Investigation of the reaction 12C(7Li, t)16O

I2.A.I:2.B]

NuclearPhysics A147 (1970) 258--272; (~) North-HollandPublishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout writtenpermissionfrom the publisher

I N V E S T I G A T I O N O F T H E R E A C T I O N lZC(TLi, t)160 F. P1]I-[LHOFER, I-L G. RITTER * and R. BOCK

Max-Planck-lnstitut fiir Kernphysik Heidelberg und Physikalisches Institut der UniversitdtMarburg and G. BROMMUNDT, I-I. SCItMIDT and K. BETIIGE

IL PhysikalischesInstitut der UniversitiitHeidelberg Received 29 December 1969 Abstract: Angular distributions of the reaction 12C(7Li, t)a60 have been measured at E~a~~ 15,

21.1 and 24 MeV with a magnetic spectrograph and a dE/dx--E telescope. From the shape of the angular distributions and the weak excitation of the 2- state at Ex : 8.87 MeV in 160 it is concluded that the reaction proceeds dominantly by a direct s-transfer. Contributions from compound nucleus formation were estimated from a Hauser-Feshbach calculation. The angular distributions were analysed by means of the DWBA, which has been modified to take into account the relative p-state between the s-particle and the triton in 7Li. Approximations valid for a surface reaction were used to simplify the theory. The calculations are able to reproduce the essential features of the angular distributions. Reduced ~-widths were extracted for some states in 160.

I E

NUCLEARREACTIONS ~ZC(TLi,t),E :15,20.5,21.1,24 MeV;measured~(Et, O).

1

160 deduced levels,/-values, reduced g-widths. Natural target.

2. I n t r o d u c t i o n

I n several investigations it has been shown that the (TLi, t) reaction can be interpreted as the transfer of a n a-particle 1-3). It could also be shown that this reaction exhibits more features of a direct reaction m e c h a n i s m t h a n the corresponding (6Li, d) reaction 1,4). This c o n c l u s i o n is based o n the shape of the a n g u l a r d i s t r i b u t i o n a n d the weak excitation of states of u n n a t u r a l parity in (7Li, t). F r o m the (7Li, t) reaction one expects i n f o r m a t i o n o n four-particle correlations in the final nuclear states. A quantitative i n t e r p r e t a t i o n of the cross sections, however, implies a calculation of the reaction dynamics. This is particularly difficult for this reaction, because the relative l = 1 state between the a-particle a n d the t r i t o n in the 7Li nucleus precludes the application of the usual zero-range D W B A . I n this paper, m e a s u r e m e n t s of the reaction 12C(7Li, t ) t 6 0 are discussed. The c o r r e s p o n d i n g (6Li, d) reaction o n the same target has already been studied 4). D W B A calculations are performed assuming a simple form of a surface reaction. The relative p-state in the projectile a n d the resulting superposition of two transferred a n g u l a r m o m e n t a are taken into account. Spectroscopic factors a n d reduced a-particle t Present address: CERN, Geneva.

258

12C(7Li, t)160 REACTION

259

widths are derived for some states of the final nucleus 160. The structure of this nucleus is known from extensive experimental and theoretical investigations 5-8). Most of the states can be sorted into rotational bands originating from intrinsic deformed states of different particle-hole configurations. The first band with positive parity consists of the levels Ex = 6.05 MeV (0+), 6.92 (2+), 10.35 (4 +) and 16.22 (6+). These states exhibit mainly a 4p-4h structure. The second positive parity band with mainly 2p-2h character is expected to start around 12 MeV excitation energy in 160. The negative parity states at 6.13 MeV (3-), 7.12 (I - ) and 8.87 ( 2 - ) have dominant spherical l p - l h configurations. An additional rotational band with mainly 3p-3h character starts at 9.61 MeV with a broad 1 - state.

