) reactions The first series of counter experiments were initiated with the advent of modem, higher intensity separated Kaon beams, and the recognition that the (K, s-) reaction could be used to produce an essentially recoiless A. Both CERN and BNL began programs using spectrometer systems to investi-

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gate hypemuclear formation via the (K, P) reaction near the so called “magic” momentum. At this momentum the A remains at rest in the lab system. Separated beams of about 104/s with a T/K ratio of lO/ 1 were typical. Spectrometer resolutions were about 2-3 MeVlc [ 1561. The early (K, T) experiments concentrated on the determination of the spin orbit strength of the A-nucleus interaction. This parameter was deduced to be small since the IPI12 to ’ Pji2 level splitting was not observed to be different from that of the nuclear core. In addition, a set of counter experiments using a stopped K- beam and y coincidence was used to determine the spin splitting of the A = 4 isodoublet. The result of this important experiment was used to set the spin-spin interaction parameter for the A-nucleus potential [ 871. To provide better resolution, a series of (K, n-7) experiments were performed on p-shell hypemuclei, initially using NaI detectors, but culminating in a search for an expected 170 keV y in ‘OB using Ge detectors [ 87,851. These experiments found hypemuclear ys associated with deexcitation in :Li, IBe 4H and ;He although in the A = 4 cases the ys were not resolved due to the fact that these hypemudlei were droduced from fission products in the ‘Li (K, n) reaction. Typical y spectra in coincidence with selected regions of hypemuclear missing mass are shown in Fig. 2. Resolution in the hypemuclear missing mass is poor due to the use of thick targets to improve the very low event rate. One can see a true hypemuclear y in coincidence with that portion of the spectrum coming from the first excited state in :Li. The y energy is close to the core excitation which would be expected for weak spin dependence of the R-N inteaction. This electromagnetic transition simply requires rearrangement of the nuclear core [ 1571. The (K, T) reaction, particularly at forward angles, has negligible spin-flip strength. However, in the case of 9Be, the (K, n-) reaction is predicted to equally excite both members of the first excited-state doublet [ 1571. Decay of these states to the ground state then produces two ys with an energy difference proportional to the spin-orbit potential in the A-nucleus interaction. Because no splitting between these transitions was experimentally observed, the best upper limit on the spin-orbit parameter is set at 40 keV. The p-shell potential parameter set predicts that the higher energy component of the ground-state doublet is the non-spin-flip component as produced in the “B( K-, T-) reaction. This is in contrast to other hypemuclei in the p-shell. Therefore, except for this particular situation, it is impossible to excite the upper member of the ground-state spin doublet. However, no y transition was experimentally observed at appropriate energies within a 90% confidence limit [ 851, indicating that the theoretical modeling of this hypemucleus is incorrect. The (K-, r”) reaction with detection of the yr” decay has been proposed as a technique to attain resolution of the order of 0.5 MeV. Because the states excited are predominantly proton-hole, Aparticle in character, the reaction is complementary to the (K-, T-) and (&, K+) reactions that involve a neutron. Comparison of results for mirror hypernuclei would permit direct investigation of the significant charge symmetry breaking in the AN interaction which is already observed in the A = 4 isodoublet [ 16,158]. In addition, information about the radial compression of the nuclear core can be extracted from a systematic study of mirror pairs. Furthermore, the Coulomb barrier is favorable, and a number of states in the residual hypemucleus can be bound whereas their analogs, produced in charged pion reactions, lie in the continuum. Detection of a low energy Z-Odoes not face the same technical difficulties as detection of a low-energy rTT-, so that masses of few-body hyperfragments might also be measured following the fission of light hypemuclei. Finally, the (K-, 1~‘) reaction

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(y, K+) studies at CEBAF, because the latter reaction emphasizes

