DHalo nuclei follow rutherford elastic scattering at energies below the barrier? the case of 11Li

Do Halo Nuclei Follow Rutherford Elastic Scattering at Energies Below the Barrier? The Case of 11Li M. Cubero, 1,2 J. P. Ferna ´ndez-Garcı ´a, 3,4 M. Rodrı ´guez-Gallardo, 3 L. Acosta, 5 M. Alcorta, 1 M. A. G. Alvarez, 3,4 M. J. G. Borge, 6, *L. Buchmann, 7 C. A. Diget, 8 H. Al Falou, 9 B. R. Fulton, 8 H. O. U. Fynbo, 10 D. Galaviz, 11 J. Go ´mez-Camacho, 3,4 R. Kanungo, 9 J. A. Lay, 3 M. Madurga, 6 I. Martel, 5 A. M. Moro, 3 I. Mukha, 4 T. Nilsson, 12 A. M. Sa ´nchez-Benı ´tez, 5 A. Shotter, 7,13 O. Tengblad, 6 and P. Walden 7 1 Instituto de Estructura de la Materia CSIC, E28006 Madrid, Spain 2 CICANUM, Universidad de Costa Rica UCR, Apartado 2060 San Jose ´, Costa Rica 3 Departamento de FAMN, Universidad de Sevilla, 41080 Seville, Spain 4 Centro Nacional de Aceleradores, Universidad de Sevilla/Junta de Andalucı ´a/CSIC, 41092 Seville, Spain 5 Departamento de Fı ´sica Aplicada, Universidad de Huelva, 21071 Huelva, Spain 6 Instituto de Estructura de la Materia CSIC, E28006 Madrid, Spain 7 TRIUMF, V6T2A3 Vancouver, British Columbia, Canada 8 Department of Physics, University of York, YO 10 5DD Heslington, York, United Kingdom 9 Department of Astronomy and Physics, Saint Mary’s University, Halifax B3H3C3, Nova Scotia, Canada 10 Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus, Denmark 11 CFNUL, Universidade de Lisboa, 1649-003 Lisbon, Portugal 12 Fundamental Physics, Chalmers University of Technology, 41296 Go ¨teborg, Sweden 13 School of Physics and Astronomy, University of Edinburgh, EH9 3JZ, Edinburgh, United Kingdom (Received 7 October 2012; published 26 December 2012) The first measurement of the elastic scattering of the halo nucleus 11Li and its core 9Li on 208Pb at energies near the Coulomb barrier is presented. The 11Li þ208Pb elastic scattering shows a strong reduction with respect to the Rutherford cross section, even at energies well below the barrier and down to very small scattering angles. This drastic change of the elastic differential cross section observed in 11Li þ 208Pb is the consequence of the halo structure of 11Li, as it is not observed in the elastic scattering of its core 9Li at the same energies. Four-body continuum-discretized coupled-channels calculations, based on a three-body model of the 11Li projectile, are found to explain the measured angular distributions and confirm that the observed reduction is mainly due to the strong Coulomb coupling to the dipole states in the low-lying continuum of 11Li. These calculations suggest the presence of a low-lying dipole resonance in 11Li close to the breakup threshold. DOI: 10.1103/PhysRevLett.109.262701 PACS numbers: 25.60.Bx, 25.60.Gc, 25.60.t One century ago, Rutherford [1] inferred the structure of the atom from the reaction data measured by Geiger and Marsden [2]. Since then, nuclear structure properties have often been deduced from nuclear reaction studies. With the advent of the first accelerated radioactive beams, new nuclear structures were discovered, such as the existence of a halo in some very loosely bound nuclei. In fact, 25 years ago, Hansen and Jonson [3] interpreted the large interaction cross section observed in 11Li with light targets by Tanihata et al. [4] as due to the high probability of the outermost nucleons to be at large distances from the central core, which they referred to as a halo structure. The halo structure is a threshold phenomenon due to the low binding energy of the last nucleons. Halo nuclei have several features in common, such as a rather compact core, an extended neutron distribution, and very few, if any, excited states. The discovery of halo nuclei brought renewed interest in the modeling of nuclear reactions. This peculiar structure should affect the reaction properties at near-Coulomb barrier energies. Due to their low binding energy, the description of reactions involving halo nuclei should incorporate the coupling into the continuum. Current approaches to reaction theory involve different approximations whose validity needs to be checked when applied to halo nuclei. The most neutron-rich bound lithium isotope, 11Li,isa fascinating case. Predicted to be unbound, it was identified in 1966 [5] and it is the archetype of a Borromean halo nucleus; i.e., the two different binary subsystems, 9Li-nand n-n, are unbound, whereas the three-body system is bound by S2n¼369:15 0:65 keV [6]. The ground state density distribution of 11Li extends well beyond its core; i.e., the rms matter radius for the 9Li isotope is 2:44 0:06 fm [7], while for 11Li reported values are one fermi larger. No bound excited states are known, but several resonances at 1.1 MeV (0:5 MeV) and 2.5 MeV (1:5 MeV) have been identified in different reaction studies with light ions (see Ref. [8] for a recent review). Theoretical models predict also different low-lying resonances with J nn ¼0þ and 1[9–13], but their existence and precise location have not been clearly