Investigation of the (d, 6Li) reaction on 16O at Ed = 80 MeV

2.B : 2.G

A306 (1978) 1-18 ; © North-Holland Publkhlng Co ., Amsterdam Not to be reproduced by photopriat or microfilm without written permission from the publisher Nuclear Physics

INVESTIGATION OF THE (d, 6 Li) REACTION ON 160 AT Ed = 80 MeV W. OELERT, A. DJALOEIS, C. MAYER-WRICKE, P. TUREK and S. WIKTOR Institut fur Kernphysik, Kemforschungsanlage Julich,

D-5170

Julich, W. Germany

Received 7 April 1978 Abtdmet: The (d, 6Li) reaction on 160 has been investigated with the 80 MeV deuteron beam of the Julich Isochronous Cyclotron. Angular distributions were obtained between 10° and 55° lab. Experimentally an excitation energy range up to 40 MeV was observed . Single states and level groups with E, < 22 MeV show up clearly in the present data . These were analysed by both zerorange and finite-range DWBA calculations . Spectroscopic factors have been obtained and compared to theoretical predictions. Evidence for other than direct transfer mechanism is discussed phenomenologically . E

NUCLEAR REACTION ' 60(d, 6Li), E = 80 MeV, measured a(E,L  B) . ' 2C levels deduced S, . Gas target . Zero-range, finite-range DWBA calculations .

1. Introduction Generally, four-nucleon transfer reactions are regarded as being useful for investigating a-clustering effects in individual nuclear states. A great deal of the fournucleon transfer measurements done up to now were carried out via the reactions (d, 6 Li) and ('He, 'Be) or ( 6 Li, d) and ('L~ t) for the pick-up or the stripping case, respectively t - t 3) . However, most of them have been performed at such low incident energies that they cover only a few low-lying excited levels. We have investigated the pick-up reaction (d, 6 Li) at a rather high incident deuteron energy, since it is of interest to see how the quartetting of four nucleons is reflected at higher excitation energy in' the residual nucleus. Throughout the literature relative spectroscopic factors extracted by using DWBA predictions have been compared with model calculations. The deviations between experimental results and calculations might be attributed to the fact that only strong correlated four-particle clusters are included in the extraction of the spectroscopic information. Furthermore such deviations may also result from compound nucleus contributions [see e.g. ref. t4)] and multi-step or sequential transfer reactions.

2

W . OELERT et al.

2. Experimental procedure In order to investigate properties of highly excited states, we used the 80 MeV deuteron beam of the Julich Isochronous Cyclotron JULIO to measure the (d, 6 Li) reaction on an 16 0 gas target . As a by-product the outgoing particles 'Li and 'Be were detected as well ts). The experiment was performed by use of a conventional dE-E detector technique in a 1 m diameter scattering chamber. Differential cross sections were taken in the angular range from 10° to 55° lab. Because of the low cross sections, fairly thick targets (350 Torr at 25°), high intensity achromatic beams and radial solid angles of 0.5° and 0.7° were used . This resulted in an energy resolution of x 300 keV FWHM . The incident beam was continuously monitored by a Ge(Li) detector at an angle of 30° relative to the beam direction. The deuterons elastically scattered into the monitor counter and the integrated charge collected in the Faraday cup served for the determination of the cross section at the various angles . The measured cross sections relative to each other are believcd to be more accurate than 10 %, as long as the statistical uncertainties do not rise above this value. For the determination of the absolute cross section an error of up to 20 % is quite realistic . Random errors (as shown in the angular distributions), which are due to counting statistics and background uncertainties alone, have to be added incoherently to the errors in normalization. An energy spectrum of the reaction `0(d, 6Li)t ZC is shown in fig. 1. The dominant features of the 6 Li spectrum are: EXCITHT13N ENERGY 30 .0 20 .0

(MEV ; 10 .0

0 .0

700 .

560 .

420 . 0

u

280 .

140 .

0 .0 600 .00

800 .00

I000 .00 CNP,VNE_ NUMBER

1290 .00

Fig. 1 . Energy spectrum of the (d, 6 Li) reaction on 160 . The solid line is drawn to indicate the lower limit of an average background .