7.3. (rr, K) reactions The (K, 7~) reaction tends to remove a neutron and replace it with a A in the same nuclear shell, so that it preferentially populates substitutional states [ 1201. Interior hypemuclear levels are not strongly excited since the K- is strongly absorbed. The (r, K) reaction was proposed as an alternative. In contrast to the (K, T) reaction, the (r, K) reaction involves substantial momentum transfer. Thus, if a valence neutron is removed, the A can be placed in any of the nuclear shells. In fact, one expects that by matching angular momentum transfer one would preferentially excite high spin states. Like all high momentum transfer reactions, the cross section falls rapidly as the scattering angle (momentum transfer) increases, and it shows little structure. At finite angles there is some spin-flip strength, so that this reaction should at least weakly produce spin-flip excitations at larger angles. At BNL the (r, K) reaction was used to investigate a series of targets ranging from 9Be to “Y [ 891. This work demonstrated the effectiveness of the reaction for the production of deeply lying hypemuclear levels. The reaction is sufficiently selective to produce spectra which may be resolved and interpreted. At the moment, however, the resolution of published results remains about 3 MeV FWHM. New experiments at KEK obtain 1-2 MeV resolution [ 111. A comparison of Fig. 8 with Figs. 3, 4, and 6 illustrates the features of the (K, v) and (r, K) reactions. In Fig. 8 one should note that the excitation strength is dominated by substitutional levels produced by the exchange of a A for a valence neutron. These states lie near threshold, and very little strength to interior hypemuclear levels is observed. In the (r, K) reaction the A is highly polarized even at forward angles. Polarization occurs through two effects [ 1591. In the first place, the elementary spin-flip amplitude leads to non-trival interference effects. Secondly, there is polarization due to absorption effects in the reaction, as is well known in other nuclear reactions. Thus, there is the possibility of producing polarized hypemuclei, and the self-analyzing weak decay of the A process provides a technique for the measurement of the residual polarization. The situation, however, is complicated, especially in the heavier hypemuclei, by the fact that the mesonic decay mode is suppressed and the asymmetry parameter for nucleon emission is model dependent. The residual hypemucleus decays electromagnetically to the ground state which can change the initial polarization of hypemuclear formation [ 1601. 7.4. Electromagnetic

production

Electromagnetic production of strange nuclear systems provides access to hypemuclear levels difficult or impossible to reach by pseudoscalar meson reactions, particularly because of the large spinflip strength in the elementary amplitudes. In addition, the color-blind, gluon-insensitive properties of the electrweak interaction should be much easier to interpret than competing hadronic reactions. On the other hand, it is expected that cross sections to specific hypemuclear levels would be several orders of magnitude below hadronic ones, and both the outgoing electron (to define the photon energy) and the kaon must be detected in coincidence [ 1611. A comparison of the spectra excited by different reactions is shown in Fig. 9.

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‘Be(K-,c,)iBe 30 15 0

> al I 3j E 2 0

40

‘60(K-,rr-)‘60 rd

20

0

30 20 10 0 40

-20

0

20

B, WV) Fig. 8. A survey of (K, z-) spectra from various nuclear targets. Note that in contrast to the (n-, K) reaction this reaction excites mainly the valence substitutional level.

In the ( y, K) reaction the minimum momentum transfer, and thus generally the higher cross section, is obtained when the angle between the photon and the kaon is zero. Typical momentum transfers range between 250-450 MeV/c. The transition form factor decreases rapidly for fi > 400 MeVlc, so that one must place the detectors at forward angles to maintain a reasonable cross section. The different production mechanisms are complementary and are required for a complete study of hypernuclear spectra.

8. Conclusions

and future prospects

Direct experimental information AN scattering data are insufficient

about the hyperon-nucleon interaction is limited. In particular, to define the interaction, even when one combines the analysis

380

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(I3= 100)

n

‘2c(tc,7t-)‘,2c

0+

0.8 GeVk

(0.396 mblsr)

l!LiL 0 - ‘- (x+,K+)

5

2;

”

1.04 GeVk

10

:

- 22’

-

(10.9 pb1s.r)

1.2 GeVlc

0

5

10

E,WV

Fig. 9. A comparison of the (K, T), (T, K), and (y, K) reactions for a 12C target. No spin splittings are included, but the complementary nature of the various reactions is clearly obvious.

with the NN data and enforces SU(3) constraints. This is readily apparent from Table 1, where the spin-dependent scattering lengths and effective ranges are observed to be poorly determined within the model space. Nonetheless, because the OPE mechanism is absent in lowest order, the shorter range nature of the AN interaction has been suggested as an area where the meson exchange and quark cluster models of the baryon-baryon force might begin to exhibit their differences. Therefore, providing as many experimental constraints as possible upon the hyperon-nucleon interaction is of fundamental importance and is required to generate a detailed understanding of the S # 0 hadronic many-body problem. A new measurement of Ap cross section and polarization observables has been suggested [ 163,164]. In addition, the PP’ --+ K+Ap reaction as measured at Satume provides an opportunity to extract information about Rp scattering from final-state interactions [ 1661. Similarly at CEBAF, one can utilize the 2H(e, e’K+)Ap reaction to explore Ap scattering in the final state. Here the weakness of the electromagnetic and K+ interactions helps to isolate the Ap final-state interaction [ 1671. Additional

