Highly excited high spin states in 28Si populated through the 12C(20Ne, α) reaction

Nuclear Physics A457 (1986) 461-476 North-Holland, Amsterdam

HIGHLY POPULATED S. KUBONO,

EXCITED

HIGH

THROUGH

K. MORITA’,

M.H.

SPIN

THE

TANAKA,

STATES

‘ZC(ZoNe, a) A. SAKAGUCHI’,

IN “Si REACTION and

M. SUGITAN13

Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo, 188 Japan S. KATO Yamagata

University,

Received

Yamagata,

18 February

990 Japan

1986

Abstract: High spin states at 12.0-17.6 MeV in ‘sSi excited through the ‘%(“Ne, CX)reaction have been investigated with a particle-particle angular correlation method. New spin-parity assignments ranging from 3- to lO+ have been made, some of which are classified into an excited prolate band reported previously. Most states in this energy region are found to decay both by alpha and proton emission. Specifically, a new 6+ state found at 12.80 MeV is identified to be the lowest excited state whch has a large fraction of g9,2 component. This is also supported by a successful reanalysis of the “Al( (x, t)**Si reaction at 65 MeV by a DWBA calculation assuming g,,, transfer. These high-lying states also are discussed in terms of coexistence of oblate and prolate shape bands in %i. The with that in %. particle decay property of these states in **Si is also discussed comparatively

E

NUCLEAR REACTION ‘*C(“Ne, a), E = 52 MeV; measured excitation energies, ~(0). aa (0), ap( 0). %i deduced branching ratios of p. Q decays, J, ?r, particle decay characteristics, coexistence of oblate, prolate bands and excited prolate band.

1. Introduction In the high excitation

energy

region

of nuclei,

coexistence

and the competition

of oblate and prolate bands I,*) and quasi-molecular band 3-6) will play an important role, and are predicted theoretically even below the threshold energy 3-6) of the molecular configuration. In addition, single particle states of higher shells or deephole states will also take p&t at high excitation. A specific effort has been made here to investigate high spin states at high excitation energies in **Si, possibly with a largely deformed shape, quasi-molecular configuration ‘*‘) or higher orbit single particle component. The ground state of 28Si is well known to have an oblate shape 9), and 28Si has long been suggested to have a prolate band with the band head state being at around 6 MeV [refs. 1-3,6)]. Glatz et al. lo) have studied 28Si with the 25Mg(a, n-y) reaction, ’ Present address: ’ Present address: 3 Present address:

Institute of Physical and Chemical Research (RIKEN), Kyoto University, Kyoto, 606 Japan Sumitomo Heavy Industry Co., Ltd., Tokyo.

0375-9474/86/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

Wako, Saitama,

351 Japan.

S. Kubono et al. / 28Si

462

and pointed

out that the band

13-18 MeV has been studied

head is the 6.69 MeV O+ state. The energy in our previous

work “,r*), suggesting

possible

region

of

8+ and

lO+ states, which seem to form a new rotational band with the band head being at around 10.3 MeV and the rotational constant k = 50 keV, where k = h*/24 and $ is the moment of inertia of the band. This band was suggested to have a prolate shape with a configuration of (fp)‘(sd)-* from a systematic study of **Si [ref. “)I and from a comparison with the cranked Nilsson-Strutinsky model calculation ‘). Therefore, it is of great interest to study further with high resolution the high spin states and the decay properties in this energy region in *‘Si specifically by using the I60 transfer reaction (*‘Ne, a), where a large parentage of the 160 + (Y configuration 14) is known for the ground state in *‘Ne. This reaction also favors excitation of high spin states as the reaction brings in a large angular momentum to the residual **Si system. We first explain the experimental setup in sect. 2, and then discuss on ‘%i with the experimental results in sect. 3. A short summary is given in sect. 4. Part of this work has been already published elsewhere I’).