2. Experimental arrangement The experiments have been performed at the Heidelberg EN tandem accelerator. The negative lithium ions were extracted from a Penning type ion source 9), the beam intensity at the target varied between 50 and 100 nA. Carbon targets of 20 and 90 /~g/cm 2 thickness were used. Angular distributions were measured at 15 MeV incident energy between 0lab = 5 ° and 40 ° and at 21.1 and 24 MeV between 5 ° and 150 °. The data at 15 MeV were taken by means of a Brown-Buechner spectrograph, whereas for the measurements at 21.1 and 24 MeV the conventional technique of particle detection and identification with solid-state detectors was applied. The resolution obtained was about 20 to 25 keV for the spectrograph exposures. This allowed a complete separation of the two states at E x = 6.05 and 6.13 MeV in a 60. The resolution of the detector telescope was about 100 keV. Absolute cross sections were determined by comparison with Coulomb scattering on the same targets. The cross section for the transition to the broad level at Ex = 9.61 keV was calculated from the measured intensity in a 120 keV wide region around the center of the line, assuming a total width of 650 keV. This procedure was only possible for the spectrograph measurement, where the background was sufficiently low. The absolute cross sections measured for this state at Elab = 21.1 and 24 MeV are certainly too small.

3. Results Spectra of the 12C(7Li, t) reaction obtained at 15 and 21.1 MeV incident energy are shown in figs. 1 and 2, the measured angular distributions are given in figs. 3 to 5. The rotational states of the 4p-4h configuration dominate in the spectra. At the incident energy of 15 MeV the 2 + state at Ex -- 6.92 MeV is most strongly excited, at 21.1 and 24 MeV the 4 + state at E X = 10.35 MeV is dominating. This is obviously a consequence of the angular m o m e n t u m matching. Because of the 4p-4h configuration of these states one expects large spectroscopic factors for an a-transfer. In addition, the high number of nodes of the radial wave function of the captured c~-particle results in a large reduced width and in a large cross section for a surface reaction.

260

F. PUHLHOFERet

al.

The small cross section for the ground state transition does not necessarily imply that this state contains only a small e-cluster configuration. The large binding energy of the e-particle as well as the small number of nodes for four particles in the p~ shell yield a small amplitude of the form factor at the nuclear surface. 3 0 0 [ 6 0 5 613

E

6.92

/-~--

712

961

t,

2ooI

9~5

12 C (7Li,t)16 0

x1/5

x112

ELi = 15 MeV 0LA B = 5 °

to

1035 MOV

rL-position on the plate

Fig. 1. Spectrum of the reaction l~C(7Li, 0160 obtained at spectrograph. 100

i

15 MeV using the magnetic

Ela b ~

"'l

12C(7Li,

8O

t)160

OLA B = 6 0

l°°

°

ELAB=21.1MeV

o

N 4o

to©

~to ~

20

.

i

i

4

6

.... . . . . .

I

1'o

12

,.

.

i

4'4

16

18

Et EMeV-]

Fig. 2. Telescope spectrum of the reaction 12C(7Li, t)I60 at E~,b = 21.1 MeV.

The states of negative parity at Ex = 6.13 MeV ( 3 - ) and 7.12 MeV (1 - ) are weaker excited than the members of the first positive parity band, but still pronounced. One could therefore conclude that these states will have comparable spectrosctopic factors, because their dominating l p - l h configuration leads to a small number of nodes for the form factor and therefore to a concentration of the e-particle in the interior of the nucleus. In the measurements at 21.1 and 24 MeV the states at Ex = 6.05 and 6.13 MeV (0 + and 3 - ) were not resolved. However, the result of the spectrograph exposures at 15 MeV and the favoured excitation of high spin states at higher born-

12C(TLi, 0160

REACTION

261

barding energies indicate that the measured intensity can be attributed in essential to the 3 - state. As pointed out earlier 1), the weak excitation of the 2 - state at E X = 8.87 MeV allows one to draw some conclusions about the reaction mechanism. Transitions to states of unnatural parity are not allowed in a direct transfer of an a-particle or in general a spin-zero cluster to a spin-zero target. F r o m the shape of the angular distri12C(7Li,t)160 L- i

Io I°

I

I

I

I

1. ~

'