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c+p scattering data are coming from KEK [ 1621, and new experiments to measure C-p and E-p scattering are planned [ 1651. Finally, a measurement of the spin dependence in the AN + IZN reaction near threshold would be extremely helpful. In the S = -2 sector there is a paucity of information. The RR interaction can only be studied in double A hypernuclei, or possibly in final-state interactions. The EN and AA couple strongly in the T = 0, S = 0 channel, so that AA +-+EN coupling in nuclei should be investigated both experimentally and theoretically in order to explore fully the baryon-baryon force. In addition, they couple to the H dibaryon for which initial searches have proven negative. Each of these S = -2 systems can be reached via the (K-, K+) reaction, but to fully exploit this double strangeness-exchange tool, new detectors and more intense beams are required. In lieu of precision scattering data in the YN or W channels, s-shell and p-shell hypernuclei must be exploited to provide major constraints upon our interaction models. Therefore, confirmation of the binding energy of the hypertriton is important. The ground state of this system constrains the s-wave spin-singlet interaction, and observation of the spin-flip i’ state, even if only in the continuum, would play an important role in constraining the s-wave spin-triplet interaction. Within the p-shell, hypemuclear spectra provide an essential test of whether the effective interaction parameterization correctly describes the physics, or for example, whether the spin-isospin dependent AN -+ XN coupling (i.e. three-body or tensor forces) preclude a state-independent parameterization of an effective A shell model potential. The non observation of the electromagnetic transition within the ground-state doublet in ,,“B indicates that our understanding of the p-shell hypemuclear manybody problem is not complete. Furthermore, even if the effective potential parameterization is valid, the parameters, particularly the tensor term, are not well defined. There is hope that the large aperture superconducting spectrometer in operation at KEK will provide much needed data on hypemuclear structure. The preliminary r*C( K-, 7~~) spectra shown in Fig. 10 demonstrates the potential usefulness of the device [ 1681. However, hypemuclear fine-structure splittings are expected to be quite small due to the weak spin dependence of the AN interaction. Thus, energy resolution much better than the l-2 MeV/c of this system will, in general, be required to delineate the structure. It is possible to obtain hypemuclear spectra with about i MeV resolution using the (K-, n-O) reaction in combination with the Neutral Meson Spectrometer (NMS) now at LAMPF. A proposal for a preliminary study using this technique is being prepared. Furthermore, resolution of the order of 200-300 keV is possible using the (e, e’K) reaction at CEBAF. Spectra measurements for heavier hypemuclei should be extended toward *O*Pb, to determine whether the elementary particle nature of the A is preserved at the nuclear matter densities found in heavier systems. Resolution is required so that one can identify and track the evolution of specific states as a function of A. An alternative to direct measurement of spectra with good resolution is to detect the ys from electromagnetic transitions between the hypemuclear states. As described earlier, this has been used to determine the level structure in A = 4, 7, and 9 hypemuclei, albeit with a few experimental difficulties. Unfortunately, the (K, r) reaction near the magic momentum transfer has no sizeable spin-flip component, and spin flip in the (r, K) reaction at forward angles is very small, so that unnatural parity states are not excited. However, it should be possible to look for the de-excitation of hypemuclear levels after nuclear fragmentation or particle emission [ 1691. Of course, the experiments and the identification of the hypemuclear species would be difficult.

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-

reliminary

-L

5

-

,.,

,,,I,

10

15

:2’3

BA ( MeV >

Fig. 10. Preliminary “i C ( K- , T- ) spectrum from KEK demonstrating the improved resolution now available.

The mass difference in mirror hypemuclear pairs provides information not only about charge symmetry breaking but also about the modification of the Coulomb energy differences as the nuclear core is distorted by the A. The latter can be used to deduce the change in the nuclear core radii due to the insertion of the A. Measurements for mirror pairs in the upper p and s-d shells are needed. The Coulomb energy also shifts the threshold for particle stability. For example, the p-shell substitutional states in i2C lie above the particle emission threshold, whereas the corresponding states in L2B would be stable. The nonmesonic decays of A hypemuclei provide a unique tool with which to probe the weak interaction. There is no other means to investigate the four-fermion weak vertex. Because hypemuclei can be used as filters, the issue of whether the AZ = i rule applies to the AN -+ NN process can be studied [ 1701. Also, the interference term between the different parity amplitudes is being investigated by measuring the weak decay of polarized hypemuclei at KEK [ 17 1 ] ; recently proposed is a new measurement using the ‘jLi(,rr+, K+p)iHe reaction. Although the asymmetry parameter is known for the mesonic weak decay of the free A, only model calculations exist for the asymmetry in the weak nonmesonic decay of hypemuclei. Questions relating to IZ hypemuclei are still open, including the parameters of the X-nucleus interaction and the resulting spin-orbit term for which naive quark models and OBE potential models differ. At present, the only evidence for a bound Z state exists in the A=4 system. Note, however,

