REVISTA MEXICANA DE FISICA 50 SUPLEMENTO 2, 101–106 DICIEMBRE 2004

Sub-barrier fusion of neutron-rich nuclei: 132Sn+64Ni

D. Shapiraa, J.F. Lianga, C.J. Grossa, J.R. Beenea, J.D. Biermanb, A. Galindo-Uribarria, J. Gomez del Campoa,P.A. Hausladena, Y. Larochellec, W. Lovelandd, P.E. Muellera, D. Petersond,

D.C. Radforda, D.W. Stracenera, and R.L. VarneraaPhysics Division, Oak Ridge National Laboratory,

Oak Ridge, Tennessee 37831, USAbPhysics Department AD-51, Gonzaga University,

Spokane, Washington 99258-0051, USAcDepartment of Physics and Astronomy, University of Tennessee,

Knoxville, Tennessee 37966, USAdDepartment of Chemistry, Oregon State University,

Corvallis, Oregon 97331, USA

Recibido el 20 de enero de 2004; aceptado el 23 de mayo de 2004

Accelerated beams of132Sn (98% pure) were used to measure sub-barrier fusion cross sections of132Sn+64Ni induced reactions down toenergies for which the cross section was as low as 3mb. The measured excitation function shows large enhancement in cross section thatcould not be accounted for by coupling of inelastic and transfer channels. A simple computational model for calculating sub-barrier fusioncross sections between neutron-rich heavy nuclei reproduces the very large enhancement observed for this system.Keywords: Nuclear Fusion; Evaporation Residues; Interaction Barrier; neutrons; flow; energy; energy loss; time of flight; ionizationchamber.

Haces de 132Sn de alta pureza fueron utilizados para medir secciones elicaces de fusion cerca y abajo de la barrera Coulombiana para lareacciones 132Sn + 64Ni. Para la energıa mas baja la seccion eficaz de fusion fue de tan solo 3 mb. La funcion de excitacion medida muestraun acrecentamiento en la seccion eficaz abajo de la barrera que no se ha podido explicar por el acoplamiento de canales inelasticos y detransferencia. Usando un modelo simple para calcular secciones de fusion abajo de la barrera entre nucleos ricos en neutrones se puedereproducir el gran acrecentamiento observado para este sistema.Descriptores: Fusion Nuclear; Residuos de Evaporacion; Barrera de Interaccion; neutrones; flujo; energıa; perdida de energıa; tiempo devuelo; camara de ionizacion.

PACS: 25.70Jj; 24.10Eq; 25.60

1. Introduction

Fusion between heavy ions at sub-barrier energies is the sub-ject of intense study since it was discovered that the magni-tude of these fusion cross sections far exceeds the expectedvalues based on quantum penetration of the one-dimensionalCoulomb barrier [1–3]. Present views hold that this enhance-ment is due to the complexity of the colliding nuclei. Nu-clear transformations prior to fusion, that take place as thenuclei approach, result in changes to the Coulomb barrierprior to fusion. The coupling of channels such as nuclearexcitation and transfer create these multi-dimensional barri-ers which lead to an enhancement of sub-barrier fusion crosssection. Such channel coupling models have succeeded inexplaining general trends of the measured yields. The caseswith the most spectacular success are those where a singlechannel or process dominates the pre-fusion stage and canaccount for the barrier distribution as extracted from fusionexcitation functions [4,5]. As more reliable data on the struc-ture of the colliding nuclei become available it is expectedthat more complex full coupled channel-calculations, willbetter describe observed increases in sub-barrier fusion crosssections [6]. With the advent of accelerated radioactive ionbeams opportunities to study fusion between exotic nucleiwill become available. The fusion between very neutron-

rich nuclei is of particular interest. In these processes thecompound nucleus is less likely to fission and stands a bet-ter chance to survive as a heavy product. It has been sug-gested that the fusion probability would be further enhancedin such reactions in part due to the large N/Z ratio leadingto reduced barrier heights and partly due to the presence ofloosely bound neutrons [7–9]. The probability for neutron-rich nuclei to fuse at sub-barrier energies may well affect ap-proaches to the synthesis of superheavy nuclei.

Spurred by such speculations we have decided to use thepure132Sn beams accelerated to energies of 4-5AMeV thathave become available at HRIBF [10] to measure fusion witha heavy neutron-rich target. With the beam energy availablethe combination of132Sn and64Ni allowed us to measureexcitation function for evaporation residue production at en-ergies above and below the Coulomb barrier. The data werefirst reported in ref. [11]. This paper will describe how thesedata were acquired and discuss a possible explanation for theobserved enhancement in the fusion cross section.