established experimentally. Due to the loosely bound structure, the neutron halo is easily polarizable in the strong electric field of a heavy PRL 109, 262701 (2012) PHYSICAL REVIEW LETTERS week ending 28 DECEMBER 2012 0031-9007=12=109(26)=262701(5) 262701-1 Ó2012 American Physical Society target such as 208Pb. In contrast to normal nuclei, where the E1response is dominated by the giant dipole resonance, large soft electric dipole (E1) strength close to the breakup threshold has been observed in halo nuclei. The strongest E1transition observed at low excitation energy was determined in an exclusive measurement of the Coulomb dissociation of 11Li at 770 MeV at RIKEN [14]. This large E1strength will induce a strong dynamic polarization effect of the 11Li projectile when scattered with a heavy target, giving rise to long-range Coulomb couplings. According to Ref. [15], this effect should manifest itself at Coulomb barrier energies as a departure from the elastic Rutherford scattering. In order to disentangle the contribution of the loosely bound structure of 11Li from the reaction process, one should know the behavior of the core, 9Li, under the same conditions. No data exist for the scattering of 11Li near the Coulomb barrier, and even for 9Li the scattering data are scarce. The cross section of 9Li on the 208Pb target was measured at 86 MeV [16], but this energy is three times the Coulomb barrier. Near the Coulomb barrier, the fusion cross section of 9Li þ208Pb was measured at centerof-mass (c.m.) energies from 23.9 to 43.0 MeV [17]. However, the elastic cross section was not reported. This Letter reports on the first measurement of the scattering of the halo nucleus 11Li on 208Pb at incident energies of 24.3 and 29.8 MeV, which are, respectively, below and around the Coulomb barrier (Vb28 MeV). To characterize the behavior of the core, the 9Li þ208Pb scattering has also been measured with the same setup and at the same c.m. energies of 23.1 and 28.3 MeV. The 11Li elastic scattering data show a stronger reduction of the cross section than predicted in Ref. [15] for this reaction. These data have been compared with four-body continuumdiscretized coupled-channels (CDCC) calculations, based on a three-body description of the 11Li nucleus, which takes into account, in addition to the dipole Coulomb couplings, other Coulomb multipoles and nuclear couplings to all orders. The experiment was performed in the postaccelerated ISAC-II line at the TRIUMF facility (Vancouver, Canada). A primary 500 MeV 100 Aproton beam produced at the TRIUMF cyclotron irradiated a Ta primary target. The secondary beams of Li isotopes were transported to the ISAC-II facility for postacceleration [18]. The average intensity of the 11Li beam, as detected in our monitor detector located 280 mm downstream of the Pb target, was 4300 11Li=s. The accelerated incoming beam impinged on a 208Pb target tilted 75with respect to the beam direction. For the 9Li study, two 208Pb targets with different thicknesses 1.45 and 1:9mg=cm2were used. Only the 1:45 mg=cm2 208Pb target was bombarded by the 11Li beam, in order to minimize the loss of energy resolution due to straggling in the target. The experimental setup consisted of four telescopes, T1-T4. Two of them, T1and T2, were placed in the target forward direction, each one consisting of a windowless 40 mthick double-sided silicon (16 16) strip detector (DSSSD) [19] acting as a Edetector and a 500 mthick Si PAD as an Edetector. Telescopes T3and T4were placed in the target backward direction, and each one consisted of a20 mthick Esingle-sided silicon (16) strip detector and a 60 mthick DSSSD (16 16) behind. The segmentation of the detector system gives information of 256 pixels per telescope either by matching front and back strips of the DSSSD for telescopes 1 and 2 or front and back detectors in telescopes 3 and 4. This configuration permitted a high angular resolution (2–3, depending upon the detector) with large angular coverage: 10to 40(T1), 30to 60(T2), 50to 100(T3), and 90 to 140(T4)[20]. Due to the compact geometry used in the setup, a refined determination of the angle subtended by each pixel of T1and T2was done based on the fact that the elastic scattering of 9Li on 208Pb at energies below the barrier follows the Rutherford scattering formula. For the 11Li þ208Pb data, the method was applied to the sum of elastic and breakup data. Further details on the setup, data processing, and event selection can be found in Refs. [20,21]. Elastic events were selected in the two-dimensional plot of Eversus EþEenergy spectra for each pixel. A clear identification of the elastic peaks and fragments, both in the 9Li and in the 11Li scattering data, was achieved. Figure 1illustrates the data obtained for 9Li and 11Li beams scattered on the same 1:45 mg=cm2thick 208Pb target and at equivalent c.m. energies. The twodimensional plot for the 11Li scattered data, on the bottom part of Fig. 1, shows the contribution of the elastic channel and the 9Li breakup