2. Experiment A 52 MeV *‘Ne4+ beam was obtained from the sector-focussing cyclotron of the Institute for Nuclear Study (INS), University of Tokyo. The targets used here were self-supporting natural carbon foils of 9 Fg/cm’ for a high resolution measurement and of 20-30 kg/cm* for correlation measurements. Singles a-spectra were obtained at 0” and 6” by using a QDD-type magnetic spectrograph 16) and a position-sensitive gas proportional counter “) in the focal plane. Some spectra are shown in figs. 1 and 2. The solid angle of the spectrograph was set to 7.6 msr at the center of the focal plane counter. This proportional counter, covered with a thin aluminum foil to stop the incident beam and inelastically scattered *‘Ne particles, provides also good particle identification with the energy loss signals which are proportional to the square of the masses of the particles at the same magnetic rigidity. A fast timing signal from a plastic scintillator placed just behind the proportional counter was used for the coincidence measurement and also for time-of-flight for additional particle identification. A typical time resolution obtained was about 40 nsec. The overall energy resolution of singles a-spectrum was 55 keV, which should be compared with 180 keV in the previous experiment “). Singles a-spectra with less background than in previous measurements “,l*) were obtained here by use of this improved counter I’) together with a better quality plastic scintillator for time resolution, a thinner target and careful beam transport. Angular correlation functions were measured for the states of *‘Si excited strongly where through the reactions ‘*C(*‘Ne, (u,)28Si(a2)24Mg and “C(*‘Ne, a,)*%i(p)*‘Al, the decay (Y’S and p’s were measured by a position sensitive solid state detector (PSD) of 500 wrn thick in the scattering chamber in coincidence with (Y, measured

S. Kubono et al. .J “Si

463

at 0” with the spectrograph. If C-X, is detected at 0” and a2 decays to a O+ state, the angular correlation functions of CY,and cy2 may be described ‘1,‘8) simply by a function of the form IP,(cos W12, where L is equal to J, the spin of the excited state in %i since all other particles have spin 0. Practically, the a.-(~ angular correlation functions obtained were fitted by a function of the form alp,-(cos 0)/*+ b, where both a and b are not negative. The PSD subtended the angular range of about 40” in the laboratory system, and it was covered with a multi-slit Ta plate of 0.5 mm thickness which had 20 slit holes of 1 mm width and 7 mm height at each 2 mm step. A typical count rate of the detector was about IO4 counts per second. The energy calibration of the PSD was obtained by use of an “‘Am(cr) source. The particle identification of the decay particles was made in two ways: first by three-body kinematics (energy versus angle), and second from the particle energy loss which was produced in a thin aluminum foil placed over one half of the detector at the forward angles. This foil also prevents enormous elastic scattering particles to enter the PSD. A schematic two-dimensional spectrum of energy versus angle expected from the kinematics and the energy loss is shown in the upper portion of fig. 3 for the decay of the 14.00 MeV state in 28Si. The proton decay measurement was limited only up to E, = 14.4 MeV, because of the thickness of the PSD. A typical energy versus angle two-dimensional spectrum of decay particles is shown in the lower half of fig. 3, which was measured in coincidence with the first (Yparticles leading to the 14.00 MeV state in **Si. The decay energies of p’s and ty’s and the energy losses are in good agreement with those expected (see figure). Thus, the decay particles were unambiguously identified. A careful determination of the excitation energies and the level widths of the states were made with the thin target by measuring separately the effects of the beam energy spread (23 keV), the resolution of the spectrograph (13 keV), the resolution of the focal plane counter (22 keV), and the energy loss in the target (43 keV). The error in the excitation energies obtained is less than 30 keV, and all the states observed were found to have the widths less than 39 keV. The excitation energies of previously known states were reproduced within the error. A silicon solid state detector was set at about 10” to monitor the beam and the target. 3. Results and discussion 3.1. NEW

