Physics Letters B 527 (2002) 187–192

www.elsevier.com/locate/npe

Strong coupled-channel effects in the barrier distributionsof 16,18O+ 58Ni

R.F. Simões1, D.S. Monteiro, L.K. Ono, A.M. Jacob, J.M.B. Shorto,N. Added, E. Crema

Instituto de Fisica DA, Departamento de Fisica Nuclear, Universidade de São Paulo, 05508-900 São Paulo, Brazil

Received 15 October 2001; received in revised form 3 December 2001; accepted 21 December 2001

Editor: V. Metag

Abstract

Quasi-elastic barrier distributions for the16,18O + 58Ni systems have been deduced from high precision measurements oftheir quasi-elastic excitation functions. The distribution obtained with this method for16O+58Ni is in complete agreement withthat deduced from fusion measurements. Contrary to present beliefs, these light systems present complex barrier distributionsthat reveal important couplings of inelastic and transfer channels to fusion. Coupled channel calculations are in good agreementwith our experimental data. 2002 Elsevier Science B.V. All rights reserved.

Keywords: Nuclear reactions;58Ni(16O, X), E = 30–50 MeV;58Ni(18O, X), E = 30–50 MeV; Measured large-angle elastic and inelasticscattering; Measured large-angle transfer reactions; Fusion barrier distributions

A remarkable characteristic of heavy ion reactionsat energies near the Coulomb barrier is the strongcoupling that sometimes occurs between the intrin-sic degrees of freedom and the relative motion. Con-sequently, fusion dynamics can be strongly affectedby intrinsic excitation of the interacting nuclei or nu-cleon transfer between them, with consequent largeenhancement of the fusion cross section [1–4]. Inother words, complex fusion barrier distributions canbe generated. Rowley, Satchler and Stelson [5] pro-posed an elegant and precise method to disclose thechannels which are responsible for the fusion cross

E-mail address: edilson.crema@dfn.if.usp.br (E. Crema).1 The work presented here is part of the PhD-project of

R.F. Simões and was supported by FAPESP.

section enhancement. It is a question of measuringthe fusion barrier distribution, which is extracted di-rectly from the experimental fusion excitation func-tion by Dfus ≡ d2[Eσfus(E)]/dE2 [6–12]. Since theinelastic barrier widths are proportional toZ1Z2βR,we expect that only heavy systems will present in-elastic (rotational or vibrational) couplings as isolatedpeaks in their fusion barrier distribution. In fact, allavailable experimental data have confirmed this pre-diction [13]. However, for lack of experimental data,the ability of Dfus to reveal the influence of transferchannels on the fusion of light systems is unknown.Recently, it has been proposed that the experimen-tal quasi-elastic excitation function can also providea barrier distribution when submitted to the opera-tion Dqe = −d[σqe(E)/σruth(E)]/dE, which shouldbe equivalent toDfus [14,15]. Since then, there have

0370-2693/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved.PII: S0370-2693(02)01171-1

188 R.F. Simões et al. / Physics Letters B 527 (2002) 187–192

been studies dedicated to a comparison of the barriersobtained with these two methods [15–17]. Their re-sults reveal that, in fact, the two distributions are iden-tical for those systems without strong coupling of thereaction channel to the fusion channel. On the otherhand, when a target or projectile excitation producesa peak in the barrier distribution, it is more evident inDfus than inDqe. Up to now, only heavy systems havebeen the object of these comparative studies. Thereare no experimental data available for light systems(Z1Z2 ≈ 224), mainly in those cases for which thetransfer channel is strongly coupled to fusion.

