The 9Be(α, 5Li)8Li(g.s.) reaction

Nucleur

Physics

A352 ( I981 ) 83 - 92; @

North-Holland

Publishing

Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

THE

9Be(a, sLi)8Li(g.s.)

Phwics

Department,

REACTION

l

N. E. DAVISON Cyclotron L&oratory,

University of Manitoba, R3 T 2.N2

Winnipeg, Manitoba.

Canada

and Institute

de Physique

GH.

lnstitut

Corpusculuire,

GREGOIRE,

de Fhysique

TH.

B-1348. Lourain-la-Neure. and K. GROTOWSKl

DELBAR

Corpusculuire.

Belgium

B- I.348. Lourain-la- Neure,

’ Belgium

and S. K. DATTA Cjclorron

Lohoruroq:

Ph~~.~icsDepartment,

L’nicersit), e/‘Munitoha, R.jT 2N2

Received 29 January (Revised Abstract:

The differential

their ground finite-range

cross section

Winnipeg.

Cunudu.

1980

16 June 1980)

for the ‘Be(z.

‘Li)“Li

reaction

leaving

states has been measured at 7 angles at an incident z-particle DWBA

Manitoba.

analysis has been performed

taking

‘Li

in

energy of 90 MeV.

both

*Li

and

A

into account the L = I nature of the ‘Li

wave function.

NUCLEAR

E

REACTION

%e(z.

I

‘Li), E = 90 MeV: measured o(E=, f&, ~(0,~~). DWBA analysis.

0,. &):

deduced

1. Introduction

Reactions producing unstable particles in the final state have been studied for some time ‘-8). but a number of important reactions, notably those producing sLi in the final state, have received little attention. An important reason for this is that the large breakup Q-value of “Li (approximately 2 MeV) causes the proton and a-particles to be emitted into large cones about the initial ‘Li direction in the laboratory frame of reference. The use of a-p coincidences to detect the production of ‘Li is thus quite ineffrcient and although the cross sections of these reactions l

Supported

in part by the National

Research Council

’ On leave from the Physics Department,

Jagellonian x3

of Canada. University.

Krakow,

Poland.

x4

X. E. Darison et al.

: YBr(z. ‘Li)RLilg..s.,

are expected to reach several mbisr [refs. 5. ‘)] for light target nuclei, the experimental effort required is considerable. To date, of those reactions yielding sLi in the final state, data are available only for the (2, sLi) reaction. Differential cross sections have been measured by Brown et al. ‘) for three angles on 4’JCa and one angle each for 90Zr and “‘Pb and by Saha et al. *) for 12C. Differential cross sections on the order of 2 mbisr were found. In many ways, the (2. 5He) reaction is similar to (3, 5Li). It has been studied for targets of “C, U, Rh and 208Pb at incident energies of 42 and 90 MeV but the only angular distribution ofwhich we are aware is that of Chenevert 2, which was subsequently studied by Pong and Austern “). The latter authors found that it was possible to describe adequately the shape of the 208Pb(r. 5He)207Pb angular distribution using a finite-range DWBA theory which took into account the L = 1 structure of the 5He wave function and the fact that 5He is unbound. Since ‘Li has a significantly shorter lifetime than has 5He. however. it is not apriori obvious that a DWBA description is also feasible for (r, “Li). It was one of the goals of the present study to determine whether a DWBA treatment is at all feasible. In the present paper, data are presented at seven angles for the 9Be(x, ‘LQ8Li reaction leaving both ‘Li and 5Li in their ground states. In light of the difficulties anticipated in using p-a coincidences, the reaction was identified as described in sects. 2 and 3, using coincidences between the recoil nucleus and the a-particle produced in the breakup of “Li. As one of the important requirements of this study was obtaining data over as large an angular range as possible, a light target was chosen so that the recoil nucleus would be sufficiently energetic to permit identilication at forward 5Li angles. From an experimental point of view, a 9Be target is quite suitable. On the other hand, previous analyses of “IIe and x induced reactions on 9Be have experienced difficulty in obtaining satisfactory DWBA tits to experimental data. This point is discussed further in sect. 4 where the results obtained in the present work are compared with those obtained in other single-nucleon transfer reactions using 9Be targets.

