p-shell Σ-hypernuclei

Nuclear PhymcsA450 (1986) 165e-178c North-HoUand,Amsterdam

1"65c

p-SHELL Y -HYPERNUCLEI V

Jan ZOFKA Nuclear Physics Institute, Czechoslovakia

v

CS. Acad. Sei., 250 68 Rez near Prague,

The impact of recent experimental E-hypernuelear data on systematies of hypernuclear spectroscopy is briefly discussed and relevant theoretical analyses are co,~aented on. Some propositions for useful measurements of ~A spin-orbit splitting are reviewed.

i. INTRODUCTION The variety of unexpected properties of long-lived states of Z-hypernuelei, observed experimentally

on several light p-shell targets at CERN, I-4 BNL 5 and

KEK 6 is a continuous challenge for existing models.

The understanding

of the

propagation of the strongly decaying particle in the nuclear medium is substantially

enriched by the E-hypernuelear

very numerous as yet.

data, even if they have not been

The study of E-hypernuclei

is also a very interesting

task as it is still at the beginning stage; every new piece of data puts new restrictions

on old models and brings new questions to be answered.

There are three main issues in Z-hypernuelei:

i) widths of ~-hypernuelear

states; the role of the strong conversion channel E I~AN; mechanisms selectivity of its suppression;

a possibility

to observe ground states of ~-

hypernuclei

or E hyperon in the is - state; ii) ~N and E-nucleus

(especially

their isospin and spin dependent components);

kinematical

iii) production processes,

selectivity,

interactions

isospln purity of

the basis for the structure description and other peculiarities hypernuclear medium;

and

of the ~-

their structural and

relative virtues and compatibility with A -

production.

All those aspects are necessarily interrelated

interpreted,

they should be treated all together.

and when

There are excellent recent

reviews available, where a thorough discussion on all or some 8 of the above issues may be found. E-hypernuclear

Moreover,

issues, as well.

several speakers at this Conference discuss Thus, to avoid overlap and repetition of what

was said in a better way before or at this Conference, present contribution to the Z-hypernuclear

the scope of the

is narrower and in fact, the main attention is paid here spectroscopy and to consequences

analogy between E and A excitation functions. 9

of the similarity and

The narrow widths of some E-

states are discussed in talks I0,II and they are used here as a fact,

0375--9474/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

166c

2ofka / p-shell E-hypernuclei

J.

confirmed

further by the experiment.

Also, a detailed discussion of ZN

interaction

is not undertaken here for Ref. 12 aims at it. 9 A previous review summarized the Z spectroscopy status in 1982 and can be

used as a useful start for a demonstration

of the progress made since then.

This is sketched in the second part, whereas the third part presents a model for extraction of the spin-orbit E-nucleus potential. propositions

2. SPECTROSCOPY

OF P-SHELL E-HYPERNUCLEI

The measurements I.

Some useful experiment

are listed in Sect. 4.

of E-hypernuclei

It is interesting

performed until now are listed in Table

to notice that there are five experiments

by x), which did not appear in the 1982 list. 9 understanding

the E-hypernuclei

even if many conclusions

Nonetheless,

has been considerable

only (denoted

the progress in

in the last three years

still need further verification. TABLE I

List of Z-hypernuclear (KW) production experiments. laboratories are indicated.)

400 (CERN')x

6Li

720 (BNL) 720 (BNL)xa

7Li 9Be

720 (CERN)

12 C

400, 45~, 720 (CERN)

160

a

0 (KZK)

450 (CERN), 0 (KEK) N 720 (BNL) *a

400 (CERN)

450 (CERN), 720 (BNL)

not quoted in Ref. 9 final results not yet available

The lightest E hypernucleus •

(Initial K- momenta and

6

.

.

.

5 .

• wzth 6 baryons, .

.

6 ° • ° rH has a slmllar excitatlon 1~

-1

functzon as ALl, wlth slmzlar znterpretatzon of observed (pEp ) and -1 . . . . 6 . (sEs ) peaks. Thezr dzfferent energy shlfts, as compared wzth ALz, reveal differences

in residual EN interaction. 12

The 13 2] cluster nature of the

16.7 MeV 5Li narrow state, on which the ~Li (sEs-l) state is built, allows to illustrate

the spin - isospln selectivity mechanism for quenching of E

J. Zofka / p-shell Z-hypernuclei wldths. 14

~Li,

167c

It is interesting to compare ~H excitation function with that 2 of

where no (sEs-l) peak is exhibited.

