Alamanos, N

Lapoux, V

Pakou, A

Sida, J L

Trotta, M

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STUDY OF SUB-BARRIER AND NEAR- BARRIER FUSIONOF HALO NUCLEIN. ALAMANOS, J.L. SIDA, V. LAPOUXCEA/DSM/DAPNIA/SPhN, Saclay, 91191 Gif-sur-Yvette Cedex, FranceA. PAKOUDepartment of Physics, The University of Ioannina, 45110 Ioannina, GreeceM. TROTTAINFN, Laboratori Nationali di Legnaro, via Romea 4, I-35020 Legnaro, Padova,ItalyCoupled channel calculations were performed to investigate the near-barrier andsub-barrier fusion cross section of light unstable nuclei and their associate sta-ble isotopes. A microscopic optical potential was used to generate the entrancechannel potential. A rather satisfactory description of the experimental data wasobtained under the condition that the optical potential is reduced for the weaklybound systems. The analysis points out some complementarymeasurementswhichare necessary to obtain a better understanding of the sub-barrier fusion processinvolving light weakly bound systems.1 IntroductionSeveral experimental and theoretical studies concerning the fusion of two asym-metric nuclei under and near the coulomb barrier were performed in the past1.Most of the times the results were interpreted adequately well under the con-text of coupled channel calculations2. With the advent of radioactive beamfacilities, the interest on such studies was renewed, aiming to reveal the struc-ture and behaviour of halo nuclei3. Such nuclei present specic features likean extended neutron tail, low-lying dipole modes and very low energy thresh-olds for breakup. Fusion, as other reaction processes should be appreciablyaected by such features. In this letter we attempt to describe into the sameframework, near-barrier and sub-barrier fusion for both stable and halo nuclei.The rst measurements with halo nuclei were visualized through the sys-tems11Be+209Bi4,6He+209Bi5and6He+238U6.The data are presented in Fig.1 together with the data of the associatedstable isotopes9Be+209Bi4,4He+209Bi7and4He+238U6;8. Cross sectionsare presented as a function of the energy divided by the coulomb barrier, Vb.In the present case Vb's were extracted via the relations of Christensen andWinther and are shown in Table 1.The presentation of all the data in Fig.1 facilitates the extraction of the1σ fusion (mb)Ecm/Vb(MeV)4,6He+238U4,6He+209Bi9,11Be+209BiX 100X 10000Figure 1: Fusion measurements for the halo systems and their associated stable isotopesfollowing conclusions. For energies higher than the coulomb barrier the crosssections for the fusion of9;11Be and4;6He on209Bi and238U targets present thesame behaviour. That is the cross sections with halo projectiles are enhancedover the cross sections with the stable ones. On the other hand, no apparentenhancement is seen for the fusion of the6He over that of4He on209Bi targets.For lower energies than the coulomb barrier, the fusion cross section for thehalo nucleus6He on238U and209Bi targets is enhanced over that of4He, nosuch enhancement is observed for the fusion of the11Be on209Bi over that of9Be .Into this paper we will perform a consistent analysis of all the above sys-2Table 1: Coulomb heights according to A. Christensen and Winther B. The BDM3Y1 po-tential and C. The BDM3Y1 potential reduced by 40%.Vb(MeV)system A B C4He+238U 22.61 22.480.24He+209Bi 20.90 21.340.29Be+209Bi 39.95 38.440.2 39.920.26He+238U 22.14 19.510.2 20.370.26He+209Bi 20.47 18.180.2 19.10 0.211Be+209Bi 39.46 35.680.2 37.400.2tems and we will try to unreveal new aspects in physics that may emerge fromthese measurements.2 The analysisIt is known that, in general, coupled channel calculations can reproduce qual-itatively and several times quantitatively the fusion results. For the stablenuclei the main ingredients of the calculations, performed with the code ECIS9are the entrance channel potential and the structure of the colliding nuclei.The real potential is calculated within the double folding model11by usingthe BDM3Y1 interaction22. This interaction was found to describe ratherwell elastic scattering for both stable and unstable nuclei10;23. The imaginarypotential simulated the incoming wave boundary condition. The densities in-volved in the real double folded potential for the stable isotopes were obtainedfrom electron