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that bumps in the cross section do not necessarily mean that a pole exists in the scattering amplitude [ 491. This also is relevant to searches for dibaryon excitations, particularly near the Z threshold. There is still no evidence for the S = -2 H dibaryon. However, the E-d -+ H +n search will have as a byproduct data on the neutron spectrum from E + d -+ A + A + n, which contains information on the AA interaction. While C hypernuclei may not exist, AA hypemuclei have been observed. Even though they are stable with respect to particle emission, the difficulty associated with their investigation lies in their production. The (K-, K’) reaction is expected to have a low cross section because of its two-step nature. In addition, the momentum transfer to at least one of the As must be larger than the Fermi momentum. However, Z h ypemuclear states couple strongly to AA hypemuclear states [ 1651, so that it may be possible to produce AA hypemuclei via nucleon emission [ 441. The study of Z hypemuclei in themselves would provide much needed information about ZN interactions. In summary, the field of hypemuclear physics offers a direct means of exploring the full SU(3) symmetry-breaking baryon-baryon interaction. The strangeness degree of freedom leads to hypemuclear structures forbidden by the Pauli principle in conventional nuclei. Existing data on the s-shell A hypemuclei demonstrate that direct extrapolation of models from the nonstrange sector fails to account for even the binding energies. If NN-NA coupling were as important in conventional nuclei as AN-CN coupling appears to be in A hypemuclei, then perhaps nuclear modeling would have encompassed more of the ingredients important to hypemuclei. In any event, hypemuclear physics is not just conventional nuclear physics with added “hype”. The physics of hypemuclei is new and different, and the challenge to understand it beckons.

Acknowledgement We wish to thank those who contributed to the material covered in this document and those provided critical comments: I.R. Afnan, PD. Barnes, B. Bassalleck, J.A. Carlson, R.E. Chrien, Davis, J.J. de Swart, C.B. Dover, H. Ejiri, H. Feshbach, A. Gal, R.S. Hayano, K.R. Maltman, McClelland, D.J. Millener, T. Motoba, K. Nakai, E. Oset, J.-c. Peng, G.A. Peterson, P.H. Pile, Rijken, F. Tabakin, H.A. Thiessen, and K. Yazaki.

who D.H. J.B. T.A.

References [ l] A. Gal, Adv. Nucl. Sci. 8, 1 ( 1977). [2] B. Povh, Ann. Rev. Nucl. Part. Sci. 28, 1 (1978). [ 31 H. Feshbach, in Proc. of the Summer Study Meeting on Kaon Physics and Facilities, ed. by H. Palevsky (BNL 18335, 1973), p. 185. [4] M. Danysz and J. Pniewski, Phil. Mag. 44, 348 (1953). [5] M. Juric, G. Bohm, J. Klabuhn, V. Krecker, F. Wysotzki, G. Coremans-Bertrand et al., Nucl. Phys. B52, 1 ( 1973). [6] D. H. Davis, in Proc. of the LAMPF Workshop on (a. K) Physics, AIP Conf. Proc. 224, ed. by B. F. Gibson, W. R. Gibbs, and M. B. Johnson (AIP, New York, 1991), p. 38. [7] M. Danysz, K. Garbowska, J. Pniewski, T. Pniewski, J. Zakrewski, E. R. Fletcher et al., Phys. Rev. Lett. 11, 29 (1963); Nucl. Phys. 49, 121 (1963). [8] D. J. Prowse, Phys. Rev. Lett. 17, 782 (1966); R. H. Dalitz, D. H. Davis, P H. Fowler, A. Montwill, J. Pniewski, and J. A. Zakrzewski, Proc. R. Sot. London, A426, 1 (1989). [9] see Proc. Summer Study Meeting on Nuclear and Hypemuclear Physics with Kaon Beams, BNL report 18335, ed. by H. Palevsky ( 1973). This volume summarizes the status of hypemuclear physics at the advent of counter