Various mechanisms were proposed,

why this state could not be oberved there (width increase by denslty, 2 1 = 3/2 channel suppression in PK ~ 400 MeV/c reglon7).

Another one may be the

difference in threshold positions for various E 1 hypernuclei.

The discrepancy

should be noted between B E of Refs. 5 and i-4. First (K, ~) reaction where narrow resonances in E spectrum were clearly seen yielded ~Be. I the A one.

It gave evidence for a E-well depth shallower than

Its pronounced cluster structure complicates the interpretation.

The link between ~He and ~Be ground states 15 may cause the ls E state in ~Be to be narrow; if it is narrow in ~He hypernucleus

(in the original ~Be

spectrum, I a small peak at B E = 0 seemed to suggest g.s. observation). 12C target yielded the most extensive ~ data.

They were used for fixing the

isospin structure of resulting hypernuclear states i.e. whether the E particle keeps its charge identity or whether isospin is a good quantum number.

In

fact, Ref. 16, by comparing various 12 Z C spectra, suggested a strong charge mixing in contrast to the conclusion of Ref. 3. An important novel mechanism for E-hypernuclear production,

capture of stopped K-, was reported in Ref. 6

and it yielded three-peak l~Be excitation function (Fig. I), which is employed in section 3 for model extraction of the spin-orblt interaction.

i

E+t85 n,/T+ E-p3a

(E-pwz)

60

K-p--E-'/'/"+

7/-+ SPECTRUM Stopped K-

in (CHJ.

Tocjged by T a

4o

~-o

r

20

i

140

160

I 0

200

220

rr + Momentum (MeV/c}

FIGURE 1 l~-Be experimental spectrum produced by capture of stopped K-. 6

J. Zofka / p-shell E-hypernuclei

168c

For that purpose, also a new analysis 4 of 16zC is used, which suggested a two 0 + peaked spectrum (Fig. 2) for (K-,~ +) reaction on 160 target at PK = 450 MeV/c.

When using PK = 713 MeV/c, 5 much broader structure (F ~ 19 MeV) is

encountered around E

~ -15 MeV, which may include an addition to 0 + states ex also, non-substitutional 2 + ones excited in view of larger momentum transfer.

r

32

i

i

|

(a

.lJLl .,

450.eV/c

24

F,-. z

i

12C(K-,~:*)l~Be

1_4 ,e,i ,2

16

gs .,,tt,1~t~

(D

t t f")"' K--,~

i

i

i

i

"

or" i,i

m 3o

450 MeV/c

i[(~ £

),

tbrt

7

2O

10 o

240

260

280 300 MHy-M A

320

340

FIGURE 2 12 16 zBe and zC evperimental spectra produced by in-flight (K-,~ +) reaction.394 3. Z-NUCLEUS SPIN-ORBIT SPLITTING The l~Be K- capture measurement 6 (Fig. I) proposed for the Z-nucleus spln-orblt splitting (SOS) in this hypernucleus a value of EZ = 5 ± 0.5 MeV. Early this year 9 a combined analysis 17 of all (K-,~ +) measurements for A = 12, 16 hypernuclei resulted in a larger eZ (twice a nucleon value).

Limitations

on EZ were further analyzed in Ref. 18, especially the interplay between eZ and residual ZN interaction, for smaller values (~ 3 MeV) of EZ9 was noticed there.

The shell-model for the description of the Z-hypernuclear Ip-shell excitations used in Ref. 17 was the same as that applied to A-hypernuclel before 13 and rely on similarity of A and Z spectra. 2

Relevant states lie

within single (i ~r~) excitation group (pA~5pr),-- the results are thus related to those which would be obtained in similar approaches to A-hypernuclei.

J. ~ofl~ / p-shell Z-hypernuclei

169c

To avoid a m b i g u i t i e s i n the r e l e v a n c e o f i s o s p i n or c h a r g e - s t a t e b a s e s , 3'16 the double charge exchange r e a c t i o n s ( K - , ~ + ) , (K-,K +) were t r e a t e d i n Ref. 17. The one-body s p l n - o r b i t i n t e r a c t i o n was i n c o r p o r a t e d i n the s i n g l e p a r t i c l e energies.

