REVISTA MEXICANA DE FÍSICA 50 SUPLEMENTO 2, 101 106 DICIEMBRE 2004 Sub-barrier fusion of neutron-rich nuclei: Sn+ 64 Ni D. Shapira a, J.F. Liang a, C.J. Gross a, J.R. Beene a, J.D. Bierman b, A. Galindo-Uribarri a, J. Gomez del Campo a, P.A. Hausladen a, Y. Larochelle c, W. Loveland d, P.E. Mueller a, D. Peterson d, D.C. Radford a, D.W. Stracener a, and R.L. Varner a a Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA b Physics Department AD-51, Gonzaga University, Spokane, Washington 99258-0051, USA c Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37966, USA d Department 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 of Sn (98% pure) were used to measure sub-barrier fusion cross sections of Sn+ 64 Ni induced reactions down to energies for which the cross section was as low as 3mb. The measured excitation function shows large enhancement in cross section that could not be accounted for by coupling of inelastic and transfer channels. A simple computational model for calculating sub-barrier fusion cross 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; ionization chamber. Haces de Sn de alta pureza fueron utilizados para medir secciones elicaces de fusion cerca y abajo de la barrera Coulombiana para la reacciones Sn + 64Ni. Para la energía mas baja la sección eficaz de fusion fue de tan solo 3 mb. La función de excitación medida muestra un acrecentamiento en la sección eficaz abajo de la barrera que no se ha podido explicar por el acoplamiento de canales inelasticos y de transferencia. Usando un modelo simple para calcular secciones de fusion abajo de la barrera entre núcleos ricos en neutrones se puede reproducir el gran acrecentamiento observado para este sistema. Descriptores: Fusion Nuclear; Residuos de Evaporación; Barrera de Interacción; neutrones; flujo; energía; perdida de energía; tiempo de vuelo; cámara de ionización. PACS: 25.70Jj; 24.10Eq; 25.60 1. Introduction Fusion between heavy ions at sub-barrier energies is the subject of intense study since it was discovered that the magnitude of these fusion cross sections far exceeds the expected values based on quantum penetration of the one-dimensional Coulomb barrier [1 3]. Present views hold that this enhancement is due to the complexity of the colliding nuclei. Nuclear transformations prior to fusion, that take place as the nuclei approach, result in changes to the Coulomb barrier prior to fusion. The coupling of channels such as nuclear excitation and transfer create these multi-dimensional barriers which lead to an enhancement of sub-barrier fusion cross section. Such channel coupling models have succeeded in explaining general trends of the measured yields. The cases with the most spectacular success are those where a single channel or process dominates the pre-fusion stage and can account for the barrier distribution as extracted from fusion excitation functions [4,5]. As more reliable data on the structure of the colliding nuclei become available it is expected that more complex full coupled channel-calculations, will better describe observed increases in sub-barrier fusion cross sections [6]. With the advent of accelerated radioactive ion beams opportunities to study fusion between exotic nuclei will become available. The fusion between very neutronrich nuclei is of particular interest. In these processes the compound nucleus is less likely to fission and stands a better chance to survive as a heavy product. It has been suggested that the fusion probability would be further enhanced in such reactions in part due to the large N/Z ratio leading to reduced barrier heights and partly due to the presence of loosely bound neutrons [7 9]. The probability for neutronrich nuclei to fuse at sub-barrier energies may well affect approaches to the synthesis of superheavy nuclei. Spurred by such speculations we have decided to use the pure Sn beams accelerated to energies of 4-5AMeV that have become available at HRIBF [10] to measure fusion with a heavy neutron-rich target. With the beam energy available the combination of Sn and 64 Ni allowed us to measure excitation function for evaporation residue production at energies above and below the Coulomb barrier. The data were first reported in ref. [11]. This paper will describe how these data were acquired and discuss a possible explanation for the observed enhancement in the fusion cross section. 2. Experimental methods The measurements were carried out at the Holifield Radioactive Ion Beam Facility (HRIBF) at Oak Ridge National Laboratory. Short-lived Sn ions were produced in proton-in-