STATES

AND

DECAY

WIDTHS

There are about 38 states observed at 0” in the excitation energy region from 12.0 to 17.6 MeV in **Si, as can be seen in fig. lb, where the excitation energies are denoted. Most peaks here are of states observed for the first time. Table 1 gives the excitation energies and the spin-parity assignments made in this work. The excitation

464

S. Kubono

12C( 20Ne,~

et al. / 28Si

) 28Si

E[ab, = 52.20MeV @lab. = 0”

12

11

10 Excitation

(

b,,” 0

500

8

9

Energy

7

6

in *‘Si

"C ( 20Ne,cX ) *'Si

5

4

(MeV)

Elab=51.93 MeV 8

n

%bioo

s

400 ul -z 3 300 0 ”

200

100 0

Ii

I I 17 16 Excitation

I 15 Energy

14 i n%i

13 ( M eV)

Fig. 1. (a) A singles cr-spectrum at 0” for an excitation energy range E,=4-13 _. ._ “C(‘“Ne, cr)% reaction measured with the spectograph. (b) A singles a-spectrum 12-18 MeV from the “C(*‘Ne, a)% reaction.

12 MeV from the at 0” for E, =

are in reasonable agreement with previous work within 30 keV as mentioned in sect. 2. Clearly, unnatural parity states like 6- are not excited in the spectrum at 0” (fig. 1). However, the 9.702 MeV 5- state, a natural parity state of the (f,,,d$) configuration, was clearly observed at 0”. A tentative 8+ state at 14.643 MeV proposed by Glatz et al. lo), possibly a member of the oblate ground state band was not observed in the present reaction at 52 MeV. One interesting observation in fig. la is that the (“Ne, a) reaction excites the band head state of the prolate configuration at 6.69 MeV with considerable cross section, which was not excited in either the (6Li, d) or (r*C, 9Be) reactions 19*20),and also excites strongly the 6+ member of the

energies

S. Kubono

‘2C(20Ne,cx)2*Si

17

18

19

Excitation Fig. 2. A single a-spectrum

465

et al. / “Si

Elab.=

16 Energy

51.88 MeV

15

1.4

in**Si

(MeV)

from the ‘*C(*‘Ne, a)‘sSi

13

reaction measured

at 6”.

prolate band lo) at 11.51 MeV as can be seen in the figure. There is a strong peak at 10.94 MeV in the figure, which was not known before. The (l*C, 9Be) reaction seems to excite more likely particle-hole high spin states 19*20),and the (6Li, d) reaction excites even parity states of smaller spins. The total widths for all states observed here were less than the experimental upper limit, of 39 keV. A measurement of particle-particle angular correlation functions for the reactions ‘*C(*‘Ne, a)28Si((u)24Mg and ‘*C(*‘Ne, a)28Si(p)27A1 at 52 MeV has been made in the excitation energy region of 12.0 to 17.6 MeV in 28Si, which is a little lower than the previous measurement ‘I). One of the interesting features observed here is that many states in the present energy region in *‘Si decay both with proton and (Y emissions. This conclusion is supported by the fact that the decay energies of the proton and (Yare, within 50 keV, consistent with both particles coming from a single state. A portion of the energy spectrum of alpha particles from the ‘*C(*‘Ne, a)*‘Si reaction, obtained with the magnetic spectrograph at O”, is shown in fig. 4 together with the coincident decay-particle yields of protons (po) to 27Al(g.s.) and alphas ( a0 and (Y~)to the ground and the first excited states in 24Mg. Here, the decay yields were obtained by extrapolating the measured angular correlation functions by best fit curves to all solid angles. The decay properties here in 28Si are clearly different from those of the states in 32S [ref. 18)], where states in this excitation energy region have measurable level widths but have no observable proton decay yield. This point will be investigated later. 3.2. SPIN-PARITY