I f needed, the f i n i t e range i n t e r a c t i o n m a t r i x e l e m e n t s f o r a l l

c o n f i g u r a t i o n s pA-5p~ may be c h a r a c t e r i z e d by two S i s t e r i n t e g r a l s F (0) and F (2) and exchange s t r e n g t h s ax, a s of c e n t r a l ~N i n t e r a c t i o n u s e d .

Possible

i s o s p i n m i x t u r e appears as a f i x e d combination V = 2/3 V ( I = I / 2 ) + I / 3 V (I

= 3/2).

The production mechanism (K-,~ +) i n - f l i g h t

was described by DWIA i n the

eikonal approximation, which works well in A-hypernuclear production.

The

K- capture at rest produces both 0 + and 2 + states (it differs appreciably f r o m ~ - and ~- capture) and is described in the impulse approximation with K-electron - llke wave functions. The experimental input into Ref. 17: a)

A new analysis of 16 EC in-fllght data 4 at PK = 450 MeV/c (Fig. 2).

It

yields two substitutional 0 + states, split by AE ~ 6.5 MeV and their fntensity ratio is IU/I L = I : 1.5 (± 30%), the lower peak being more pronounced. 4 b)

In-flight (K-,~ +) production 3 of l~Be at PK = 450 MeV/c (Fig. 2). Again, due to a small transferred momentum qtr = 70 MeV/c, it yields one narrow substitutional 0 + peak (at MHy - M A = 279 MeV) and a broad shoulder (at I to 17 MeV higher).

c)

At-rest (K-,~ +) capture leading to l~Be,- which yielded three peaks 5 MeV apart and decreasing intensity ratios (see Fig. I).

Purposefully, the absolute positions of (pEp -1 ) states in various hypernuclei were not compared in Ref. 17 (this would introduce as free parameters:

E - E and F(0)). p s It is important to start with 16 ~C analysis as the target of 160 has the

closed Ip shell to a good approximation; description of 0 + spectrum in 16 zC necessitates two hole states only and both 0 + level splitting and their intensity ratio are simple functions of energy e = EZ - 6.18 MeV and interaction matrix element v :.VI1.:.V22 = V 1 2 ~ 2 . of four parameters ax, as, F (U), F tZ). displayed graphically in Fig. 3.

v is a single mixture

The solutions are straightforward and

The ellipses are contours of a given

(measured) splltting AE, whereas straight lines are contours of a given peak intensity ratio.

Thus, two regions (emphasized on the ellipses of AE = 6.5

MeV) correspond to the experimentally found "'1~Cspectrum. 4

They yield two

possible values of Z hyperon P3/2 - P1/2 splittings, namely 12.5 MeV and -0.5 MeV.

The upper one corresponds to a small value of v.

Remarkably enough,

variations in v or lu/I L around found values do not change E appreciably.

170c

.L

Zofka / p-shell F~-hypernuclei

The ambiguity of the solution is to be removed and the A-dependence

of the

applied parametrization

of the residual VyN shown to be weak in analogy 12 with A-hypernuclei and normal nuclei. The target C may seem very appropriate 8 with its approximate P3/2 structure. The p,d) experiments (cf. Fig. 4a) and shell model intermediate

coupling calculations

demonstrate~

however~

a need to

consider three "hole" states 3/2- (GS), 1/2- (2 MeV), 3/2- (4.8 MeV) instead of one in IIc (11B) 19, The spectrum of 12AC does not contradict

it~ as the

spin exchange of AN interaction and small SOS result in enhancing the first state and the other pap -I states are not pronounced even in 2 + spectrum (Fig. 4h with E = 0 displays it).

Thus, A~I2 E hypernucleus

cannot be treated in an

equally simple model as that for A=16~ but the diagonalization with VZN interaction was to be performed.

For a rough orientation,

Figs. 4b, c, d

depict how some appreciably populated 0 + and 2 + states in 12Be "travel" through spectrum when changing SOS EP(and the residual central interaction

is

switched off, VyN = 0). In order to get three stronger peaks 5 MeV apart in 12 the at-rest EBe spectrum~ SOS of at least of 5 MeV would be needed. Changing VEN t one can notice that the existence of one pronounced 0 + peak in the in-flight spectrum of 12 EBe 3 suggests a large negative value of a s (of the order of -0.2 to -0.6). and <0,5>,

respectively,

Varying now a and F(2)/F (0) in intervals <-i, i> x so that v is kept in the emphasized areas~ the

message on SOS remains essentially the same.

