Large-angle enhancements in the 16O(6Li, α)18F reaction at 48 MeV

Nuclear Physics A415 (1984) 114126 @ North-Holland Publishing Company

LARGE-ANGLE ENHANCEMENTS IN THE 160(‘jLi, a)“F REACTION AT 48 MeV J. COOK and L. C. DENNIS Department of Physics, Florida State University’, Tallahassee, Florida 32306, USA

K. W. KEMPER Department of Physics, Florida State University ‘, Tallahassee, Florida 32306, USA and Department of Nuclear Physics, IAS, The Australian National University, Canberra, Australia

T. R. OPHEL and A. F. ZELLER’ Department of Nuclear Physics, IAS, The Australian National University, Canberra, Australia

and C. F. MAGUIRE and Z. KUI** Departmeni of Physics and Astronomy, Vanderbilt Universily t, Nashville, Tennessee 37235, USA

Received 7 March 1983 (Revised 23 August 1983) Abstract: The elastic scattering of 6Li+‘60 at 48 MeV has been measured and fitted with an optical model calculation. Measurements have been made of the ‘60(6Li, a)‘*F reaction at 48 MeV populating the 1+ g.s., 3+ 0.927 MeV and 5+ 1.122 MeV states in “F. The data exhibit cross sections at large angles comparable to those at forward angles, and have been compared with exact finite-range DWBA calculations. Exchange contributions were included for the 1’ g.s. and were unable to account for the large-angle data. Calculated statistical compound nucleus cross sections were approximately a factor of 100 below the data. The same conclusions are reached for previously published data at 34 MeV.

E

NUCLEAR REACTIONS ‘60(6Li, 6Li), (6Li, a), E = 48 MeV; measured o(B). Finite-range DWBA analysis, including exchange.

+ Work supported in part by the National Science Foundation. ++ Work supported in part by the US Department of Energy. * Present address: National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA. ** Permanent address: Institute of Atomic Energy, Beijing, China. 114

J. Cook et al. 1 Large-angle

enhancements

115

1. Introduction For incident energies around 34 MeV, it has been shown I- 3, that the (6Li, a) reaction on lp-shell target nuclei produces back-angle cross sections (0 = 160”-170“) that are as large as those at forward angles. In early studies “) of the (6Li, a) reaction on i2C, large back-angle cross sections were reported for bombarding energies between 2 and 5.5 MeV. These enhanced back-angle cross sections were attributed to contributions from the “heavy-particle-stripping” mechanism. The interpretation of the low-energy data was made more difficult by the presence of resonance-like behavior thought 5, to arise from the resonant transfer of clusters between the target and projectile. Around 34 MeV, the excitation functions is2) for the (6Li, a) reaction do not exhibit large variations in cross section, so that resonant-cluster transfer is not an important contribution to the cross section. Selective population of final states is observed at large angles in the higher energy works ’ -3), thus ruling out statistical compound nuclear processes as the primary source of the enhanced cross sections. It was proposed 2, that exchange effects produce the enhanced large-angle cross sections at the higher energies also, and subsequent calculations 6, ‘) supported this conjecture. In the present work, a measurement of the 160(‘jLi, a)18F reaction at Q6Li) = 48 MeV is reported. The calculations of ref. 6, were repeated for this higher-energy data so that the relfability of the spectroscopic factors for the exchange process could be studied further. Elastic scattering measurements for 6Li+ I60 were carried out at 48 MeV to provide the optical model parameters necessary for the DWBA analysis.

2. Experimental procedure The 48 MeV ‘Li3+ beam used for this study was produced by the ANU 14 UD Pelletron tandem accelerator. The 6Li and a-particles were detected with a gas proportional counter *) after momentum analysis by an Enge split-pole spectrograph. The polar acceptance angle of the spectrograph was 0.7”. Initially aluminium oxide targets were used, but because of persistent rupture in the beam, they were later replaced with tungsten oxide targets. The oxygen content of the targets was determined by scattering 1.75 MeV He+ from them and assuming the elastic scattering to be Rutherford. The He+ beam was produced with the ANU 2 MV van de Graaff. The absolute error in the cross section is f 12 % with the principle contributions to the uncertainty being from the determination of the target thickness and target non-uniformity (- 8 %), detector solid angle (- 8 %), and charge integration (- 3 %).