2. Experimental

data

The experiment was carried out using an r-particle beam extracted from the Louvain-la-Neuve cyclotron. The momentum analyzed beam had an energy spread estimated to be several tens of keV (much less than the resolution sought). Typical currents on target were on the order of 100 nA limited primarily by the requirement that total deadtime not exceed 15 7”. The target consisted of a self-supporting beryllium foil of thickness I .O mg/cm2. A novelty of the present measurement lies in the fact that the reaction was identified on the basis of a-‘Li coincidences. Since the cone about the 5Li direction

N. E.. Davison ef al.

/)9Befs, ‘Li)‘Li/g.s.)

TABLE

Detector

85

I

characteristics Thickness

Telescope

Detector

alpha

AE E veto

500 2000 500

recoil

AE E veto

22 300 500

(pm)

into which a-particles are emitted is much smaller than that into which protons are emitted, the efficiency of coincident detection is greatly increased. It is possible to obtain coincident detection efficiencies of the order of 5 7: while still maintaining angular resolution of approximately ) lo. In addition, the 8Li direction determines the initial direction of the sLi within a small uncertainty due to the sLi mass spread. This greatly facilitates reduction of the data to a single differential cross section. Reaction products were detected and particle identification performed with AE- E telescopes using surface barrier detectors. Table 1 shows the characteristics of the detection system. In all cases, the cc-telescope was placed at the angle at which the 5Li would emerge in coincidence with a 8Li particle emitted toward the recoil telescope. Consequently, those a-particles were detected that were emitted close to parallel or antiparallel to the initial ‘Li direction. Data were recorded event by event on magnetic tape for subsequent off-line processing. During the experiment, no particle identification requirements were imposed so that many “uninteresting” events principally a-a coincidences were also recorded. Dead-time corrections were made by feeding a pulser signal into a scaler as well as into the test inputs of the AE and E detectors in each telescope at the rate of one count per second. Pileup events were detected and counted in scalers; corrections for pileup were found to be unimportant.

3. Results 3.1. EXPERIMENTAL

COINCIDENCE

SPECTRA

In the raw data a true to random coincidence ratio of approximately 5 to 1 was obtained. The majority of the random events were found to be due to a-a coincidences and when the requirement of an a-Li coincidence was imposed, the number of random events ivas found to be less than 1 ‘A of the true coincidences. Since 5Li has a very short lifetime, it usually decays while still at a high electrostatic potential with respect to the recoil nucleus. As the a-particle has a lower

h’. E. Duckon

X6

et ul.

9Bc~l~, sLi,RLi(g.,s.

j

charge-to-mass ratio than does the 5Li, its energy, observed far from the recoil nucleus, is lower than it would be if the decay had occurred at low potential. This energy shift is expected to be on the order of 500 keV or less depending on the sep aration of the ‘Li and ‘Li when 5Li decays and has not been taken into account in the calculation of kinematics or the efficiency of coincident detection as described below. The particle identification resolution in the recoil telescope was insufficient to obtain clean separation of events producing lithium ions of masses 6, 7 and 8, and it was therefore necessary to rely on kinematics to achieve this separation. Fig. 1 shows a two-dimensional representation of experimental data for the case 0, = 37.5O, 0, = 59.5” (lab) (subscript “r” signifying “recoil”) as well as projections of the COUNTS

'Be+a

E,

(MeV)

Fig. I. Experimental spectra for “Be+2 at I?~ = 90 MeV with spectra projected onto the a-particle energy (E,) and recoil energy (E,) axes. The projected Emspectrum used only data between the two arrows on the right side of the two dimensional spectrum so as to emphasize the (2. sLi) events. Loci are shown for the ‘Be(a, 21). ‘Beta, ad) and “Be(z, ap) reactions to the ground state of the residual nuclei and for the “Be(a, cm) reactions leading to the sBe states at excitation projected