Namely,

in order to get three

peaks as in Fig. i, a large SOS is needed (5 or I0 MeV) and a reasonable V~N alone (allowed by constraint on v) cannot simulate it. 4e - 4f demonstrates interactions

A comparison of Fig.

how little the inclusion of very different residual

VyN changes intensities

and energy positions.

the first peak (0 + and 2 + ) is still beyond the experimental Variations

spectra,

reach.

of F (2) and a

influence mainly the splitting of 0 + and 2 +

In this respect~

a comparison of in-flight data with e.g. ( ~

x states and cannot be unambiguously available.

The structure of

extracted from the data presently

for which a large transfer is typical

K +)

(qtr J" 370 MeV/c for p~ ~ 1500

MeV/c), would be useful. Problems with a sufficient

intensity in the second peak of l~Be- spectrum

(cf. Figs. I and 4) were mentioned in Ref. 17 and emphasized again in Ref. 18.

Indeed~ E~ ~

10 MeV generates a strong third peak and depletes the second

one to some extent.

When adopting E E ~" 5 MeV~ as preferred in Refs. 16 and

18~ the second peak is strong enough~ hut then only a very weak third peak arises.

J. ~,ofka / p-shell Z-hypernuclei

171 c

o 3I 1I ~3II TI

IIIII illll

51353 7 ~73 'f ~o 312

i ii

e

1

IMeVl [MeV}

Z

i 3

3

15

\

c

! _

•

i

e

i

•

f

I

i

i

i

l

-8 -3

3

3

1 =r

I

I

I

I

I

I

3

2

1

0

-1

-Z

I

v [MeV]

0

FIGURE 3 Map of SOS £ vs matrix element v at constant 0+ peaks splitting (ellipses) and their i n ~ n s l t y ratio (straight lines).

4

8

12

AE [MeVI

FIGURE 4 0+ and 2+ peaks excited by KmeSg~cCapturelz on 12C target: a) hole spectrum; b) s = O , V y N = O ; c) c=5 MeV, VyN=O ; d) effil0MeV, VyN=O; e,f,g) e=10 MeV, V ~ 0 ; h) ~=0 MeV, VAN#0.

Details of the residual Z N interaction are not vital for extraction of eZ at e~ 5 MeV, 18 which is the range under consideration in Ref. 17.

Calculation

of Affil6Z-hypernucleus using microscopically based OBEP potential yielded AE 6 MeV 20 with expected preference for small e Z .

In fact, the use of OBEP

motivated Z N interactions should prevent an extraction of large (eZ > £N) SOS value of e Z .

,L Zofka / p-shell E-hypernuclei

172c

Summing up:

•

the experlment

6

yields a strong evidence for excluding values

of CZ close to zero 9 preferring cZ around 5 and 10 MeV for A=12 mass region. Ref. 4 would then be evidence for E~ 6- ~

12 MeV.

Even if 6~2- ~

10 MeV does

not yield quite correct intensity pattern in ~2Be, a smaller value c~ 2 ~ 5 MeV corresponds to a too strong A dependence of E Z.

This contradicts the

experience with normal nuclei and A-hypernuclei and the notion of the mean field (if this is applicable for Z hypernuclei at all).

A larger E~ 2- ~

10

MeV should be thus preferred on the basis of the combined A=I2, 16 analysis. In view of relatively large experimental uncertainties in energy~ positions 18

and intensities~ extracted EZ should bear errors of the order of 2 MeV.

Thus~ the reasonable phenomenological representation of the presently available experimental data seems to be E~ 6- = 12 ± 2 MeV and E~2- = i0 ± 2 J 5 16 L MeV. (It islworthwhile to notice that the measurement of z C does not contradict 6~6 value quoted above 9 as seen in Fig. 5. at 9° and 1 ~ , oI~2 = -I, ~

Also~ flat "spectra"

in E-H 6 seen in Ref. 5 might reflect the appearance of

P3/2 J structure shifted by large E~ between substitutional resonances.