'05F I L = I ~

15 M e V

I

I

I

I

I

,.. Ex=Z12 1-

÷

+

\

L = O* 2 ~_~_.,.,,

-+ 1.~'X~ ,5

#

I \

,I,

20 °

+÷÷+

.f-

1.~--'~

Ex=9.61, I-

"~

Ex=10-35, 4+-~

1. 0o

÷ ~, ~ E×=8.87,2-

.~-

40 ° 822 °

0°

I

I

20 °

I

I

I

l

40 ° @60 °

Fig. 3. A n g u l a r distributions o f the reaction x2C(7Li, t ) 1 6 0 at Elau = 15 MeV. T h e curves are D W B A calculations.

butions in figs. 4 and 5 it was concluded that this level is mainly excited via a compound nucleus process. The measured angular distributions are nearly symmetric to 0 = 90 °. A Hauser-Feshbach calculation was based on this transition in order to estimate the compound nucleus contribution to the other transitions. The procedure has been described in a previous paper +). The optical-model parameters used for the calculation of the transmission coefficients were taken from optical-model fits of elastic scattering data also measured at 21.1 MeV. They are listed in table 1, which also contains the optical-model parameters for the exit channel [from ref. t o)]. The calculated compound nucleus contributions are given in figs. 4 and 5 together with the values of the integrated experimental cross sections in table 2. It should be

262

F. PUHLHOFER et al.

12C (7Li,t)160

0.01

ELA B = 21.1MeV

1

=

"~ '~ ~-'~

Ex =6.13MeViJ3[ =3" (Ex=6.05MeVi jJT =0+)

o..~..~

,

~..~__;___

;

%

1" I

~.~

~

Ex=6.92MeViJ3T .2 +

~o

i'~

I'

L =

Lb.

1.

1+3

E x =7.12MeVj J J'T =1"

0.1L--~

,=o-2

~

/

~ D W B A

E x :8,87MeV i jJT = 2 "

0.1

z {

0.01~ i O*

i

=

I~

i

30 °

' ' 6 ' 0 ' ' o' 0

9 o

(a)

. . .120.= . . 150 . °.

9CM

Fig. 4. Angular distributions of the reaction 12C(7Li ' t)160 at E~ab = 21.1 MeV. The curves represent D W B A calculations for the direct part of the reaction and I-Iauser-Feshbach calculations for the c o m p o u n d nucleus contributions. F o r the absolute cross section of the 9.61 MeV state see sect. 2.

t2C(TLi, t)t60 REACTION

L

12C(7Li,t)160

ELA B=21.1MeV

°,L

~{\ i

,.-o.,

i

-

~:

0.1 ~ :

263

~DWBA

Ex =9.85MeViJJf =2* ~{ ~ ! ~

~

\

L=1+3 {z ~z

,

{

i j

,

0.01.-

,XX, "~

~,_-,o.,,Mev,J~_-4.

i ~

L =3+5

OA-

o*

30*

so*

90"

(b) Fig. 4.

~200

1so* OCM

264

r. POHLHOFER et al.

12C (7Li, t ) 1 6 0 ELA B = 2 4 MeV I

I

I

I

I

I

1

I

I

I

I

I

I

I

I

I

I

I

i

i

i

i

i

i

i

i

i

i

I

i

i

i

i

I

I

1.O

1.0 ~ ~ X !

61103,sMMeeVv ? 3~==30÷,

F o.11-

-

J~Ex

=9.61 MeV ; 3~ =1-

,44,,

10.:

D'WBA -

1.O X E × = 6 . 9 2

\

MeV ~ 3~ ~2÷

0.1 -

% E x = 9.85 MeV, 3"~=2*

-

--,,,

.F

o, 7--..

~

I~l

10 :.

7.12MeV ; 3~=1-

~

,% DWBA ~ f ~ ×=lO'35Mev'3~=4÷ -

1.O

I-IF

'J f

HF

i 1.0 t

~! t Ex=8.87MeV ; 3~=2 0.1 "

HF~

--'~ 1.0 ~...~

Ez,=11.10MeV~3n =4 ÷ O~

~ 0.1t

0°

HF -E

I

I

I

30 °

I

I

I

60 °

I

I

i

I

90*

I

I

,

I

I

i

"~~DWBA I

120° 150* ®CM

Oo

I

I

I

30 °

I

I

I

60 °

I

I

t

90 °

i

t

t

~ I

I

I

I

120° 150 ° OC~

Fig. 5. Angular distributions of the reaction 12C(7Li, 0160 at Elab = 24 MeV. (See caption of fig. 4.)

