-Particle Production in the Reaction 6Li + 28Si at Near-Barrier Energies

VOLUME 90, N UMBER 20

PHYSICA L R EVIEW LET T ERS

week ending 23 MAY 2003

-Particle Production in the Reaction 6 Li 28 Si at Near-Barrier Energies A. Pakou,1 N. Alamanos,2 A. Gillibert,2 M. Kokkoris,3 S. Kossionides,3 A. Lagoyannis,1 N. G. Nicolis,1 C. Papachristodoulou,1 D. Patiris,1 D. Pierroutsakou,4 E. C. Pollacco,2 and K. Rusek 5 1

Department of Physics, The University of Ioannina, 45110 Ioannina, Greece 2 DSM/DAPNIA CEA SACLAY, 91191 Gif-sur-Yvette, France 3 National Research Center, Demokritos, Greece 4 INFN Sezione di Napoli, I-80125, Napoli, Italy 5 Department of Nuclear Reactions, The Andrzej Sołtan Institute for Nuclear Studies, Hoz˙a 69, 00-681 Warsaw, Poland (Received 27 January 2003; published 19 May 2003) The production of particles in the 6 Li 28 Si reaction was studied at near-barrier energies. Angular distributions were performed at four bombarding energies, namely, 7.5, 9, 11, and 13 MeV. The distributions were characterized by a Gaussian shape, which was integrated in order to obtain -particle cross sections. Our results were compared with previous data of 6 Li scattering on various heavier targets and found to exhibit a universal behavior. Present continuum-discretized-coupledchannel calculations support the obtained data. The consequences of the systematic behavior of the -particle production on the unusual behavior of the imaginary potential observed previously in elastic scattering of weakly bound systems is discussed. DOI: 10.1103/PhysRevLett.90.202701

PACS numbers: 25.70.Bc, 24.10.Eq, 25.60.Gc, 25.70.Hi

At energies close to the Coulomb barrier, coupled channel effects appear strong and are manifested in various reaction channels, e.g., in near-barrier and subbarrier fusion as a cross section enhancement or in elastic scattering as a threshold anomaly in the optical potential. For stable systems, the above picture is to some extent well understood while for the weakly bound ones and moreover the exotic nuclei with halo or skin structures this is not true, since an additional coupling due to the influence of breakup effects complicates the situation. Concerning the elastic scattering of weakly bound systems, it was suggested before [1] that the threshold anomaly, which appears as a localized peak in the strength of the real potential, associated with a sharp decrease in the strength of the imaginary potential, may disappear. Subsequently, several studies have been undertaken to resolve the issue [2 –8]. In a very recent study [9] on the elastic scattering of 6 Li 28 Si, an unusual behavior in both the real and imaginary parts of the optical potential was established at near-barrier energies. More explicitly, the normalization factor of the real part of the doublefolding potential was found to remain constant and reduced by 40% exhibiting the same behavior as the one which is established for weakly bound nuclei at energies well above the Coulomb barrier [2,4,10 –13]. The normalization factor of the imaginary potential was found to present an increasing trend with decreasing energy. Therefore, it was suggested that the influence of an additional strong breakup and/or transfer channel developed around the barrier produces a more repulsive, possibly energy-dependent, polarization potential which compensates the attractive part of the real potential. Into this context, we report in the present Letter the measurement of the -particle production channel cross section in the 6 Li 28 Si system at energies near the Coulomb barrier