In order to study the effect of transfer channels onlight system fusion we have compared the fusion bar-rier distributions of16,18O + 58Ni. A high precisionquasi-elastic excitation function has been measuredfor each system atθlab = 161◦. As all transfer chan-nels in16O + 58Ni have large negativeQ-values, weexpected that fusion at energies near the Coulomb bar-rier should be weakly influenced by transfer couplingsand that the mean barrier should be a good referencefor the calculation with a one-dimensional barrier pen-etration model (BPM). On the other hand, the one andtwo neutron stripping in the18O + 58Ni system haveQ1n = +0.956 MeV andQ2n = +8.20 MeV. If bothprocesses were to produce barriers in the distribution,the large difference of theirQ-values would allow usto distinguish them. The comparison of these differ-ent neutron transfers would be an opportunity for dis-cussing the still open question: is multi-neutron trans-fer a simultaneous or sequential process? Finally, sincethe fusion barrier distribution for16O + 58Ni was de-duced directly from the fusion excitation function byKeeley et al. [18], it would be of great interest to com-pare, for the first time,Dfus andDqe for a light system.

The experiment was carried out with16O and18Obeams from the 8 UD Pelletron Accelerator at theUniversidade de São Paulo. The accelerated beamshad energies in the range 30–48 MeV, with steps of0.5 MeV over most of the energy range, and intensi-ties in the range 10–100 pnA. A 90◦ analyzing mag-net defined the beam energy with an uncertainty of≈ 40 keV. Before taking data, the analyzing magnetwas properly recycled, and during the measurementsthe energy was decreased only. The self-supportingtarget was 80 µg/cm2 of isotopically enriched58Ni(99.9%). The identification of the scattered nuclei atθlab = 161◦ was extracted fromE–�E spectra, where

�E was provided by the energy loss in a gas propor-tional counter which was backed by a silicon surface-barrier detector measuring the residual energy of thedetected nuclei. The resolution inZ allowed the un-ambiguous identification ofZ = 6,7,8 present in thespectra. However, as expected in that case, the en-ergy resolution wasn’t sufficient to resolving the elas-tic scattering and inelastic scattering from the low-est excited states of the target. Three silicon surface-barrier detector, located at angles±30◦ and−45◦ withrespect to the beam direction, were used to monitor thebeam direction and for normalization purposes. Threequasi-elastic excitation functions were calculated withthe three monitors and their results coincide withinthe experimental uncertainties. The statistical uncer-tainties associated with the measurements are lessthan 1%, except at the highest energies (45–48 MeV)where they are≈ 3%.

In the data analysis, quasi-elastic scattering wasdefined as the sum of all elastic, inelastic and transferevents. When transfer processes were observed, theZ = 6 channel was always the most probable. Athigher energies,Z = 7 events are also present in the18O + 58Ni spectra. The inelastic excitations as wellas neutron transfer processes were not resolved inthe spectra, but they were included by summing thecounts in the residual energy range of−5 MeV and+8 MeV around the elastic peak. AllECM valueswere corrected by the centrifugal potential energyat 161◦ [15]. The measured quasi-elastic excitationfunctions are shown in Fig. 1(a), as a function ofECM/VB, whereVB is the height of the average barrierextracted from the barrier distribution. The valuesare 31.55 MeV for16O + 58Ni, and 30.75 MeV for18O + 58Ni. The distributions are similar for nearlythe entire energy range investigated, but there areimportant differences near and below the Coulombbarrier. This could be a sign that, at these energies,a larger quasi-elastic flux is deviated to fusion in the18O+ 58Ni system.

As usual, the experimental barrier distributionswere extracted using a point-difference approxima-tion, with energy steps of�Elab = 2.0 MeV, whichare shown in Fig. 1(b), where a barrier penetrationmodel calculation (BPM) for the system16O + 58Niis also plotted. This simple calculation is unable to ex-plain the data. As theoretically expected, the total ar-eas of both distributions are≈ 1. However, it is sur-

R.F. Simões et al. / Physics Letters B 527 (2002) 187–192 189

Fig. 1. (a) The measured excitation functions for quasi-elasticscattering atθlab = 161◦ relative to Rutherford scattering. Theerror bars shown correspond to the statistical uncertainties. (b) Thecorresponding experimental distributionsDqe(E). The dotted curveis a barrier penetration model calculation for the system16O+58Ni.

prising that such light systems present such differentbarrier distributions. While the low energy part of the16O + 58Ni distribution is well adjusted by BPM, the18O + 58Ni distribution is flattened below the meanpeak which is much less pronounced. This barrier dis-tribution is very similar to those of much heavier sys-tems,16O+ 186W for example [15]. In this latter case,the explanation was the large prolate deformation ofthe 186W nucleus. Obviously, this is not the case for58Ni and we must search for other kinds of couplings.