16O(d

6Li)12C

3

The rather selective excitation of three peaks with excitation energies of 0.0, 4.43 and 14.08 MeV. (b) The minor yields of the known 7.66 MeV 0 + and 9.64 MeV 3 - states in '2C. (c) The observation of broad, structured bumps, one underlying the 14.08 MeV state, the other centered at 19.5 MeV and possibly a third one ranging from 22 to 27 MeV excitation energy . It seems that these broad bumps have fine structure and may therefore be due to groups of levels. Only an integral extraction of the cross section for these bumps could be carried out with confidence . (a)

3. Parameters for DWBA calculations In the framework of an a-cluster model zero-range (ZR) DWBA and finite range (FR) DWBA calculations have been performed using the computercodes DWUCK 16) and LOLA "), respectively. Even for such fairly simple-minded cluster calculations various uncertainties arise. These are discussed in several papers throughout the literature of a-like transfer reactions, see e.g. ref. ") . Some of these problems are: (a) Unambiguous optical model parameters are not available for the 6 Li particles at the relative high energy used. (b) If a cluster description for the four nucleons to be transferred can be used, the bound state wave function for both the cluster in the target and the cluster in the 6 Li outgoing particle has to be determined . The geometrical size for calculating this wave function is not known. In the one-step DWBA calculations performed for the reaction "O(d, 6 Li) ' 2C , a-cluster form factors were created assuming (0p)4 pick-up for all positive parity states and (0s)'(0p)' pick-up for negative parity states . In the cluster approach the configurations (n;, l;) for the four transfered nucleons are the same throughout the reaction process. Therefore - following from conservation of angular momentum and energy (Talmi-Moshinsky transformation) - the relative motion quantum numbers N, L, for an s = 0 four-nucleon cluster relative to the core are given by the expression : 2N+ L = 1a 1 (2n; + l). 3 .1 . INFLUENCE OF OPTICAL MODEL PARAMETERS

Since there are no optical model parameters available which have been determined at the energy of the present experiment several potential sets ' 9-26 ) have been tested. Eight different deuteron potentials ' 9-2 ') have been employed, along with the 6 Li potential by Chua et al. 22). A representative selection of angular distributions obtained for the g.s. to g.s. transition is shown in fig. 2. For these calculations a radius parameter of 1 .33 fm was used for determining the depth of the bound state potential for both, the "a-cluster" in the target and (in the FR calculations) in the 6Li ion. Regarding the shape of the ZR DWBA angular distributions (left-hand side)

W. OELERT et al.

4

eC.M .

Fig. 2. The DWBA calculations for the ground state transition of the reaction '6O(d, 6Li)"C, employing different deuteron potentials : (a) ref. 3 °), set 1 ; (b) ref. 2 °), set 1' ; (c) ref. 2°), set 2' ; (d) ref. l9) ; (e) ref. 19) with V, ., . = 0. Zero-range and finite-range calculations are shown on'the left- and right-hand sides. respectively .

FINITE -RANGE

e le.m. )

DWBA

e (C .m)

Fig. 3. The DWBA calculations for the ground state transition of the reaction "O(d, 'Li) 12 C employing different 'Li optical model potentials : (a) ref. 27); (b) ref. 2°) ; (c) ref. 26) ; (d) ref. 22). Zero-range and finite-range calculations are shown on the left- and right-hand sides, respectively .

16O(d, 61,i) 12c

5

a rather structureless pattern is observed with a decrease by about one order of magnitude for a 15° increase of angle. With respect to the absolute cross section, however, a deviation of up to a factor oftwenty is observed. Exact FR DWBA calculations, as shown on the right-hand side of fig. 2, have a similar tendency up to 80° c.m. However, the theoretical curves show slightly less decrease with increasing angle up to 60° c.m. than in the case of the ZR calculations and at 80-85° c.m . they develop a deep relative minimum. In general they are only significantly different from each other in absolute magnitude. While the choice of the deuteron optical potentials used for DWBA calculations seems to be rather insensitive t with respect to the shape of the theoretical angular distribution, a strong dependence is observed in using different 6Li optical potentials . Fig. 3 shows ZR and FR DWBA calculations on the left- and right-hand sides, respectively, using the deuteron optical potential set of ref. t 9) neglecting the spinorbit term, and four different 6Li optical potentials selected from those potentials deduced and used in refs. zz-z6). Here patterns of angular distributions are observed ranging from strongly oscillating to nearly smooth decrease with increasing angle . A good determination of 6Li parameters appears to be essential for future investigations. 3 .2. THE BOUND STATE RADIUS OF THE "ALPHA-CLUSTER"