2. Experimental methods

The measurements were carried out at the Holifield Radioac-tive Ion Beam Facility (HRIBF) at Oak Ridge National Lab-oratory. Short-lived132Sn ions were produced in proton-in-

102 D. SHAPIRAet al.

FIGURE 1. Detector arrangement in the experiment. The beam defining detectors were about 1m apart. Target to 3rd timing detector distancewas about 20 cm. Typical flight times from target to the last timing detector are 13 ns for evaporation residues and 9 ns for the beam.

duced fission of238U and were extracted using the isotopeseparator on-line technique. Isobars of mass A=132 weresuppressed by extracting molecular SnS+ from the ion sourceand subsequently breaking it up in the charge exchange cellwhere the SnS+ was converted to Sn− [10]. The132Sn ionswere post accelerated by the 25 MV tandem electrostaticaccelerator. The beam intensity was measured by particlecounting with a combination of a foil and a micro-channelplate detector. The beam passed through a 10µg/cm2 car-bon foil and the secondary electrons emitted from the foilwere steered to a micro-channel plate (MCP) detector andcounted. The average beam intensity during our experimentwas 2×104 particles per second (pps) with a maximum near3×104 pps. The purity of the132Sn beam was monitored bymeasuring the energy loss of the beam ions in an ionizationchamber (IC); typically, the contaminants were at a level be-low 2%. Moreover, all the measurable impurities had a higheratomic number (Z) than Sn. (Lower Z isobars have muchshorter lifetimes and, therefore, less of a chance to get outof the ion source.) This impurity (of higher Z elements) hasnegligible influence on the measurement because the higherCoulomb barrier suppresses the fusion of the contaminantsin the beam with the target. Because of the low intensityof radioactive beams, the measurement was performed witha thick, 1 mg/cm2 self-supporting highly enriched (99.8%)64Ni foil target.

The evaporation residues (ERs) were detected along withbeam particles by a timing detector and a gas filled ioniza-tion chamber at 0◦, as shown in Fig. 1. They were identifiedby their time-of-flight and energy loss in the IC. In the time-of-flight measurement, the coincidence between the two up-stream timing detectors provided the time reference (beamtiming). The data acquisition was triggered by the scaleddown beam singles or the ER-beam particle coincidences.With this pre-triggering scheme we were able to reduce therandom background in our selected data and measure cleanevaporation residue data. The pretriggering scheme also re-duced the load on the data acquition computer system. Wewere able to run with an overall dead-time of less than 5%and measure ER cross sections done to energies where thecross section was less than 5 mb.

3. Data reduction and results

The ERs were very forward focused because of the inversekinematics conditions which resulted in good product collec-

tion efficiency. One of the disadvantages of using a thick tar-get is the multiple scattering of the beam and reaction prod-ucts in the target material. This results in a broadening of theangular distribution. The efficiency of the apparatus was esti-mated by Monte Carlo simulations using the statistical modelcodePACE [12] to generate the angular distribution of ERs.The efficiency of the apparatus changes from95±1% for thelowest beam energy to98± 1% for the highest energy.

The ER excitation function for132Sn+64Ni (solid circles)is compared to those of64Ni on even stable Sn isotopes mea-sured by Freemanet al. [13] in Fig. 2. Our measurementusing the124Sn guide beam is shown by the open circle andagrees well with the measurement of Ref. [13] as shown bythe open triangles. In Fig. 2 the energy is scaled by the fu-sion barrier (VB) predicted by the Bass model [21] and theER cross section is scaled by the size of the reactants usingR = 1.2(A1/3

p + A1/3t ) fm, whereAp (At) is the mass of the

projectile (target). At energies below the barrier, the ER crosssections for132Sn+64Ni are found to be much enhanced com-pared to those of64Ni+112−124Sn which cannot be explainedby nuclear size effects.

FIGURE 2. Detector arrangement in the experiment. The beamdefining detectors were about 1m apart. Target to 3rd timing detec-tor distance was about 20 cm. Typical flight times from target tothe last timing detector are 13 ns for evaporation residues and 9 nsfor the beam.

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SUB-BARRIER FUSION OF NEUTRON-RICH NUCLEI:132Sn+64Ni 103

4. Analysis

The measured ER cross sections are compared to coupled-channel calculations using the codeCCFULL [15] in Fig. 3.Since fission was not measured in our experiment, it was es-timated byPACE. The input parameters were determined byreproducing the ER and fission cross sections of64Ni+124Snin Ref. 16. The calculations predict that fission is negligiblefor 132Sn+64Ni and64Ni+124Sn at Ec.m. ≤ 160 MeV. There-fore, the following discussion will be restricted to the datapoints at Ec.m. ≤ 160 MeV where the ER cross sections aretaken as fusion cross sections.

