Elastic scattering and total reaction cross sections for the 12B+58Ni system

Angular distributions for elastic scattering of radioactive 12B projectile on 58Ni target have been measured for the first time. They were obtained at two energies, ELab = 30.0 and 33.0 MeV, close to the Coulomb barrier. These angular distributions were analyzed with the conventional optical model using Woods-Saxon shape and double-folding São Paulo potentials. The total reaction cross sections were extracted from this analysis and compared with other similar masses systems.


Introduction
The structure of stable nuclei has been extensively investigated through direct reactions. However, nowadays, a great interest has been devoted to the study of properties of light proton and neutron rich nuclei away from the stability valley. Some of these radioactive nuclei can be called exotic due to their anomalous structures. Nuclei such as 6 He, 8 B, 11 Li, 11 Be, and 15 C can exhibit large radial extension, as compared to the stable ones, in which the valence nucleons extend outside the binding potential, forming a halo structure [1]. Elastic scattering measurements at low energy are very useful tool to investigate the static effects (nuclear structure) of the nuclei involved and dynamic effects (coupling of reactions channels) in the collisions [2,3]. In the recent past years, several experiments have been dedicated to the investigation of elastic scattering induced by these light radioactive nuclei [2,4]. The elastic scattering of the proton-rich exotic nucleus 8 B on 58 Ni has been investigated and, from optical model analysis and continuum discretized coupled channels calculations, the halo structure for this weakly-bound nucleus (S p =0.138 MeV) has been established [5,6]. Recently, elastic scattering of the two stable and tightly-bound boron isotopes, 10,11 B, has also been investigated with interesting results in terms of deformation and spin-orbit effects [7,8]. To complete the study on the boron isotope chain we investigate the elastic scattering of the neutron-rich 12 B on the same 58 Ni target. The 12 B nucleus is radioactive, with ground-state spin J π = 1 + and it has a . This nucleus has a predominant configuration given by a 11 B+n, with separation energy of S n =3.370 MeV. Due to this separation energy one can say this nucleus is in the border to be considered weakly or tightly bound nucleus. For weakly bound nuclei, the breakup channel may strongly complete with the elastic scattering and coupled-channel analysis would be required to describe the cross sections. For stable and tightly bound nuclei the optical model analysis of the elastic scattering angular distribution can be useful to extract some information such as radius and deformations. The optical model approach with Woods-Saxon (WS) and double-folding São Paulo potentials (SPP) were used to analyze the measured angular distributions.

The experiment
Angular distributions for the 12 B+ 58 Ni elastic scattering were measured for the first time at energies close to the Coulomb barrier, E Lab = 30.0 and 33.0 MeV. These measurements were performed at Pelletron Laboratory of the University of So Paulo, Brazil. The 12 B secondary radioactive beam was produced with the 9 Be( 11 B, 12 B) transfer reaction in the RIBRAS facility [9]. The 9 Be production target and the 58 Ni reaction target had 14 µm and 2.1 mg/cm 2 of thickness, respectively. The 11 B primary beam had an intensity of about 300 nAe. The produced 12 B secondary radioactive beam was focused by the first solenoid of the RIBRAS in the 58 Ni target, which was mounted in the scattering chamber and had an average intensity of 2 × 10 5 pps. Runs with gold target, 4.6 mg/cm 2 thick, were also performed for the overall normalization purpose since, at these energies, the elastic scattering on gold target is purely Rutherford. The detection system consisted of two ∆E − E telescopes with silicon planar detectors of 25 and 1000 µm in thickness, for the measurements at forward angles, and one 1000-µm thick E planar silicon detector, for measurements at backward angles. The telescopes and the single E detector had circular apertures that subtended a solid angle of about 16 msr (±4.0 • ). Since only one solenoid was used for this measurement, some particles other than 12 B, such as 9 Be, 6,7 Li, 4 He and others were also present in the cocktail beam. However, these particles could be separated and identified in the ∆E − E spectrum, as shown in Fig. 1.  . We performed optical model calculations using Woods-Saxon (WS) and double-folding São Paulo Potential (SPP) [10]. All the calculations were performed with code FRESCO [11]. The results of the OM analysis with the WS potential are shown in Figs. 2 and 3. The WS potentials were obtained by adjusting the parameters which best reproduced the elastic scattering data. The obtained parameters are listed in Table I. As can be seen in the Figs. 2 and 3 the agreement with the data is excellent, in particular at the Fresnel peak. The results of the analysis with the SPP are also show in Figs. 2 and 3. The SSP is a potential of double convolution on the nuclear densities of the projectile and target and it can then be used in association with the optical model, with N R and N I as the normalization for the real and imaginary part, respectively. From a large systematic, the values of N R =1.00 and N I =0.78 were adopted for nucleus with normal density (diffuseness a=0.56) [10]. By adopting these values for the normalization of the SPP we could not describe the experimental angular distributions, as can be seen in Figs. 2 and 3. By performing a searching procedure for the best values of these normalization which describe the data, we obtained: N R =0.99 and N I =0.36 for the angular distribution at 30.0 MeV and N R =0.66 and N I =0.28 for the one at 33.0 MeV. The departure from the systematic normalization is a clear indication of the influence of static and/or dynamic effects. Possible static effects could be checked by using a better value for the 12 B matter density, which could be obtained by measurement or detailed microscopic structure calculation. However, this is out of the scope of the present preliminary results. The dynamic effect could be investigated by the identification of the important channels, which by its turn can be obtained by a coupled-channel calculation. This coupled-channel analysis has already been performed for this system, with interesting results [12]. Table 1. Parameters for the Woods-Saxon potential used in the OM calculations.