ZR DWBA calculations . The potential depth for determining the wave function of the bound state a-cluster in the target nucleus (and for FR in the outgoing 6 Li nucleus) was adjusted to reproduce the a-particle binding energy in the nucleus. In this procedure the geometrical size seems to be a free parameter t 8). To investigate this question in more detail, eight different deuteron potentials t9-2 t) have been tested along with the 6Li potential of ref. 22) in the rather economic Z') ZR DWBA calculation . The radius parameter ro (R = roA}) was varied from 1 .33 to 1 .90 fm . As mentioned; some calculated angular distributions for the ground state to ground state transition are shown in fig. 2, using ro = 1 .33 fm. Only one theoretical ZR DWBA curve (case e in fig. 2) gives a good fit to our data . This curve of the L = 0 ground state transition is shown as a solid line along with the experimental data in the upper part offig. 4, the lower part of this figure shows the angular distribution of the L = 2 transition to the 4.44 MeV state. When the radius parameter of the bound state potential is increased from 1 .33 to 1 .65 fm the quality of the L = 0 fit decreases, whereas the one for the L = 2 transition increases as is shown by the dashed curves in fig. 4. This general observation is still valid even if only the five deuteron optical model sets given by Hinterberger et al. s°) are taken into account. Examples for ro = 1 .33 (dotted curve) and ro = 1 .90 (crosses) are shown in fig. 4 using the dpotential 2* of ref. 'o) and the 6Li potential of ref. z3) (table 1, set II). It seems that t Note that none of those potentials were really determined for 80 MeV deuteron energy.

ec.m.

Fig. 4. Comparison between experimental angular distribution data (for the populations of the 0 + g.s . and of the4.44 MeV 2+ state) and ZR DWBA calculations using differentradius parameters ro (r = roA `13 ) for the bound state wave function . Two optical model potential set combinations are tested as given in table 1 ; (a) and (b), ref. ") and ref. 22) ; (c) and (d), ref. 2 °) and ref. 23) .

even a higher ro value than 1 .90 fm would be appropriate for this combination of potential sets. It turns out that (a) the variation of the radius parameter changes the absolute cross section drastically (in fig. 4 the theoretical curves are arbitrarily normalized to the data points in the range of 15-25°); (b) in the given range of the bound state radius parameter the relative spectroscopic factor changes by less than 20 % for the case of the 2+ state, but by x 50 % for the case ofthe 4+ state; and (c) for each potential set and transition there is an optimum value for the parameter ro of the bound state potential . From all ofthe DWBA calculations performed, which yield a reasonable fit, there is a general tendency that larger radius parameters are required for the transition to the L = 2 state than for the ground state (fig. 4). The optimum value for the transition to the 4+ state in' ZC seems to be in between. The ratios of these different radius parameters, however, are not constant with respect to different potential sets .

16 O(d, 6Li)12C

7

From FR DWBA calculations the same quality of fits to the present data can be achieved . However, slightly larger radius parameters for the bound state potentials seem to be required. Again it turns out that each transition regarded has its own optimum radius value for the best possible fit. The following average parameters (radius, diffuseness and Coulomb radius) have been chosen for the "a-cluster" in the target and the "a-d" --+ 6Li system : R = 1.65A} fm, a = 0.65 fm and R c = 1.40A} fm. The optical model potentials chosen were : the d-potential of ref. 19) since these "global fit" potentials span a wide range of target masses and energy, and the 6 Li potential of ref. ") since these potentials are determined at rather high energy (E6L, = 50.6 MeV) and for several target nuclei . These parameters are given in table 1 . TABLE 1

Optical model potentials used (potential strengths in MeV, lengths in gym) Set

Part .

VR

rR

as

W,

r,

a,

I

d 6Li

-76.20 -214 .00

1 .15 1 .30

0.78 0.70

-3 .97 -26.80

1 .33 1 .70

0.69 0.90

II

d 6Li

-76.80 -173 .20

1 .25 1 .21

0.75 0.802

-8 .90

2.18

0.94

1 .65 b)

0.65

bound state

')

The analytical expression of the potential is V = V,+VR1(r,

RR, alt) + iW1J(r, R a,)+iWp4a,

WD

r,

a,

r.

Ref.

9.62

1 .33

0.69

1.30 1.40

19)

3.97

1 .25

0.75

1.30 1.30

22) 20 ) 23)

1.40

d f(r, R a,),

withj(r, RN, aN) = 1+(exp[(r-RN)IaN])-`, RR . 1 = rR .1A113 . ') Adjusted by the computer code to fit the a-particle separation energy . b) For this parameter see the discussion in the text .

3.3 . QUANTUM NUMBERS OF THE BOUND STATE WAVE FUNCTION

The bound state wave functions for the "a-cluster" depend on the geometrical properties of the a-bound-state potential, as discussed in subsect. 3.2 . The relative motion quantum numbers N, L of the a+ 12C = 160 system are determined for positive parity states by the relation 2N+L = 4 and for negative parity states by 2N+L = 3. Higher values are possible when including the sd shell for the ground state configuration of 16 0. However, it was found that there is no significant difference in the shape of the angular distribution for different values of 2N+ L.

Some controversy and uncertainty arises in the literature on how to describe the relative motion in the 6 Li system, i.e., OS, 1S and OD states are suggested 28-31).