data. The pixels contributing to the selected angular ring of ð14 1Þare displayed on the lefthand side of the figure. The relatively large contribution of the breakup channel observed at this low energy and forward angle is remarkable. In Fig. 2, we show the two-dimensional plot corresponding to 9Li þ208Pb scattered data at a c.m. energy of 28.3 MeV for a pixel of telescope 4 centered at 128.2. It is remarkable that, at this near-threshold energy, one can identify 8Li events likely corresponding to the transfer reaction 208Pbð9Li;8LiÞ209Pb (Q¼0:1 MeV) and the possible contribution of 7Li þ210Pb (Q¼3 MeV) and  production from transfer or breakup, observed at very high energies [22]. The contribution of these channels, when present, has been removed in order to extract the elastic scattering data. The differential cross section for each detector was calculated by the sum of the counts in each pixel divided by the sum of their solid angles corresponding to a given angular ring. The measured elastic angular distributions for 9Li and 11Li on 208Pb are displayed in Fig. 3, relative to the PRL 109, 262701 (2012) PHYSICAL REVIEW LETTERS week ending 28 DECEMBER 2012 262701-2 Rutherford cross section. The upper and lower panels correspond to Ec:m:¼23:1and 28.3 MeV, respectively. For the lower energy (below the Coulomb barrier), the 9Li data are very close to the Rutherford cross section, whereas, for the higher energy, a Coulomb-nuclear interference maximum starts to be visible at c:m:75, accompanied by a smooth decrease beyond this angle. This is reminiscent of the Fresnel-type pattern characteristic of the scattering of ‘‘normal’’ nuclei near the Coulomb barrier. On the other hand, the 11Li data show a strong reduction with respect to Rutherford, even at the energy below the barrier. Moreover, the departure from Rutherford scattering at both energies starts at very forward angles. This behavior has been observed previously in the scattering of 6He [23] and 11Be [24], although the observed reduction was not as striking as in the 11Li case. For a more quantitative understanding of this behavior, we have compared the 11Li þ208Pb data with four-body CDCC calculations. The CDCC method [25,26] is a generalization of the coupled-channels formalism traditionally used in the analysis of inelastic reactions populating excited states of the projectile or target. In CDCC, the model space is extended so as to include the unbound states of the projectile, thus allowing the evaluation of the projectile breakup and its effect on the elastic scattering. Since the positive energy states form a continuum, a discrete representation in terms of a finite set of square-integrable functions is commonly used. Due to the Borromean structure of the 11Li nucleus, we use here a recent extension of the method appropriate for three-body projectiles (four-body CDCC). This kind of calculation has successfully been used to describe several 6He induced reactions [27–29]. FIG. 2 (color online). Two-dimensional plot of Eversus EþEfor 9Li cattering on a 1:9mg=cm2 208Pb target at Ec:m:¼28:3 MeV for a pixel at 128.2. Note the presence of breakup channels already at this energy. FIG. 3 (color online). Elastic differential cross section of 9Li and 11Li on 208Pb, plotted as a ratio to the Rutherford cross section. In the upper part, it is shown for energies below the barrier, Ec:m:¼23:1 MeV, and in the bottom part for Ec:m:¼ 28:3 MeV. The optical model (OM) calculation for the 9Li þ 208Pb system is also shown in each panel. For details on the fourbody CDCC calculations, see the text. FIG. 1 (color online). Two-dimensional plot of Eversus EþEin T1displayed for the pixels illustrated on the left part of the figures. The scattered 9Li þ208Pb data are shown in the upper part for only one pixel centered at 13.9. In the bottom figure, the scattered 11Li þ208Pb data are shown in the angular sector of ð14 1Þ. Contributions from the elastically scattered 11Li and 9Li reakup data are distinctly separated. The data correspond to the same c.m. energy of 23.1 MeV. PRL 109, 262701 (2012) PHYSICAL REVIEW LETTERS week ending 28 DECEMBER 2012 262701-3 To describe the 11Li nucleus, a three-body structure is assumed with an inert and spinless 9Li core surrounded by two valence neutrons. The 11Li states were obtained solving the Schro ¨dinger equation in hyperspherical coordinates. We took the two-body interactions P4from Ref. [30]. In addition, an effective three-body force was included and adjusted to reproduce the experimental twoneutron separation energy. This gave a ground state wave function with a rms of 3.30 fm, assuming a rms of 2.44 fm for the 9Li core [7]. Continuum states were grouped into energy bins, up to a maximum energy of 5 MeV, following the average method, recently extended to the three-body continuum [29]. Continuum states with J nn ¼0þ,1,2þ, and 3were included. The elastic differential cross section for this reaction is very sensitive to the BðE1Þstrength close to the threshold and, in particular, to