PRL 96, 162701 (2006)PHYSICAL REVIEW LETTERS week ending28 APRIL 2006Deep Sub-Barrier Fusion Enhancement in the 6 He206 Pb ReactionYu. E. Penionzhkevich, V. I. Zagrebaev, S. M. Lukyanov, and R. KalpakchievaFlerov Laboratory of Nuclear Reactions, JINR, Dubna, Moscow Region, Russia(Received 13 January 2006; published 28 April 2006)The fusion of 6 He with 206 Pb has been studied at energies close to and below the Coulomb barrier. Theexperiment was carried out at the Dubna Radioactive Ion Beams complex of FLNR, JINR. The 6 He beamintensity was about 5 10 6 pps, the maximum energy being 60:3 0:4 MeV. The yield of the 210 Poisotope, produced in the 2n-evaporation channel, demonstrates an extremely large enhancement of thesub-barrier fusion cross section as compared with the 4 He208 Pb reaction. This enhancement is mostlikely due to the mechanism of ‘‘sequential fusion’’ with an intermediate neutron transfer from 6 He to thePb nucleus with positive Q values.DOI: 10.1103/PhysRevLett.96.162701Introduction.—The reactions with halo nuclei during thepast 10 years have been of increased interest from experimentaland theoretical points of view. In particular, mucheffort has been devoted to studying near-barrier fusion oflight weakly bound nuclei. Unusual effects are expectedhere both from the halo structure of these nuclei and fromthe specific tunneling mechanism of the composed weaklybound system which is of common interest for quantumtheory.Some model calculations have shown that the weakbinding energy of the nuclei could significantly reducethe near-barrier fusion cross section [1,2]. In comparisonwith the fusion of ordinary nuclei, the breakup and transferchannels with positive Q values could be very importanthere. The extended ‘‘halo’’ structure of exotic nuclei, suchas 6 He or 11 Li, may also influence the fusion probability. InRefs. [3–5] a large enhancement of the fusion probabilityfor weakly bound nuclei was found due to the excitation ofa low-lying soft-dipole mode and the strong coupling withthe breakup channels. On the other hand, the weak bindingof these nuclei leads to an increase in the probability oftheir breakup that may be accompanied by the consequentfusion of the residual nucleus (the core) with the targetnucleus or by the transfer of nucleons without any furtherinteraction between the nuclei. The variety of possibleprocesses makes it difficult to analyze the experimentaldata and requires the consideration of all possible reactionchannels. For this reason, no matter how surprising it mayseem, but until now there is no consensus (neither in theorynor in experiment) on the extent to which the sub-barrierfusion of weakly bound nuclei differs from fusion ofordinary ones.The great interest in this type of investigations arosewhen in 1995  in the study of the fusion-fission crosssection for the 6 He209 Bi reaction, a significant enhancementwas observed, especially in the sub-barrier region,compared to the one expected according to the standardmodel. Soon after the first experimental paper , a newseries of experiments was undertaken on the near-barrierfusion of 6 He with 209 Bi  and 238 U  that also announceda significant enhancement of the fusion probabil-PACS numbers: 25.60.Pj, 21.10.Gv, 24.10.Eq, 25.60.Jeity for 6 He compared to 4 He. However, it is rather difficultto make an unambiguous interpretation of this result. Onereason is that when comparing the evaporation residuecross sections for the 6 He 209 Bi and 4 He 209 Bi fusionreactions, one has to take into account that compoundnuclei are produced that differ both in excitation energyand decay properties. In addition, in a fusion-fission reactionsuch as 6 He238 U (with detection of fission fragmentsonly) it is difficult to distinguish the process ofcomplete fusion from other channels giving contributionto the total yield of the fission fragments. From a subsequentmore careful analysis of this reaction, by involvingthe measurement of the fission fragments in