Nuclear Physics A478 (1988) 113c-125c

113cNorth-Holland, Amsterdam

NUCLEAR PHYSICS W

STRANGE PROBES

ityugo S. HAYANO

Department of Physics, Faculty of Science, University ofTokyo, 7-3-1Kongo, Bunkyo-ku, Tokyo 113, Japan

Abstract: Hyperons in a nucleus can be regarded as a test probe marked by strangeness. It is hoped thatquark degrees of freedom in nuclei may be revealed by the use of such probes, but the experimentaldata are rather poor at present. The current puzzles concerning E hypernuclei are described, andthe new data from KEK on '=C (stoppedK-, r*) are presented, which are analyzed in terms of.he E-nuclear interaction parameters.

1 . Introduction

It is almost 40 years since the discovery of strange particles. Kaons, hyperons,hypernuclei, etc ., which used to be the main subject of high-energy physics in the50's and 60's, arenow attracting the renewed interest of nuclear physicists, especiallyin conjunction with the quark degree of freedom in nuclei .We believe today that quantum chromodynamics (QCD) is the correct theory of

strong interactions, and we know that nucleons have quark-gluon sub-structures .Does it mean that we can expect to see some quark degree of freedom in nuclei?Should nuclear physics be reconstructed in terms of QCD?The discovery of the EMC effect is considered as providing evidence for the quark

degree of freedom in nuclei, and triggered both theoretical and experimental studiesof "quarks in nuclei". Interesting possibilities such as nucleon swelling, partialquark deconfinement, mufti-quark bag, modification of nucleon mass andmagneticmoment in nuclei, etc., have been talked about. Although the nuclear physics basedon point-like nucleons plus mesons is of great success, it is appealing to understandnuclei based on a more fundamental theory.An interesting question to ask would be whether or not the quark degree of

freedom is visible even at the low momentum transfer regime . It is hoped thathyperons embedded in nucleimaybe useful tools to study the effect of quark degreesof freedom in nuclei.The hyperon-nucleus spin-orbit interaction is said to beagoodplace to look for

such effects, because of its short range nature . The study of A hypernuclei hasestablished that the A spin-orbit interaction is weak (V"-0) [ref. Z)] and quark-inspired models'') can describe the smallness of the A spin-orbit splitting. However,the predictions for the Y spin-orbit splitting are rather different and its experimentaldetermination is eagerly awaited .A hyperon in a nucleus is usually assumed to be distinguishable from other

nucleons . Unlike neutrons and protons, none of the hyperon's shell-model orbits

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is Pauli blocked ; in principle, we should be able to observe shell-model levels allthewaydownto theground state. This aloneis quiteinteresting, sincetheobservationofthe lowest-lying shell-model states in nuclei is not possible except in light nuclei.The measurement of the single-particle energy of thelowest s-orbitby using nucleonknockout, for instance, would not work because the width of the highly excitedresidual nuclear level having a deep hole state is very broad.

If the hyperon embedded in the nucleus overlaps with nucleons, Pauli blockingat the quark level should occur; when the u- and d-quarks in the hyperon becomePauliblocked, ananomalous shiftin thesingle particle energies in heavyhypernucleimay take place.

In this context, it has been argued that Pauli blocking at the quark level may bea clue to understanding the anomalously small A binding energy in ,;He [ref.')] .Instead of viewing AsHe as consisting of 2 protons, 2 neutrons and 1 A, it may bealternatively viewed as made up of 7 u-quarks, 7 d-quarks and 1 s-quark. Since theOs quark orbit canaccommodate only6quarks, one u-quark and one d-quark withinA become Pauli blocked; the A would then become less bound, and the wavefunction of A would be pushed out of the "He core .The radial distribution of A in ,;He should have a readily observable effect, i.e .,

enhancement of the pionic decay rate of this hypernucleus. It is expected that themesic decay rate of ,S,He should be hindered due to Pauli blocking of the protonor neutron emitted in the mesic decay. However, if the A wave function has lessoverlap with the 'He core, mesic decay is not so much suppressed . Note that thesame phenomenon canbe alternatively described byusingthe language of standardnuclear physics6), namely, in terms of a repulsive core in the hyperon-nucleusinteraction .Apart from such exciting possibilities, the study of hypernuclei is important in

understanding the flavour dependence ofbaryon interaction, since hypernuclei aretheonly practical means currently available in extracting hyperon-nucleon interac-tion parameters.