trying to enlighten further the situation. Previous work concerning the -particle channel in the scattering of 6 Li on heavier targets [3,7,14,15] is also considered. We also report continuum-discretized-coupled-channel calculations (CDCC) for the production for the systems 6 Li 28 Si and 6 Li 208 Pb. Our experimental setup was described in detail in a previous work [9] and only a short summary pertinent to this work is given here. A 6 Li2 beam was delivered by the TN11/25 HVEC 5.5 MV Tandem accelerator of the National Research Center of Greece-Demokritos at four bombarding energies, namely, 7.5, 9, 11, and 13 MeV. Beam currents were of the order of 30 nA. The beam impinged on a 180 m thick, self-supported natural silicon target tilted by 40 (depending on the detector position) and the reaction products were detected in two solid state surface barrier telescopes (the E silicon detector was 10 m thick, while the E detector was 300 m thick) in an angular range 27 up to 60 in the laboratory system. The alpha group was well discriminated in the forward detectors with the E-E technique. The detectors were set 30 cm far from the target on a remote control rotating table, one on the left and the other on the right hemisphere of the chamber to compensate for possible noncentrality beam problems. Tantalum masks were placed in front of each telescope and each detector and an angular resolution of 0:7 was obtained. This angular uncertainty was estimated to be 2 due to the beam divergence. The subtending solid angle was 1:2 104 sr. An overall normalization was obtained at each energy by placing two monitor Si(Li) detectors, 300 m thick, at 15 , fixed on a top table concentric to the bottom rotating one and measuring the elastic scattering of lithium. The scattering at 15 , with the present bombarding energies, can be considered as being pure

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 2003 The American Physical Society

0031-9007=03=90(20)=202701(4)$20.00

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Rutherford. A liquid-nitrogen cold trap close to the target holder minimized the target contamination on carbon. This was confirmed at the end of the runs in a separate Rutherford backscattering experiment [16] during which the carbon contaminant was estimated and the target thickness was established. In Fig. 1, a two dimensional E-E spectrum is displayed, observed at 13 MeV by a detector set at lab 60 . Three different groups of reaction products are well separated. One of them corresponds to alpha particles the origin of which may be attributed to the following reactions: (i) exclusive breakup of 6 Li 28 Si into d (or p n) with Q 1:475 MeV and (ii) n and/or p transfer 28 Si6 Li; 5 Li 5 Li ! p 29 Si and 28 Si6 Li; 5 He 5 He ! n 29 P with Q 2:81 and 1:84 MeV correspondingly. An energy spectrum obtained by setting a contour around the -particle group is shown in the inset of Fig. 1. The dominant feature of the spectrum is a broad continuum characteristic of three body interactions. For angles less than lab 30 a sharp peak was also seen on the top of the broad continuum which may be attributed to two-body final state interactions (sequential decay via a resonant state of 5 Li). Since our measurements were limited down to 27 this peak was not further considered. Angular distributions corresponding to the alpha group are shown in Fig. 2, exhibiting a bell shape. Parameters (centroids and widths) obtained as best fits to this bell shaped part assuming a Gaussian distribution are given in Table I. An energy dependence of both centroid and width is apparent. In fact, while for the lower bombarding energies, centroids are closer to the grazing angle [9], moving to higher energies the maxima of the distributions diverge towards larger angles than the grazing one, indicating a strong absorption. The widths of the distri-

butions are narrow at low energies and wide at higher energies. Narrow widths suggest a time scale for the emission comparable to the collision time between the incoming projectile and target. This may be the case if transfer occurs and it is supported by a calculation reported previously for the 6 He 209 Bi system [17]. The broad widths may indicate the contribution of breakup through sequential decay at higher energies. For a more quantitative explanation of the energy dependence of both centroids and widths additional data are required, on pure breakup and transfer. In the same table cross sections obtained from the integration of the Gaussian part of the distribution are compared with total reaction cross sections obtained by fitting elastic scattering measurements [9]. (The influence of the constant part of the distribution was negligible and is omitted.) The assigned errors to these values result from a sensitivity analysis performed in the above cited work. In Fig. 3, present results of -production cross sections are compared with previously published ones concerning 6 Li scattering on various targets, as a function of lithium bombarding energy over the Coulomb barrier. As is seen, present and previous data of lithium scattering on 28 Si, 58 Ni, 118 Sn, and 208 Pb [14,15] present a very good consistency among them. In fact, all data, except the ones of 6 Li 208 Pb by Kelly et al. [7] which level off as a function of the bombarding energy earlier than the other points, present a universal behavior. To get a more comprehensive idea about the situation, we performed CDCC calculations for the systems; 6 Li 28 Si and 6 Li 208 Pb. Our goal was to determine -production cross sections (total fusion ) rather than pure breakup reported previously [3,7], in order to obtain meaningful comparisons with the data.