8

W . OELERT et al.

for example, gives the following numbers for the spectroscopic factors : =0.44. Furthermore, a more simple 1 S relative motion wave function is predicted by the antisymmetrized cluster model a9) and by the shell model. However, even if the probability for OS and OD contributons for the 6 Li g.s. are small, they have to be kept in mind. Since the components of the wave functions would have to be added coherently, interference effects can modify the shape of the experimental angular distributions. Fig. 5 gives examples for FR DWBA calculations assuming the outgoing 6 Li to be either in a 1S state (dashed line), in a OS state (solid line) or in a OD state (dasheddotted line). In fact, comparing these curves to the experimental data only calculations for the 1 S relative motion ofthe d-a system fit the ground state angular distribution. In the case of the transition to the 2 + 4.44 MeV state no clear distinction can be made between the 1S and the OD shape of the calculated angular distributions, which both tentatively fit the data. Finally, for the case of the 14.08 MeV 4 + state none of the theoretical curves gives really a complete fit. However, the 1 s curve shows at least the correct increase and decrease in the angular ranges 10-25° and 35-50°, respectively, as shown below (fig. 8). Ref.

3° ),

Va(I S) = 0.69; Sa!'a(OD) = 0.04 ; and S,'itt.(1 S)

ad

of

ed et: .m.

Fig . 5 . Angular distributions of FR DWBA calculations for final states in "C excited by the 16 O(d, 6 Li)'?C reaction . Different configurations for the relative motion of the a+d system forming 6 Li are employed .

16O(d 6Li)12C

9

4. Results and discussion 4 .1 . TRANSITION TO SINGLE STATES IN 12 C ; DWBA ANALYSIS

Using for the DWBA calculations the parameters given in table 1, the spectroscopic factors Sa were extracted by comparison between the theoretical and the experimental results. The post representation was employed in the LOLA calculations . The following expressions were used for the "a-cluster" pick-up reaction on the 0 + target t 6 0 [projectile and ejectile have the same spin value, implying that the S.6 , d S) spectroscopic factor is unity] ZR DWBA dv(0) _ _ ' N ' S `21+1 CddSl a(e) JDWUCx' da(0) d12 Je=p L N2S .(21 + 1 ) Wz ( l IJ1' 1 2 .12+ ' ; sn x`lI WIT nr s

1

16)

FR DWBA t ') .

10 2

10 0

.61

()CM . Fig. 6. Angular distributions from the population of the 0* states in 12C at 0.00 and 7.66 MeV, excited by the 16O(d, 6Li) reaction . The FR and ZR DWBA curves are shown by the solid and dashed lines, respectively .

W. OELERT et al .

10

The experimental angular distributions of observed single states in ' ZC are shown in figs. 6-8, along with the theoretical curves obtained from ZR (dashed lines) and FR (solid lines) DWBA calculations . As a general experimental feature it can be stated that not much structure appears. By both of the DWBA calculations the monotonic decrease and the slight wiggles in the experimental angular distributions are rather well reproduced for each of the two L = 0 cases in fig. 6 (E,, = 0.0 and 7.66 MeV).

to e

t N to

Fig. 7. See caption to fig. 6, but now foAhe case of the 4.44 MeV 2+ state.

Fig. 8. See caption to fig. 6, but now for the cases of the 9.64 MeV 3 - and 14 .08 MeV 4 + states in ' 2 C.

The situation is similar for the results concerning the 2 + state at 4.44 MeV excitation energy (fig. 7). Possibly by a matter of chance, the data are fit slightly better by the ZR rather than by the FR calculations, at least for angles lower than 40° c.m . Moreover, at the deuteron energy of the present experiment, the shape of the experimental L = 2 angular distribution is not characteristically different from those shown for the L = 0 cases in fig. 6. In fact an L = 0 theoretical curve would pass through the data points almost as well . It should be mentioned, however, that the data ofref.') and ref. sz) measured with 19.5 and 35.0 MeV incident deuteron energy showed characteristically different shapes . Our results are presumably due essentially to the strong momentum mismatching conditions at 80 'MeV incident deuteron energy . In addition possible other effects of reaction mechanism and/or nuclear

