A study of 16O by the reaction 14N(3He, p)16O

(l.D.1:2.4

Nuclear Physics A176 (1971) 645-656; Not to be

@ North-Holland

Publishing

Co., Amsterdam

reproduced by photoprint or microfilm without written permission from the publisher

A STUDY R. WEIBEZAHN,

OF 160 BY THE REACTION H. FREIESLEBEN,

Physikalisches

Institut

“N(3He,

F. PUHLHOFERt

der Universitc’it Marburg,

Received 21 September

p)160

and R. BOCKtt Germany

1971

Abstract:

The structure of the states of I60 has been studied by means of the (3He, p) reaction on 14N. Angular distributions were measured between 8lab = 5” and 60” at 18 MeV incident energy. The data were analyzed using DWBA and the shell-model wave functions of Zuker, Buck and McGrory. The transitions to the negative-parity lp-lh states at E, = 6.13, 7.12, 8.87 and 10.95 MeV are described very well. The 4p-4h structure of the positive-parity states at 6.05, 6.92 and 10.35 MeV is confirmed by their low cross sections. The 2+ state at 9.85 MeV and the positive-parity states between 11.08 and 13.66 MeV are found to contain only a small part of the 2p-2h strength and it is suggested to identify these states with Arima’s 4p-4h states with an excited 12C core. The 2p-2h states seem to lie mainly above 14 MeV excitation energy.

E

NUCLEAR

REACTIONS 14N(3He, p), E = 18 MeV; measured a(E,, 0). I60 levels deduced L, p-h configurations.

1. Introduction The spectrum of the doubly magic nucleus I60 has been experimentally well studied I). About 70 states are known up to an excitation energy of about 20 MeV and most of them have spin and parity assigned. The nucleus 160 has also been the subject of extensive theoretical investigations. The excited states are described in terms of particle-hole excitations. These calculations have to explain the fact that positiveparity states, which have to be 2p-2h or 4p-4h excitations, appear at about the same energy as the negative-parity lp-1 h states. In fact, the first excited state is a Of state and is generally believed to have a dominant 4p-4h configuration. The relatively low excitation energy of the multiparticle excitations is apparently connected to their collective character and they are therefore often described as deformed states ‘), in contrast to the spherical lp-1 h states. Recently, Zuker, Buck and McGrory “) ttt (ZBM) were able to give a shell-model theory of both the negative- and positiveparity states. These calculations are of particular relevance here, because wave functions in a shell-model basis are directly applicable fox predicting spectroscopic factors for transfer reactions. In the present work, I60 has been studied by means of the reaction 14N(3He, p)160, measured at 15 and 18 MeV incident energy. At this energy, the reaction proceeds via a transfer of a proton-neutron pair and, since the target nucleus has a two-hole cont Present address: Lawrence Radiation Laboratory, University of California, Berkeley, USA. tt Present address: GSI, Darmstadt, Germany. ttt In this paper the wave functions of the BNL report have been used (matrix elements and singleparticle energies Al). 645

I

646

R. WEIBEZAHN

et nl.

figuration relative to i60, it selectively populates Op-Oh, lp-lh and 2p-2h states. Excitation of 3p-3h and 4p-4h configurations is forbidden, and the reaction is therefore expected to immediately give information about the configuration of the final states. Two-nucleon transfer reactions and, in particular, (3He, p) and (t, p) reactions have been shown to be a successful means for testing nuclear wave functions. It was, therefore, interesting to see if a DWBA analysis using the ZBM wave functions is able to explain the (3He, p) cross sections. Similar transfer-reaction studies have been published recently. We use in particular the results of Bohne et al. “) and Fulbright et al. “) [‘5N(3He, d)r60], Mendelson et al. “) [r70(p, d)r60], Zisman et al. ‘) [14N(a, d)i60], DBtraz et al. “) [19F (3He, 6Li)‘60], Piihlhofer et al. ‘) [‘2C(7Li, t)‘“O] and McGrath et al. lo) [“Ne(d, 6Li)160] f or comparison. As a consequence of the selectivity discussed above, the “N(3He, p)“jO reaction is expected to lead to new results. It is mainly a means of investigating the lp-lh component in the negative-parity states of 160 and the 2p-2h component in the positive-parity states. To be sure, only those 2p2h components in which the two pt holes are coupled to l+, T = 0 are excited, but the different 2p-2h components will generally mix strongly. The one-nucleon transfer reactions populate mainly the negative-parity states and measure their lp-lh strength. The selection rules for the (CI, d) and (3He, p) reactions are, of course, very similar. However, the different kinematic conditions, i.e. the low momentum transfer in the (3He, p) reaction, make the latter in general more suitable for a DWBA analysis. The a-transfer reactions populate in principle all the configurations mentioned. They have a different type of selectivity because of their sensitivity to four-nucleon correlations.