Angular

ASSIGNMENTS

correlation

functions

states, fig. 6 for even-parity

states,

of (Y~and

CY*are shown pin fig. 5 for odd-parity

fig. 7 for the 14.00 MeV state, and fig. 8 for the

466

S. Kubono et al. / 28Si

Position

Sensitive

12C(*‘Ne,a,

>

Detector

)28Si(a2)24Mg

E(*‘Ne)

( P )27Al = 51.93 MeV

Ex( hi)

= 14.00 MeV

4 i2 t

h

I

I

20

30

II 40

I

I

50

60

*

@lab.(deg.) Fig. 3. The upper portion is a schematic two-dimensional spectrum of energy versus angle expected from the three-body kinematics and the energy loss. A thin aluminum foil put on the left-hand half produces kinks for the loci in the middle. The lower half is the experimental two-dimensional spectrum for a- and p-decays from the 14.00 MeV state in % excited through the ‘2C(Z0Ne, cz) reaction. The dashed lines are the calculated curves for the decay particles.

12.80 MeV state. All the correlation

functions and the decay yields were compared for the upper half and the lower half of the peaks in the energy spectrum. They are almost identical, except for the 14.00 MeV state, within statistics. It should be a very small chance that all peaks excited are multiplets of p- and a-states. Thus, the most states seen here would not be a multiplet. This point is discussed in more detail for the 12.80 MeV state in ref. 15).

467

S. Kubono et al. I 28Si TABLE 1 Levels in *8Si

E* (MeV) 12.00 12.21 12.80 13.17 13.62 14.00 14.32 15.01 15.91 15.97

0.18 0.79 0.58 0.17 0.20 0.30 0.17

0.22 0.21 0.42 0.83 0.70 0.53 0.53

0.10 0.17 0.30

17.40

P&=

0.46 0.60 1.8 3.1 0.60 1.2

kc& Ft( UC) + Gt( WC) ’

pc=Gxu+ r,+T,,(E,S

L

PLS

ZP&WL

ZP&WL

(eV)

(eV)

18.5

(h)

(fi)

(4+) 6+

(4) 6

3.05 x 1o-6 1.30x 1ov

28.5 12.2

(3_) (8++9-)

(3) (8+9)

4.71 x 1ov

4.4 x lo4

5(1F)

5 (li

6.35 x 1O-2 2.34 x 1O-4

5.93 x lo3 219

(6+)

(6)

2.1

44 r=

.I

reoir r,,ir r,,ir r=,ir,

WL=3h

2~.Rf’

R, = 1.40 x ( Ai’3 + A:“) 13.17 MeV) and r=

fm

,

rq+l’_,+rpO

(13.62~ E,s

14.32 MeV) were assumed.

There is a state excited at 12.00 MeV in the (“Ne, a) reaction. A reliable spin-parity assignment was not made for this state because the a0 decay particles were discriminated instrumentally at some angles. J” = 5- is clearly assigned to the 15.01 MeV state, as is shown in fig. 5 together with a best fit curve of (PLES(cos fI)(*. Previously, this state was seen also in the energy spectrum, but the spin was not determined because of high background in the 0” spectrum rl). The peak at 15.97 MeV observed previously “) is found to be a doublet of states at 15.91 and 15.97 MeV. Although 9- is assigned here to the 15.91 MeV fig. 5, the summed yield of the two states is still dominated by the 15.97 state, and so is the correlation function. However, the branchig ratios table 1 are clearly different from each other, indicating the peak to be

state as in MeV (lo+) I’,,/T,O in a doublet.