2. Lambda hypernuelel

Lambda hypernuclei have been studiedextensivelyby usingthe so-called "recoil-less" method') (at PK-550MeV/c, momentum transfer is almost zero) . In thismethod, hypernuclear states of substitutional configuration of the type [(Ij)P'(lj)n,i .e., the A occupying the same shell-model orbit as the neutron struck by the K-,are preferentially populated.The search for the "A EMC effect", by which I mean the possible modification

of A in nuclear medium (due to deconfinement etc), can be best carried out byproducing low-lying levels of heavy A hypernuclei. To produce a hypernuclearground state from a heavy target nucleus, we usually need to convert a neutronoccupying an orbit with an appreciable angular momentum, into a A in the Os,/2

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orbit. Angular momentum as well as momentum transfer is therefore necessary forsuch a reaction to occur. Unfortunately, with the limited kaon intensity availabletoday, it is impractical to perform the (K-, ir-) in-flight reaction at angles satisfyingthe angular momentum matching condition.An alternative method, (ir+,K+), is now being actively pursued at BNL8) and

at KEK9). In this method, the small cross section is morethan compensated by thestrong pion beam intensity . A systematic survey of the A hypernuclear signalsthroughout the periodic table has recently been trig at BNL, and results arepresented at this conference') . Possibilities of measuring the magnetic moment ofA hypernuclei by using the (v+, K+) reaction are also being investigated ' 0) .

Production ofA hypernuclei by using kaon absorption at rest is also suitable topopulate low-lying states, since kwon absorption occurs preferentially on surface(usually least-bound) nucleons, and since the A production via (stopped K-, it )involves relatively large momentum transfer (q=250 MeV/c) ").Thelifetime of the A hypernucleus is another interesting topic, and is extensively

covered by the next speaker 12). Here, I only mentionthat thelifetimes ofvery heavyA hypernuclei have recently been measured at LEAR (Low Energy AntiprotonRing), by using a recoil distance method") .

3.1 . DATA

3. Sigma hypernuclei

The sigma hypernucleus was first discovered in 1979 at CERN in the (K-, ar -)reaction on 9Be at PK=720 MeV/c and 9� =0° [ref. ")]. Approximately 80 MeVabove the 'Be peaks, two peaks of width <8 MeV were found. Those peaks wereassigned as due to the production of FbBe. Such a finding was quite unexpectedsince, unlike A, E in the nucleus can decay via strong interaction EN->AN. It wasnaturally expected that E-hypernuclear structure, if it existed, would be as broadas r-25 MeV [ref. 15 )] .

Subsequently, (K-, ir+) spectra were taken at BNL on 'Li and 'e0 at p�=713 MeV/c for several forward angles''). The data on 6Li revealed twopronouncedenhancements. The suppression of the conversion width in this case was viewed asan evidence for the spin-isospin selectivity mechanism' s) .At CERN, a very short kaon beam line called K26 (only 11 .5 m in total length)

was constructed in order to study Z hypernuclei near recoilless condition, thewell-established method for studying A hypernuclei . The (K-, .r') as well as(K-, ir-) spectra taken on C and O targets are shown in fig. 1 [refs . '7.")] . In the(K-, ir+) spectrum on '2C, asingle excitation at AM -278 MeVwas observed (whichcorresponds to about -3 MeV in the binding energy of E-), and was assigned asa [(P3/2)P'(p3/2)S-]0+ substitutional state. In the (K-, or+) spectrum on 160, twoexcitations at AM - 277 and AM=284MeV were suggested, and were assigned as

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wcU

OwÂEz

3.2. CURRENT PUZZLES

-

f#0

4 ~.

240 260 280 300 320 340MHY-MA

Fig. 1 . (K-, ar+) data on 1ZC and 6̀0 [ref.'s )] .

due to [(P3/2)_1(P3/2)X_10+ and [(P1/2)P1(P1/2)â-0+ respectively. Since the[(p1/2)P1(Pl/2)x-]0+ peak appears about 6 MeV above the [(P3/2)p t(p3/2)x-10

+ peak(just the reverse of the situation in A hypernuclei), it was concluded that the äspin-orbit strength in the p-shell was about 12MeV, or twice that of the nucleon.At KEK, a stopped-kaon 12C(K-,w+) experiment was done "), and a method to

'tag' 2', - hypernuclei was developed . The idea is as follows: the E- trapped in anucleus will eventually convert to A. By detecting the A decay products (pv ornv ), the continuum due to E- quasi-free production (E escaping) can be sup-pressed.