Another very interesting result comes from thequalitative comparison presented in Fig. 2, where ourdistributionDqe for 16O + 58Ni is exhibited togetherwith Dfus obtained by Keeley et al. [18] for the samesystem. This is the first time that this kind of compari-son is done for a light system. The agreement betweenthe two representations is impressive. All character-istics of Dfus can be equally identified inDqe, eventwo weak structures located at≈ 1 MeV and≈ 2 MeV

Fig. 2. Comparison of the experimental barrier distributions for16O + 58Ni deduced from fusion and quasi-elastic excitationfunctions. The fusion data were measured by Keeley et al. [18].

above the Coulomb barrier. The only discrepancy be-tween them is the amplitude of the structure located at≈ 5 MeV above the main barrier. Although this peakis more pronounced inDfus, it is not completely ab-sent inDqe, as in the16O + 144Sm case [14]. It hasbeen shown by ECIS as well as by the eigenchannelmodel calculations that the second peak inDfus is dueto couplings of the lowest octupole- and quadrupole-phonon states of144Sm. Nevertheless, these two the-oretical calculations predicted a second peak also inDqe, which was not confirmed by the data. In order tofit the experimental barrier distribution, it was neces-sary to include a surface imaginary potential for ab-sorbing the flow of the direct channels not directly in-cluded in the coupling matrix [15,19]. However, in oursystem16O+ 58Ni, the second peak inDqe is present.The error bars ofDfus make a more accurate compar-ison between their amplitudes difficult. The remark-able agreement ofDfus andDqe over most of the en-ergy range investigated gives confidence in the analy-sis presented below and suggests that these two barrierrepresentations are more nearly equal in light systemsthan in heavy ones. It would be interesting to confirmthis hypothesis by measuring other light systems, be-causeDqe has the advantage of smaller errors at higherenergies.

190 R.F. Simões et al. / Physics Letters B 527 (2002) 187–192

In order to reveal the origin of the barriers observedin the experimental distributions, calculations havebeen done within the coupled-channels approach,using the CCFULL code [20]. This code employs theisocentrifugal approximation, uses the incoming waveboundary condition inside the barrier, takes account ofthe finite excitation energies of the coupled modes, andincludes the effects of inelastic nonlinear coupling toall orders. The program includes one transfer couplingbetween the ground states and uses the macroscopicform factor given byFtrans(r) ≡ Ft dVN/dr, whereFt is the coupling strength. The nuclear potentialused was a proximity potential prediction with smallvariations to fit the main peak of the distribution:V0 = 53 MeV; r0 = 1.29 fm and 1.28 fm; anda0 = 0.49 fm and 0.51 fm for16O + 58Ni and18O + 58Ni, respectively. They were deep enough toavoid reflection effects at the highest energies. Thecalculations for both systems with no couplings areshown in Figs. 3 and 4 by the thin lines. We havebegun calculating the influence of16O excitation onthe 16O + 58Ni distribution. In agreement with otherstudies [21], we found that in our system the couplingto the 3− octupolar vibration state of the16O producesonly an energy shift in the entire distribution withoutchanging its shape.