Em spectrum. (a, ‘Li)

arrows

indicate

energies of 17.64 and I II. IS MeV.

the limits used in summing

On the

the two peaks corresponding

events, and the solid line shows the assumed background.

to

N. E. Darison et al. / 9Be(x, 5LiisLilg.s.)

87

data onto the E, and E, axes. Kinematic loci for the 9Be(a, crt), ‘Be(r, Id). 9Be(r. rp) and ‘Be(a, an)8Be reactions are also shown. No evidence for the ‘Be(r. xt)(‘Li reaction was found and the ‘Be(a, ad)‘Li reaction was weak except in the kinematic region where the (to, ad) reaction passes through the 6Li nucleus in its unstable 4.3 MeV state. This state gave an enhancement on the (a, ad) locus which served to verify the energy calibrations of the a and recoil telescopes. The 9Be(a, ‘He)‘Be reaction is also a possible contaminant. Although the Qvalue of the ‘Be(cc, 5He)sBe(g.s.) reaction is 16.2 MeV higher than is that of ‘Be(a, ‘Li)‘Li(g.s.), ‘Be has states at 17.64 and 18.15 MeV which have strong y-decay branches to the ground state of 8Be. The kinematics of the (a, 5He) reactions leading to these states are thus similar to the (a, 5Li) kinematics. In addition, the ‘Be d E- E particle identification locus is similar to that of ‘Li when both a-particles from ‘Be are detected in the recoil telescope. The efficiency of detecting ‘Be recoils was low in this experiment because the 94 keV breakup energy caused the a-particles to be emitted into a cone of approximately 5 msr while the recoil detector telescope subtended only about 0.3 msr. However, the relative cross sections of the (a, ‘Li) and the (a, 5He) reactions are not known, and hence the (a, ‘He) reaction cannot a priori be excluded. The (a, 5He) reactions can, however, be eliminated on the basis of three body kinematics. As shown in fig. I, the enhancements supposedly due to the (a, 5Li) reaction have a large spread in E, due mainly to energy loss in the target. One thus expects the more energetic recoils to coincide with the (a, ap) locus as is observed. The energies of the more energetic recoils (- 17 MeV) also agree well with the energy range expected for ‘Li nuclei produced in a two body ‘Li + ‘Li final state. On the other hand, the observed enhancements are some 3 MeV too energetic to agree with the (a, an) locus. The region within the (a, ap) locus is nearly filled by events possibly due to reactions involving the broad first excited J” = $- state of 5Li or to (a, ad) reactions populating various states in ‘Li. A weak enhancement was seen at some angles in the kinematic region where the first excited state of ‘Li(J” = I+, E, = 0.98 MeV) is expected. This enhancement, however, rests on a strong background and no attempt was made to extract an angular distribution for the excited state of ‘Li. 3.2. ANGULAR

DISTRIBUTION

FOR ‘Be(a, ‘Li)‘Li

In order to convert the observed number of a-particles into a differential cross section for the (a, ‘Li) reaction, it is necessary to know the efftciency for the coincident detection of the reaction products. This was calculated using a Monte Carlo program in which it was assumed that the 5Li broke up isotropically in its c.m. Overall efficiencies for detection were calculated to be on the order of 5 %. Reduction of the data to a single differential cross section in terms of the angle of emission of the 5Li was simplified by the fact that the direction of the *Li recoil nucleus defines, to within a small uncertainty due to the spread in the 5Li mass, the direction of emission of the 5Li.

xx

N. E. Davison et al.

I ‘Belr,

5Li]BLi(g.s.j

qBe(a,5Li)8Li(g

s.)

E,= 90 MeV

Fig. 2. Angular

distribution

for the ‘Be(r,

sLi)aLi(g.s.)

reaction.