Li+28Si

6

dσ/d Ω(mb/sr)

ELi=13.0 MeV *7.0 ELi=11.0 MeV *5.5 ELi=9.0 MeV *8.0 ELi=7.5 MeV *9.0

Θc.m. FIG. 1 (color online). E-E two dimensional spectrum taken at 13 MeV, 60 for the system 6 Li 28 Si. The energy spectrum, shown as an inset, corresponds to the -particle group.

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FIG. 2 (color online). Angular distributions of the group at various bombarding energies measured in the present work. The curves are the best Gaussian fits to the bell shaped part of the distribution.

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TABLE I. Best fit parameters (C: centroid, W: width) obtained via a Gaussian fit of the bell shaped part in the angular distributions of Fig. 2. The cross sections deduced by integration of this Gaussian part are also shown and are compared with total reaction cross sections obtained in a previous publication [9]. Ebomb (MeV) (mb) reaction (mb) 7.5 9.0 11.0 13.0

20 14 86 13 424 52 533 76

298 21 603 25 954 35

C (deg)

W (deg)

53:9 1:0 13:3 5:9 54:8 1:0 19 2 60:0 2:1 34 10 47:6 3:2 44:9 9:8

σ (mb)

These calculations were performed using version FRXP.18 of the code FRESCO [19] at laboratory energies 29, 33, 39, 42, 48, 52, 100 MeV for 208 Pb and at 7.5, 9, 11, 13 MeV for 28 Si. The model used was very close to that of Refs. [3,7]. It was assumed that the nucleus 6 Li has a twobody d cluster structure. Couplings between resonant and nonresonant cluster states corresponding to the d relative orbital angular momentum L 0; 1; 2

E/VC.b FIG. 3 (color online). particle cross sections in reactions involving 6 Li scattering on various targets. Present data: 6 Li 28 Si are designated with solid circles. Previous data: 6 Li 58 Ni, 6 Li 118 Sn, 6 Li 120 Sn, and 6 Li 208 Pb [15] are designated with solid stars, up and down solid triangles, and solid boxes, correspondingly. Previous more recent data on 6 Li 208 Pb obtained by Signorini et al. [14] are designated with open boxes and data obtained by Kelly et al. [7] are designated with open circles. Calculated production cross sections (see text) are designated with the solid curve for the system 6 Li 208 Pb and with the dash-dotted curve for the system 6 Li 28 Si. Data concerning the system 6 He 209 Bi [17] are designated with open stars. Coulomb barriers were obtained from the measurements of Refs. [9,15] as 6.2, 11, 16.5, 16.5, and 25 MeV in the center of mass for the targets 28 Si, 58 Ni, 118 Sn, 120 Sn, and 208 Pb correspondingly. These barriers are 12% lower than values according to the Broglia relation [18]. In that respect the barrier adopted for 6 He was 18.1 MeV in the center of mass.