102 D. SHAPIRA et al. FIGURE 1. Detector arrangement in the experiment. The beam defining detectors were about 1m apart. Target to 3rd timing detector distance was 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 of 238 U and were extracted using the isotope separator on-line technique. Isobars of mass A= were suppressed by extracting molecular SnS + from the ion source and subsequently breaking it up in the charge exchange cell where the SnS + was converted to Sn [10]. The Sn ions were post accelerated by the 25 MV tandem electrostatic accelerator. The beam intensity was measured by particle counting with a combination of a foil and a micro-channel plate detector. The beam passed through a 10 µg/cm 2 carbon foil and the secondary electrons emitted from the foil were steered to a micro-channel plate (MCP) detector and counted. The average beam intensity during our experiment was 2 10 4 particles per second (pps) with a maximum near 3 10 4 pps. The purity of the Sn beam was monitored by measuring the energy loss of the beam ions in an ionization chamber (IC); typically, the contaminants were at a level below 2%. Moreover, all the measurable impurities had a higher atomic number (Z) than Sn. (Lower Z isobars have much shorter lifetimes and, therefore, less of a chance to get out of the ion source.) This impurity (of higher Z elements) has negligible influence on the measurement because the higher Coulomb barrier suppresses the fusion of the contaminants in the beam with the target. Because of the low intensity of radioactive beams, the measurement was performed with a thick, 1 mg/cm 2 self-supporting highly enriched (99.8%) 64 Ni foil target. The evaporation residues (ERs) were detected along with beam particles by a timing detector and a gas filled ionization chamber at 0, as shown in Fig. 1. They were identified by their time-of-flight and energy loss in the IC. In the timeof-flight measurement, the coincidence between the two upstream timing detectors provided the time reference (beam timing). The data acquisition was triggered by the scaled down beam singles or the ER-beam particle coincidences. With this pre-triggering scheme we were able to reduce the random background in our selected data and measure clean evaporation residue data. The pretriggering scheme also reduced the load on the data acquition computer system. We were able to run with an overall dead-time of less than 5% and measure ER cross sections done to energies where the cross section was less than 5 mb. 3. Data reduction and results The ERs were very forward focused because of the inverse kinematics conditions which resulted in good product collection efficiency. One of the disadvantages of using a thick target is the multiple scattering of the beam and reaction products in the target material. This results in a broadening of the angular distribution. The efficiency of the apparatus was estimated by Monte Carlo simulations using the statistical model code PACE [12] to generate the angular distribution of ERs. The efficiency of the apparatus changes from 95 ± 1% for the lowest beam energy to 98 ± 1% for the highest energy. The ER excitation function for Sn+ 64 Ni (solid circles) is compared to those of 64 Ni on even stable Sn isotopes measured by Freeman et al. [13] in Fig. 2. Our measurement using the 124 Sn guide beam is shown by the open circle and agrees well with the measurement of Ref. [13] as shown by the open triangles. In Fig. 2 the energy is scaled by the fusion barrier (V B ) predicted by the Bass model [21] and the ER cross section is scaled by the size of the reactants using R = 1.2(A 1/3 p + A 1/3 t ) fm, where A p (A t ) is the mass of the projectile (target). At energies below the barrier, the ER cross sections for Sn+ 64 Ni are found to be much enhanced compared to those of 64 Ni+ 112 124 Sn which cannot be explained by nuclear size effects. FIGURE 2. Detector arrangement in the experiment. The beam defining detectors were about 1m apart. Target to 3rd timing detector distance was 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. Rev. Mex. Fís. 50 S2 (2004) 101 106
SUB-BARRIER FUSION OF NEUTRON-RICH NUCLEI: Sn+ 64 Ni 103 4. Analysis The measured ER cross sections are compared to coupledchannel calculations using the code CCFULL [15] in Fig. 3. Since fission was not measured in our experiment, it was estimated by PACE. The input parameters were determined by reproducing the ER and fission cross sections of 64 Ni+ 124 Sn in Ref. 16. The calculations predict that fission is negligible for Sn+ 64 Ni and 64 Ni+ 124 Sn at E c.m. 160 MeV. Therefore, the following discussion will be restricted to the data points at E c.m. 160 MeV where the ER cross sections are taken as fusion cross sections. Large sub-barrier fusion enhancement can be seen for both Sn+ 64 Ni and 64 Ni+ 124 Sn as compared to the barrier penetration model (BPM) predictions shown by the dotted curves in Fig. 3. The dashed curves are the result of coupling to inelastic excitation (IE) of the projectile and target. As shown in the right panel of Fig. 3, the calculation reproduces FIGURE 3. Comparison of measured ER excitation functions with CCFULL calculations. The left panel is for Sn+ 64 Ni and the right panel is for 64 Ni+ 124 Sn [13]. The measured ER cross sections are shown by the filled circles and open triangles for Sn+ 64 Ni and 64 Ni+ 124 Sn, respectively. See text