In the wo-tagged spectrum (fig. 2) a narrow excitation at AM-278 MeV (corre-sponding to thepeak seen in theCERN data) wasfound.In addition,twoexcitationswere suggested at AM =282 MeV and at AM-287 MeV. The peaks at 278MeVand at 282MeV were assigned as due to [(P3/2)D1(P3/2)x-10+, 2+ and to[(P3/2)P 1(P1/2)x-12+, respectively. From this spacing, the spin-orbit splitting ofex _5t0.5 MeV was deduced, while the third peak was left unexplained.

Forthe E- hypernucleus alone, the followingproblems arefarfrom beingsettled :Width. Since all the 2 hypemuclear excitations identified so far lie in the 2

continuum, the suppression of 2 escape width in addition to the E conversionwidth must be explained.

771e depth of the centralpotential. Since no ground state peak has been observedso far, it is difficult to deduce the depth of the potential.

3.3 . STOPPED K DATA

70

s

U 3

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R.S. Kayano / Strangeprobes

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Be (MeV)20 10 0 -10 -20

(Stopped K;7r+ ) [n (CHI .'- I' --nv° KP~~x,Togged by 7r®

8

NAA

vlove

255~

-

0 2260 270 280 290 300Mtnr - MA (MeV)

Fig. 2 . (stopped K- , a') data on "C tagged by fro [ref. ' 9)] .

Spin orbit splitting. 7Li was once proposed as a good nucleus to determine thespin-orbit splitting 2° ) and data were collected at BNL, but no peak was found 21).

No consensus exists at present on what is the best method to determine the spin-orbitsplitting.

Unfortunately, all the existing data on E hypernuclei are characterized by poorstatistics, in spite of the considerable efforts of experimental groups. There haveeven been questions raised of whether or not some of the observed structures are

really due to genuine X hypernuclear excitations 22) . Therefore, when it comes tothe interpretation of the data, the situation is quite confusing.

In 1986, we started a new series of hypernuclear spectroscopy by using stoppedkaons at KEK. In what follows, I present some of our new results . Our data as wellas the CERN in-flight data at pK=450 MeV/c will be compared with full DWIA(distorted wave impulse approximation) calculations which recently becameavailable.

To begin with, let me mention a few words about the usefulness of the stoppedkaon data, especially at this stage ofthe E hypernuclear investigation. In the stoppedK- method, we can achieve high statistics hitherto unattainable, especially for theE hypernuclear data. This is because wecan fully utilize the kaonbeamby stopping

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RS. Hayano / Strange probes

kaons in a thick target (3-5 g/cm2). Hyperons are abundantly produced by kaonabsorption.Of course, a large fraction of hyperons do not form hypernuclei, but contribute

to a so-called quasi-free continuum. Nevertheless, if the Z -> A conversion widthissufficiently small, we should be able to see a rich structure in the pion spectrum aswill be shown later.

It is also expected that the stopped K- method can populate the ground state ofZ hypernuclei rather efficiently. If indeed the conversion width is small, apeak dueto the formation of the ground state should become visible. Then the Z bindingenergy canbe readily obtained.The key point of the experiment is to use a thick target to achieve high kaon

stopping efficiency, without deteriorating the hypernuclear mass resolution. Thismeansthat thekaon reaction pointin thethick target should be preciselydetermined,so that the pion energy loss can be corrected for. The use of a stack of plasticscintillators to determine the kaon reaction point, as in theprevious experiment "),limits the applicability of the stopped kaon method to the study of ' 2C only . In thepresent experiment, we employ vertex reconstruction by using muldwire chambersas depicted in fig. 3.

Fig . 3. Schematic view of thetarget region of the present experiment.

The mass resolution of the present experiment in the X hypernuclear region hasbeen measured to be 2 MeV (FWHM). The check was made by using a plasticscintillator as a target, and by looking at the peak due to kaon absorption onhydrogen in the scintillator, K_p-sE-i+ (p,* =173 MeV/c) .

In fig . 4, we present inclusive or + momentum spectrum from kaon absorption on' ZC, corrected for the spectrometer acceptance, pion loss due to decay in flight andto the interactionwithin thetarget material.The prominent peak at pR =185 MeV/ c,and tails on both sides of the peak are due to E' -* or''n . E+ is produced in thequasi-free (stopped K- , r-) reaction. The tails are due to the Z* decay in flight,while the peak is due to the E' decay at rest after slowing down in the target. Thebroad bump below pn-170 MeV/c corresponds to the production ofE_ on tZC.The contribution of the 3r+ decay background underneath the X- production

region canbe reliably subtracted by using the observed shape of the higher momen-tum tail (pn>185 McV,'c), and assuming that X's are ejected isotropically fromthe target nucleus.The background-subtracted spectrum is plotted in 6g. 5, in the scale of the

transformation energy

where MHY is the hypemuclear mass, MA is the target nuclear mass, (MHY-MN)is the difference of hyperon massandnucleonmassand BHYand BN arethehyperon

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MHY-MA= (MHY- MN)- (BHY-BN) ,

(K-.n+) spectrum

(Target : C)

150 200a+ momentum (MeV/o)

Fig . 4. Inclosive (stopped K', rr+ ) data on 12C.