116

J. Cook et al. / Large-angle enhancements

3. Elastic scattering Optical model parameters for 6Li+ I60 scattering have been determined earlier ‘) for a bombarding energy of 50.6 MeV. To make certain that no rapid change in the elastic scattering occurs in this energy range, 6Li+ I60 was measured at 48 MeV, the bombarding energy of the reaction study. An optical model analysis of the data, using standard volume Woods-Saxon potentials, was performed with starting values for the parameters of the potentials. Only slight adjustments to the parameters were necessary to get good tits to the data. The results show that no reasonably rapid changes in the elastic scattering occur in this energy range. The form of the potential interaction assumed is given in table 1 of ref. ‘). The potential parameters found here are listed at the bottom of table 1. The calculated elastic scattering angular distribution and the experimental data are given in fig. 1. TABLE 1 Optical model parameters Ref.

System

V 010 u

G ULio

ULio

34 MeV 48 MeV

191 191

0.946 0.946

0.540 0.540

33.0 33.0

0.946 0.946

0.520 0.520

0.778 0.778

11 11

194 223 198

1.60 0.703 0.773

0.600 0.800 0.700

15.0 11.8 20.8

1.87 1.17 0.964

0.500 1.04 1.02

1.60 0.755 0.813

? 12) present work

“) R, = r&if+&).

4. The 160(6Li, a)‘*F reaction The DWBA of nuclear reactions, in which both direct and exchange processes are included, has already been described elsewhere 6*‘, lo); only the essential features are reproduced here. The reaction A(a, b)B has a direct mode in which the outgoing clusber b has arisen entirely from the cluster a ; A+(a = b@x) --+(B = A@x)+b,

direct mode,

(1)

where a and B are the bound states, and x is transferred as a cluster from b to a. The largest exchange term is expected to be where b originates entirely in A ; (A = b@y)+a

+ (B = a@y)+b,

exchange mode.

(2)

J. Cook et al. / Large-angle enhancements

117

.*_I . lIY!!J ‘60(6Li.6Li)

‘“+-----l

IO0

cc

\bto-’ b

48MeV

.

G2

I O-3o

Fig. 1. Optical model tit to 6Li + I60 elastic scattering data at 48 MeV.

Here A and B are the bound states, and y is the transrerled cluster. The direct and exchange DWBA transition amplitudes are

Tl~l,“,,, =
r.AWa(rbxWA>~

(3)

The $‘s are elastic scattering distorted waves and the 4’s are bound state wave functions characterized by the quantum numbers nl. The differential cross section is given by the expression da -_= dSZ

1 PiPr kr (5@7~(2J,+1)(2JA+1)

where the p’s and k’s are the reduced masses and asymptotic wavenumbers respectively. SL, is a spectroscopic amplitude for cluster i with the bound-state

118

J. Cook et al. i Large-angle en~ncem~nts

quantum numbers nl, and is the square root of the corresponding spectroscopic factor. N is the number of nucleons in cluster b, and {v} denotes the set of magnetic quantum numbers of the four nuclei. For the ‘%t6Li, a)‘*F reaction, the direct mode and its corresponding transition amp~tude are r60+ (6Li = cr@d) + (iaF = r60@d)+ol, TD = (fJV,, + V,,-

The exchange mode and its corresponding (I60 = ‘2C@a)+6Li

(5)

U,,li).

(6)

transition amplitude are

+ (i*F = ‘zC@6Li)+ot,

(7)

TE = (f 1V,, + V,,i - U,,li’).

(8)

In eqs. (6) and (8), U,, is the optical potential which generates the final state distorted wave, V,, and V,, are potentials which give rise to the 6Li and 160 bound states, and V,, and VELi are core-core interactions. The potential parameters, bound state quantum numbers, and spectroscopic amplitudes used in this work are given in tables 1 and 2. At 34 MeV they are the same as those used in ref. “) although note that ‘*F = “C @ 6Li should have the quantum numbers 4s, 3d rather than Ss, 4d as in ref. 6). The only difference at 48 MeV is in the entrance channel optical potential ULio. Initially, DWBA calculations of the ‘60(6Li, u)i8F (1 + g.s.) reaction at 34 MeV were made, in an attempt to reproduce the calculations of ref. 6). Two independent TABLE

2

Bound-state parameters “) and spectroscopic amplitudes State

S

Ref.

(& 6Li = a@d (1 + g.s.) I60 = ‘*C@a(O+ g.s.) l*F = 160&ld (l+ g.s.)

(3+ 0.927 MeV) (5+ 1.122 MeV) ‘*F = ‘*C@6Li(l + g.s.)