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experiments. It is interesting to read the review articles to see how much (and how little) progress has occurred in the intervening years. [lo] C. Milner, M. Bartlett, G. W. Hoffmann, S. Bart, R. E. Chrien, P. Pile et al., Phys. Rev. Lett. 54, 1237 (1985). [ I I ] A. Hashimoto, T. Nagae, T. Fukuda, S. Homma, T. Shibata, Y. Yamanoi et. al., Nuovo Cimento 102A, 679 ( 1989). [ 121 R. E. Chrien, Nucl. Phys. A478, 705~ (1988). [ 131 R. E. Chrien and C. B. Dover, Ann. Rev. Nucl. Part. Sci. 39, 113 ( 1989). [ 141 D. J. Millener, in Proc. of the LAMPF Workshop on (r, K) Physics, AIP Conf. Proc. 224, ed. by B. F. Gibson, W. R. Gibbs, and M. B. Johnson, ( AIP, New York, 1991)) p. 128. [ 151 H. Ejiri, in Proc. of the LAMPF Workshop on (n-, K) Physics, AIP Conf. Proc. 224, ed. by B. F. Gibson, W. R. Gibbs, and M. B. Johnson, (AIP, New York, 199 1) , p. 185. [ 161 J. c. Peng, in Proc. of the LAMPF Workshop on (rr, K) Physics, AIP Conf. Proc. 224, ed. by B. F. Gibson, W. R. Gibbs, and M. B. Johnson, (AIP, New York, 1991), p. 141. [ 171 J. J. deSwart, M. M. Nagels, T. A. Rijken, and P. A. Verhoven, Springer Tracts in Modern Physics 60, 138 (1971). [ 181 G. Alexander, U. Karshon, A. Shapira, G. Yekutiel, K. Engelmann, and H. Filthuth, Phys. Rev. 173, 1452 (1968). [ 191 B. Sechi-Zom, B. Kehoe, J. Twitty, and R. A. Bumstein, Phys. Rev. 175, 1735 ( 1968). [20] R. Engelmann, R. Filthuth, V. Hepp, and E. Kluge, Phys. Lett. 21, 587 (1966). [21] J. A. Kadyk, G. Alexander, J. H. Chan, P. Gaposchkin, and G. H. Trilling, Nucl. Phys. B27, 13 ( 1971). [22] M. M. Nagels, T. A. Rijken, and J. J. de Swart, Ann. Phys. (NY) 79, 338 ( 1973); Phys. Rev. D 15, 2547 ( 1977); Phys. Rev. D 20, 1633 (1979). [23] P. M. Maessen, T. A. Rijken, and J. J. de Swart, Phys. Rev. C 40, 2226 ( 1989). [24] R. Biittgen, K. Holinde, B. Holzenkamp, and J. Speth, Nucl. Phys. A450,403c ( 1986); B. Holzenkamp, K. Holinde, and J. Speth, Nucl. Phys. A500, 485 (1989); K. Holinde, Nucl. Phys. A479, 197~ (1988); K. Holinde, in Proc. of the LAMPF Workshop on (r, K) Physics, AIP Conf. Proc. 224, ed. by B. F. Gibson, W. R. Gibbs, and M. B. Johnson, ( AIP, New York, 199 1), p. 101. [25] A. Reuber, K. Holinde, and J. Speth, Czech. J. Phys. 42, 1115 ( 1992); K. Holinde, Nucl. Phys. A547, 255~ ( 1992). [26] R. H. Dalitz, Nuclear Physics, ed. by C. deWitt and V. Gillet (Gordon & Breach, New York, 1969), p. 701 [ 271 T. A. Rijken, P. M. M. Maessen, and J. J. de Swat-t, in Proc. of the LAMPF Workshop on (7~, K) Physics, AIP Conf. Proc. 224, ed. by B. F. Gibson, W. R. Gibbs, and M. B. Johnson, (AIP, New York, 1991), p. 153. [ 281 J. J. de Swart, P. M. M. Maessen, and Th. A. Rijken, in Properties and Interactions of Hyperons, ed. by B. F. Gibson, P. D. Barnes, and K. Nakai (World Scientific, Singapore, 1994) p. 37. [29] A. Reuber, in Properties and Interactions of Hyperons, ed. by B. F. Gibson, P. D. Barnes, and K. Nakai (World Scientific, Singapore, 1994) p. 159. [30] M. Oka, K. Ogawa, and S. Takeuchi, in Properties and Interactions of Hyperons, ed. by B. F. Gibson, P. D. Barnes, and K. Nakai (World Scientific, Singapore, 1994) p. 169. [3 I] R. Timmermans, in Properties and Interactions of Hyperons, ed. by B. F. Gibson, P. D. Barnes, and K. Nakai (World Scientific, Singapore, 1994) p. 179. [32] R. H. Dalitz, Nucl. Phys. A354, 101~ (1981); R. Karplus and L. S. Rodberg Phys. Rev. 115, 1058 (1959); H. G. Dosch and V. Hepp, Phys. Rev. D 18, 4071 ( 1978). [33] A. Gal, J. M. Soper, and R. H. Dalitz, Ann. Phys. 63, 53 (1971); 72,445 (1972); 113,79 (1978). [34] J. V. Noble, Phys. Lett. B 89, 325 ( 1980). [35] H. J. Pimer, Phys. Lett. B 85, 190 (1979); 0. Morimatsu et al., Nucl. Phys. A420, 573 (1984); F. Wang and C. W. Wong, Nucl. Phys. A438, 620 (1985); Y. He, F. Wang, and C. W. Wong, Nucl. Phys. A448,652 (1986); A451, 653 ( 1986); A454, 541 (1986). [36] 0. Morimatsu, Nucl. Phys. A424,412 (1984); K. Yozaki, Nucl. Phys. A479, 217~ (1988). [37] C. B. Dover and H. Feshbach, Ann. Phys. (N. Y.) 198, 321 ( 1990). [38] C. B. Dover, D. J. Millener, and A. Gal, Phys. Rpt. 184, 1 ( 1989). [39] C. B. Dover and A. Gal, in Prog. Part. Nucl. Phys. 12, ed. by D. H. Wilkinson (Pergammon, Oxford, 1984), p. 171 [40] A. R. Bodmer, Q. N. Usmani, and J. A. Carlson, Phys. Rev. C 29, 684 (1984); A. R. Bodmer and Q. N. Usmani, Nucl. Phys. A477, 621 (1988). [41] 1. R. Afnan and B. F. Gibson, Phys. Rev. C 41, 2787 (1990). [42] For example, see A. Gal and C. B. Dover, Phys. Rev. Lett. 44, 379 (1980). [43] C. B. Dover and A. Gal, Ann. Phys. (NY) 146 309 (1983).