On the other hand, the target excitations are able togenerate new barriers in the distribution. Couplings tothe lowest vibrational states 2+ (1.454 MeV) and 3−(4.475 MeV) of58Ni generate the barrier distributionthat has the same shape as the experimental, except forthe second peak at 36 MeV, as shown by the dashedline in Fig. 3. It must be stressed that the 2+ stateplays the major role in this result. The deformationparameters used (β2 = 0.1828 andβ3 = 0.190) wereobtained from Refs. [22,23]. Several combinations ofexcited states of the target and projectile were triedbut the best fit was obtained including only the 2+and 3− vibrational couplings discussed above. Thenwe investigated the effect of some transfer couplingon barrier distributions. The best result was obtainedfor one α-particle stripping (Q = −3.792 MeV andFt = 0.28) coupled together with the lowest 2+vibrational state of the58Ni with the experimentalvalue β2 = 0.1828. The result is the excellent fitplotted with the full line in Fig. 3. The inclusionof the 3− state has little influence on this fit. Ourresult is consistent with our experimental data which

Fig. 3. The experimental barrier distributions for16O + 58Nideduced from quasi-elastic excitation functions. The curves are theresults of coupled-channel calculations (see the text).

Fig. 4. The experimental quasi-elastic excitation function for18O + 58Ni. The lines correspond to cc-calculations and are dis-cussed in the text.

present theα-particle stripping as the most probabledirect transfer. Besides, theFt value is consistent withtheoretical predictions [26].

R.F. Simões et al. / Physics Letters B 527 (2002) 187–192 191

Therefore, our result differs from the16O+ 144Smcase. In the16O+ 58Ni system, the equivalent theoret-ical calculation, including the same vibrational statesof the target and one transfer channel, does not pre-dict the amplitude of the second peak observed in theexperimentalDfus. On the contrary, the theoretical dis-tribution is very close to the experimentalDqe, as canbe seen in Fig. 2. Of course, the inevitable large er-ror bars ofDfus in the high energy region makes amore accurate comparison difficult, but it is impres-sive that in the light system the coupled-channel cal-culation reproduces quite well the quasi-elastic distri-bution. This could indicate that in light systems thedirect reaction channels not explicitly included in thecoupled-channel calculation do not produce an impor-tant reflected flux at energies above the Coulomb bar-rier. We have already measured other light systems andthey confirm this result [24].

Now, we turn our attention to the more complexbarrier distribution of the18O + 58Ni system, whichis very different from that of the neighboring system16O + 58Ni. The presence of two weakly bound neu-trons in the projectile (compared to16O) generated fu-sion barriers in the energy region below the Coulombbarrier and reduced the amplitude of the main peak.So, the obvious processes that we may invoke to ex-plain the data would be the coupling to one- and two-neutron transfer. We started with one-neutron transfer(Q = 0.956 MeV); the result of the coupled-channelcalculation withFt = 0.33 is the dotted line in Fig. 4.This Ft value is also consistent with Ref. [26]. Thecomparison with the bare barrier distribution showsthat this coupling alone has a strong influence on thefusion process. In addition, when one neutron strip-ping is coupled with the lowest 2+ vibrational exci-tation of 58Ni the quality of the fit is improved in thehigh energy part of the distribution as well as in itslower part. This can be seen by the full line in Fig. 4,which is the best fit that we have achieved with one-neutron transfer. We were unable to fit the data by in-cluding the projectile vibrations.

Two-neutron transfer with its very largeQ-value(8.2 MeV), compared to the Coulomb barrier, is diffi-cult to be treated correctly in the calculation. Even so,we tried to fit the data with two-neutron transfer as thecoupled-channel in the calculation. A fit was achievedonly if the parameters of the bare potential are changedto unreasonable values, which do not fit the elastic ex-

citation function. Therefore, the fit obtained with two-neutron transfer is artificial and we must be aware ofthe ambiguities in the potential choices. So, within alllimitations of the calculation employed here, the reac-tion mechanisms that generate the barriers observed inthe experimental distribution of18O + 58Ni would beone-neutron stripping and the 2+ vibration of the tar-get. The lowest positiveQ-value transfer mechanismwould be more easily coupled to the fusion process inthis system, in other words the more adiabatic transferprocess would be an easy path to fusion of18O+ 58Niat sub-barrier energies. If this conclusion is correct, itwould be evidence for the possibility of a neutron-pairbreakup before fusion occurs. This would also indicatethat, in this case, sequential neutron transfer is a possi-ble reaction mechanism that could improve still morethe fit to the experimental barrier distribution at lowerenergies. Meanwhile, a more precise coupled channelcalculation is needed to confirm this result. This hy-pothesis is also supported by a precise coupled chan-nel calculation that was done by Rowley, Thompsonand Nagarajan [25] in order to decide between sequen-tial or simultaneous neutron transfer. The shape of thebarrier distribution in18O+ 58Ni is similar to that pre-dicted for sequential neutron transfer.