scattering data by adopting standard procedures11. For the ra-dioactive nuclei shell model densities12, and HF densities13were used for6Heand11Be correspondingly.The calculation for the system4He+238U has been performed within therotational model. Couplings to the rst excited states of238U were consideredwith deformations extracted from B(E2)'s reported previously14. In additionto our previous calculation6we have used now not only multipolarities with=2 but also with =4. The calculation for the system4He+209Bi includescoupling to the two excited levels of209Bi, E=0.896 MeV(=2) and E=1.608MeV (=3) with deformations reported in the compilation16. Finally forthe system9Be+209Bi, we have taken into account the excited state of9Be,E=2.430 MeV (=2). The B(E2) for the transition to this state, was obtained3σ fusion (mb)Ecm/Vb(MeV)4He+238U4He+209Bi9Be+209BiX 100X 10000Figure 2: Fusion cross section for stable nuclei.recently by Rudchik et al.17.The coulomb barriers and radii of the potentials are shown in Table 1. Itis obvious that potential heights of systems with radioactive nuclei present areduction of  3 MeV relatively to the heights of systems with their associatedstable isotopes. This is a well known eect, and a quantitative understand-ing has been achieved in terms of the halo structure18. The consequence ofa reduced height is the enhancement of the sub-barrier fusion cross sections,sometimes by several orders of magnitude. The results of the calculation forthe stable projectiles are shown in Fig.2 together with the same data which arepresented in Fig.1. The ts are adequately good, for both the4He+238U and44He+209Bi systems. We point out the additional data indicated in Fig.2 withsquares, obtained previously19. These data concern the 1n evaporation chan-nel of the reaction,209Bi(,n)212At. The addition of these points make thet excellent. On the other hand, the calculations for the system9Be +209Bi,overestimate highly the results. The same eect was reported before for thesystem9Bi+209Pb20and it can be well assigned to the coupling to the contin-uum. The nucleus9Be presents a very low threshold to one neutron emission(Sn=1.67 MeV). Elastic scattering of such nuclei with a weak binding energy,has been described by Satchler and Love11, into a microscopic description witha reduced potential than the one describing elastic scattering of stable nuclei.The eect was studied also by Sakuragi et al.21into a context of discretizedcoupled channel calculations and was attributed to the coupling to the contin-uum due to their weak binding energy. Moreover into a recent study by Tracheet al.23for elastic scattering of light elements including9Be, it was found thatthe description of9Be can be successfully done via a potential reduced by afactor of 40%. It has to be pointed out here that Trache et al.23have beenusing the microscopic potential BDM3Y1, which is used in the present work.Into this context, it is clear to us that two types of calculations can anticipatethe reduction of the potential height and describe sub-barrier and near-barrierfusion. The rst is the method of discretized coupled channel calculations21;24which is probably the most accurate method but which depends on severalparameters not known for each system. The second one involves a reducedreal potential, which is a local representation (not exact) of the discretizedcoupled channel calculation. It is obvious that the eect of the coupling tothe continuum may not be represented by a simple reduction of the entrancechannel potential but may also aect its shape27.Adopting the over simplied point of view that couplings to the continuumaect only the height of the potential and with the experience of the calcula-tion on the case of9Be we have proceeded with the analysis of the unstablesystems. The performed calculations with a standard potential (solid line) anda reduced one by 40% (dashed line) are presented in Fig.3. The calculationsinvolve coupling to the excited states of the targets as before, and the followingcouplings to excited states of the projectiles. For6He we considered couplingwith the rst excited state at 1.87 MeV (=2) with deformation extracted fromour recent inelastic scattering results6He(p,p')6He12; 25. For11Be the excitedstate E=0.320 MeV (=1) with a B(E2)=0.116 e2fm4was