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[44] C. B. Dover, A. Gal, and D. J. Millener, Nucl. Phys. Axxx, xxx ( 1994), BNL preprint 49584; K. Ikeda, T. Fukuda, T. Motoba, M. Takahashi, Y. Yamamoto, INS-Rep.-986 (June 1993) [45] A. Aoki, S. Y. Bahk, K. S. Chung, S. H. Chung, H. Funahashi, C. H. Hahn, et al., Prog. Theor. Phys. 85, 1287 ( 1991); C. B. Dover, D. J. Millener, A. Gal, and D. H. Davis, Phys. Rev. C 44, 1905 ( 1991). [46] A. R. Bodmer, Q. N. Usmani, and J. A. Carlson, Nucl. Phys. A422, 510 (1984). [47] P J. G. Mulders et al., Phys. Rev. D 25, 1269 ( 1982); 26, 3039 ( 1982); R. L. Jaffe, Phys. Rev. D 15, 267 ( 1977); A. T. M. Aerts, P. J. G. Mulders, and J. J. de Swart, Phys. Rev. D 17, 260 ( 1978) ; 21, 1370 ( 1980); 19, 2635 ( 1980); E. Lomon, Phys. Rev. D 26, 576 ( 1982); M. P Lecher, M. E. Sainio, and A. Svorc, Adv. Nucl. Phys. 17, 47 (1986). [48] R. J. Oaks, Phys. Rev. 131, 2239 (1963). [49] I. R. Afnan and B. F. Gibson, Phys. Rev. C 47, 1000 (1993). [SO] R. L. Jaffe, Phys. Rev. Lett. 38, 195 ( 1977). [ 511 C. B. Dover, in Properties and Interactions of Hyperons, ed. by B. E Gibson, P. D. Barnes, and K. Nakai (World Scientific, Singapore, 1994) p. 1. [52] M. Oka, K. Shimizu, and K. Yazaki, Phys. Lett. B 130, 365 (1983). [53] A. T. M. Aerts and C. B. Dover, Nucl. Phys. B253, 116 (1985). [ 541 G. Toker, A. Gal, and J. M. Eisenberg, Nucl. Phys. A362, 405 ( 1981); G. Pigot, J. P. de Brion, A. Caillet, J. B. Cheze, J. Derre, G. Marel, et al., Nucl. Phys. B249, 172 (1985); H. Piekarz, Nucl. Phys. A479, 263~ (1988); K. Johnston, E. V. Hungerford, T. Kishimoto, B. W. Mayes, L. G. Tang, S. Bart, et al. Phys. Rev. C [55] K. Miyagawa and W. Glockle, Phys. Rev. C 48, 2576 ( 1993). [56] H. Berger, Mehr-Baryon-Systeme mit Strangeness im Quark-Cluster-Model, Ph. D. thesis (Friedrich-AlexanderUniversitat Erlangen-Numberg). [57] A. Bamberger, M. A. Faessler, V. Lynen, H. Piekarz, J. Piekarz, J. Pniewski et al., Nucl. Phys. B 60, 1 ( 1973). [58] M. Bejidian, E. Deseroix, J. Y. Grossiord, A. Guichard, M. Gusakow, M. Jacquin et al., Phys. Lett. 83B, 252 (1979). [59] B. F. Gibson and D. R. Lehman, Nucl. Phys. A329, 308 ( 1979). [60] B. F. Gibson, Nucl. Phys. A450, 243~ (1986). [ 611 B. F. Gibson and D. R. Lehman, Phys. Rev. C 22, 2024 ( 1980). [ 621 G. A. Miller, B. M. K. Net-kens, and 1. Slaus, Phys. Rpt. 194, 1 ( 1990) ; J. A. Nolen and J. P. Schiffer, Ann. Rev. Nucl. Part. Sci. 19, 471 (1969). [63] R. H. Dali& and F. von Hipple, Phys. Lett. 10, 153 ( 1964); A. R. Bodmer and Q. N. Usmani, Phys. Rev. C 3 1, 1400 (1985). [64] B. F. Gibson, Nucl. Phys. A479, 115~ (1988); B. F. Gibson and D. R. Lehman, Phys. Rev. C 37, 679 (1988). [65] J. A. Carlson, in Proc. of the LAMPF Workshop on (g, K) Physics, AIP Conf. Proc. 224, ed. by B. F. Gibson, W. R. Gibbs, and M. B. Johnson, (AIP, New York, 1991), p. 198. [ 661 R. H. Dalitz, R. C. Hemdon, and Y. C. Tang, Nucl. Phys. B47, 109 ( 1972); R. C. Hemdon and Y. C. Tang, Phys. Rev. 153, 1091 (1967); 159, 853 (1967); 165, 1093 (1968). [ 671 E. V. Hungerford and L. C. Biedenhom, Phys. Lett. 142B, 232 ( 1984). [68] B. F. Gibson, in Hadronic Probes and Nuclear Interactions, AIP Conf. Proc. 133, ed. by J. R. Comfort, W. R. Gibbs, and B. G. Ritchie (AIP, New York, 1985), p. 390. [69] C. B. Dover and A. Gal, Phys. Rev. Lett. 44, 379 (1980); Phys. Lett. B 110,433 (1982). [70] C. B. Dover, in Proc. of the LAMPF Workshop on (n-, K) Physics, AIP Conf. Proc. 224, ed. by B. F. Gibson, W. R. Gibbs, and M. B. Johnson, (A. I. P. New York, 1991). p. 3. [71] R. S. Hayano, T. Ishikawa, M. Iwasaki, H. Outa, E. Takada, H. Tamura, A. Sakaguchi, M. Aoki, and T. Yamazaki, Phys. Lett. B 23 1, 355 ( 1989); Nuovo Cimento A 102,437 ( 1989). [72] T. Harada and Y. Akishi, Phys. Lett. B 262, 205 ( 1991). [73] T. Harada, S. Shinmura, Y. Akaishi, and H. Tanaka, Soryusiron-Kenkyu 76, 25 (1987); Nuovo Cimento A 102,473 (1990); Nucl. Phys. A507, 715 (1990). [74] P. A. Katz, K. Bunnell, M. Derrick, T. Fields, L. G. Hyman, and G. Keyes, Phys. Rev. D 1, 1267 (1970). [75] R. H. Dalitz, D. H. Davis, and A. Deloff, Phys. Lett. B 236, 76 (1990) [76] M. Barakat and E. V. Hungerford, Nucl. Phys. A547, 157~ ( 1992). [77] B. F. Gibson, A. Goldberg, and M. S. Weiss, Phys. Rev. 181, 1486 ( 1969). [78] D. J. Millener, A. Gal, C. B. Dover, and R. H. Dali&, Phys. Rev. C 31, 499 ( 1985).