16 O( d 6Li)12C

structure as e.g . non-negligible contributions from the OD relative state in 6 Li (see fig. 5) remain to be further investigated. The overall slope of the angular distributions concerning the 3 - and the 4 + states at 9.64 and 14 .08 MeV excitation energy, respectively (see fig. 8), decreases much less than in the cases shown before. The FR DWBA curve tends to fit the 3 angular distribution somewhat better than the ZR curve. However, the quality of the fits is only fair in all cases shown in fig. 8. In the case of the 4+ state, higher energy resolution would be useful in order to be able to distinguish better between the peak and the underlying broad structure (see fig. 1) . The results of the analysis for the single states in t ZC are given in table 2. Only the relative spectroscopic factors of columns five and six are considered for further discussion ; their uncertainty is estimated to be at least 20 %. According to these results the predictions of Kurath as) and Rotter ") (column 7 in table 2) seem to favour the L = 2 and L = 4 transition strength too much, whereas the ratio of the two L = 0 S a values is in good agreement with our result. Good agreement is found 35) and our relative between the relative Sa predictions of the "a-chain model" spectroscopic factors for the L = 2 and L = 4 transition strengths. TABLE 2 The a-spectroscopic factors for states in 12C populated by the transfer reaction 16O(d, En

L

N 1 SDWUCK a

N 2 S1.°LA n

S°rCK o ral

0.00 4.44 7 .66 9.64 14.08

0 2 0 3 4

0 .45 1 .46 0 .10 0 .19 0 .72

0 .76 2 .43 0 .14 0 .43 1 .45

1 .00 3 .24') 0 .22 0 .42 1 .60

SLOLA n rel

1 .00 3 .18 0.18 0.56 1 .90

6Li)"C

Srhenr b) n rel

5th= e) n

1 .00 5 .54 0 .26

1 .00 3 .16

10 .16

1 .97

The "absolute spectroscopic factors" in column three and four are only listed for completeness. Since these results are strongly model dependent their values have no real significance . ') An analysis with several different d optical potentials results in an average spectroscopic factor of 3 .5 f 0 .5 . 33 .34) . °) Ref. ") . b) Refs . 4.2 . THE BROAD STRUCTURED BUMPS AROUND 14.1 AND 19 .5 MeV EXCITATION ENERGY

The experimental angular distributions obtained from the broad structures (see fig. 1) are given in fig. 9. Only in the case of the broad bump around 14.1 MeV excitation energy are the theoretical curves for L = 1 to L = 4 transitions shown. The shape of the angular distribution extracted from the broad structure around 19 .5 MeV coincides with the one around 14.1 MeV, as can be seen in fig. 9. Furthermore, both of them are similar to the data of the angular distribution leading to the 3- state at 9.64 MeV displayed in fig. 8. If only one L-transfer is responsible for the observed shapes of the angular distributions in fig. 9 only the L = 3 DWBA curve can be

fft"

10 1

brood structure at 19.5 :15MW

'444,} 100

1 0

2d

co'

f

sd

ecm.

Fig. 9. Experimental angular distribution of the observed broad structures around 14 .1 and 19 .5 MeV excitation energy . Since both of the angular distributions are rather similar to each other FR DWBA curves for L = 1 to L = 4 transitions are shown for one case only .

accepted. This tends to suggest that octupole strength is observed in a-transfer between the nuclei t6 0 and tZ C. However, the quality of the "fit" shown in fig. 9 between the L = 3 FR DWBA calculation and the experimental data is not convincing enough to make this to a definite statement. Nevertheless, according to the E x = 32A} MeV law 36) for excitation energy of low-lying octupole strength (x 14 MeV in tZ C) and according to theoretical results 37 .38) observation of E3 strength would not be unexpected . The question remains, whether (in the experiment performed) shapes which look like an L = 3 DWBA angular distribution necessarily lead to states with . total angular momentum 3. Alternatively, the data may be interpreted in terms of (a) an incoherent superposition of an L 5 2 with an L Z 3 theoretical curve and (b) contributions from multi-particle/multi-hole structure of the target nucleus. 4.3 . THE BROAD STRUCTURES IN COMPARISON TO OTHER EXPERIMENTS

In this section we discuss another possible reaction mechanism for the excitation of the main yield of the two broad structures, observed in the 'Li spectrum as shown in fig. 1. The same kind of population mechanism for both of them may be assumed, since experimentally it was found that the angular distributions (see fig. 9) show the same kind of overall slope. Furthermore, the angular distributions extracted from the yields on the left- and right-hand sides (not explicitly shown here) of the broad

16ad 6Li) 12C

13

structure around 14.1 MeV excitation energy have the same relative shape within the random errors . In the excitation energy range of 11 .5-14.0 MeV (i.e. the low excitation energy part of the broad structure underneath the 14.08 MeV 4+ state) only 1+ and 2 - unnatural parity states with isospin T = 0 are known 39). For the other side of the bump, ranging from 14.1 to x 17 MeV excitation energy, only T = 1 states are established 39). Therefore, direct population of these known states is ruled out in a a-cluster transfer picture in the framework of ZR DWBA considerations, i.e. higher order processes may be important. Fig. 10 shows a comparison of our (d, 6 Li) spectrum with (a) a (d, a) reaction spectrum on 14N [ref. 40 )] and spectra of (b) (a, a') and (c) ('He, 3 He') inelastic scattering experiments on 1sC [ref. 41 )] . Quite a striking similarity in the overall structure between both the (d, 6Li) and the (d, a) spectra is observed, when one disregards some strongly populated peaks in the (d, a) case as for instance the peak at 12.7 MeV excitation energy . This peak, however, corresponds to a known 1 + state and is therefore preferentially populated in the (d, a) experiment with the 1 + 14N target nucleus, and not in the "a" transfer reaction .