taken into account.We have to keep in mind, that the aim of the present calculations was theachievement of an unied description, in a qualitative basis, for the rst sub-barrier and near-barrier fusion data involving halo nuclei. As it is seen fromFig.2 the systems4He+209Bi and4He+238U need no reduction of the poten-5σ fusion (mb)Ecm/Vb(MeV)6He+238U6He+209Bi11Be+209BiX 100X 10000Figure 3: Fusion cross section for unstable nuclei.tial as it is expected for well bound nuclei. On the contrary, a 40% reductionis necessary to describe the systems9Be+209Bi,6He+209Bi and11Be+209Bi,although for energies well above the coulomb barrier the later system is betterdescribed with non reduced potential calculations. The situation is more com-plex for6He+238U. Above the coulomb barrier this system is probably betterdescribed with calculations with non reduction of the potential, whereas wellbelow the coulomb barrier the calculations fail to reproduce the data. It has tobe noticed however that this is the rst system for which sub-barrier fusion, forenergies well below the coulomb barrier, has been measured. A new experimentis planned to investigate in more details sub-barrier fusion of6He+238U.6From this discussion we can draw the conclusion that coupled channel cal-culations reproduce the gross properties of near-barrier fusion involving halonuclei. The agreement of the calculations with the data is particularly spec-tacular in the case of9Be+209Bi and11Be+209Bi.3 ConclusionsWe have performed coupled channel fusion calculations for several systems withhalo and their associated non-halo projectiles. A description of the weaklybound stable system (9Be+209Bi) and the halo systems was qualitatively ob-tained, by making use of a reduced potential. The reduction of the potentialcan be understood in terms of breakup processes due to the weak binding en-ergy of the stable nucleus9Be and the halo nuclei. The reduction of potentialwas justied before via elastic scattering of weakly bound nuclei and in partic-ular of9Be on dierent targets. In this context elastic scattering measurementsfor halo nuclei are highly requested. These measurements would help to pindown a possible variation of the strength and eventually of the shape of theentrance channel potential.In general it has to be stressed out that additional measurements includingelastic scattering, complete fusion (without contributions due to incompletefusion) and break-up are necessary to enlight the subject of near-barrier andsub-barrier fusion of halo nuclei.AcknowledgmentsOne of the authors (N.A) acknowledges Dr R. Wolski for the discussions hehad with him and for pointing out the reference with the209Bi(,n)212At data.References1. M. Beckerman Rep. Progr. Phys. 51, 1047 (1988).2. S.G. Steadman and M. J. Rhoades-Brown, Ann. Rev. Part. Sc. 36, 649(1986).3. P.G. Hansen et al, Ann. Rev. Part. Sc. 45, 591 (1995).4. C. Signorini et al, Eur. Phys. J. A2 227, 157 (1998).5. J.J. Kolata et al, Phys. Rev. Lett. 81, 4580 (1998).6. M. Trotta et al, Phys. Rev. Lett. 84 , 2342 (2000 ).7. W.J. Ramler et al, Phys. Rev. 114, 154 (1959).8. V.E. Viola and T. Sikkeland, Phys. Rev. 128, 767 (1962).9. J. Raynal, Phys. Rev. C 23, 2571 (1981).10. V. Lapoux, to be published and PhD thesis, University of Orsay 1998.711. G. R. Satchler and W.G Love, Phys. Reports 55, 183 (1979).12. S. Karataglidis et al, Phys. Rev. C 61, 024319 (2000); private commu-nication.13. H. Sagawa, Phys. Lett. B 286, 7 (1992).14. Mc Gowan et al, Phys. Rev. Lett. 28, 1741 (1971)15. C.E. Bemis et al,Phys. Rev. C 8, 1466 (2000).16. Nuclear Data Sheets 63, 723 (1991).17. A. T. Rudchik et al, Nucl. Phys. A 662, 44 (2000).18. N. Takigawa and H. Sagawa, Phys. Lett. B 265, 23 (1991).19. A. R. Barnett and J.L. Lilley, Phys. Rev. C 9, 2010 (1974).20. M. Dasgupta et al, Phys. Lett. B 82, 1395 (1999).21. Y. Sakuragi et al, Phys. Rev. C 35, 2161 (1987).22. D.T. Khoa, G.R. Satchler and von Oertzen Phys. Rev. C 56, 954 (1997).23. L. Trache et al, Phys. Rev. C 61, 02461 (2000).24. M. S. Hussein et al, Phys. Rev. C 29, 2383 (1984).25. A. Lagoyannis et al, to be published.26. K. Hagino et al, Phys. Rev. C 61, 037602 (2000).27. V. Lapoux et al, to be published.8

Study of sub-barrier and near-barrier fusion of halo nuclei

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