Large sub-barrier fusion enhancement can be seen forboth132Sn+64Ni and64Ni+124Sn as compared to the barrierpenetration model (BPM) predictions shown by the dottedcurves in Fig. 3. The dashed curves are the result of couplingto inelastic excitation (IE) of the projectile and target. Asshown in the right panel of Fig. 3, the calculation reproduces

FIGURE 3. Comparison of measured ER excitation functions withCCFULL calculations. The left panel is for132Sn+64Ni and the rightpanel is for64Ni+124Sn [13]. The measured ER cross sections areshown by the filled circles and open triangles for132Sn+64Ni and64Ni+124Sn, respectively. See text for details.

the64Ni+124Sn cross sections fairly well at low energies. For132Sn+64Ni, the calculation significantly under predicts thesub-barrier cross sections as shown in the left panel of Fig. 3.

For the 132Sn-induced reaction, the Q values are pos-itive for 64Ni picking up two to six neutrons whereas in64Ni+124Sn, the (64Ni,66Ni) reaction is the only transferchannel which has a positive Q value. This suggests thatthe observed fusion enhancement may be attributed to multi-nucleon transfer similar to that observed in40Ca+96Zr [4].Coupled-channels calculations including one-neutron trans-fer and IE are in good agreement with the fusion cross sec-tions for 64Ni+124Sn near and below the barrier, as can beseen by the solid curve in the right panel of Fig. 3. Results ofcalculations including IE, and multi-nucleon transfer chan-nels (nXFR) assuming clusters of neutrons transferred to theground state are shown by the solid curve in the left panelof Fig. 3. The calculation cannot account for the cross sec-tions near and below the barrier, nevertheless, it illustratesqualitatively the enhancement of sub-barrier fusion due tothe coupling to multi-nucleon transfer. More realistic cal-culations which also consider sequential transfer, as pointedout in Ref. [4], may account for the discrepancy. It is notedthat the codeCCFULL is suitable for reactions where multi-nucleon transfer is less important than IE [15] as is the casein 64Ni+124Sn.

While these efforts are still under way [17] one must re-alize that most of the neutron transfer channels to be incor-porated into the coupled channel code have not been mea-sured yet and are unlikely to be measured in the near future.An alternative, simple model that will account for the sub-barrier fusion cross section in systems with neutron-rich nu-clei is therefore desirable. Such a model was first introducedabout a decade ago [18, 19]. In this model enhanced fusioncross sections, at sub-barrier energies, are calculated usinga uniform barrier distribution ranging from a threshold bar-rier to the full Coulomb barrier. In the original papers andin subsequent publications [20] it was shown that the thresh-old barriers extracted from the measured cross sections werecorrelated with the neutron separation energy in the collidingnuclei.

The underpinnings of this simple model are illustrated inFigs. 4 and 5. Fig. 4 shows the nucleus nucleus potential in acollision of 132Sn with64Ni. The Coulomb barrier reaches aheight of∼150 MeV at an inter-nuclear distance of∼12 fm.Fig. 5 shows the combined shape of the two neutron wellsof the approaching nuclei at an inter-nuclear distance near15 fm (indicated by the vertical line in Fig. 4). At this dis-tance the depression in the combined nuclear wells reachesthe same level that matches the separation energy of a sin-gle neutron in132Sn. At this point, and beyond it at closerinter-nuclear distances where the depression in the combinednuclear well deepens further, the neutron can flow freely be-tween the two nuclei. The inter-nuclear distance (∼15 fm)corresponding to this onset of neutron flow is indicated by avertical line in Fig.4. The Coulomb barrier height at this ra-dius (∼130meV) corresponds to a threshold barrier. This is

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the distance at which the nuclei begin to interact; if conditionsfor neutron flow are maintained this may lead to neck forma-tion. The separation energies for neutrons in131Sn and65Niare indicated in Fig. 6. Obviously neutron flow conditionscontinue to be maintained also after the first neutron transferhas occurred. Using a simple algebraic formula sub-barriercross sections can then be calculated for a flat barrier distri-bution ranging from the threshold barrier to the full Coulombbarrier. This formalism proved successful in predicting thecross section in several cases involving lighter systems withmoderate barrier shifts [18–20]. It has also been shown thatthreshold barriers extracted from the experimental data trackthe dependence on neutron separation energy in the collidingnuclei [20]. Using this simple model we tried to apply it toa large body of sub-barrier fusion data [11,13,14] for Sn iso-topes colliding with64Ni. Fig. 7 shows the results from suchan attempt. The calculation does not involve any free param-eter. The nucleus-nucleus potential is calculated using pub-lished systematics [22] and the neutron well parameters werefixed and are listed in the caption of Fig.5. It is obvious thatthis model predicts very large enhancements but falls short ona few counts. The predicted cross sections are much higherthan the measured ones and while the predicted magnitudefor the stable isotopes tend to cluster just as the data doesthe model fails to predict the extra enhancement observed for132Sn+ 64Ni. There is clearly something amiss.