TABLE 1 Optical potentials

12C+7Li 160+t

Elab (MeV)

U (MeV)

ro ffm)

a (fm)

WD (MeV)

rt (fro)

ai (fm)

21.1

50.0 143.0

1.47 1.42

0.83 0.54

8.65 17.4

1.86 1.56

0"80 0.55

The notation is the same as in ref. 14), particularly R = roAtarget{-.

rc (fro) 2.30 1.40 ref. 1°)

12C(7Li, t)160 REACTION

265

TABLE 2

Integrated experimental cross sections of the reaction 12C(7Li, 0160 at E~.b ~ 21.1 and 24 MeV, obtained from a Legendre polynomial fit to the angular distributions. The Hauser-Feshbach cross sections are also given Level in 160 -~x

Ela b =

JTr

(MeV) 0.00 6.05 6.13 6.92 7.12 8.87 9.61 9.85 10.35 11.10

21.1 MeV

Elab = 24 MeV

O-exp

O-HF

O-exp

O-HF

(mb)

(mb)

(mb)

(rob)

0+ 0_+}

0.41 a) 2.59

2+ 12-12+ 4+ 4+

4.74 0.84 0.63 0.71 ~) 1.13 11.20 3.75

3.01 1.10 0.37 0.51 0.15 0.37 2.08 1.47

3.58 b) 1.33 b) 1.05 1.11 c) 1.69 19.08 6.36

1.99 0.60 0.63 0.25 0.65 4.84 3.46

a) E~ab = 20.5 MeV, integrated only between 5° and 90° c.m. b) Integrated only between 40 ° and 180 c.m. c) See discussion in sect. 2.

noticed that the direct part o f the differential cross section in the forward direction is an order o f magnitude larger in strong transitions.

4. D W B A analysis of the angular distributions A significant feature o f the angular distributions o f the (7Li, t) reaction (figs. 3 to 5) is the difference between the oscillating curves o f transitions to the 0 + states in 160 a n d the s m o o t h behaviour for higher final spins. This is related to a peculiarity o f the (7Li, t) reaction. In contrast to the conventional transfer reactions with light projectiles, the particle to be transferred in this reaction is b o u n d in a relative p-state (l 1 = 1) in the projectile. As a consequence, the transferred angular m o m e n t u m 1, which determines the shape o f the angular distribution, is no longer identical with the angular m o m e n t u m 12 o f the captured particle. Instead, l is given by the condition ! = 12+11,

11 = 1,

with the restriction by the parity selection rule

(-ly= These relations are well k n o w n f r o m heavy-ion reactions. F o r the (7Li, t) reaction they will be derived below. In the reaction 12C(7Li, t) 160 two/-values are in general possible, namely l = 124-1. The superposition o f these transferred angular m o m e n t a

266

F. P(JHLHOFER et al.

obviously leads to the structureless angular distributions. The only exceptions are the transitions to 0 ÷ final states, where only l = 1 is allowed since 12 = JB = 0. Because of the relative p-state between the a-particle and the triton in 7Li the usual zero-range DWBA cannot be applied for (TLi, t) reactions. As shown in fig. 6, the replacement of the product of the interaction potential V(rl) and the relative wave tunction ¢(r1) by a delta function at the origin is no longer justified. The solution of the finite-range problem was avoided here by using the following assumptions: (i) The reaction is localized at the nuclear surface. (ii) Only those spatial configurations, where the a-particle is in a collinear position between target nucleus and outgoing triton, contribute to the transition amplitude.

Fig. 6. Radial wave function of the relative motion of or-particle and triton in the JLi. The first assumption follows from the strong absorption between projectile and target, the second one is justified because of the quick drop of the wave function of the bound a-particle at the nuclear surface and the absorption of the triton near the target nucleus. The distance a between the e-particle and the triton in 7Li was kept fixed, in the order of the second maximum of the wave function ~b(rl) in fig. 6. The inner part of ¢ ( r l ) is again neglected because of the strong absorption. In order to derive the transfer cross section, we start from the transition amplitude T =

fdri

drl ~(-)*(rf)(Bbl VlaA)~(+)(ri).