2. Experimental

method

The experiments were performed using the 3He beam from the EN tandem Van de Graaff of the Max-Planck-Institut fur Kernphysik in Heidelberg. The proton spectra were analyzed with a broad-range magnetic spectrograph. The protons were easily separated from other reaction products by means of absorber foils in front of the nuclear emulsion plates. A sandwich target containing adenine (C5N5H5) was used. The adenine was evaporated onto a carbon backing and protected from decomposition under bombardment by a thin layer of gold. The 14N content was about 30 pg/cm’. Since the (3He, p) reaction on the “C impurity of the adenine target complicated the study of states at high excitation in 160 a selfsupporting TiN target was used additionally. This target contained only a very small amount of “C, but, unfortunately, as much ’ 6O as ’ 4N. Attempts to reduce the oxygen content failed. Angular distributions at E3,, = 18 MeV were measured between 5” and 60” using the adenine target. Absolute cross sections were determined from the elastic 3He scattering at 17.4 MeV and &, = 40”. The absolute elastic cross section at this point

.

B 8 ,’

2

:

100

0

s

0

5

35

'LN(3He,p)'60

LO

“or?

6

Fig. 1. Proton spectrum of the reaction

- 50

-

“E E :: X

E,

N

“N(3He,

45

!q

7

55

9

60

10

65

11

70

12

75

60

05

the

14

postion on

13

plate

cm

t-W

p)160 at eLab= 5” and EsHc = 18 MeV. The excitation energies are taken from ref. ‘).

50

0

648

R. WEIBEZAHN

et al.

was taken from an optical-model fit to data of Artemov et al. ‘l). The energy resolution, typically about 70 keV, was mainly determined by the target thickness. Exposures at a few forward angles were made at 15 MeV incident energy using the TIN target in order to study the states in I60 between 13 and about 18 MeV excitation energy.

3. Results A spectrum of the reaction 14N(3He, p)i60 obtained at Oiab = 5” is shown in fig. 1. One of the striking features is the low cross section for the transitions to the states of the rotational band based on the first excited state (Of E, = 6.05 MeV, 2+ E, = 6.92 MeV, 4+ E, = 10.35 MeV). This may be taken as a direct experimental evidence for the dominant 4p-4h character of these states. As expected this band is very strongly populated in a-transfer reactions on “C [refs. 9pI’)]. Most of the strongly excited states of positive parity are at higher excitation energy. We observe a relatively high cross section for the states 2+ E, = 9.85 MeV, 3+/4+ E, = ll.OS/ll.lO MeV, 2+ E, = 11.52 MeV, O+ E, = 12.05 MeV and If E, = 13.66 MeV. These states have to have 2p-2h admixtures in order to be excited. Whether this configuration is the dominant one will be discussed in a quantitative analysis of the cross sections (see sect. 4). As expected for the lp-lh configurations of the lowest negative-parity states, we observe strong excitation of the states 3- E, = 6.13 MeV, l- E, = 7.12 MeV, 2- E, = 8.87 MeV and O- E, = 10.95 MeV. These four states arise from a coupling of a p, hole and a d, and s3 particle. They have large spectroscopic factors in the (3He, d) reaction 4*“). The equally large (3He, p) cross sections for the states lE, = 12.44 MeV and 2- E, = 12.53 MeV indicate lp-lh components in these states configuration for the state at E, = 12.53 also. The suggestion of a dominant d,p,-i MeV by Fullbright et al. “) will be discussed in sect. 5. The state at 12.44 MeV also seems to be more complicated and to have a s3pi1 and pt hole components in its wave function 4*5, “). The measured angular distributions are shown in fig. 2. Most of the transitions and, in particular, all strong ones show typical stripping patterns. Because of the spin the proton1’ of the target nucleus i4N and because of the necessity of transferring neutron pair in an S = 1 state to excite T = 0 states in i60, the angular distributions contain, in general, several contributions with different values of the transferred angular momentum L. Although the lowest L-value is favored kinematically this often leads to very complicated shapes. Only the O- state at E, = 10.95 MeV has a pure L = 1 angular distribution. In the transitions to the l- states at E, = 7.12 and E, = 12.44 and to the 2+state at E, = 9.85 MeV the lowest L-value seems to dominate. The shapes of the angular distributions for the states 2+ E, = 6.92 and 4+ E, = 10.35 MeV, which are only weakly excited, indicate a more complicated reaction mechanism than a simple two-nucleon stripping. Unfortunately, we were not able to obtain