for details. the 64 Ni+ 124 Sn cross sections fairly well at low energies. For Sn+ 64 Ni, the calculation significantly under predicts the sub-barrier cross sections as shown in the left panel of Fig. 3. For the Sn-induced reaction, the Q values are positive for 64 Ni picking up two to six neutrons whereas in 64 Ni+ 124 Sn, the ( 64 Ni, 66 Ni) reaction is the only transfer channel which has a positive Q value. This suggests that the observed fusion enhancement may be attributed to multinucleon transfer similar to that observed in 40 Ca+ 96 Zr [4]. Coupled-channels calculations including one-neutron transfer and IE are in good agreement with the fusion cross sections for 64 Ni+ 124 Sn near and below the barrier, as can be seen by the solid curve in the right panel of Fig. 3. Results of calculations including IE, and multi-nucleon transfer channels (nxfr) assuming clusters of neutrons transferred to the ground state are shown by the solid curve in the left panel of Fig. 3. The calculation cannot account for the cross sections near and below the barrier, nevertheless, it illustrates qualitatively the enhancement of sub-barrier fusion due to the coupling to multi-nucleon transfer. More realistic calculations which also consider sequential transfer, as pointed out in Ref. [4], may account for the discrepancy. It is noted that the code CCFULL is suitable for reactions where multinucleon transfer is less important than IE [15] as is the case in 64 Ni+ 124 Sn. While these efforts are still under way [17] one must realize that most of the neutron transfer channels to be incorporated into the coupled channel code have not been measured yet and are unlikely to be measured in the near future. An alternative, simple model that will account for the subbarrier fusion cross section in systems with neutron-rich nuclei is therefore desirable. Such a model was first introduced about a decade ago [18, 19]. In this model enhanced fusion cross sections, at sub-barrier energies, are calculated using a uniform barrier distribution ranging from a threshold barrier to the full Coulomb barrier. In the original papers and in subsequent publications [20] it was shown that the threshold barriers extracted from the measured cross sections were correlated with the neutron separation energy in the colliding nuclei. The underpinnings of this simple model are illustrated in Figs. 4 and 5. Fig. 4 shows the nucleus nucleus potential in a collision of Sn with 64 Ni. The Coulomb barrier reaches a height of 150 MeV at an inter-nuclear distance of 12 fm. Fig. 5 shows the combined shape of the two neutron wells of the approaching nuclei at an inter-nuclear distance near 15 fm (indicated by the vertical line in Fig. 4). At this distance the depression in the combined nuclear wells reaches the same level that matches the separation energy of a single neutron in Sn. At this point, and beyond it at closer inter-nuclear distances where the depression in the combined nuclear well deepens further, the neutron can flow freely between the two nuclei. The inter-nuclear distance ( 15 fm) corresponding to this onset of neutron flow is indicated by a vertical line in Fig.4. The Coulomb barrier height at this radius ( 130meV) corresponds to a threshold barrier. This is Rev. Mex. Fís. 50 S2 (2004) 101 106
104 D. SHAPIRA et al. the distance at which the nuclei begin to interact; if conditions for neutron flow are maintained this may lead to neck formation. The separation energies for neutrons in 131 Sn and 65 Ni are indicated in Fig. 6. Obviously neutron flow conditions continue to be maintained also after the first neutron transfer has occurred. Using a simple algebraic formula sub-barrier cross sections can then be calculated for a flat barrier distribution ranging from the threshold barrier to the full Coulomb barrier. This formalism proved successful in predicting the cross section in several cases involving lighter systems with moderate barrier shifts [18 20]. It has also been shown that threshold barriers extracted from the experimental data track the dependence on neutron separation energy in the colliding nuclei [20]. Using this simple model we tried to apply it to a large body of sub-barrier fusion data [11, 13, 14] for Sn isotopes colliding with 64 Ni. Fig. 7 shows the results from such an attempt. The calculation does not involve any free parameter. The nucleus-nucleus potential is calculated using published systematics [22] and the neutron well parameters were fixed and are listed in the caption of Fig.5. It is obvious that this model predicts very large enhancements but falls short on a few counts. The predicted cross sections are much higher than the measured ones and while the predicted magnitude for the stable isotopes tend to cluster just as the data does the model fails to predict the extra enhancement observed for Sn + 64 Ni. There is clearly something amiss. While very intuitive, this model fails to account for the fact that as a result of the neutron