(1)

The reaction is denoted by A(a, b)B, where a = b + a; ~(+), ~(-) are the distorted waves in the entrance and exit channels, A, a, B and b the internal wave functions of the corresponding nuclei. We restrict ourselves to targets with JA = 0. The coordinates are defined in fig. 7. We write for the wave function of the projectile nucleus 7Li I//a = E (jbmb, 11 m~[jama)@bt~¢(rl)ihYt,m,(P~).

(2)

rtll

This implies that only the (a + t) cluster structure of the 7Li is important here. In a similar way, we factorize the internal wave function of the final nucleus B:

CB -- 7 ~A ~'. u(/.2) i,2~2m2(~2 ) + . . . . /'2

(3)

12C(7Li, t)160

REACTION

267

Eq. (3) defines the spectroscopic factor or relative reduced width 72, which determines the probability of finding the (12C + e) cluster structure in 160. The reduced e-width 0~, which will be discussed in sect. 4, gives this probability for the nuclear surface. It is defined by O~ = 72½r2u2(r2), r2 = 5.4 fro. (4) For simplicity, we assume that the internal structure of the e-cluster in the final nucleus is similar to that in 7Li. According to assumption (ii), the product of the interaction V(rl) and the wave function ~b(rl) is replaced by a delta function at the distance r 1 = a (fig. 6): V(rl)(#(I'I)Y/lmI(Pl)

= Da3

r 1 -a

Yt~mt(ri).

(5)

Fig. 7. C o o r d i n a t e s for the D W B A t r a n s i t i o n a m p l i t u d e .

All coordinates can therefore be expressed by functions of ri: r 1 =a

Yi , ?'i

r 2 --~ r i - m b a r i ' 1TIa r i r e = MAMB -~ri+a

(1

MA mbt ri

MB real r~

(6)

After inserting eqs. (2), (3) and (5) into eq. (1) and integrating over rx, we find for the effective interaction: ~ A .11 (BbIVlaA) = rDa(jbmb, lamlljama) u(r2) z• --12 Yt2m2(ri)' Yl,m,(Pi).

(7)

r2

The product of two spherical harmonics with the same argument can be simplified by y (

r.ml(OV,2.2(O = - 1 )

t , , 1 / ( ~ I + 1)(212+ 1)

V

X

(I 1 ml, 12 mzll- m)(l, OlzOllO)Yt*(P).

(8)

268

F. PUHLHOFER

et al.

Then the transition amplitude is given by

T = y D , ( - 1 ) m2-m-mb+A - - 1 x/(2j. + 1)(212 + 1)(j. rn., J b - mblll rnl) x 2 i"-t2+'(l 1 - m~, l a ,,,211m)(1~ o, 12Ollm)fl,,,,

(9)

l

firm --

z

1

( d r i ~(-)*(rf) u(r2) i_,yz.(~i)~(+)(ri), ~/(2l + 1 ) J rz

(10)

rt and r 2 are to be taken according to eq. (6). The quantity l has the meaning of a transferred angular momentum. The differential cross section is then:

da _ mira f kf zDZ(2lz+l) ~,(1, O, izOllm)ZElfl,m(O)12" (2nh2) 2 kii r ~ , m

dO

(11)