Similarly large splitting (15 MeV vs. 10 MeV for A) between those substitutional states may reflect large EZ.) 12.5 (Y)

ir

0A -2.5 (Z)

]

-B

-4

0

4

8 AE [MeV]

FIGURE 5 Predicted 160 spectra in K- capturel7~ Ev are indicated

Z Zofka / p-shell ~,-hypernuclei

173c

4. USEFUL EXPERIMENTS To test further various ~ hypernuclear characteristics and especially to verify the value of spin-orbit splitting EZ, many experimental results may be used, but only some of them are simply and straight forwardly related to e. The latter ones may be "divided" into three types of productions on structurally interesting targets: A)

substitutional recoilless; (K-,~) for AL. = 0, qtr << qF reactions;

B)

non-substitutlonal (qtr >> 0, AL ffi 2, (K-9~) at 8 # 0°, (~,K+), Kcapture) reactions;

C)

exotic atoms.

For A and B, the double charge exchange reaction (K-,W +) often simplifies considerably the produced spectra and thus also extraction of e. Reaction (K-,W +) on isospin I

= 1/2, I

O

= - 1/2 targets prepares IN = 1 Z

nuclear core which is then coupled to IHy = 2 of resulting Z-hypernucleus. In addition to 7Li (where (szs -I) configuration may complicate the e extraction 21 using K- capture) and 13C targets, suggested in Ref. 18, also 9Be and lib target are of interest.

They have two close I

Z

= -i narrow proton hole states

(0.7 and 3.4 MeV apart, respectively). Reaction A produces one 3/2 -I (substruetured) state (Pz P3/2 ), whereas B would yield two states

(4/2

A).

18

.

. "

and .

.

s p l i t by

. .

(fore

÷

"

.

.

Reactlons wlth qtr >> 0 (as e.g. (~, K )) yleld preferentlally the

latter ones.

To get e, one then uses B or a comparison of B with A

productions.

The target 15N is well suited for seeing both p3~2- a~d pli2-

in a single A measurement (especially when eZ ~ eN, when one coherent state is produced). Targets with I ° = 19 I z = -I are even better suited as they yield a single narrow hole state at I 15 MeV and A, B produce Z hypernuclear states with IRy = 5/2.

Thus 14C appears as an ideal target for extraction of eZ in A and B

comparison.

Target 10Be has a similar property.

Comparison of A = 12, 13, 14

carbon Z hyperisotopes might further reveal the isospin structure of ZN interaction. Fig. 5 displays also spectra of A=I6 hypernuclei with varying e (the relative 0 + vs. 2 + intensities correspond to at-rest kinematics, (W+,K +) and (K-,K +) would trace 2 + states only). case, the insertion e

To see how the scheme works in a known

0 corresponds to I 0 hypernucleus, which exhibits

only 0 + and two 2 + pap -I states (seen e.g. in (K-,~-) angular distributions at ~

~ 150). eA = 0 is corroborated here further by a schematic spectrum of 1~C (Fig.

4h), where the excitation function of 2 + states (taken at ~ exhibits one peak only.

= 15° in Ref. 22)

174c

J.

2ofka I p-shell ~-hypernuclei

Different numbers of peaks for E = 5 MeV and c = 12.5 MeV (3 and 4, respectively)

are to be noticed~ because repeating Tokyo at-rest ( K - ~ +)

experiment on oxygen target should clearly distinguish

it.

And the distance

of two last 2 + states is practically equal to E. It is worthwhile

to illustrate the usefulness

production of both A- and E-hypernuclei. 23~ its experimental Ref. 24.

Its theory has been outlined in Ref.

feasibility has been even experimentally

demonstrated

in

Its main interest lies in practically exclusive population of 2 +

states with still applicable cross-sectlons. instrument 25 for verifications Fig. 5.

of (~gK +) reaction for

It is thus a very suitable

of estimates of Ey and VyN as it follows from

Figure 6 summarizes elementary

(7 9K+) cross-sections 26 in " the region

of i GeV/c to 2 GeV/c and allows choice of the best kinematics (e.g. p + I 1.5 + GeV/c for E + production; p~ I 2 GeV/c for Z ° production). Further 9 Fig. 7 compares

the ~- and A-hypernuclear

production on 12C target.

i) relatively high production cross-section

(especially

It demonstrates:

in view of higher

meson fluxes available) 9 ii) practically exclusive AL = 2 population, for indicating

certain levels and edges of energy regions

needed

(this is due to high

qtr ).