All angles and solid ang!es refer to the

Initial direction of the sLi nucleus. The upper four curves represent the sum of differential

cross sections

calculated for the allowed angular momentum transfers. The solid line represents calculations carried out usmg thepotentialset(S,+S,); the heavydashedlinewith(M,+ M,,); thelight dashed linewith(D,+D,,), and dash-dot

line with (D,+D,,).

curves show the three differential the (D, + D,,,)

potential

are displaced downward

The curves are normalized

at the -

40” point.

cross sections for given angular momentum

set. These three curves are correctly

normalized

with respect to the data and other calculations

The lower

three

transfers (l) obtained with

with respect to each other, but so as to avoid confusing

the

diagram.

The differential cross section angular distribution for the “Be(r, “Li)‘Li reaction leaving both ‘Li and ‘Li in their ground states is shown in fig. 2. The curves represent DWBA fits obtained with the potentials listed in table 2 and discussed below. All calculations were carried out using the finite-range DWBA code LOLA lo) and simplifying assumptions also discussed below. The errors on the cross sections are on the order of IO ‘4 of which approximately 8 Y0comes from statistical uncertainty and background subtraction. The remaining error is primarily due to an assumed 5 % uncertainty in the Monte Carlo calculation of detection efficiency. Although the number of events calculated far exceed that reflected by a 5 % uncertainty, the lack of explicit justification for the-assumption of isotropic breakup of the ‘Li prompted the addition of an uncertainty in excess of that based on statistical considerations alone. Uncertainties in current integration, dead-time corrections, pileup, solid angles and target thickness were small compared to the two errors

N. E. Davison et al. / ‘Be(a,

89

5Li)aLi(g.s.)

TABLE 2 Potential

Normalization

set

0.25 0.60 1.05 1.20

%+% Mm+& J’,+J’,, D,+%

mentioned above. Taken together they amount to less than 3 %. All errors were added in quadrature to obtain the errors shown in fig. 2.

4. Analysis and discussion The analysis has been performed using the finite-range computer program LOLA lo). It was assumed that a pt proton in 9Be was picked up to leave ‘Li. Although pickup from other levels is not excluded especially as 9Be is deformed, the p+ level is expected to dominate or at least to be of major importance. Since ‘Li is an unstable particle of short half-life, one should in principle integrate over the relative momenta of the proton and cc-particle that constitute the 5Li. In addition, calculation of the DWBA form factor 4, 5’9, ii 3I’) should include a generalized density-of-states function dependent on the range of the p-a interaction, the p-cl phase shifts and the relative momenta of the proton and a-particle. This procedure is essential if the normalization of the calculated cross sections is to be correct. In the preliminary analysis presented here, however, the 5Li has been treated as slightly bound and the parameters of the binding potential adjusted so as to yield a wave function matching closely the wave function of 5He used by Pong and Austern in their analysis ‘) of *O’Pb(a, ‘He)*“Pb. This procedure is expected to yield approximately the correct shape for the angular distribution, but the absolute normalization will be inaccurate. All calculations have therefore been adjusted to the experimental data at Q,.,, z 40”. As the relative normalizations may, however, be of interest, table 2 gives the multiplicative factors applied to each calculated angular distribution shown in fig. 2. The optical potentials listed in table 3 were obtained in the following manner. The cc-particle potential M, was calculated by fitting 9Be(a, a), E, = 89 MeV data using the optical-model code SEEK, These data and the optical-model fits will be published elsewhere. A well depth in the vicinity of 90 MeV was chosen because of similarity to the best potential obtained by DeVries i3) for ‘Be(cr, c(), E, = 104 MeV. A 5Li potential was subsequently generated from the a-potential by increasing the real central well depth by 25 % and leaving all the other parameters unchanged. These parameters are shown in table 3 as potential M,.

90

N. E. Ducison z/ ul.

, qBelz, ‘Li/“Liig..s.,

TADLE 3 Optical

Particle

Potential

potentials ‘)

V

W

(MN

s,

a

‘Li

P+l p+‘Li

(MeV)

- 50.0

1.55

0.48

_

(tz,

_

(;I$

_ _

_.

R, (fm)

_

- 27.0

1.55

0.48

1.25

M,

-x9.5

1.34

0.69

- 37.9

1.20

0.97

1.25

D,

- 207. I

1.55

0.48

- 27.0

1.55

0.4R

1.25

- 55.0

1.60

0.50

- 32.0

1.60

0.50

I .25

MI.