The correlation function for the 15.97 MeV state in fig. 6 is not so clear, but is consistent with a J” = lO+ assignment. Thus, only a tentative assignment of lO+ can be made for the 15.97 MeV state. Previously, 8+ was tentatively assigned to the state at 14.00 MeV [ref. I’)]. The present measurement also shows strong particle decay, but the (Y-CYcorrelation function is not characterized by a single Legendre function as shown in fig. 7, although it is not in contradiction with J” = 8+. The data were best fitted by assuming a doublet of 8+ and 9- states, which is shown by a solid line in the figure. The previous data had a large background with worse energy resolution and also the

S. Kubono ei al. / “Si

468

12C ( *ONe,a ) 28Si EL = 51.93 MeV Q_ = o”

Er

in

28S;3(MeV)

‘*

Fig. 4. A singles a-spectrum from the ‘%(“Ne, (x)%i reaction and the coincident decay yields to the ground (a,,) and the first excited ((I,) states in 24Mg and those to the ground state (p,,) in *‘Al.

incident

energy used was slightly different. These would have changed

the correlation

function. This could be true also for the 15.97 MeV state as discussed above. Thus, only a tentative spin assignment, 8++9-, is made for the 14.00 MeV peak.

3.3. THE

12.80MeV

STATE

AND

A g,,,

SHELL

COMPONENT

Most states below 14.4 MeV are found to decay also by proton emission as mentioned earlier. The decay widths provide, in principle, spectroscopic information on proton single particle components. The state at 12.80 MeV has a very clear correlation pattern of jPL,,(cos 13)1’,as is shown in the upper half in fig. 8, which has been partly reported in ref. i5). This state also shows a comparable proton decay yield, which also can be seen in the lower half of the figure. In the proton decay from 6+ to 2’ states, L = 4 contributes almost uniquely since the penetrabilities for L> 6 are so small. Thus, the proton single particle state is of the g-shell, and most

S. Kubono ef al. I 28Si

469

Ex = 15.91MeV

40

60

80

100

0c.m. (deg.) Fig. 5. CX-oangular correlation functions measured for the decays from the odd parity states denoted.

probably g9/2 in this energy region in 28Si. From penetrability and Wigner limit considerations and assuming gYf2 proton decay, a large fraction of the g-shell component has been confirmed in this state, about 30% of the spectroscopic factor of a (gqt2d$) configuration. A DWBA analysis also has been made for the 12.82 MeV state which were observed in the 27Al(a, t)28Si reaction at 65 MeV [ref. “‘)I. The angular distribution for this state in fig. 9 is much better reproduced by assuming g9,2 transfer, rather than L = I+3 transfer as previously assumed 21). This analysis

470

S. Kubono

I

I

I

I

I

et al. / 28Si I

‘*C( *ONe,N, 10 -

I

I

I

I

I

I

I

I I

I

I !

r-

I

I

1 28Si(CX2 )24Mg

Ex = 12.21 MeV -L=4

T

I

I

Ex = 15.97

MeV

-L=lO

I I

Ex z

17.4

MeV

-L=6 ________. L = g

I

60

80

100

120

I

140

8c.m. (deg. 1 Fig. 6. (I-(I angular

correlation

functions

measured

for the decays

from the even parity

states denoted.

gives a spectroscopic factor of S (g9,J = 0.2, which is consistent with the present decay measurement. This is the first and direct evidence for a considerable gcomponent in this energy region in medium sd-shell nuclei. Detailed discussion will be found elsewhere 15)-. Although other states in this energy region also decay with a proton emission, the decay angular momenta are not uniquely determined and thus no further analysis is made here.

S. Kubono et al. / 28Si I

-

I

I

‘*CC *‘Ne,a,)

I

471

I

I

I

I

*%i(Q2’Mg(gs)

Ex = 14.00 MeV ___-__

60

L=8+9 L =8

80

100

0c.m. (deg.) Fig. 7. cr-a angular correlation function measured for the decay from the 14.00 MeV state. The solid line is the result of an incoherent sum of L = 8 and 9 with equal amplitudes.