d.F~. [~blsr]

(~, K÷ )

100

/

\

\\/

/

.,

rr

1

A

)'

°

Z

_.eob

1.5 FIGURE 6 (~+,K+)v cm cross sections

2

OeVlC

Z 2ofka / p-shell Z-hypernuclei

10

175c

2+

2~

2÷

LII- i-

i

o+I2÷

1"

Ii + 2+

d8" l-" d

10

2+ (~+K+}~C

I2+

I-

I"

I

10

I Eex[MeV]20i"

FIGURE 7 I~C and I~C comparison, as produced in (w +, K +) reaction The lower insertion in Fig. 5 may be used further for illustration of possible excitation function of E- hyperoxygen, when using proposed value of c=.

Analysis of binding energies and da/d~ of (K-gK +) production reaction

given in Ref. 27 shows the possibility of population of their spectra in planned kaon factories.

Relatively weak interaction E-N and SOS

ratio EE/¢ N = -I13 make it possible~ to use Figs. 4 and 5. again suppresses 0 +.

Large qtr in (K-~K +)

Thus l~Be spectrum would contain one 2 + peak only.

More useful would be (K-~g+)-reaction on 160 target yielding three 2 + peaks when a good resolution is attained. evidences the ~

The distance of the last two peaks

value.

An interesting example of an effect of type "C"~ sensitive to the ZA spinorbit interaction9

is the hyperfine structure of Z- exotic atoms.

When

supposing the existence of a near threshold resonance Z state in the field of the core nucleus, one may derive a relation between AE shift and r~ width of the E-atomlc level and E energy and r width of the single particle Z hypernuclear level 28 hypernucle£~

In particular~

for p-states relevant for p-shell

the following holds. AE2p - ir2p/2 Ec

3

m 2 a3 Z 3

28 r l ( E

i r/2)

J. Zofka /p-shell E-hypernuclei

176c

where E c = m c 4 Z2/~ 2 , m = (mZ • mA)/(m Z + m A) ,

r 1 is the effective range and Z is the charge. Z

was considered

there.

In Ref. 281 the system lIB +

Adopting values from Ref. 6, the atomic values

obtained are:

bE (2P3/2) = - 8 keV,

F (2P3/2) = 17 keV,

bE (2Pl/2) = - 2 keV,

r (2PI/2) = 1.6 keY,

Thus, a splitting of X-rays from 3d ÷ 2pj transitions however masked by widths of split levels. observing

appears, which may be 28 for

The most suitable case

the splitting should be the exotic atom X-4He.

5. CONCLUSION All the information on properties isospin and spin structure,

of ~N and EA interactions,

strengths)

extracted by many authors from observed E-hypernuclear is essential,

but often needs further experimental

is also true for the spin-orbit EA interaction, much larger than A A one and comparable

(notably,

and E behavior in the nuclear medium, excitation

verification.

functions This

which is suggested

to be

to or larger than NA one.

In spite of an extensive similarity between E and A hypernuclei, remains to be done for E-hypernuclei of the same models

than for A-hypernuclei.

(as e.g. bound shell model)

more

Even the use

for both is ascertained

only

posteriori. Thus also suggestions reactions

on new experiments

on interesting

(K-,~) and (~,K +) in eollinear and non-collinear

Z--atoms have been reviewed here.

Performing

targets using geometry,

as well as

at least some of them would help

to verify what a value the spin-orblt E-nucleus

splitting should have.

ACKNOWLEDGEMENTS Useful suggestions H. B a n d ~

and discussions

on various aspects of ~ hypernuclei with

A. Bouyssy, R.E. Chrien, C.B. Dover, R.A. Eramzhyan,

L. Majling, V.E. Markhushin,

D.F. Measday,

T. Yamazaki are greatly acknowledged. Sotona in preparing

B. Povh~ O. Richter, M. Sotona and

Collaboration with L. Majling and M.

this manuscript was very useful.

Support from organizers

of 1985 HF&K BNL Conference rendered the authors participation particular

V.N. Fetisov,

the help by R.E. Chrien is very much appreciated.

possible,

in

Z ~ofka /p-shell 7~-hypernuclei

177c

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2)

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3)

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4)

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7)

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