While very intuitive, this model fails to account for thefact that as a result of the neutron being transferred from the132Sn nucleus to the64Ni nucleus a neutron pair is broken in132Sn and a neutron state in65Ni must be occupied as indi-cated in Fig. 5 (long dashed line).

FIGURE 4. Nucleus-nucleus one dimensional potential for132Sn+64Ni. The critical angular momentum for this system isLorb=102~. The curves show that a few units of angular momen-tum will not have much effect on the barrier to fusion at low ener-gies.

FIGURE 5. The combined neutron wells of132Sn(left) and64Ni(right) calculated at the distance corresponding to zero thresh-old (see vertical line in Fig.4). Indicated in the figure are the sep-aration energies of neutrons in the two approaching nuclei. Theneutron wells are parameterized with a Woods-Saxon shape andthe parameter used for all systems are: depth V=50 MeV, radiusR=1.24*A1/3 fm and well diffuseness a=0.68 fm.

FIGURE 6. The combined neutron wells of132Sn(left) and64Ni(right) calculated at the distance corresponding to zero thresh-old (see vertical line in Fig.4. The separation energies indicated inthe figure are for the system after one neutron is transferred from132Sn to64Ni. The neutron wells are the same as in Fig. 5.

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SUB-BARRIER FUSION OF NEUTRON-RICH NUCLEI:132Sn+64Ni 105

FIGURE 7. Comparison of predicted sub-barrier fusion cross sec-tions with data taken for several Sn isotopes [11,13,14]. The rangeof data for the stable isotopes is represented by vertical bars in thepicture.

A simple way to incorporate this fact into the neutron flowmodel comes from realization that the initial transfer step re-quires that the neutrons have extra energy (the Q-value for theneutron transfer reaction) above the depression in the com-bined neutron well to make the transition from the initial stateto the final state. For this to happen the depression has to getdeeper,i.e., the colliding nuclei must be closer. Once thisinitial transfer has occurred further flow is facilitated sincethe neutron separation energies in131Sn and65Ni are muchsmaller. We therefore modified the model to incorporate thisrequirement in the calculation of threshold barriers. The re-sults from this calculation, shown in Fig. 8, account very wellfor the trends seen in the data. The clustering of the stableisotope data as well as the enhancement in the132Sn resultsare well reproduced. It turns out that this recasting of theneutron flow model also addresses some of the shortcomingsnoted in the original publication regarding the cross sectionof 112,116,122Sn on40Ar [19]. It also predicts correctly thatthe sub-barrier cross section for112Sn+ 64Ni is higher thansome of the other systems, after nuclear size effects are re-moved.

There are several assumptions made in this model thatshould be noted:

• The degree of nuclear overlap is still small enough thatthe two neutron shells are separate and independent.

• The flow conditions are initiated by the transfer of asingle neutron, not a pair.

• The change in nuclear spin of the transferred neutronis ignored.

• The barrier distribution resulting form the initiation ofneutron flow is flat.

FIGURE 8. Comparison of predicted sub-barrier fusion cross sec-tions to data for several Sn isotopes. Cross sections are calculatedwith the neutron flow model where flow is initiated by the sharingof a single neutron between the two nuclear wells. The model al-lows for the difference in neutron separation energies in the twopositions. The data are from [11, 13, 14] and the range of data forthe stable isotopes is represented by vertical bars in the picture.

It is obvious that by its nature this model ignores any as-pects of nuclear structure affecting the neutron transfer; oncethe critical distance is reached the probability to transfer isunity. As can be also seen in seen in Fig. 4 a change of afew units of orbital angular momentum does not affect theheight of the barrier to fusion, allowing us to ignore changesin the spin state of the transferred neutron. One must realizethat other processes affect the barrier distribution as well, andmay produce a barrier distribution that is not flat. The aim ofthis calculation was to present a simple schematic model thatwould be suitable for predicting the degree of enhancement(order of magnitude) one might expect for sub-barrier fusionwith unstable neutron-rich nuclei.

5. Summary

We have presented new data on fusion of64Ni with 132Snwhich show a large enhancement in sub-barrier fusion crosssections which could not be explained by size effects or bysimple coupling orfr direct reaction channels to the fusionprocess. We also suggest a simple model that can account forthe large enhancement observed in sub-barrier fusion crosssections for this system.

Acknowledgments

This research was sponsored by the Office of Science, U.S.Department of Energy under contract DE-AC05-00OR22725managed by UT-Battelle, LLC.

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