3.4. COEXISTENCE

OF OBLATE

AND

PROLATE

BANDS

The present experimental results are plotted in fig. 10 by closed circles together with the states from other references 13). The data with parentheses mean that the spin assignments are not conclusive. The state at 12.80 MeV is identified to have 6+, and in the figure it just follows the J(J+ 1) rule for the excited prolate band of the (fp)2(sd)-2 configuration proposed previously ‘*) from the Nilsson-Strutinsky calculation. Furthermore, this state decays with a large a-width similar to the 8+ and lO+ members of the excited prolate band 11-‘3). Therefore, the 12.80 MeV state possibly is a 6+ member of the band. Although this band has been suggested to have a dominant component of (fp)2(sd)-2 [ref. 3)], these states are found to decay with large a-widths. Thus, this band could be characterized rather by the (fp)4(sd)-4 configuration, which is also predicted to exist quite close to the 2p-2h band ‘). The 12.80 MeV state has a large amplitude of a shell-model component of (gd-‘) as discussed in subsect. 3.3. Thus, the 6+ state could have both components of (gd-‘),+ and ((fp)*(sd)-*),+ or ((fp)4(sd)-4),+. The 12.21 MeV (4+) state is a little high in energy, but rather close to the line of the excited prolate band in fig. 10. Furthermore, the particle decay yields of the state are large, and are similar to those in the 6+ state discussed above. Thus, these two states possibly belong to the same band. These results support the previous suggestion for the excited prolate band 3*‘2)in terms of energy. The 12.80 MeV state could have such a large gg12 component if the state is strongly deformed. However, the lower spin members of the band (J” = O+ and 2+) have not yet been identified. In this excitation energy region there are some candidates which are excited very strongly in the “C(“Ne, cy)*%i reaction. These

472

S. Kubono

I

I

I

I

“C( 20Ne,a,)

10 -

“Si

et al. / “Si

I

I

I

I

I

(&2)2’Mg(g,s.)

Ex = 12.80 MeV L q6

____ c

5 -

j$;

:

!I

9

-0 3’ -0

+$&q

ytQ.. I

c

I

/_ 10 -

I

I

I

: I

I

I

,

,

1 28Si( p) 27Al(g.s.)

“C(“Ne,&

5-

tii+tttii..ittjt,i 0

Fig. 8. Angular

40

60

100

1

120

correlation functions for e-decay (upper part) and p-decay (lower part) the 12.80 MeV state. The solid line is the best fit curve with L = 6.

measured

for

states should be studied with other methods since they are close to or lower than the a-particle threshold. The proposed excited prolate band has the rotational constant k = 50 keV, and the deformation constant j3 = 0.54. This shape is of such a large positive deformation that it has a considerable overlap with 12C+ I60 or 12C+ (Y+ 12C configurations “). Theoretical calculations for the particle decay widths would be very useful to investigate further the quasi-molecular nature of these states.

3.5. PARTICLE

DECAY

PROPERTY

OF HIGH-LYING

STATES

IN 28Si AND

32S

two nuclei 28Si and 32SI*) show a distinct difference in the decay properties of the presently investigated excitation energy region. As shown in table 1 the states in 28Si decay both with proton and LYemissions but have small total widths, whereas the states in 32S decay mostly through an CYemission and have measurable level widths. This fact can be understood as follows. Suppose all states have the same The