coincidencewith particles, produced after the breakup of 6 He, it wasconcluded that the observed enhanced yield of the fissionfragments at sub-barrier energies could be attributedmainly to 2n-transfer reactions to the excited states of240 U (with its subsequent fission) and, thus, there is noenhancement of the fusion probability for 6 He . Thereare a few more papers reporting on fusion reactions with6 He [10,11]. However, these measurements require theinclusion of more information on the different exit channelsand higher statistics in order to be considerably morereliable.Neutron transfer cross sections are known to be ratherlarge at near-barrier energies of heavy-ion collisions andthere is a prevailing view that coupling with the transferchannels should play an important role in sub-barrier fusionof heavy nuclei. For weakly bound nuclei (the twoneutronseparation energy for 6 He is less than 1 MeV) astrong coupling with the breakup channels is also evidentand it should influence significantly the fusion probability.However, while the role of collective degrees of freedom(rotation of statically deformed nuclei and/or vibration ofnuclear surfaces) in the sub-barrier fusion reactions is wellstudied in many experiments and well understood theoretically,the role of neutron transfer and breakup channels isnot so clear.Such a controversial situation in the experimental dataon sub-barrier reactions can be explained by a series ofdifficulties. First, experiments with radioactive beams are0031-9007=06=96(16)=162701(4)$23.00 162701-1 © 2006 The American Physical Society
PRL 96, 162701 (2006)PHYSICAL REVIEW LETTERS week ending28 APRIL 2006rather complicated. One problem is the low intensity of thesecondary beams. This makes measurements in the regionof the Coulomb barrier extremely time consuming, if highstatistics is to be obtained. Second, in the experimentalstudy of the effect, we need to compare the fusion crosssections of different combinations of nuclei, which amongother things have different collective properties, and it isnot so easy to single out the role of breakup and/or neutrontransfer from the whole effect of sub-barrier fusion enhancement.At last, it is very difficult, for many reasons, totake into account explicitly the breakup and transfer channelswithin the consistent channel coupling approach usedsuccessfully for the description of collective excitations inthe near-barrier fusion processes. As a result, we are stillfar from good understanding of the subject and additionalexperimental and theoretical studies are needed.Recently in Ref.  a new mechanism has been proposedfor the sub-barrier fusion of weakly bound nuclei, inwhich an intermediate rearrangement of valence neutronswith positive Q values may lead to a gain in kinetic energyof the colliding nuclei and, thus, to enhancement of the barrierpenetrability. Within this ‘‘sequential fusion’’ mechanism,the fusion enhancement in the reactions 40 Ca48 Ca(compared with 48 Ca 48 Ca), 40 Ca 96 Zr (comparedwith 40 Ca 90 Zr), and 18 O 58 Ni (compared with 16 O60 Ni) has been successfully explained. In Refs. [12,13] anexperiment was proposed for measuring and comparing theevaporation residue cross sections in the 6 He206 Pb and4 He 208 Pb reactions leading to the same compound nucleus.The yield of polonium isotopes at the same subbarriercenter-of-mass energy of 15 MeV was predicted tobe 3 orders of magnitude larger for the first reaction ascompared to the second one .New opportunities arose when secondary beams of radioactivenuclei with relatively high intensity ( 10 7 pps)became available and when a considerable sensitivity ofthe experimental techniques applied for detecting the reactionproducts was achieved. Thus, in first experimentsperformed at the Dubna Radioactive Ion Beams (DRIBs)complex , it was possible to measure the excitationfunctions for the 6 He197 Au (above-barrier) and 6 He206 Pb (sub-barrier) fusion reactions, and on the transfer of xneutrons when bombarding 197 Au with 6 He, with the sensitivityfor the cross section not worse than 100 nb in thevicinity of the Coulomb barrier . In the present Letter,we study a possible enhancement of the deep sub-barrierfusion of 6 He with 206 Pb in the energy interval E c:m:15–24 MeV.Experimental method.