2s Id 3s 2s 3s 2d 2d lg 4s 3d

1.47

1.05

0.65

0.8 0.2

131

7.53 7.16

1.29 1.20

0.65 0.60

15 14;

6.59 6.40 13.22

1.20

0.60

0.90 0.23 0.556 0.097 0.592 0.603 0.54 1.08

“) All bound-state parameters from ref. 6). bf R, = r&At+&; Coulomb radius & = R,.

?I

J. Cook et al. / Large-angle enhancements

16016Li ,a ) 18F

119

34 MeV

*_._.-.-_-*-.__ 30

60

e90tde;;0 cm.

150

180

Fig. 2. Finite-range DWBA calculations of the 160(6Li, a)‘sF (l+ p.s.) reaction at 34 MeV compared with the data of ref. ‘). The calculated cross seciions have been multiplied by 0.46 to tit the forwardangle data.

calculations were made using the computer programs NICOLE ’ 6, and DAISY ’ ‘), suitably modified to include the exchange processes and all three of the interaction terms in eqs. (6) and (8). Agreement between the programs, and also between the post and prior representations, was within about 5 %. The transition amplitudes calculated by these programs were stored on disc and then summed to produce the total differential cross sections in a program which would allow the spectroscopic amplitudes to be varied to fit the data. The results of such calculations are shown in fig. 2, compared with the 34 MeV data of ref. ‘). It is immediately noted that the exchange process is three orders of magnitude too small at large angles to reproduce the experimental cross section. This is in complete contrast to the calculations of ref. 6, where it is claimed that the exchange process accounts for the large cross sections at backward angles. However, the same overall normalization of 0.46 applied to the calculated cross sections to tit the forward-angle data was found. In order to try to resolve this discrepancy we have carefully examined the calculations. Goldfinger et al. 6, assumed that the bound state i*F = 12C @ 6Li had the quantum numbers 5s and 4d, while the Talmi-Moshinsky energy conservation relation gives 4s and 3d states. The different quantum numbers result in different shapes for the exchange contributions, but the magnitudes are roughly the same. Moore and Kemper *) used a different set of 6Li = CY@ d bound state parameters, which give similar results for the 6Li 2s state, but a significant weaker Id contribution. Thus different conclusions are drawn about the importance of the Id state, but this does not alter the observation that both the

J. Cook et al. 1 Large-angle enhancements

120

direct and exchange processes are too small at large angles. Because our initial calculations disagreed with those previously published, considerable checking has been done of the calculations presented here. The calculations were made by two independent groups at Florida State University and Vanderbilt University using different programs, which calculated the DWBA transition amplitudes by different methods, running on different computers, without communication of the results until after the calculations were completed. The excellent agreement between the programs, and between the post and prior representations, gives us confidence in the present results. We conclude, therefore, that there is an error in the calculations of ref. (j), possibly in the exchange-mode bound-state radii which would alter the magnitude of the exchange cross sections, and that exchange processes are not able to account for the observed cross sections at large angles. The same DWBA calculations were now made for the l+ g.s. at 48 MeV, and are compared with the data in fig. 3. To maintain consistency with the 34 MeV calculations, the same optical model parameters, bound-state potentials and spectroscopic amplitudes as before were used, except for the entrance channel where the 48 MeV optical potential found in sect. 3 was used. Although the 34 MeV 6Li + I60 optical of ref. “) does not fit the elastic scattering data at 48 MeV, it produces a very similar angular distribution for the (6Li, a) reaction, with the same normalization. It is found that the overall normalization is still 0.46, implying that the direct spectroscopic amplitudes for the ground state are not energy dependent. Also, as at 34 MeV, both the direct and exchange contributions are far too small at large angles compared with the data. DWBA calculations of the direct component only were also made for the 3+

‘“0(6Li.a)‘8F

48MeV 0.0 MeV

._

+*+‘,“H

Total ---- Direct -.-.- Exchange

/.-~‘~’

, ,-6 I”

0

30

---‘--.-. I

60

-i._.. I

.C._

._,__

J...

1 I

-90 120C&-,.@ed

,

/

‘\

150

.‘.

i

180

Fig. 3. Comparison of data for the 160(6Li,~) “F (l+ gs.) reaction at 48 MeV with finite-range l... n “L ,- c+ ll.- C^_..“..A--“IDWBA calculations. I-L- mlr..ln*~~ ,...,.^” i,%,.&...”h,...- _” . ....1t...x.%rl

121

J. Cook et al. / Large-angle en~an~e~nts

105~ 0 30

60

90 120 O,.m.(deg.)

150

18.0

Fig. 4. Comparison of data for the ‘60(6Li , a)‘*F reaction at 48 MeV with tinite-range DWBA calculations. The calculated cross sections have been multipli~ by 0.18 and 0.15 to tit the forward-angle 3+ 0.927 MeV and 5+ 1.122 MeV data, respectively.