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2000

1500

0250

IllI . Y1Ii

}. . i . . I

~ ~ 1111111

111111111

it11

1 11;11

111i1111111

Illlll.

280 270 280 m0 900 910,r -

® (9®n)Fig. 5. Background due to V-" rr*n is subtracted from the inclusive pion spectrum shown in fig. 4.

and nucleon binding energies. On the same figure, the E binding energy (Bx) scaleis also indicated . For t2C, Bx-=0 corresponds to (MHy-MA ) u�n-275 MeV.The spectrum thus obtained is an unbiased inclusive pion spectrum, which can

be readily compared with the results of recent full DWIA calculations. A MonteCarlo simulation of the (stopped K- , w+) spectrum (fig. 6) indicates that thecontribution of the K - in-flight reaction during slowing down in the target is lessthan 3 .5%, and that of K- decay in flight is practically negligible . Note that it isinappropriate to compare the so called "tagged" spectra, such as presented in ref.with those theoretical results.

3.4. FULL DWIA CALCULATION OF (STOPPED K-, -rr') SPECTRA

In tog . 7, I present spectra expected from DWIA calculations for several differentpotential parameters, calculated by using the Green function method of Morimatsuand Yazaki 23) . The following assumptions are made as in ref. 23 ) : K- is assumedto be captured from 3d atomic orbit. Only the proton in the Op3/2 is assumed tocontribute to the process and the proton wave function is generated by the Woods-Saxon form with radius parameter to=1.27A 113 fm and the diffuseness parametera=0.67 fm. The depth of the potential V0N was taken to be -61 MeV and thespin-orbit strength V'N -= 27 MeV in the parametrization of ref. 2°) is used . Withthese radius parameters, the ground state energy of the AC hypernucleus can bereproduced with VA--30 MeV.

1500

1000

1500

1000

500

0

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400

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13îc

(stopped K-,it*

3-body decay of K-(x100)

f

I (in-flight K-,7r*')

F0 50 100 150 200 250

momentum

Fig. 6. A Monte Carlo pion momentum spectrum of the (stopped K-, or*)reaction. Thecontributionsof the K- reaction in flight andthe K- decay to the spectrum are foundto be insignificant .

270 880 2h90r ~ 900

270 280 200 9~M(i* - M(A) (NOV)

MQM- 11(A) (NOV)

Fig.7. Pion spectracalculated forseveraldifferentpotential parameters ~) arecompared with the presentdata.

(a) V--5M*V (b) V--5Y®VA--9MGV. Vl®-0 Wm-BMOV, Vls-

N Ni

i i ! üii i i11

11444.111 + b1N

t""a

(o) V--10MOV (d) V--15MOV11--9MoV. Ws- W--3Mev, Vls-0

If i i11 14#0 111 1t4N

~N [[

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To describe the B-nucleus strong interaction, an optical potential with imaginarypart was used

U.(r)= (Vol+iW°s)p(r)/po .

where po(=0.17 fm -') is the nuclear matter density, and the same Woods-Saxonform as above is used for p(r) . The imaginary part of the potential takes care ofthe I-> A conversion.As the figures indicate, it should be quite possible to obtain information on the

_Y-nucleus potential parameters by studying the (stopped X-, ar') spectrum. Forexample, with V°E=-10 MeV(shallower than that of theA-nucleuscentral potential,as usually assumed), VI = VN (spin-orbit twice as strong as the nucleon) andW= -3 MeV (weakE-A conversion, corresponding to the width in nuclear matterof about 6 MeV), a spectrum as shown in fig. 7c is predicted. Clearly, our data lookquite different from such a spectrum.By comparing our data with the various curves drawn for different sets of

potentials, we can set constraints on the potential parameters.(i) Firstof all, thecentralpotential depthhasto be shallowerthan about -12MeV

to avoid an excessive strength in the BE > 0 region . For V°<-15 MeV, the[p(N'p(i)j levelwouldbebound in thepresentradius parameters, in total disagree-ment with the observed spectra.