14N(3He, p)160

649

REACTION

angular distributions for the four lowest T = 1 states and for states above E, = 13.66 MeV, mainly because of the carbon impurity of the target. Some qualitative remarks on these states will be made in sect. 5.

4. DWBA analysis The calculations were performed with a standard DWBA code 13) using a twonucleon form factor calculated separately by the program FOCAL. The details of the form-factor calculations have been described previously ’ “). The optical potentials used are listed in table 1. For the exit channel we assumed a potential obtained from TABLE 1

Optical-model Particle

Energy (MeV)

3He P

P P P P P

32 26 24 22 20 18

parameters used in the DWBA

(Mk)

(2)

170.0

1.272

0.687

47.0 47.9 48.1 48.4 48.7 49.0

1.141 1.141 1.141 1.141 1.141 1.141

0.715 0.715 0.715 0.715 0.715 0.715

(M:)

calculation

(M%)

7.94 8.85 8.20 7.78 7.35 6.82 6.20

$I) 2.098

0.417

1.3

1.26 1.26 1.26 1.26 1.26 1.26

0.42 0.42 0.42 0.42 0.42 0.42

1.3 1.3 1.3 1.3 1.3 1.3

the elastic scattering of protons on 160 [ref. 15)], taking into account the energy dependence of the real and imaginary potential depth. The Gaussian potential of ref. 15) was replaced by an equivalent derivative Woods-Saxon potential. For the entrance channel we were not able to find a potential which described the published elastic scattering data 1 ’ “) of 3He on 14N and the (3He, p) reaction simultaneously. We adopted one which describes our measurements of the elastic scattering of 3He on 14C at 15 MeV as well as the (3He, p) reaction on this nucleus. The success of this potential might be due to the fact that the excitation energy of the compound nucleus in the latter reaction is about 13 MeV higher at the same incident energy. The form factor for the (3He, p) reaction was calculated from the shell-model wave functions of Zuker, Buck and McGrory “) for the states in 160. The configuration space of the ZBM theory consists of all four-particle configurations in the pt, d, and s+ shells outside an inert 12C core. In order to be consistent we calculated the wave function of the target nucleus in the same configuration space and using the same interaction and obtained:

r,

14N(1+, T = 0) = 12C(O+,T = 0) @ (0.99p;+O.O8

d;-0.07

sf) (I+, T = 0).

Woods-Saxon single-particle wave functions with the parameters r,, = 1.25 fm and a = 0.65 fm were used in the form-factor calculation. Their energies were adjusted to

650

R. WEIBEZAHN

et al.

2**

* *;

‘:__;,_.:/y. ‘.

_._.-.---‘-‘~~~

.I-

_-.

k

14N(3He, p)r60

651

REACTION

TABLE 2

Comparison

of experimental

and theoretical cross sections of the reaction 14N(3He, p)160

J”

negativeparity states

positiveparity states

-5 6-M)

do/dQ (exp) da/dQ (talc)

312-

6.13 7.12 8.87

5.83 6.90 8.34

2.1 0.8 1.1

O12-

12.44 10.95 12.53

(12.47) 10.22 (13.42)

(:::) (3.9)

0.00

0.00

6.05 6.92 10.35 9.85 11.08/ 11.10 11.52 12.05 13.66

6.19 7.39 10.66 (10.27) (12.45)/ (12.03) (11.77) (12.48) (11.91)

1.1 weak, no stripping

0+ 0+ 2+ 4+ 2+ 3+/4+ 2+ 0+ 1+

Dominant configuration

closed shell 4p-4h

(0.2) (0.2)

‘2C2+ @I“Ne,,+

(0.2) (0.5) (0.1)

rzc2 + @ 20NeZ + i

A common normalization factor is included in the calculated cross section. Ratios in parentheses are calculated if the experimental states are tentatively identified with states of ZBM; the last column gives the suggested dominant configuration.