the presence of a dipole resonance. Since the precise location of this resonance has not yet been firmly established, we have adjusted the position of this resonance to the energy that best reproduces the elastic and breakup cross sections. The latter will be presented in a separate work [31]. This gives Eres ¼0:69 MeV (i.e., 0.32 MeV above the breakup threshold). To place the dipole resonance at the desired position, the three-body force has been adjusted for the 1continuum. This model predicts a large E1strength at low energies, even larger than that extracted experimentally [14]. For the scattering calculations, the nþ208Pb and 9Li þ 208Pb interactions are also required. The former was taken from the global parametrization of Koning and Delaroche [32]. The real part of the 9Li þ208Pb potential was generated microscopically, using the double-folding Sa ˜o Paulo potential [33], with the 9Li matter density from Ref. [7] and the 208Pb density from a Hartree-Fock calculation. The imaginary part was parametrized using a Woods-Saxon potential for which the parameters (Wv,ri,ai), along with the normalization of the real part (Nr), were adjusted in order to reproduce the present 9Li elastic data at Ec:m:¼ 28:3 MeV, giving rise to the parameters Nr¼1:0,Wv¼ 46:5 MeV,ri¼1:33 fm, and ai¼0:47 fm. The optical model calculations for 9Li þ208Pb are compared with the data in Fig. 3(for further details about the procedure, see Ref. [20]). The CDCC coupled differential equations were solved with the code FRESCO [34], including both nuclear and Coulomb couplings between the target and the projectile to all orders. The four-body CDCC calculations are compared with the 11Li þ208Pb data in Fig. 3. To illustrate the effect of the coupling to the breakup channels, we have included also the calculation in which these couplings are omitted (dotted line). This four-body CDCC calculation without coupling to the continuum follows the 9Li data up to 90but then decreases faster than the 9Li data beyond this angle, as illustrated in the lower part of Fig. 3. This reduction is due to the absorptive effect arising from the interaction of the halo neutrons with the target and also to the extended size of the 11Li ground state. This diminution, however, is found to be insufficient to explain the 11Li data. Including the coupling to the continuum produces an additional reduction, and the resulting angular distribution is found to describe very well the data at both energies. At Elab ¼24:3 MeV, the CDCC calculations underestimate the data at the largest angles. Inclusion of continuum states of even larger angular momenta (e.g., J nn ¼4þ) could increase the calculated elastic cross sections even further. Our CDCC calculations indicate that the main interactions responsible for the reduction of the elastic cross section and the subsequent disappearance of the Coulomb-nuclear interference peak are the dipole Coulomb couplings. This special behavior of 11Li has been associated with the effect of Coulomb dipole polarizability [15]. The weakly bound 11Li, in the strong Coulomb field of the target, gets distorted and eventually breaks up. This reduces the elastic cross sections similarly below (Ec:m:¼23:1 MeV) and at the barrier top (Ec:m:¼28:3 MeV), where the absence of the Coulomb-nuclear interference peak is extraordinary. In summary, the first measurement of the elastic scattering of the halo nucleus 11Li and its core 9Li on 208Pb at energies below and on top of the Coulomb barrier is presented. The 9Li þ208Pb scattering data follow the expected behavior for well-bound nuclei, obeying the Rutherford formula below the barrier and exhibiting a Fresnel-like diffraction pattern above the barrier. On the other hand, the 11Li þ208Pb elastic cross section departs significantly from the standard behavior of a well-bound nucleus such as its core 9Li, showing a strong reduction with respect to the Rutherford cross section both below and around the Coulomb barrier. Four-body CDCC calculations, using a three-body model of 11Li and including Coulomb and nuclear couplings to all orders, reproduce satisfactorily the experimental elastic angular distributions. The reduction of the cross section with respect to the Rutherford scattering is attributed to the strong dipole coupling between the ground and the continuum states in 11Li. The presence of a low-lying dipole resonance, close to the breakup threshold, is found to improve the agreement with the data. This work has been partially supported by Spanish National Projects No. FPA2009-07387, No. FPA200907653, No. FPA2009-08848, and No. FPA2010-22131C02-01, by the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042), and by the U.K. Science and Technology Facilities Council through Grant No. EP/ D060575/1. M. C. acknowledges the support of the CSIC-UCR and FCT Grant No. ISFL-2-275. *[email protected] [1] E. Rutherford, Philos. Mag. 21, 669 (1911). [2] H. Geiger and E. Marsden, Proc. R. Soc. 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