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were included. The continuum above the 6 Li ! d breakup theshold was discretized into momentum bins. The width of most of the bins was set to k 0:26 fm1 . In the presence of the 3 , 2 , and 1 , L 2, resonant states the binning scheme was suitably modified in order to avoid double counting. For the 208 Pb target, the d continuum was truncated at momentum k 0:78 fm1 while for the 28 Si this upper limit was slightly reduced according to the lower c.m. energy of the scattered system. All the diagonal and coupling potentials were generated from empirical target and d target optical model potentials for the corresponding target nucleus by means of the single-folding technique. For the 208 Pb target these potentials were the same as in Ref. [3], while for the 28 Si target the corresponding potentials were adopted from Refs. [20,21]. In this way the following quantities were extracted: elastic scattering cross sections, total reaction cross sections, and breakup cross sections. The elastic scattering calculations described well all the measured angular distributions of the differential cross sections for 6 Li elastic scattering for both Si and Pb target nuclei [2,3,9]. In addition, fusion cross sections were also extracted from our CDCC calculations, but by using the method described in Ref. [22] by means of the barrier penetration model. For this purpose, effective potentials were obtained for each of the investigated systems and for each energy. Optical model calculations with these effective potentials reproduced well the CDCC result for the elastic scattering. Our results concerning the production are shown in Fig. 3, where we plot the difference between the calculated total reaction cross section and the fusion cross section by a dash-dotted line for the system 6 Li 28 Si and a solid line for the system 6 Li 208 Pb. It is seen that the calculation for the system 6 Li 208 Pb is compatible to the universal behavior of the data. On the other hand, the calculation for the 6 Li 28 Si system declines by 40%. This was unexpected and may suggest that the calculated fusion cross section for the light target is overestimated under the present model. Fusion cross section measurements in this energy range with light targets are necessary to disentagle this point. Calculated ratios of pure breakup cross sections over production are displayed in Fig. 4(a). It is seen that while for the heavy target breakup plays a major role in the production, especially around the barrier, for the light target breakup is of minor importance and other reaction channels are dominant. This fact might have played a decisive role in the overestimation of the fusion cross section for the light target. Finally, the -production cross section of 6 He 209 Bi [17] is also displayed in Fig. 3 to point out the striking difference between the behavior of the weakly bound nucleus 6 Li and its ‘‘associate’’ halo nucleus 6 He. The -production cross section of 6 He differs by an order of magnitude from 6 Li. To clarify further this point, we 202701-3



b.

σα-production/σreaction

σbreak/σα-production

a.

E/VC.b FIG. 4 (color online). (a) Ratios of CDCC calculated breakup cross sections over -production cross sections for the systems 6 Li 28 Si (dash-dotted line) and 6 Li 208 Pb (solid line). (b) Ratios of measured -production cross sections over total reaction cross sections for some of the systems displayed in Fig. 3 and according to the same symbols. Total reaction cross sections were obtained from calculations concerning elastic data reported previously [9]. The line is a linear best fit to the data and it is there to guide the eye.

present in Fig. 4(b) the ratio of -production cross sections over the total reaction cross sections as a function of bombarding energy over the Coulomb barrier. As is seen approaching the Coulomb barrier the -particle production in respect to the total reaction cross section, for both 6 Li and 6 He projectiles, presents an increasing behavior. This fact implies that transfer and/or breakup accounts for the increasing behavior of the imaginary potential obtained previously [9,17]. In conclusion, we have measured near-barrier -production cross sections for the weakly bound nucleus 6 Li on 28 Si. Our results exhibit the same universal behavior obtained previously by the 6 Li scattering on heavier targets, excluding a strong dependence on the mass number of the target. The measurements are supported by CDCC calculations for the 6 Li 208 Pb system, while calculations for the 6 Li 28 Si decline by 40% perhaps due to overestimation of the fusion cross section for light targets into the present model. A comparison of calculations for breakup and -production cross sections indicates that, at near-barrier energies, breakup is a substantial reaction channel for the heavy target while for the light one this channel is negligible and transfer plays

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the major role. It was also demonstrated that approaching the Coulomb barrier, the -production yield either due to breakup or/and to transfer almost exhausts the total reaction cross section. This systematically occurs for the 6 Li scattering on various targets as well as the 6 He scattering on 209 Bi. Therefore we can suggest that the unusual behavior observed previously in the elastic scattering of 6 Li on various targets is directly related with the behavior of production. Similar behavior can be expected for weakly bound radioactive nuclei. We warmly acknowledge Mr. John P. Greene from Argonne National Laboratory for providing the silicon targets and the personnel of NPL-Ioannina and Demokritos for helping with the experiment. One of us (K. R.) acknowledges partial support by State Committee for Scientific Research (KBN) of Poland via Grant Polonium No. 4335.

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