reproduce the correct asymptotic behavior of the two-nucleon form factor according to the separation energy of the cluster. The comparison between the experimental and the arbitrarily normalized calculated angular distributions is shown in fig. 2. No cut-off has been used in the radial integration. The DWBA fits are satisfactory, mainly for the negative-parity states. In table 2, a comparison between the experimental and the calculated cross sections is given. The latter contain an arbitrary DWBA normalization factor (Di = 52 x lo4 MeV’ - fm3 as defined in ref. 14)), w h’ic h was chosen to reproduce the cross sections of the negative-parity states. The table shows that with this choice it is possible to get fairly good agreement for the four lowest lp-lh states simultaneously. However, the calculated cross sections for the positive-parity states are then typically a factor of 5 too large. In order to see if this might be due to the DWBA we varied the optical potentials and bound-state parameters systematically, but we were not able to obtain an essential improvement with reasonable parameters. We conclude that the disagreement is due to an inadequacy of the wave functions used for i60. Since the negative-parity states are generally the less complicated ones and are usually well described in the shell model, we believe that the 2p-2h strength is by far too strong in the theoretical wave functions. In other words, the last six positive-parity states in table 2 should not be identified with the 2p-2h states calculated by ZBM [ref. 3)] at about this excitation energy.

652

R. WEIBEZAHN

et al.

It may be mentioned that the calculated cross sections for the states 2+ E, = 6.92 MeV and 4+ E, = 10.35 MeV are also larger than the measured ones by a similar amount. In view of the obviously more complicated reaction mechanism in these cases, however, this is not conclusive. In order to make sure that the disagreement found for the (3He, p) cross sections is in fact due to the reason mentioned above we investigated the accuracy of various assumptions made in the calculations of the wave functions. Because of the wellknown sensitivity of two-nucleon transfer cross sections to small components in the wave functions, truncations of the configuration space sometimes have a severe influence. As mentioned, the ZBM theory considers only the p+, d, and si shells and assumes an inert “C core for the excited states of 160. In order to get a feeling for the importance of the pt hole and d, particle admixtures we studied their influence on the (3He, p) cross sections of the four lowest negative-parity states of table 2. We used the lp-lh wave functions calculated by Kallio and Green 17) and Giltet and Vinh Mau la) for 160 and the 14N ground state wave function calculated by True 19) but modified by the inclusion of a Ip+ component by Mangelson et al. ‘O). We find that the inclusion of neither d, nor p+. nor both shells simultaneously leads to a significant increase of the calculated cross sections for these negative-parity states. This confirms our assumption that the wave functions of the negative-parity states are essentially correct. d, admixtures in the positive-parity states are expected to lead to an increase of the calculated cross sections, and this would make the discrepancies even worse. We estimated the effect by adding d, admixtures of the same size and phase as in ‘*F or 180 states “) to the 2p-2h wave functions and found changes of the order of 30 “/6.The only remaining possibility to explain the relatively low cross sections found experimentalty is to assume that p+ admixtures, or in other words excitations of the “C core, are important in the positive-parity states 2+ E, = 9.85 MeV and the five states between I.?, = 11.08 and 13.66 MeV. Such states are not included in the ZBM theory. However, they were predicted by Arima et al. 22) on the basis of a weakcoupling model. Their dominant configuration should be 12C(2+, E, = 4.43 MeV) @,“Ne(O+, 2+, . . .) and their approximate excitationenergies in I60 are about 10.5 MeV for the first 2+ state and 12 MeV for a quintuplet with spins 0’ to 4’. Since these states occur not far below where the 2p-2h states are expected they can mix. This, would explain the relatively small cross sections, since configurations involving an excited “C core are not populated in the (3He, p) reaction on i4N. A further consequence would be the existence of other states which carry the rest of the 2p-2h strength. Some strongly excited positive-parity states have been observed in the range E, = 14.8 to 18.1 MeV (see sect. 5) and Zisman et al. ‘) found strong excitation of a state at 14.40 MeV with probable spin 4+ or 5+ in the (CI,d) reaction on 14N. This state was obscured by reactions on target impurities in our meas~ements. Our conclusion about the structure of the posit.ive-parity states at 9.85 MeV and between I 1.08 and 13.66 MeV is not in contradiction with the finding of Mendelson et aL6)