-111.8

1.34

0.69

- 37.9

1.20

0.97

I.25

D 1.1 D 1.1

- 250.0 - 250.0

1.60 I.60

0.50 o.so

- 32.0 - 64.0

1.60 I.60

0.50 0.50

I.25 I.25

S,

- 0.20 h)

I .43

0.15

- 16.89 h,

1.20

0.50

‘) The optical model potential

was of the form:

(j(r)

= Vf(r. rO. a,) + iW/(r.

r&Q+.) + V,.,“,.

where /(r. r,. 0,) is a Woods-Saxon volume form factor with the usual notations and Vcnu, is the Coulomb potential for a spherical charge distribution of radius RCA’ ‘.

h, Binding energy. The DWBA

program calculates a well depth V so as to reproduce the binding energ).

Several other potentials were also generated on the basis of the “C(p, z)~B study by Li and Hird 14). The potential D, is taken directly from that work. A shallow a-particle potential S, was generated by simply reducing the real central potential to 50 MeV while keeping the other parameters fixed. The potential Dt., was generated by increasing the real central potential of D, by roughly 25 ‘$,, and rounding off the geometric parameters. Potential DLz differs from D,, by having twice the absorptive well depth. This potential was included since 5Li may be envisaged as a very fragile particle and one might anticipate a large probability of breakup as it emerges from the nucleus. Finally, a shallow ‘Li potential S, was generated by arbitrarily taking a 55 McV well depth. Only the potentials M, and D, are based on experimental data. and for 5Li, only M,, and D,, have been generated by a reasonably simple algorithm. A comparison of angular distributions obtained with the potentials of table 2 should thus indicate the extent to which simple algorithms allow one to obtain potentials that are significantly better than those obtained by arbitrary means. In fig. 2, the calculated DWBA cross sections are compared with experimental data. The potential set (Sz+S,,) yields a quite satisfactory fit to the data. Calculations using the sets (D, + D,, ,) and (D, + D,,2) also reproduce the data reasonably well. On the other hand, calculations using medium potentials for both the a-particle and “Li (M,+ ML) yield a cross section that is apparently too large at large angles. It is interesting that the angular distributions arc almost devoid of structure. Finite range calculations generally have non-zero amplitudes for more than one

‘V. E. fkll~i.W~l c/ ol.

QErl 1. ‘Lii “Li/q.s.,

91

angular momentum transfer. and these amplitudes add incoherently in the absence of spin-orbit coupling potentials. As has been observed in finite-range calculations elsewhere I’), the angular distributions calculated taking only one angular momentum transfer into account at a time show marked oscillatory structure. However. the even and odd /-transfer cross sections are almost exactly out of phase so that the summed angular distributions show little structure. The separate angular distributions for each angular momentum transfer are shown in the lower portion of fig. 2 for the (D,+ D,,) potential set. Although the present calculations reproduce the experimental data reasonably well. it must be pointed out that this could be fortuitous. Since the ‘Li has a very short lifetime, a significant fraction of the ‘Li nuclei may decay before leaving the tail of the nuclear matter distribution. Although part of this effect can be taken into account by deepening the absorptive potential for the ‘Li, rescattering processes may well be important. Some information on this point might be obtained by measuring the shift of the mean r-particle energy from that expected if the ‘Li decayed at a large distance from the residual nucleus. Since the energy shift is related to the distance from the recoil nucleus at u.hich decay. occurred. such a measurement might indicate whether the decay took place in a region of appreciable nuclear density. In the present experiment this measurement was not practical because.of the low charge of the ‘Li recoil nucleus. In addition, it should be noted that the DWBA has tended to yield rather poor fits to data for “He and r induced single-nucleon transfer reactions on ‘Be. For the 9Be(3He. d) reaction. EIHc = 33 MeV [ref. I)] tits to the differential cross section angular distributions were satisfactory. but the calculated analyzing powers bore little resemblance to the data. In the case of the ‘Be(‘He. 2) reaction I). also at 33 MeV, the tits to both the differential cross section and analyzing power data were poor. The average slopes of the differential cross section angular distributions were generally reproduced in the latter reaction. but oscillatory structure was not. in the present case of ‘Be(r. 5Li). the angular distribution is structureless. and, therefore, the fact that a reasonable fit was obtained may not be an indication that the DWBA theory is adequate. In the case of the “Be(x. t) reaction at E, = 27 MeV [ref. Ih)] the differential cross section angular distributions were in general poorly fitted. the difficulty being ascribed partly to the complexity of, the “Be target and partly to the assumption that the reaction is describable by a simple one-step DWBA calculation. In order to assess whether the apparently satisfactory tits obtained in the present work are indeed real, more rigorous calculations must be performed. in particular, to calculate the absolute magnitude of the cross section. These calculations are in progress.