In conclusion, the precisely measured quasi-elasticexcitation function for the systems16,18O + 58Niproduced very different fusion barrier distributionswhich reveal important coupled-channels effects, de-spite their lowZ1Z2 values. The experimental barrierdistributions extracted from fusion and quasi-elasticmeasurements for the system16O+ 58Ni are very sim-ilar and, using a simplified coupled channel calcula-tion, a very good fit was obtained by coupling the low-est 2+ vibrational state of the58Ni and oneα-particlestripping. Finally, the more surprising results were thecomplex fusion barrier distribution obtained for the18O + 58Ni and its explanation by one neutron strip-ping coupled with the 2+ vibrational excitation of the58Ni. However, more precise calculations are need toconfirm these conclusions.

Acknowledgements

The authors wish to thank Dr. W.A. Seale and Dr.J.R. Lubian for useful discussions. This work is a partof the PhD Thesis of R.F. Simões, was supported by

192 R.F. Simões et al. / Physics Letters B 527 (2002) 187–192

the Fundação de Amparo à Pesquisa do Estado de SãoPaulo (FAPESP).

References

[1] W. Reisdorf, J. Phys. G 20 (1994) 1297.[2] M. Beckerman, Rep. Prog. Phys. 51 (1988) 1047.[3] S.G. Steadman, M.J. Rhoades-Brown, Annu. Rev. Nucl. Sci. 36

(1986) 649.[4] C.H. Dasso et al., Nucl. Phys. A 405 (1983) 381;

C.H. Dasso et al., Nucl. Phys. A 407 (1983) 221.[5] N. Rowley et al., Phys. Lett. B 254 (1991) 25.[6] J.X. Wei et al., Phys. Rev. Lett. 67 (1991) 3368.[7] R.C. Lemmon et al., Phys. Lett. B 316 (1993) 32.[8] J.R. Leigh et al., Phys. Rev. C 47 (1993) 437.[9] C.R. Morton et al., Phys. Rev. Lett. 72 (1994) 4074.

[10] C.R. Morton et al., Phys. Rev. C 52 (1995) 243.

[11] J.R. Leigh et al., Phys. Rev. C 52 (1995) 3151.[12] A.M. Stefanini et al., Phys. Rev. Lett. 74 (1995) 864.[13] M. Dasgupta et al., Nucl. Phys. A 630 (1998) 78c, and

references therein.[14] H. Timmers et al., Nucl. Phys. A 584 (1995) 190.[15] N. Rowley et al., Phys. Lett. B 373 (1996) 23.[16] H. Timmers et al., Nucl. Phys. A 633 (1998) 421;

H. Timmers et al., Phys. Lett. B 399 (1997) 35.[17] O.A. Capurro et al., Phys. Rev. C 61 (2000) 037603.[18] N. Keeley et al., Nucl. Phys. A 628 (1998) 1.[19] A.T. Krupa et al., Nucl. Phys. A 560 (1993) 845.[20] K. Hagino et al., Comput. Phys. Commun. 123 (1999) 143.[21] K. Hagino et al., Phys. Rev. Lett. 79 (1997) 2014.[22] J.K. Tuli, Nucl. Data Sheets 56 (1989) 683.[23] R. Spear, At. Data Nucl. Data Tables 42 (1989) 55.[24] E. Crema et al., to be published.[25] N. Rowley et al., Phys. Lett. B 282 (1992) 276.[26] C.H. Dasso, G. Pollarolo, Phys. Lett. B 155 (1985) 223.