“N(3He,

p)160

REACTION

653

that there is little p+ strength in the states of ’ 6O below 18 MeV. They measured the “O(p, d) reaction and, consequently, their statement refers mainly to negativeparity states of dominant lp-lh configuration. In fact, their result that the (p, d) cross section of the states 2’ E, = 9.85 MeV and 4’ E, = 10.35 MeV is much lower than expected from the ZBM wave functions is consistent with the assumption of large admixtures of configurations with an excited 12C core. In the reaction 12C(‘Li, t)160 a relatively large cross section has been measured for the doublet 3+/4’ at E, = 11.08/l 1.10 MeV [ref. ‘)j. This suggests that the 4+ member of the quintuplet mixes with the nearby 4+ state at 10.35 MeV, which has mixing the simple 4p-4h configuration with an inert “C core. A similar configuration seems to occur in the 2+ state at 9.85 MeV [ref. ‘“)J.

5. States above 13 MeV excitation energy Because of the experimental problems mentioned above we were not able to study higher excited states in 160 as extensively as the lower ones. Two exposures were made at 15 MeV beam energy and 8 = 5’ and 20” using the TIN target. One of the spectra is shown in fig. 3. The discussion of the positive-parity levels between 11 and 14 MeV excitation energy already showed that the configurations of these states become complicated and that they are not described by, available calculations. Therefore, we have to restrict our further discussion to some qualitative remarks. The negative-parity states in this region are expected to have dominant 3p-3h configurations, which cannot be excited in (3He, p). This is consistent with our data, apart from two obvious exceptions. The strong excitation of the 2-, T = 0 state at E, = 13.98 MeV and the l-, T = 1 state at 17.14 MeV suggests a lp-lh configuration for these states, in particular d,p;’ for the former. This is in contradiction with the result of Fulbright et al. ‘) that the 2- state at 12.53 MeV already contains most of the d, strengths. The dominant positive-parity states in the region between 13 and 18 MeV excitation energy are the states 2+ E, = 13.02 MeV, 4+ E, = 14.92 MeV and 4+ E, = 18.02 MeV. These states have to have dominant 2p-2h configurations. However, part of the large cross sections is due to the small binding energy of the proton-neutron cluster at these excitation energies. DWBA calculations showed that this effect enhances the cross section for a 4+ state at 18 MeV by a factor 4 compared to a state with the same configuration at 10 MeV excitation energy. The complete absence of the state at 18.02 MeV in the (u, d) spectrum ‘) suggests a T = 1 assignment for this state.

6. Summary The reaction 14N(3He, p)160 is essentially a means of studying the lp-lh configuration in negative-parity states and the 2p-2h configuration in positive-parity states of 160. A DWBA analysis allows us to do this quantitatively and to compare

50

2

0

60

3

1

4

70

2

e

60

3

!

1

position

on

the

90

i

plate

5

cm

E,

(‘*F

E, (“N) I

Fig. 3. Spectrum of the reaction “N(3He, p)160 to states above 12 MeV taken at elab = 5” and ,?I& = 15 MeV using a TiN target. All final states in 160, ‘*F and 14N are indicated by lines above the spectrum. There are no important contributions from the reaction 48Ti(3He, P)~OV to transitions being discussed in sect. 5, based on the results of ref. 23).