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[79] D. J. Millener, A. Gal, and C. B. Dover, Phys. Rev. C 38,270O (1988). [ 801 Y. Yammato, H. Bando, and J. Zofka, Prog. Theor. Phys. 80, 757 ( 1988). [ 811 V. N. Fetisov, L. Majling, J. Zotka, and R. A. Eramzhyan, “Effective AN-Interaction and Spectroscopy of Low-Lying States of lp-Shell Hypemuclei,” Z. Phys. A 339, 399 (1991). [82] E. Satoh, Nucl. Phys. B49, 489 (1972); A. R. Bodmer and Q. N. Usmani, Nucl. Phys. A477, 621 (1988); B. F. Gibson, Nucl. Phys. A479, 11% ( 1988); B. F. Gibson and D. R. Lehman, Phys. Rev. C 37, 679 ( 1988); A. R. Bodmer, Phys. Rev. 141, 1387 (1966). [ 831 A. Gal, in Proc. of the LAMPF Workshop on (r, K) Physics, AIP Conf. Proc. 224, ed. by B. F. Gibson, W. R. Gibbs, and M. B. Johnson (AIP, New York, 1991), p. 173. [ 841 W. Bruckner, M. A. Faessler, T. J. Ketel, K. Kilian, J. Niewisch, B. Pietrzyk, Phys. Lett. 79B, 1.57 ( 1978); M. May, H. Pickarz, R. E. Chrien, S. Chen, D. Maurizio, H. Palevsky et al., Phys. Rev. Lett. 47, 1106 (1981); R. E. Chrien and C. B. Dover, Ann. Rev. Nucl. Sci. 39, 113 (1989). [85] R. E. Chrien, S. Bart, M. May, P. H. Pile, R. J. Sutter, P. Barnes et al., Phys. Rev. C 41, 1062 (1990). [86] M. May H. Pickarz, R. E. Chrien, S. Chen, D. Maurizio, H. Palevsky et al., Phys. Rev. Lett. 47, 1106 ( 1981). [ 871 M. May, S. Bart, S. Chen, R. E. Chrien, D. Maurizio, I? Pile, et al., Phys. Rev. Lett. 51, 2085 ( 1983). [88] T. Motoba, H. Bando, K. Ikeda, and T. Yamada, Prog. Theor. Phys. Suppl. 81,42 (1985). [ 891 P H. Pile, S. Bart, R. E. Chrien, D. J. Millener, R. J. Sutter, N. Tsoupas, et al. Phys. Rev. Lett. 66, 2585 ( 1991). [90] T. Motoba, H. Bando, and K. Ikeda, Prog. Theor. Phys. 70, 189 ( 1983). [91] R. H. Dalitz and A. Gal, Phys. Rev. Lett. 36, 362 ( 1976); Zong-ye Ahang, Huang-lie Li, and You-wen Yu, Phys. Lett. B 108, 261 (1982). [92] E. H. Auerbach, A. J. Baltz, C. B. Dover, A. Gal, S. H. Khana, L. Ludeking, and D. J. Millener, Phys. Rev. Lett. 47, 1110 (1981). [93] B. Mayer, Nukleonika 25, 439 (1980). [94] R. Bertini, P. Birien, K. Braune, W. Bruckner, G. Bruge, H. Catz, et al., Phys. Lett. B 158, 19 (1985). [95] R. Bertini, D. Bing, P. Birien, W. Bmckner, H. Catz, A. Chaumeaux, et al., Phys. Lett. B 90, 375 (1980); R. Bertini, P. Birien, K. Braune, W. Briickner, G. Bruge, H. Catz, et al., Phys. Lett. B 136, 29 (1984). [96] H. Piekarz, S. Bart, R. Hackenburg, A. D. Hancock, E. V. Hungerford, B. Mayes, et