—The beam of accelerated 6 Heions was provided by the Dubna accelerator complex forradioactive beams DRIBs  at FLNR (JINR). The detailsof producing the 6 He beam and the beam diagnosticsystem are presented elsewhere [ and referencestherein]. The optimization and transport of the 6 He 2 -ionbeam made it possible, without applying any additionalcollimation, to have a (7 7)-mm beam spot on the physicaltarget, the beam energy being E 60:3 MeV, the162701-2energy spread 0:4 MeV, and the intensity 5 10 6 pps.The energy of the beam was measured using the MSP-144magnetic spectrometer .The measurement of the yield of the products of thefusion reaction with the evaporation from the compoundnucleus of 2 neutrons, 206 Pb 6 He; 2n 210 Po, was performedby the activation method. A stack of six 206 Pb targets, each600–700 g=cm 2 thick, with 20 m Al foils inserted inbetween so as to reduce the beam energy from 23 to13 MeV, was irradiated giving the six data points shownin Fig. 1. In order to tune the 6 He beam and to measure itsintensity and spatial distribution, a multiwire proportionalchamber for beam diagnostics was placed in front of thestack. After passing through the stack, the beam entered themagnetic spectrometer MSP-144, which gave a precisemeasurement of the residual energy. The 6 He energy andthe energy loss in each layer of the stack were calculatedwith the LISE code  and the calculated residual energywas compared to the value measured by the magneticspectrometer. In this way, in spite of the rather large energydispersion of the beam at the end of the stack [ 3 MeV,this is the FWHM of the energy distribution measured withthe magnetic spectrometer after both (Au and Pb) stacks offoils], the absolute value of the energy was determinedwith good accuracy (not worse than 1 MeV).The fusion of 6 He with 206 Pb was studied by measuringthe yield of 210 Po nuclei formed in the 2n-evaporationchannel of this reaction in the beam-energy range13–24 MeV (the Coulomb barrier is 20 MeV). The 210 Poisotope was identified by observing its decay activity(the -particle energy E 5:3 MeV) and its half-life(T 1=2 138 d). The energy resolution of the spectrometerwas about 50 keV, and the total efficiency of registrationof the particles was about 50%.Results and analysis.—On the basis of the measuredyields, taking into account the 6 He beam intensity andFIG. 1. Cross sections for the production of 210 Po in the 6 He206 Pb fusion reaction (solid squares, 2n channel) and 211 Po in the4 He 208 Pb fusion reaction  (open circles, 1n channel).Solid curves are the theoretical predictions taken from .Long dashed curve includes the effect of the energy spread.Arrows at the energy axis show the corresponding Coulombbarriers for 6 He (left) and 4 He (right).
PRL 96, 162701 (2006)PHYSICAL REVIEW LETTERS week ending28 APRIL 2006the target thicknesses, we could determine the cross sectionfor the formation of the isotope 210 Po in the206 Pb 6 He; 2n 210 Po reaction and its dependence on theincident energy. The measured excitation function is presentedin Fig. 1. One can see that 210 Po is produced with across section of about 10 mb at the incident energy 133 MeV, i.e., much lower than the Coulomb barrier.In Fig. 1 the measured cross sections for production of210 Po nuclei in the 6 He 206 Pb fusion reaction  areshown compared with the 4 He 208 Pb fusion reaction and with the theoretical predictions of Ref. . At abovebarrierenergies the fusion cross sections in both reactionsare quite comparable. However, at deep sub-barrier energiesthe fusion probability of the weakly bound nucleus6 He with Pb target is several orders of magnitude largerthan the fusion probability of 4 He. At sub-barrier