1

r4N(3He, p)r60

REACTION

655

with the predictions of structure calculations. In the present work, the shell-model calculations of Zuker, Buck and McGrory “) have been used for this purpose. We summarize our results in the following. The positive-parity states Of E, = 6.05 MeV, 2+ 6.92 MeV and 4+ 10.35 MeV are very weakly populated in this reaction. This is experimental evidence for their dominant 4p-4h configurations, which follow from various theoretical models. The states 2+ E, = 9.85 MeV, 3+ E, = 11.08 MeV, 4+ E, = 11.10 MeV, 2+ E, = 11.52 MeV, Of E, = 12.05 MeV and l+ E, = 13.66 MeV do not have a dominant 2p2h configuration, although they are excited through such admixtures. The cross sections are smaller by a factor of 5 than predicted for the 2p2h states calculated by ZBM. It is suggested that these states be identified with those predicted consisting of an excited 12C core by Arima et al. ‘“) which h ave a configuration coupled to four particles in the s-d shell. This is a special type of 4p-4h configurations, with at least one hole in the p+ shell. Most of the 2p-2h strength seems to lie at excitation energies above 14 MeV, since very strong transitions to positive-parity states were observed there. A mixing between the configurations with an excited “C core and the lower 4p-4h band is also a likely explanation for the overestimate of the (3He, p) cross sections of the latter states by the ZBM wave functions. Strongly excited negative-parity states have been found: 3- E, = 6.13 MeV, lE, = 7.12 MeV, 2- E, = 8.87 MeV and O- E, = 10.95 MeV. These states have dominant lp-lh configurations. They arise from a coupling of a p+ hole to a d, and s+ particle. The ZBM wave functions describe the (3He, p) cross sections of these states very well, only the cross section of the 3- state being slightly underestimated. The large cross section measured for the 2- state at E, = 13.98 MeV suggests a dominant d,p, -I configuration for this state. The authors are indebted to Professor W. Gentner and Professor U. Schmidt-Rohr for the hospitality at the Max-Planck-Institut fur Kernphysik. We thank Dr. A. P. Zuker for helpful discussions and instructions in the use of his wave functions and M. Zisman for discussions and many useful comments. We also gratefully acknowledge the support of the Deutsches Bundesministerium fiir Bildung und Wissenschaft.

References 1) F. Ajzenberg-Selove, Nucl. Phys. Al66 (1971) 1 2) G. E. Brown and A. M. Green, Phys. Lett. 15 (1965) 168; L. S. Celenza, R. M. Dreizler, A. Klein and G. J. Dreiss, Phys. Lett. 23 (1966) 241 3) A. P. Zuker, B. Buck and J. B. McGrory, Phys. Rev. Lett. 21 (1968) 39; BNL report 14085/ PD-99 and private communication 4) W. Bohne, H. Homeyer, H. Lettau, H. Morgenstern, J. Scheer and F. Sichelschmidt, Nucl. Phys. A128 (1969) 537 5) H. W. Fulbright, J. A. Robbins, M. Blann, D. G. Fleming and H. S. Plendl, Phys. Rev. 184 (1969) 1068 6) R. Mendelson. J. C. Hardy and J. Cerny, Phys. Lett. 31B (1970) 126 7) M. S. Zisman, E. A. McClatchie and B. G. Harvey, Phys. Rev. C2 (1970) 1271

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8) C. D&raz, C. E. Moss, C. D. Zafiratos and C. S. Zaidins, Nucl. Phys. Al67 (1971) 337 9) F. Ptihlhofer, H. G. Ritter, R. Bock, G. Brommundt. H. Schmidt and K. Bethge, Nucl. Phys. Al47 (1970) 258 10) R. L. McGrath, D. L. Hendrie, E. A. McClatchie, B. G. Harvey and J. Cerny, Phys. Lett. 34B (1971) 289 11) K. P. Artemov, V. J. Goldberg, B. I. Islamov, V. P. Rudakov and I. N. Serikov, Sov. I. Nucl. Phys. 1 (1965) 450 12) A. A. Ogloblin, Proc. of the Int. Conf. on nuclear reactions induced by heavy ions, Heidelberg, 1969, p. 231 13) W. R. Gibbs, V. A. Madsen, J. A. Miller, W. Tobocman, E. C. Cox and L. Mowry, Direct reaction calculation, NASA TN D-2170 (1964) 14) F. Piihlhofer, Nucl. Phys. All6 (1968) 516 15) J. M. Cameron and W. T. H. van Oers, Phys. Rev. 184 (1969) 1061 16) B. T. Lucas, D. R. Ober and 0. E. Johnson, Phys. Rev. 167 (1968) 990 and private communication 17) A. Kallio and A. M. Green, Nucl. Phys. 84 (1966) 161 18) V. Gillet and N. Vinh Mau, Nucl. Phys. 54 (1964) 321 19) W. W. True, Phys. Rev. 130 (1963) 1530 20) N. F. Mangelson, B. G. Harvey and N. K. Glendenning, Nucl. Phys. All7 (1968) 161 21) T. T. S. Kuo and G. E. Brown, Nucl. Phys. 85 (1966) 40 22) A. Arima, H. Horiuchi and T. Sebe, Phys. Lett. 24B (1967) 129 23) C. Shin, K. Schadewaldt, P. Wurm and B. Povh, Phys. Rev. Lett. 22 (1969) 1124