N. E. Davison er 01. /I ‘Be(z, ‘Li,“Li/g.s.)

5. Summary

and conclusions

An angular distribution has been obtained for the ‘Be(a, 5Li)*Li reaction leaving both ‘Li and 5Li in their ground states. The angular distribution is reproduced by finite-range distorted wave calculations, but in the present case the normalization of the calculations is not obtained due to simplifications employed in the analysis. Within the context of the present preliminary analysis, the magnitudes of the cross sections are sensitive to the optical potentials chosen, but until more detailed calculations are carried out, the significance of this sensitivity is difficult to evaluate. Calculations taking into account the correct normalization of the unbound ‘Li particle are in progress and will be reported in due course. Two of the authors (N.E.D. and K.G.) wish to acknowledge the hospitality of le Laboratoire du Cyclotron where this work was carried out and to thank the cyclotron and computer personnel for their considerable efforts to ensure that this work could be completed in the time available.

References

I) 9. L. Cohen, E. C. May. T. M. O’Keefeand C. L. Fink, Phys. Rev. 179 (1969) 962 2) G. M. Chenevert. N. S. Chant, I. Halpem, C. Glashausser and D. L. Hendrie, Phys. Rev. Lett. 27 (1971) 434 3) C. Pirart, M. Bosman, P. Leleux, P. C. Macq and J. P. Meulders, Phys. Rev. Cl0 (1974) 651 4) D. R. Brown. I. Halpem, J. R. Calarco, P. A. Russo, D. L. Hendrie and H. Homeyer, Phys. Rev. Cl4 (1976) 896 5) U. Janetzki, Q. K. K. Liu, D. Hahn, H. Homeyer and J. Scheer, Nucl. Phys. A267 (1976) 285 6) P. D. Kunz, A. Saha and H. T. Fortune, Phys. Rev. Lett. 43 (1979) 341 7) D. R. Brown. J. M. Moss, C. M. Rozsa, D. H. Youngblood and J. D. Bronson, Nucl. Phys. A313 (1979) I.57 8) A. Saha, R. Kamermans, J. van Driel and H. P. Morsch, Phys. Lett. 79B (1978) 363 9) W. S. Pong and N. Austem, Nucl. Phys. A221 (1974) 221 IO) R. M. DeVries, University of Rochester (1974). unpublished I I) R. M. DeVries, Phys. Rev. CIJ (1973) 951 12) N. Austem, R. M. Drisko, E. C. Halbert and G. R. Satchler, Phys. Rev. 133 (1964) B3 13) R. M. DeVries. J.-L. Perrenoud, I. Slaus and J. W. Sunier, Nucl. Phys. Al78 (1972) 424 14) T. Y. Li and 9. Hird, Phys. Rev. 174 (1968) II30 IS) 0. Karban, A. K. Basak, J. 9. A. England, G. C. Morrison, J. M. Nelson. S. Roman and G. G. Shute, Nucl. Phys. A269 (1976) 312 16) K. W. Kemper, S. Cotanch, G. E. Moore, A. W. Obst, R. J. Puigh and R. L. White, Nucl. Phys. A222 (1974) 173