being transferred from the Sn nucleus to the 64 Ni nucleus a neutron pair is broken in Sn and a neutron state in 65 Ni must be occupied as indicated in Fig. 5 (long dashed line). F IGURE 4. Nucleus-nucleus one dimensional potential for Sn+64 Ni. The critical angular momentum for this system is Lorb =102~. The curves show that a few units of angular momentum will not have much effect on the barrier to fusion at low energies. F IGURE 5. The combined neutron wells of Sn(left) and Ni(right) calculated at the distance corresponding to zero threshold (see vertical line in Fig.4). Indicated in the figure are the separation energies of neutrons in the two approaching nuclei. The neutron wells are parameterized with a Woods-Saxon shape and the parameter used for all systems are: depth V=50 MeV, radius R=1.24*A1/3 fm and well diffuseness a=0.68 fm. 64 F IGURE 6. The combined neutron wells of Sn(left) and Ni(right) calculated at the distance corresponding to zero threshold (see vertical line in Fig.4. The separation energies indicated in the figure are for the system after one neutron is transferred from Sn to 64 Ni. The neutron wells are the same as in Fig. 5. 64 Rev. Mex. Fı s. 50 S2 (2004) 101 106
SUB-BARRIER FUSION OF NEUTRON-RICH NUCLEI: Sn+64 Ni F IGURE 7. Comparison of predicted sub-barrier fusion cross sections with data taken for several Sn isotopes [11, 13, 14]. The range of data for the stable isotopes is represented by vertical bars in the picture. A simple way to incorporate this fact into the neutron flow model comes from realization that the initial transfer step requires that the neutrons have extra energy (the Q-value for the neutron transfer reaction) above the depression in the combined neutron well to make the transition from the initial state to the final state. For this to happen the depression has to get deeper, i.e., the colliding nuclei must be closer. Once this initial transfer has occurred further flow is facilitated since the neutron separation energies in 131 Sn and 65 Ni are much smaller. We therefore modified the model to incorporate this requirement in the calculation of threshold barriers. The results from this calculation, shown in Fig. 8, account very well for the trends seen in the data. The clustering of the stable isotope data as well as the enhancement in the Sn results are well reproduced. It turns out that this recasting of the neutron flow model also addresses some of the shortcomings noted in the original publication regarding the cross section of 112,116,122 Sn on 40 Ar [19]. It also predicts correctly that the sub-barrier cross section for 112 Sn + 64 Ni is higher than some of the other systems, after nuclear size effects are removed. There are several assumptions made in this model that should be noted: The degree of nuclear overlap is still small enough that the two neutron shells are separate and independent. The flow conditions are initiated by the transfer of a single neutron, not a pair. The change in nuclear spin of the transferred neutron is ignored. The barrier distribution resulting form the initiation of neutron flow is flat. 105 F IGURE 8. Comparison of predicted sub-barrier fusion cross sections to data for several Sn isotopes. Cross sections are calculated with the neutron flow model where flow is initiated by the sharing of a single neutron between the two nuclear wells. The model allows for the difference in neutron separation energies in the two positions. The data are from [11, 13, 14] and the range of data for the stable isotopes is represented by vertical bars in the picture. It is obvious that by its nature this model ignores any aspects of nuclear structure affecting the neutron transfer; once the critical distance is reached the probability to transfer is unity. As can be also seen in seen in Fig. 4 a change of a few units of orbital angular momentum does not affect the height of the barrier to fusion, allowing us to ignore changes in the spin state of the transferred neutron. One must realize that other processes affect the barrier distribution as well, and may produce a barrier distribution that is not flat. The aim of this calculation was to present a simple schematic model that would be suitable for predicting the degree of enhancement (order of magnitude) one might expect for sub-barrier fusion with unstable neutron-rich nuclei. 5. Summary We have presented new data on fusion of 64 Ni with Sn which show a large enhancement in sub-barrier fusion cross sections which could not be explained by size effects or by simple coupling orfr direct reaction channels to the fusion process. We also suggest a simple model that can account for the large enhancement observed in sub-barrier fusion cross sections for this system. Acknowledgments This research was sponsored by the Office of Science, U.S. Department of Energy under contract DE-AC05-00OR22725 managed by UT-Battelle, LLC. Rev. Mex. Fı s. 50 S2 (2004) 101 106
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