al., Phys. lett. B 110, 428 (1982). [97] T. Yamazaki, T. Ishikawa, K. H. Tanaka, Y. Akiba, M. Iwasaki, S. Ohtake, et al., Phys. Rev. Lett. 54, 102 (1985). [98] L. G. Tang, E. Hungerford, T. Kishimoto, B. Mayes, L. Pinsky, S. Bart, et al., Phys. Rev. C 38, 846 ( 1988). [99] J. A. Johnstone and A. W. Thomas, Nucl. Phys. A392, 409 ( 1983). [ 1001 J. Dabrowski and J. Rozynek, Phys. Rev. C 23 1706 ( 198 1). [ 1011 W. Stepein-Rudzka and S. Wycech, Nucl. Phys. A362, 349 (1981); [ 1021 H. Brockman and E. Oset, Phys. Lett. B 118, 33 (1982); Nucl. Phys. A450, 353~ (1986). [ 1031 L. S. Kisslinger, Phys. Rev. Lett. 44, 968 (1980). [ 1041 V. B. Belyaev, S. E. Brewer, E. M. Gandy, A. L. Zubarev, and B. F. Irgaziev, J. Phys. G 8, 903 (1982). [ 1051 R. E. Chrien, E. V. Hungerford, and T. Kishimoto, Phys. Rev. C 35, 1589 (1987). [ 1061 D. Halderson and R. J. Philpott, Phys. Rev. C 37, 1104 (1988). [ 1071 M. Kohono, R. Hausmann, P. Siegel, and W. Weise, Nucl. Phys. A470,609 1987; Phys. Lett. B 199, 17 ( 1987). [ 1081 R. Wunsch and J. Zofka, Phys. Lett. B 193,7 (1987). [ 1091 R. Sawafta, “Proceedings of the Conference on Hypemuclear and Strange Particle Physics,” (Vancouver, Canada, July 4-8, 1994) [ 1 lo] D. H. Wilkinson, S. J. St. Lorant, D. K. Robinson, and S. Lokanathan, Phys. Rev. Lett. 3, 397 ( 1959). [ 11 l] A. Bechdolff, G. Baumann, J. P. Gerber, and P. Cider, Phys. Lett. B 26, 174 ( 1968). [ 1121 J. Catala, F. Senent, A. F. Tejerina, and E. Villar, in “Proceedings of the International Conference on Hypemuclear Physics,” Vol. 2, ed. by A. R. Bodmer and L. G. Hyman (Argonne 1969) p. 758. [ 1131 A. S. Mondal, A. K. Basak, M. M. Kasim, and A. Husain, Nuovo Cimento A 54, 333 ( 1979). [ 1141 W. H. Barkas, M. A. Dyer, and H. H. Heckman, Phys. Rev. Lett. 11,429 ( 1963). [ 1151 B. Bhownik, Nuovo Cimento 29, 1 ( 1963). [ 1161 S. Sakata, Prog. Theor. Phys. 16,686 ( 1956). [ 1171 T. Goldman, K. R. Maltman, G. J. Stephenson, Jr., and K. E. Schmidt, Nucl. Phys. A481, 621 (1988). [ 1181 C. B. Dover and G. E. Walker, Phys. Rep. 89, 1 (1982); H. Bando, Prog. Theor. Phys. Suppl. 81, 1 (1985)

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[ 1191 H. Bando, T. Motoba, and J. ZoIka, J. Mod. Phys. A 5, 1 ( 1990).

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M/Physics

Reports 257 (I 995) 349-388

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