(ii) If V°E -10 MeV, the imaginary part of the potential must be deeper thanabout -6 MeV. Otherwise, the ground state peak would be clearly visible.

(iii) If V°z is as shallow as >5 MeV, the shape of the spectrum is not very muchsensitive to the depth of the imaginaryryr potential, since the spectrum is alreadyquitestructureless anyway.

(iv) Very large spin-orbit splitting (Vz =2 Viv) is not favoured . If W°s is small,priminent peak structure appears. As the imaginary part is increased to wash outsuch structure, the strength in the BE <0 region become excessive. Only whenV°£ < -5 MeV and Woz < -9 MeV or so, the spin-orbit coupling can be made aslarge as 2VN.

It is interesting to seeifthepresentdata areconsistent with thepotential parametersdetermined by the analysis of IN atomic X-ray data"). A best fit to the existingdata is obtained with an effective scattering length a=0.35+i0.19fm, and anempirical optical potential,

V(r) =-[28+i15] MeVp(r)/po,

is obtained in terms of the nuclear matter density. This suggests a large widthrz "--2Wz -30 MeV. However, it should be noted that the fit results dependstrongly on the choice of the radius parameter. In order to determine the potentialdepths for the radius parameters ro=1.27A1/3fm and diffuseness a =0.67fm usedin the E hypernuclear calculations presented above, I fitted the F atomic X-raydata, and obtained V°o--10MeV and W°E --9MeV. In fig. 8, 1 present the

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123c

Fig. 8. The potential parameters obtained by fitting to E- atomic data are used to calculate the pionspectrum (a), and other sets of parameters which can also reproduce the present data fairly well (b)-(d) .

calculated hypernuclear spectrum with the parameters thus obtained . The data can

be fairly well fitted with such parameters.

3 .5 . COMBINED ANALYSIS OF STOPPED AND IN-FLIGHT DATA

Kohno et al. 26) have recently performed acomprehensive DWIAcalculations onthe E - hypernuclear spectra both for the case ofpK-450 MeV/c in-flight kinematics

(corresponding to the CERN datate) and stopped Kcondition . Such a calculation

is of particular importance, since it makes it possible to analyze thetwoindependentexperiments with different kinematics on the same footing.

Instead of using an imaginary potential to represent the X -sA conversion process,they employed a coupled channel approach. A fit to the X atom data yielded

Vosj -10 MeV, and VxA of similar magnitude.As shown in figs . 9c, d, the CERN in-flight data can be reasonably reproduced

with parameters Voa--5- -10MeV avid VxA -0-5 MeV. The stopped K- datacan be very well reproduced with Vol - -5 MeV and VxA = 5 MeV, but not withVox=-10 MeV and VxA =0 MeV.

4. Discussion

From the analyses presented above, the following conclusions may be reachedon ï-Be hypernucleus, within theframework of the modelbeing used :

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Fig . 9 . The same set of potential parameters is used to calculate both stopped K and in-flight (pic=450 MeV/c) pion spectra 36), and are compared with the present and the CERN'a) data.

(i) The E - -nuclear interaction is weak . Much weaker than the mean field felt bya nucleon in the nucleus, and probably weaker (<0.5) than the A-nuclear interaction.

(ii) The stopped K data seem to favor non-negligible ZA conversion strength.However it is difficult to draw a firm conclusion on this point since there exists astrong correlation between the central potential depth and the conversion strengthon the shape of the spectrum. From the experimental side, the key point would beto measure the ratio of ZA conversion to E escape . Such a possibility is beingpursued .

(iii) The potential parameters derived from the analysis of Z atomic X-ray datacan reproduce both the in-flight and the stopped K data fairly well.

Further studies are needed both theoretically and experimentally to find out ifother existing data ('Be and "Li) can be similarly understood. Also important wouldbe an effort to look for a bound X peak. In this regard, the study of 4 He(K-, v- )looks promising; a few-body calculation predicts that there exists a shallow boundstate (B -3 .6MeV) with a narrow width (l' -3 .8 MeV) [ref. ")] . An experiment isbeing prepared at KEK.

I would like to thank themembers of the E117 collaboration (Tokyo-Heidelberg-KEK) collaboration at KEK. I benefited verymuch from discussion with ProfessorsT. Yamazaki, B. Povh, K. Yazakiand H. Bando. Thanks are also due to Professors

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T. Nishikawa, H. Sugawara, H. Hirabayashi, K. Nakai of KEKand the operating

crew of the KEKPS.

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