500-

16 0(d.6L0 uC Ed =80 MeV eun.=15 °

250-

uN(d .a')ttC Ed =40 MeV 0 1m.= 8°

500U) z O U

'

25012C(a. a" )

500-

1

12C

Ea=172 .5 MeV

250-

k,b. =16°

12C(3He .3HeT2C =135MeV 5010- E3H e Oi,b.=10°

T 1

2510-

Ex (MeV)

30

20

10

0

Fig. 10. Experimental energy spectra from different reactions leading to the final nucleus 12C.

14

W . OELERT et al.

The overall similarity in the gross structure between the (d, 6 Li) and the (d, a) spectra tends to suggest that a similar selective process is involved in both types of reactions. Reaction mechanisms following selection rules like those observed in the two-nucleon transfer may be due for the excitation of both sides of the broad structure around 14.08 MeV excitation energy in the (d, 6Li) reaction . The assumption of such a mechanism, by which population of unnatural parity states and of isospin mixed T = 1 states [see ref. 4z)] may be understood, is supported by the fact that also in other cases parallelism of excitation strength between fourand two-nucleon transfer reactions has been found 41,44) . Regarding the second broad structure in our (d, 6Li) spectrum, ranging from x 18 to x 21 MeV excitation energy, it should be noticed, that in the case of the inelastic scattering experiments a lack of yield above the background is observed . Only at the lower (18.4 MeV) and at the higher (21 .3 MeV) edge of this excitation energy range are peaks observed, which in the case of a-scattering follow rather nicely an L = 2 DWBA angular distribution calculation 4i) . These states apparently have structure which cannot be excited in the transfer reactions. In the case of the (d, a) reaction two well populated peaks at 19.6 and 20.6 MeV excitation energy have been observed 4°) . The authors determined spin and parity for these peaks as being 2' or 3 + . Since these peaks are strongly excited in the d-transfer they should have isospin T = 0. On the other hand, they show only minor population in the (a, a') case if at all, and the angular distribution of the broad structure in (d, 6 Li) does not fit an L = 2 DWBA curve. Therefore, a spin, parity and isospin assignment as (2 + , 0) is not necessarily ruled out, but seems unlikely. Tentatively a 3 + assignment could be possible for the main part of the strength observed in the second bump of our (d, 6 Li) data . 5. Contributions from other reaction mechanisms The question has been raised to which extent compound nucleus contributions have to be considered in the a-transfer on nuclei of different shells '¢). Actually, for the unnatural parity 2 - state at 8.88 MeV in 160 a nice deuteron angular distribution symmetric around 90° c.m., has been observed in the ( 6 Li, d) reaction 4S). We tried to follow up the question by extending the measurements of the (d, 6 Li) reaction into the angular rangeof 140-163° lab. As examples, fig. l l shows two angular distributions for the population of (a) the 4.44 MeV 2 + state (along with DWBA calculations) and (b) of the second broad structure around 19.5 MeV excitation energy . A pronounced increase of the cross section with increasing angle is observed in the backward region for the 2 + state, while this is not as pronounced for the broad structure (this also applies for the other bump at x 19.5 MeV). Since for compound nucleus contributions an angular distribution symmetric around 90° c.m . is expected our data show that this reaction mechanism must be of minor importance for the population of states in ' Z C in the excitation energy range under investigation up to x 20 MeV.

160(d

6

Li) 12 C

15

,63

Fig. 11 . Experimental angular distributions including data points for the angle range 15(r to 170° c.m . for the 4.44 MeV 2+ state and for the broad structure around 19.5 MeV excitation energy in 12 C. The FR and ZR DWBA curves are given by the solid and dashed lines, respectively .