Eq. (11) for the cross section contains several contributions with different/-values, even though the angular momentum 1z of the captured particle is unique. The weight of the different contributions is given only by the Clebsch-Gordon coefficient (110, lz0110) and is therefore independent of the structure of the participating nuclei. The previously mentioned selection rules follow immediately. The information on the structure of a particular level in the final nucleus is contained in the spectroscopic factor 72 and the wave function u(r2)/r 2 (form factor) of the bound e-particle. A similar expression for the cross section has been derived by Buttle and Goldfarb 1~) for transfer reactions between heavy nuclei under somewhat different assumptions. The amplitudes firm of eq. (10) are similar to those of the zero-range DWBA ~2), but the arguments of the distorted waves and of the form factor are different. For our calculations we used a suitably modified DWBA code ~3). Differential cross sections for the reaction ~2C(7Li, 0 1 6 0 were calculated from eq. (11). The optical-model parameters are given in table I. The parameters for the entrance channel have been obtained by least-square fits of the elastic scattering of 7Li on 12C at 21.1 MeV using the program JIB 3. From the large number of potentials obtained we have chosen one set with surface absorption which is consistent with those from systematical investigations of the elastic 7Li scattering on various target nuclei t 4). Using parameter sets with volume absorption always resulted in angular distributions less steep than the measured ones. The wave function of a particle of mass 4 in a Woods-Saxon potential with r o = 1.25 fm and a = 0.65 fm was used as form factor. The number of nodes n2 was calculated from the energy condition 2n 2 + l 2 = ~(2vi+2~), where the sum runs over the four transferred nucleons. The ground state of ~60 was regarded as doubly closed, for the excited states we adopted the configurations mentioned in sect. 1. The binding energies were increased arbitrarily by 5 MeV in order to include the transitions to the unbound states above the x-threshold at Ex = 7.16 MeV into the calculation, Only in the analysis of the 15 MeV data, the transitions to the bound states have been cal-

12c(TLi ' t) 160 REACTION

269

culated using the correct binding energies. Further parameters in the calculations are the distance a = 1.5 fm between a-particle and triton in 7Li and the lower cut-off radius r c = 4.4 fm for the radial integrals. It should be mentioned that the shape of the calculated angular distributions is insensitive against a variation of all mentioned I

I

I

~_--,-~,

'%~.\

10

r~ 5 b

I

i

I

I

I

I

DWBA 12C(TLi,t)16O 2- E =e.92. v

-

-

[

\~ " ~

,j

ELAB=21.1MeV

" - / " 't~£~..~.W, L. 3 1.o

£

Cl 0.1

O°

I I I I I I l l l l l 2°o 4 °o 6 °o 80°

1°0o ®CM

Fig. 8. Superposition o f two /-values in the calculated a n g u l a r distribution for t h e 2 + state at Ex = 6.92 M e V in a60.

e.m.

Fig. 9. D e c o m p o s i t i o n o f the m o m e n t u m o f the projectile nucleus 7Li.

parameters, particularly of the binding energy. It is also not seriously altered by using different optical-model parameters, as far as they have surface absorption and describe the elastic scattering. However, the normalization for the D W B A and in some cases also the relative cross sections depend strongly on the parameters. The superposition of two angular distributions with different/-values is shown for one example in fig. 8. The comparison between experimental and calculated angular distributions is given in figs. 3 to 5. The D W B A describes the structureless decrease for transitions to final states with spin JB > 0. The calculated curves for transitions to 0 + states exhibit a much more pronounced structure, but the relative position of the oscillations is in disagreement with the experiment, in particular for the ground

E. PUHLHOFERet al.

270

state transition. It is difficult to discuss the r e a s o n for that failure. In the case of the first excited 0 + state this is certainly a consequence o f an a n g u l a r m o m e n t u m mismatch, which can be d e d u c e d f r o m the reflection coefficients o f the distorted waves. The g r o u n d state t r a n s i t i o n is distinguished by a very small value o f the linear m o m e n t u m transfer q = k i - k f ~ 0.1/fm in f o r w a r d direction. This m o m e n t u m transfer is, on the o t h e r hand, connected with the relative m o m e n t u m k , o f the a-particle in the 7Li nucleus by q ~4 - k l - k , (fig. 9). It c o u l d be possible t h a t because o f the restriction b y k , ,,~ x/l~(l~ + 1)/a the values o f k~ are not sufficiently large for this react i o n at the surface o f VLi. T h a t these k i n e m a t i c a l effects p l a y an i m p o r t a n t role is further indicated by the great difference o f the two l = 1 transitions to the g r o u n d state a n d first excited state in 16 0 a n d the fact t h a t our calculations p r o v i d e g o o d fits to the l = 1 transitions in the (7Li, t) reaction on ~3C, which have different Q-values [ref. 15)].