0.927 MeV and 5” 1.122 MeV states. The calculations are compared with the data in fig. 4, and are two or three orders of magnitude too small at large angles. The normalizations required to fit the forward-angle data were 0.18 and 0.15, respectively. These are consistent with the finite-range calculations of ref. *) at 34 MeV where it was found that the normalizations for the 3+ and 5+ states were about 3 of that for the 1+ ground state. Using the 6Li bound state parameters of table 2 produces a d-state contribution which is of similar magnitude to the s-state contribution at forward angles. When Moore and Kemper’s 2, parameters are used for the 6Li bound state, the d-state contribution is much smaller and results in improved fits to all three states for 9c.m. 5 30°. The absolute normalizations with these parameters are smaller by nearly a factor of two compared with those above, but the relative normalizations are consistent. Direct DWBA calculations for the ground state have also been made using different 6Li and CI optical potentials but these produce little change in the magnitude and shape of the large-angle cross sections. The intermediate-angle cross sections are, however, sensitive to the choice of optical potentials. The bound-state wave functions were obtained from a Woods-Saxon well, and this is

122

J. Cook et al. / Large-angle enhancements

clearly a simplification, in particular for the light nuclei in question. The form factor Fad(r) (which may be thought of as the product Vord(r)4,&r)) for 6Li + a + d has been calculated on a microscopic basis using a properly antisymmetrised cluster wave function and a realistic nucleon-nucleon force and has been shown to provide a good description of the (6Li, d) and (d, 6Li) reactions “). However, use of this microscopic form factor does not increase the magnitude of the large-angle (6Li, a) cross sections. 5. Statistical

model calculations

In light of the inability of the DWBA calculations to reproduce the backwardangle data for the ‘60(6Li a)‘sF reaction it is important to determine if statistical compound-nucleus calculations can reproduce the data. The statistical model calculations reported here were carried out using the computer code HELGA i9). Details of the method of calculation and the choosing of parameters for Li-induced reactions can be found in refs. “,‘i ). As can be seen in figs. 5 and 6 the calculated cross sections are significantly lower than the experimental data at both 34 and 48 MeV and for all the levels shown. Naively one can postulate two possible explanations for the observed difference in calculated and measured cross sections: (i) the parameters used in the compound-nucleus calculations were not chosen properly, and (ii) there is some mechanism present other than compound nuclear decay which contributes strongly to the observed cross section. As with all statistical model calculations there are three sets of parameters that can -affect the magnitude of the calculated cross sections; they include (i) the entrance and exit channel transmission coefftcients; (ii) the level density parameters, and (iii) the compound-nucleus formation cross section. Fortunately experimental information is available to help in the determination of these parameters. Level density parameters can be calculated from the known level schemes 21), transmission coefficients can be obtained from optical model analyses bf elastic scattering and the compound-nucleus formation cross section can be inferred from measured fusion cross sections. Such methods have been applied previously to determine the parameters for statistical model codes and have given good results for Li-induced reactions 20*21). Some of the parameters used for the 160(6Li, a)“F reaction are shown in table 3. All of the parameters, except the level density parameters for the 19Ne and 21Na residual nuclei, have been used in the 6Li + “C, 6Li + ’ 3C, ‘Li + “C, 7Li + 13C or 7Li + 160 reactions with good results. For the 6Li+ 160 reaction the fusion cross section has not been measured. Reasonable estimates of the fusion cross section can be made using a Glass and Mosel parameterization 23) with the parameters suggested by Kovar et al. 24) or the parameters determined for the 6Li + “C and 6Li + 13C reactions. 25) Both Kovar’s 24) parameters and the parameters of ref. 25) yield fusion cross sections of 800 mb+50 mb at both 34 and 48 MeV.

I23

160( ?_i.cr)

‘*F

34MeV

_ .

-5 1; icT4E - IO0 g *-.

t

‘60(6Li.~) 18F 48MeV *- .***. I+ O.OMeV t,tvtt

‘i; Id’ - ‘**.. -0

,62

(. +

. ..-

Id5 I

0

30

!

60

90

,

120

t

150

180

%ddeg.) Fig. 5. Comparison of the data for the ‘60(6Li,a)18F (l+ g.s.) reaction at 34 and 48 MeV with statistical model calculations. Details of the calculation are found in the text.