Total reaction cross section
The total reaction cross section can be extracted from the optical model analysis. These values can be used to compare with those obtained from other systems with similar target. However, to better compare the total reaction cross sections for the different systems we used the reduction procedure suggested by P. R. Gomes et al. in Ref. [13]. This prescription is valid when the compared systems has very similar masses [14,15], as the case of the systems compared in the present work. In this proposed receipt, the reduced total reaction cross section and reduced energies are given by: and In these equations, σ R is the total reaction cross section, E CM is the energy in the center of mass framework and A P (A T ) and Z P (Z T ) stand for mass and charge of the projectile (target), respectively. With this normalization (reduction), the geometrical effects are, in principle, removed and the eventual anomalous values of the reduced radii (r 0 ) in the radius definition for a normal nucleus, R=r 0 × (A 1/3 P +A 1/3 T ), which should be related to physical processes, are not washed out. The obtained total reaction cross sections for 12 B with WS potential are listed in Table 1. These values are similar to those obtained with SPP. In Figure 4, we plotted the reduced total reaction cross sections for several systems as a function of the reduced energy. Considering this plot one can infer, for instance, about the role of the breakup in the elastic scattering, since projectiles with different breakup threshold energies are involved, from weakly bound nucleus ( 6 Li, 7 Li, 7 Be and 9 Be), tightly-bound ( 10 B, 11 B and 16 O) and exotic nuclei ( 6 He and 8 B). As we can see in the figure, the reduced cross sections for the exotic nuclei lie above those for the weakly-bound normal nuclei and much above than for the tightly-bound projectiles. For the 12 B nucleus, with binding energy of S n =3.337 MeV, the reduced total reaction cross sections lie on the tightly-bound nuclei region.

Conclusion and summary
We have investigated the elastic scattering of the radioactive nucleus 12 B on 58 Ni target at energies close to the Coulomb barrier (V B ≈ 27 MeV). The elastic scattering for this projectile has been measured for the first time. The angular distributions measured at 30.0 and 33.0 MeV were analyzed with the optical model using Woods-Saxon and double folding São Paulo potentials. The angular distributions were very well described with these potentials when the parameters were varied. However, the static effects of the projectiles and the dynamic IOP Conf.  Figure 4. Reduced total reaction cross sections as a function of the reduced energies for the system indicated. The figure has been taken from Ref. [16] and updated with data from 10 B [7], 11 B [8], and 12 B from the present work. The curves are just to guide the eye joining sets of data with similar behavior.
effects of the process are embedded in these parameters. Considering the São Paulo Potential, the departure from the standard normalization (N R =1.0 and N I = 0.78) is an indication of the importance of coupling of other direct reactions channels in the elastic scattering. The identification of the important channels can be achieved only by coupled-channel calculation analysis. Total reaction cross sections could be extract from the OM analysis for the 12 B+ 58 Ni system, and from the comparison with the cross sections from some other light nuclei, in particular from boron isotopes ( 8 B, 10 B, 12 B) indicates that 12 B resembles more a tightly-bound nucleus.