energiesthe fusion cross section is falling exponentially and theenergy spread distorts significantly the experimental data.To estimate this effect we averaged the calculated crosssections for 2n channel (solid curve in Fig. 1) over thebeam spread assuming its Gaussian distribution with thewidth of 3 MeV. The result is shown by the long dashedcurve in Fig. 1. At the beam energy of 12.5 MeV this effectincreases the cross section almost by 2 orders of magnitude.However, at deep sub-barrier energies the bare fusionprobability of 6 He is at least 1000 times larger as comparedto the fusion of 4 He.Such a great effect may be explained by the largepositive Q values for the transfer of two valence neutronsfrom 6 He to 206 Pb: 6 He 206 Pb ! 5 He 207 PbQ 0 4:9 MeV ! 4 He 208 Pb Q 0 4:8 8:313:1 MeV ! 212 Po. Of course, the probability for neutrontransfer to the ground states is rather small, but the totalpossible gain in energy is very high compared to the heightof the Coulomb barrier ( 20 MeV) and, therefore, has tomanifest itself in the fusion probability of 6 He. This effectis absent in the interaction of 4 He with 208 Pb.To estimate the effect of intermediate neutron transfer onthe fusion probability we may assume that the incomingflux penetrates the Coulomb barrier in all the possibleneutron transfer channels with different Q values. Denoteby x E; l; Q the probability for the transfer of x neutronsat the center-of-mass energy E and relative motion angularmomentum l in the entrance channel to the final state withQ Q 0 x , where Q 0 x is the Q value for the ground stateto ground state transfer reaction. Then the total penetrationprobability is written ascollective degrees of freedom, P HW B; E Q; l is theusual Hill-Wheeler formula  for the estimation of thequantum penetration probability R of the one-dimensionalpotential barrier B, N trPk k E; l; Q dQ is the normalizationconstant, and 0 Q .The de Broglie wavelength of 6 He206 Pb relative motionis about 2.5 fm, whereas the Coulomb barrier distance,R B , is 11 fm. In that case a semiclassical approximationmay be used, in principle, to estimate roughly the neutrontransfer probability. Assuming predominance of sequentialneutron transfer mechanism, which means multiplicationof transfer probabilities, one gets x E; l; Q e 2 D E;l ,where D E; l is the distance of closest approach of the twonuclei and 1 2 x for sequentialtransfer of x neutrons, i 2 n i =@ 2 , and i ispthe separation energy of the ith transferred neutron.Experiments show that the transfer probability becomesvery close to unity at a short distance between the twonuclei, when their surfaces are rather overlapped. Wedenote this distance by D 0 d 0 A 1=31 A 1=32 and willuse for parameter d 0 the value of about 1.40 fm . Inheavy-ion few-nucleon transfer reactions the final stateswith Q Q opt are populated with largest probability dueto mismatch of incoming and outgoing waves. For neutrontransfer Q opt is close to zero. The Q window may be2approximated by the Gaussian exp C Q Q opt withthe constant C R B 12 = @ 2 2E B , where 12 isthe reduced mass of the two nuclei. Finally, the transferprobability may be estimated in the following wayx E; l; Q N x e C Q Q opt2e 2 D E;l D 0 ; (2)where N x f R Q 0 xE exp C Q Q opt 2 dQg 1 and thesecond exponent has to be replaced by 1 at D E; l
PRL 96, 162701 (2006)PHYSICAL REVIEW LETTERS week ending28 APRIL 2006gain in the relative motion energy for Q>0. In otherwords, an intermediate neutron transfer to the states withQ>0 is, in a certain sense, an ‘‘energy lift’’ for the twointeracting nuclei. This looks quite different from the wellknownfusion enhancement due to surface vibrations orrotation of nuclei leading to decrease of potential barrier insome channels.A schematic picture of the described ‘‘sequential fusion’’mechanism in sub-barrier collision of 6 He with206 Pb is shown in Fig. 2 taken from . When the collidingnuclei approach, two neutrons may be transferred from6 He to the ground and low-lying states of 208 Pb with asmall but not negligible probability. In that case, thecharged core finds itself with kinetic energy well abovethe Coulomb barrier and may easily fuse with the target.Conclusion.