Mechanisms as for example '°B rather than a-transfer have not been considered. A recent theoretical paper 46) gives arguments for this kind of contribution (for Ed = 35 MeV), resulting in a significant backward angle increase of cross section for the 12C ground state population. We could not observe such a backward increase for the ground state transition . However, the transitions to the 4.44 MeV 2 + state and to the broad structures around 14.1 and 19.5 MeV excitation energy, see fig. 11, have cross sections in the range 150° to 170° c.m ., which cannot be explained by DWBA calculations . Whether such heavy particle transfer processes and/or structure effects are responsible for this observation remains a question for further investigations. 6. Conclusions

The (d, 6Li) reaction on 160 leading to the final nucleus 12 C has been investigated . A corresponding excitation energy range up to 40 MeV has been observed. The

16

W . OELERT et al .

members of the ground state band (0+, 2 +, 4+ ) are selectively excited. Several other levels are populated with minor yields . Extensive ZR and FR DWBA analyses have been made. In general rather good fits between theoretical curves and experimental angular distributions could be achieved. General agreement between both kinds of analyses is obtained. However, in any case the results are very sensitive to the choice of 6Li optical model parameters . Even the relative spectroscopic factors for the members ofthe g.s. band are dependent on these parameter sets . Using the sets of refs . l9 . az) (set I in table 1) results in higher quality fits to the experimental data and in better relative agreement between a comparison of ZR and FR DWBA than for example the sets of refs. z°z3) (set II in table 1). Likewise, the radius parameter used for the bound state wave functions turned out to be sensitive not only with respect to the absolute spectroscopic strength . In the case of potential sets I of table 1 the extracted relative spectroscopic factors remain constant within a 20 % limit when varying the radius of the bound state potential within the limits as given above. Larger variations have been observed for potential set II of table 1 . With respect to the average quality of fits, potential sets I demand this radius to be lower by 25 % compared to that ofpotential sets II oftable 1 . Accordingly it must be stated that in the DWBA model as used the results obtained are in fact radius dependent. Itshould be notedfurthermore, thatdeviations between the experimentally observed angular distributions and theoretical DWBA predictions may be due to coherent contributions of other than (1S) wave function modes in the relative motion description used for the 6Li(d+a) system . Within the framework described, the following observations have been made (table 2): (a) Good agreement is obtained for the relative spectroscopic factors of the excitation of the two 0 + states in "C, when comparing our data with the predictions of Kurath et al . 33) and Rotter 34) . (b) Fairly large deviations, however, have been observed for the relative population strength of the 2 + and 4+ states. (c) Good agreement is achieved for the relative spectroscopic strengths of the 2+ and 4+ states between our results and the "a-chain" treatment of Ichimura et al. 3s) . The angular distributions of the broad structures around 14.1 and 19.5 MeV excitation energy are fitted best by L = 3 DWBA theoretical curves . However, in spite of the structureless experimental angular distributions these fits are not convincing enough. Alternatively, other than direct DWBA mechanisms have been discussed. An excitation mechanism in terms oftwo "two-nucleon transfer" probabilities has been considered for the observed broad structures . Contributions from compound reactions have been shown to be of minor importance. The authors would like to thank Drs. G. Baur, M. Betigeri, W. Chung and F. Osterfeld for helpful discussions, and Dr. D. Haenni for reading the manuscript .

16O(d , 6Li)12c

17

References 1) 2) 3) 4)