For the calculated cross sections shown in figs. 5 and 6 somewhat higher compound-nucleus cross sections of 850 mb and 875 mb were used at 34 and 48 MeV, respectively. This insured that the calculated cross sections were upper estimates of the actual cross sections (assuming all other parameters are fixed). When all of the required parameters are determined as described above the calculated statistical compound-nucleus cross sections are approximately a factor of 100 below the data. Since the most uncertain of the parameters is the fusion cross section, calculations were done for the 48 MeV data with the fusion cross section equal to the reaction cross section (N 1450 mb). With this fusion cross section the statistical model calculations were still too low by factors of 10, 8 and 2 for the 0.0, 0.927 and 1.12 MeV levels respectively. On the basis of these calculations we conclude that statistical compound nuclear decay is not the cause for the enhanced backward-angle cross sections.

J. Cook et al. / Large-angle enhancements

124

IO0

I

,()-I _-.

I

I

I

I

160(6Li,a)‘eF 48MeV,

e-**

3+ 0.927

’ ‘*’

-2_

l

MeV ”

*_

<’

lo-’ -r/-a lO-2

_

l

2.’

.*~V’..

.

.”

5+

-

.-c

1.122MeV

163‘ lo-4lo -5

I 60

I 30

0

1 90

I 120

I 150

180

%ded Fig. 6. Comparison

of the data for the 160(6Li , a) t*F (3+ 0.927 MeV) and (5+ 1.122 MeV) reactions 48 MeV with statistical model calculations.

TABLE

Optical

model and level density

3

parameters

used in statistical

Channel

‘60+6Li n+2’Na p+“Ne d+*‘Ne t+“Ne ‘He+“F a+‘sF sBe + r4N

model calculation

Type’)

210.0 48.0 47.20 117.0 152-0.17E 152-0.17E 121.0 7.50 + 0.4E

3.28 3.64 3.45 3.12 3.20 3.20 3.77 5.95

0.70 0.66 0.65 0.86 0.72 0.72 0.52 0.45

‘) Potentials were either Woods-Saxon b, Pairing energy. ‘) Level density.

25.0 9.6 7.5 189 41.7-033E 41.7-U.33E 17.5 0.4+0.125E

(volume)

4.28 3.49 3.45 3.64 3.74 3.74 3.77 5.95

or Woods-Saxon

0.90 0.47 0.70 0.68 0.88 0.88 0.52 0.45

d “) (MeV)

volume surface volume volume volume volume volume volume

derivative

(surface)

5.0 2.5 2.5 5.0 2.5 2.5 0.0 0.0

form.

(Mz?r)

1.89 2.96 3.00 2.76 3.15 3.20 2.82 2.03

at

J. Cook et al. / Large-angle enhancements 6.

125

Conclusions

Elastic scattering cross sections for 6Li+ 160 have been measured at 48 MeV and fitted with the optical model. Measurements have been made of the ‘60(6Li, a)‘*F reaction at 48 MeV and compared with finite-range DWBA calculations including exchange and statistical model calculations. At large angles the cross sections are of comparable magnitude to those at forward angles, and are about two orders of mag~tude greater than the direct contribution. The exchange process is too small to account for the large-angle cross sections both at 48 MeV and for reanalyzed 34 MeV data2), contrary to a previously published study6) where it was concluded that the exchange mechanism was responsible for the large cross sections at backward angles. The spectroscopic amplitudes for the direct calculations were found to be independent of energy. Furthermore, the statistical model calculations are about a factor of 100 smaller than the data. The authors wish to express their gratitude to Dr. C. S. Newton for his aid in the target thickness measurements and to Dr. P. J. A. Buttle for providing the exchange modi~cations to DAISY.

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J. Cook et al. / Large-angle enhancements

20) K. M. Abdo, L. C. Dennis, A. D. Frawley and K. W. Kemper, Nucl. Phys. A377 (1982) 281

21) 22) 23) 24)

L. C. Dennis, A. Roy, A. D. Frawley and K. W. Kemper, Nucl. Phys. A359 (1981) 455 A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43 (1965) 1446 D. Glas and U. Mosel, Nucl. Phys. A237 (1975) 429 D. G. Kovar, D. F. Geesaman, T. H. Braid, Y. Eisen, W. Henning, T. R. Ophel, M. Paul, K. E. Rehm, S. J. Sanders, P. Sperr, J. P. Schiffer, S. L. Tabor, S. Vigdor, B. Zeidman, and F. W. Prosser, Jr., Phys. Rev. C20 (1979) 1305 25) L. C. Dennis, K. M. Abdo, A. D. Frawley and K. W. Kemper, Phys. Rev. C26 (1982) 981