—We have presented the results of the firstmeasurement of the cross section for the sub-barrier fusionof the weakly bound exotic nucleus 6 He with 206 Pb, performedat the accelerator complex DRIBs with the6 He-beam intensity reaching 5 10 6 pps. The fusionprobability (the yield of Po nuclei) in the studied reaction,6 He 206 Pb, was found to be about 3 orders of magnitudelarger than in the 4 He208 Pb fusion reaction at the samedeep sub-barrier center-of-mass energy of E c:m:15 MeV. Such enhancement is caused, in our opinion, bythe mechanism of ‘‘sequential fusion’’ with significantlowering the energy of the valence weakly bound neutronsof 6 He when they fall into the field of the 206 Pb target. Thisgives a gain in the kinetic energy of relative motion of thecharged cores and plays a role of an ‘‘energy lift’’ for thetwo interacting nuclei. In the forthcoming experiments, the6 He-beam intensity is expected to reach 10 8 pps. Then weplan to measure in detail at energies close to the Coulombbarrier the behavior of the excitation functions for the oneandtwo-neutron evaporation channels in the interaction of6 He with 206 Pb and 197 Au, as well as the excitation functionsfor the transfer of one and two neutrons and the totalreaction cross section. Many other combinations of stableand unstable nuclei should reveal a noticeable enhancementof the sub-barrier fusion cross sections due to intermediateneutron transfer with positive Q values. To avoidadditional ambiguities caused by other effects, one maypropose to measure the fusion cross sections in the followingreactions: 4;6 He 14;12 C, 12;14 C 42;40 Ca, 16;18 O42;40 Ca, 40;48 Ca 124;116 Sn, 9;11 Li 208;206 Pb, which havepositive Q 0 values of the 1n and/or 2n-transfer channels forone combination and negative or zero Q 0 values for anotherone. Direct comparison of the corresponding experimentalfusion cross sections may display immediately suchan enhancement, if it exists.Additional enhancement in sub-barrier fusion of weaklybound neutron rich nuclei can be used, in principle, forsynthesis of new superheavy nuclei in future experimentswith accelerated fission fragments. The enhancement effectin deep sub-barrier fusion probability of light weaklybound nuclei may be very important also for astrophysicalestimations. M. S. Hussein, M. P. Pato, L. F. Canto, and R. Donangelo,Phys. Rev. C 46, 377 (1992). L. F. Canto, R. Donangelo, P. Lotti, and M. S. Hussein,Phys. Rev. C 52, R2848 (1995). N. Takigawa and H. Sagawa, Phys. Lett. B 265, 23(1991). C. H. Dasso and A. Vitturi, Phys. Rev. C 50, R12(1994). K. Hagino, A. Vitturi, C. H. Dasso, and S. M. Lenzi, Phys.Rev. C 61, 037602 (2000). A. S. Fomichev et al., Z. Phys. A 351, 129 (1995). J. J. Kolata et al., Phys. Rev. Lett. 81, 4580 (1998). M. Trotta et al., Phys. Rev. Lett. 84, 2342 (2000). R. Raabe et al., Nature (London) 431, 823 (2004). A. Di Pietro et al., Phys. Rev. C 69, 044613 (2004). A. Navin et al., Phys. Rev. C 70, 044601 (2004). V. I. Zagrebaev, Phys. Rev. C 67, 061601(R) (2003). R. Kalpakchieva, Yu. E. Penionzhkevich, and H. G.Bohlen, Phys. Part. Nucl. 30, 627 (1999). Yu. Ts. Oganessian and G. G. Gulbekian, in NuclearShells - 50 Years, edited by Yu. Ts. Oganessian et al.(World Scientific, Singapore, 2000), p. 61. Yu. E. Penionzhkevich et al. JINR Report No. P7-2005-106, 2005 (to be published). N. K. Skobelev et al., Nucl. Instrum. Methods Phys. Res.,Sect. B 227, 471 (2005). O. Tarasov et al., http://dnr080.jinr.ru/lise/. A. R. Barnett and J. S. Lilley, Phys. Rev. C 9, 2010(1974). D. L. Hill and J. A. Wheeler, Phys. Rev. 89, 1102(1953). W. von Oertzen et al., Z. Phys. A 326, 463 (1987). R. A. Broglia, G. Pollarolo, and A. Winther, Nucl. Phys.A361, 307 (1981). V. I. Zagrebaev, Prog. Theor. Phys. Suppl. 154, 122(2004).162701-4