S. Kubono et al. / “Si

Et=

27Ai~~,t%i 12.82

473

64.5

MeL

MeV State gg,2 tranrfer

%

-----

*

ITlt transfer

~~~~~~~~. da12 transfer

0

40

20

60

~~,~dogrrrs) Fig. 9. Angular distribution of tritons from the z’Ai(cx, t)‘sSi reaction Ieading to the 12.82 MeV state at 64.5 MeV. The data are taken from ref. *I). The solid line is the DWBA result assuming gsjz transfer, the dashed line is for f,,2 transfer, and the dotted line for d,,, transfer.

particle reduced width. Fig. 11 compares the decay probability of the two nuclei by a quantity of 2PL x (Wigner limit), where PL is the penetrability for L. For instance, a 6+ state at 13 MeV in 28Si can decay by proton emission as well as by LYemission with roughly the same yieids, whereas a 6+ state at the same excitation energy in 32S would decay by a-emission with a probability larger than for proton emission by two orders of magnitude. This is largely due to the different intrinsic spins of the residual nuclei, 3’ in 27Al(g.s.) and $” in 3’P(g.s.). The figure also indicates that much larger decay widths are expected for the states in 32Sthan in “Si in this energy region. These facts are in good agreement with the present experimental results and the results for 32S in ref. 18).

474

S. Kubono

et al. / 28Si

’ t2xcIIea (0)

prolate

4

1

,I

02

4

6

8

10

Spin J Fig. 10. The levels of %i observed in the present experiment are displayed by closed circles, and other data taken from references by triangles “), dotts lo) and crosses lo). The lines are drawn through the states which could be classified into certain rotational bands. The dotted line is the curve predicted by a rigid rotor of (Y+ 24Mg configuration. 4.

Summary

High spin states at 12.0-17.4 MeV in 28Si have been investigated by the particleparticle angular correlation method for the (*‘Ne, (u) reaction on “C. A new spin-parity assignment has been made for some states in *‘Si. Although a possible new band structure of large moment of inertia below the ‘*C+ 160 threshold is suggested in **Si from the spin-parity assignments and the (Y- and p-decay branching ratios, the nature of the states remains open. A new 6+ state found at 12.80 MeV has a considerable g-shell component of 20-30% and also supports the band structure. The authnors are grateful to M. Yasue and M. Igarashi for valuable discussions. They are also indebted to K. Omata for the on-line program, I. Sugai for the target

S. Kubono

!=

I

I

I

I

E 2BS?~24Mg +a

127AI + p

I

et

I

al. /

475

28Si

1, SF ‘I

I

I

I

, /‘Lp

=6

I 14

I 15

I

I

4

I 16

17

32s*-7-?esi

-

+o(

Q’P

____

+

-

p ---

Lp= o____-C--r

/

loo'

1; c

' 13

I 14

/I 15

I 16

17

Excitation Fig. 11. 2P, x (Wigner

1 ;I 18 11

Energy

I 12

I 13

/

(MeV)

limit) are plotted for some angular momenta high-lying states in 28Si and %

for the proton

and a decays

from

preparation, and the staffs of the INS cyclotron. Most analyses have been made at the main computer facility of the Institute for Nuclear Study, University of Tokyo.

References 1) 2) 3) 4) 5) 6) 7) 8) 9)

S. Das Gupta and M. Harvey, Nucl. Phys. A94 (1967) 602. I. Ragnarsson, S. Aberg and R.K. Sheline, Phys. Scripta 24 (1981) 215 I. Ragnarsson and S. Aberg, Phys. Lett. 114B (1982) 387 P.G. Zint and U. Mosel, Phys. Rev. Cl4 (1976) 1488 S.J. Krieger and C.Y. Wong, Phys. Rev. Lett. 28 (1972) 690 W. Bauhoff, H. Schultheis and R. Schultheis, Phys. Rev. C27 (1983) 2414 T. Ando, K. Ikeda and A. Tosaki-Suzuki, Prog. Theor. Phys. 64 (1980) 1608 D. Baye and G. Reidemeister, Nucl. Phys. A258 (1976) 157 G.C. Ball, 0. Hausser, T.K. Alexander, W.G. Davies, J.S. Forster, I.V. Mitchell, J.R. Beene, D. Horn and W. McLatchie, Nucl. Phys. A349 (1980) 271 10) F. Glatz, J. Siefert, P. Betz, E. Bitterwolf, A. Burkard, F. Heidinger, Th. Kern, R. Lehmann, S. Norbert and H. Ropke, Z. Phys. A 303 (1981) 239 11) S. Kubono, M.H. Tanaka, S. Kato, M. Yasue, M. Sekiguchi, H. Kamitsubo and T. Tachikawa, Phys. Lett. 103B (1981) 320

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