K. Bethge, Ann. Rev. Nucl . Sci. 20 (1970) 255, and references therein A. A. Oglobin, Part . and Nuclei 3 (1973) 467 C. Detraz, H. H. Duhm and H. Hafner, Nucl . Phys . A147 (1970) 448 H. W. Fulbright, C. L. Bennett, R. A. Lindgren, R. G. Markham, S. C. McGuire, G. C. Morrison, U. Strohbusch and J. Toke, Nucl . Phys . A294 (1977) 329, and references therein . 5) J. D. Cossairt, R. D. Bent, A. S. Broad, F. D. Beechetti and J. Jinecke, Nucl . Phys. A261 (1976) 373 6) F. L. Milder, J. Jinecke and F. D. Becchetti, Nucl . Phys . A276 (1977) 72 7) H. H. Gutbroad, H. Yoshida and R. Bock, Nucl . Phys. A165 (1971) 240 8) G. Audi, C. Detraz, M . Langevin and F. Pougheon, Nucl. Phys . A237 (1975) 300 9) J. R. Comfort, W. J. Braithwaite, J . R. Duray, H . T. Fortune, W. J. Courtney and H. G. Bingham, Phys. Lett . 40B (1972) 456 10) G. D. Gunn, R. N. Boyd, N. Anantaraman, D. Shapira, J. Toke and H. E. Gove, Nucl. Phys. A275 (1977) 524 ; N. Anantaraman, H. E. Gove,-J. Toke and J. P. Draayer, Nucl . Phys . A279 (1977) 474 11) O. Yu . Gorgunov, V. N. Dobri Kov, O. F. Nemets, E. P. Reuk and A. T. Rudchik, Sov. J. Nucl . Phys. 21 (1975) 1 12) t. 1. Dolinskii, V. V. Turovtsev and R. Yarmukhamedov, Sov. J. Nucl . Phys . 19 (1974) 514 13) R. L. McGrath, D. L. Hendrie, E. A. McClatchie, B. G. Harvey and J. Cerny, Phys . Lett . 34B (1971) 289 14) H. W. Fulbright, Nukleonika 22 (1977) 235 15) W. Oelert, A. Djaloeis, C. Mayer-B6ricke, P. Turek and S. Wiktor, Annual Report 1976, KFA-IKP 10/77(1977)16 16) P. D. Kunz, Zero-range DWBA code DWUCK, University of Colorado Boulder, unpublished 17) R. M. DeVries, Finite-range DWBA code LOLA, Phys. Rev. C8 (1973) 951 18) P. Nagel and R . D. Koshel, Phys . Rev. C14 (1976) 1667 19) J. D. Childs, W. W. Daehnick and M . J. Spisak, Phys. Rev. C10 (1974) 217 ; Report of Current. Research, University of Pittsburgh (1975-76) p. 55 20) F. Hinterberger, G. Mairle, U. Schmidt-Rohr, G. J . Wagner and P. Turek, Nucl . Phys . Al 11 (1968) 265 21) M. D. Cooper, W. F. Hornyak and P. G. Roos, Nucl . Phys. A218 (1974) 249 22) L. T. Chua, F. D. Becchetti, J. Jinecke and F. L. Milder, Nucl . Phys. A273 (1976) 243 23) P. Schumacher, N. Ueta, H. H. Duhm, K. I. Kubo and W. J. Klages, Nucl . Phys . A212 (1973) 573 24) M. Bedjidian, M. Chevalier, J. J. Crossiord, A. Guichard, M. Gusakow, J. R. Pizzi and C. Ruhla, Nucl. Phys . A189 (1972) 403 25) P. Martin, J. B. Viano, J. M. Loiseaux and Y. Le Chalony, Nucl . Phys. A212 (1973) 304 26) A. E. Ceballos, M. J. Erramuspe, A. M . J. Ferrero, M . J. Sametband, J. E. Testoni, D. R. Bbs and E. E. Maqueda, Nucl . Phys. A209 (1973) 617 27) U. Strohbusch, ,G. Bauer and W. W. Fulbright, Phys . Rev. I.ett . 34 (1975) 968 28) A. K. Jaim, J. Y. Grossiord, M. Chevallier, P. Gaillard, A. Guichard, A. Gusakow and J. R. Pizzi, Nucl . Phys . A216 (1973) 519 29) Yu . A. Kudegarov, I. V. Kurdyumov, V. G. Neudatchin and Yu . F. Smirnov, Nucl . Phys . A163 (1971) 316 30) M . F. Werby, M. B. Greenfield, K. W. Kemper, D. L. McShan and S. Edwards, Phys . Rev. C8 (1973) 106 31) K. H. Passler, Verhandlungen der Deutschen Phys . Gesellschaft 1/1973, D2 .5 (1973) 41 32) A. Van der Molen, Ph.D. thesis, The University of Michigan, 1975 (unpublished) and analyzed in ref. 's) 33) D. Kurath, Phys . Rev. C7 (1973) 1390 34) I. Rotter, Nucl . Phys . A204 (1973) 225 35) M. Ichirnura, A. Arima, E. (7 . Halbert and T. Terasawa, Nucl . Phys. A204 (1973) 225 36) J. M. Moss, D. H. Youngblood, U. M. Rozsa, D. R. Brown and J . D. Bronson, Phys . Rev. Lett. 37 (1976) 816 37) J. S. Dehesa, Ph .D . thesis, KFA-IKP (1977)

18 38) 39) 40) 41) 42) 43) 44) 45) 46)

W. OELERT et al . H. V. v. Geramb, private communication F. Ajzenberg-Selove, Nucl . Phys. A248 (1975) 59 A. van der Woude and R. J. de Meijer, Nucl . Phys. A258 (1976) 195 P. Turek, A. Kiss, C. Maher-B6ricke, M. Rogge and S. Wiktor, Annual Report 1976, KFA-IKP 10/77 (1977) 4 ; and to be published J. M. Lind, G. T. Garvey and R. E. Tribble, Nucl . Phys . A276 (1977) 25 F. L. Milder, J. Janecke and F. D. Becchetti, Nucl . Phys. A276 (1977) 72, and references therein O. Hansen, J. V. Maher, J. C. Vermeulen, L. W. Put, R. H. Siemssen and A. van der Woude, Nucl . Phys . A292 (1977) 253, and references therein K. Bethge, K. Meier-Ewert, K. Pfeiffer and R. Bock, Phys . Lett . 24B (1967) 663 Y. Kudo, Conf. on nuclear structure, Tokyo (1977), p. 566