5. Discussion The f o r m a l i s m described in sect. 4 is able to represent the m e a s u r e d a n g u l a r distributions. This suggests t h a t the basic a s s u m p t i o n o f an c~-transfer t a k i n g place in a surface reaction is a d e q u a t e to this (VLi, t) reaction. In particular, the d e p e n d e n c e o n the transferred a n g u l a r m o m e n t u m is r e p r o d u c e d . The exceptions can be explained b y m i s m a t c h i n g effects. C o n t r i b u t i o n s f r o m c o m p o u n d nucleus f o r m a t i o n have been estimated to a c c o u n t for only a b o u t 10 % of the differential cross section in f o r w a r d direction for strong transitions. TABLE 3 Spectroscopic factors 72 and reduced c~-widths of states in 160

Level in 160 Ex (MeV)

da dR (max) (mb/sr)

72

0~2

j~r DWBA

exp

0.00

0 + 0p-0h

0.7

0.2

0.3

0.07 a)

6.05 6.92 10.35

0+~ 2 +}4p-4h 4+1

7.5 16.6

1.2 11.0 6.0

0.2 0.7

0.05 0.18 0.1-0.3 b)

6.13

3-/lp-lh

2.5

1.3

0.5

0.03

7.12

1-/

100

14

014

0.025

a) No DWBA fit. b) Unbound state, 0~ is extrapolated. ~2 is given by the ratio between experimental and DWBA cross section. 0~ is defined in sect. 4. It is independent of the assumed configuration. The values are obtained from the analysis of the 15 MeV data. The results at 21.1 MeV incident energy are similar. 72 and 0~ may both contain an unknown normalization factor.

12C(TLi, t)160 REACTION

271

The 4p-4h rotational band in 16 0 is, as expected, most strongly excited in this reaction. The cross sections for the 2p-2h states are comparably small. On the other hand, the l p - l h states at 6.13 and 7.12 MeV are the most strongly excited negative parity states. Consequently, they must have more or similar four-particle correlations compared to the higher-lying 3p-3h states. A quantitative interpretation of these facts, i.e. the determination of reduced c~-particle widths, is difficult. First, our D W B A results for the ground state transition are not reliable. In addition, there are fundamental problems for D W B A calculations of transitions to the unbound states above the ~-threshold at 7.16 MeV in 160. A comparison with the results from the reaction 12C(0(, (z)lZC is therefore generally not possible. For the remaining states we cali 2 culated the spectroscopic factors ]j2 and the reduced widths 10,. The results are presented in table 3. The calculations were performed using the correct binding energies. Since the D W B A is in practice unable to calculate absolute cross sections for this reactions, all values of ,~2 and 02 may still contain an unknown common factor. In order to have at least one possibility to compare with the results of resonance scattering analyses the reduced width 02 for the 4 + state at Ex = 10.35 MeV was calculated using several bound states as form factors for the D W B A and then extrapolated to the actual unbound state. 02 should be nearly independent of the form factor. The value obtained is in rough agreement with the result 02 = 0.26 of Bittner and Moffat 16). Possibly all our values of 72 and 02 have to be multiplied by a factor of the order of 1.5 or 2. The comparison of our data with the results of Loebenstein et al. 17) show only poor agreement. These authors have estimated reduced c~-widths from the reaction 6Li(lzC, d) 160, but their analysis is complicated by the presence of strong compound nucleus contributions. Our results certainly require further justifications. For example, a comparison with reduced e-widths from structure calculations of 16 0 could be informative. One simple conclusion can be drawn immediately. The assumption of one well-defined intrinsic state for a rotational band would yield the same reduced c~-particle width for all states of this band. The values in table 3 indicate that this picture is too simple. The greater width of the 2 + and 4 + level in the 4p-4h band reflect the fact that a considerable mixing with the 2p-2h band is present. This was also found in the calculations of Celenza et al. 6). We thank Professors W. Gentner and O. Haxel for their interest in this work.

References 1) 2) 3) 4) 5) 6)

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