Energy dependence of optical potential in the near barrier elastic scattering of 11B from 232Th

The elastic scattering cross sections of 11B projectile on the 232Th target have been measured at different bombarding energies close to the Coulomb barrier. The data has been analyzed for this system using the optical model ECIS code with phenomenological Woods-Saxon forms of the optical potentials. The energy dependence of the volume type real and imaginary parts of the optical potentials are derived from the best fit of the experimental angular distribution data. The total reaction cross sections are obtained from optical model


Introduction
The rich interplay between the intrinsic structure and the reaction dynamics of the interacting nuclei has been a hall-mark of near-barrier heavy-ion interactions [1]. One of the manifestations of this feature is a strong energy dependence of the optical model potential deduced from analyses of elastic scattering angular distributions at energies around the Coulomb barrier [1,2]. The study of elastic scattering angular distributions determine parameters of the real and imaginary parts of the nuclear interaction potential. From systematic analysis of elastic scattering measurements involving tightly bound nuclei, the so called "threshold anomaly" (TA) has been observed in a number of systems [1]. This has been understood in terms of couplings of elastic channel to the direct reaction channels that generate an additional attractive real dynamic polarization potential. The study of the TA is important to investigate the influence of the breakup and other reaction mechanisms on the elastic and fusion channels [3][4][5].
In the present work, the elastic scattering angular distribution measurements have been carried out for 11 B + 232 Th system at energies from 4% below the Coulomb barrier (V lab ∼ 54 MeV) to approximately 20% above the barrier. The total reaction cross sections for this system have also been derived to understand the role of projectile breakup on the total reaction cross sections. The present article has been organized in the following way. The experimental set up is described in Sec.2. Data analysis using the Wood-Saxon potential (WSP) to determine the energy dependence of potential parameters have been disa corresponding author:dcbiswas@barc.gov.in cussed in Sec.3. In Sec.4, a systematic study of total reaction cross section for 11 B + 232 Th system has been discussed. In Sec.5, the summary and conclusions of the present work are reported.

Experimental procedure
The experiment was performed at the 14UD BARC-TIFR Pelletron facility at Mumbai using beams of 11 B in a wide energy range around the Coulomb barrier, i.e., 52, 53, 54, 55, 56, 57, 59, 61 and 65 MeV for 11 B + 232 Th system. The observed uncertainty in the beam energy was about 1% for all the selected energies. A self supporting 232 Th target of thickness 1.5 mg/cm 2 was placed at the center of the general purpose scattering chamber and the elastically scattered 11 B particles were detected by silicon ΔE-E telescopes mounted on a movable arm of the chamber. Four telescopes of thickness (T 1 ) with ΔE = 25 μm and E = 300μm, (T 2 ) with ΔE = 40 μm and E = 300 μm, (T 3 ) with ΔE = 25 μm and E = 300 μm and (T 4 ) with ΔE = 25 μm and E = 300 μm were used in the experiment. The detector telescopes were placed at an angular separation of 10 • and two silicon detectors with thickness around 300 μm were mounted at fixed angles ±18 • with respect to beam direction for absolute normalization and beam monitoring. The angular distributions were measured in steps of 5 • in the angular range from 35 • to 170 • . The uncertainty on the angular range of each telescope was ±0.81 • .

Optical Model Analysis Of Elastic Scattering
The optical model fits to the elastic scattering data have been performed using the ECIS code [6]. The phe- nomenological Woods-Saxon form of the interaction potential with only volume terms have been used in the analysis. To obtain the starting parameters, a global best fit procedure for all energies were performed, using the three parameters characterized by real and imaginary depth of the potential, reduced radii (r o ) and diffuseness (a v and a w ). Thereafter, in order to avoid a fit procedure with too many parameters, the real and imaginary reduced radii were fixed at 1.06 fm for the 11 B + 232 Th system, similar to the value used earlier [4,5]. Using this radius, and varying the diffuseness parameters a v and a w ( real and imaginary respectively) within the interval from 0.67 fm to 0.75 fm, an attempt was made to obtain the best possible parameters of the optical potential that best describe the elastic scattering angular distribution. In the present work, the best possible fitted values were obtained for a v , a w = 0.71 fm. The real and imaginary radius parameters (r o = 1.06 fm) and diffuseness parameters (a v , a w = 0.71 fm) were fixed for all energies. The depths of real and imaginary potentials were varied to obtain minimum value of χ 2 for the 11 B + 232 Th system. The potential parameter values for the best fit and the total reaction cross sections are shown in Table-I. The best fit optical model parameters show significant energy dependence as reflected from Table-I, which is a characteristic feature of the elastic scattering. The solid lines in Fig. 1 show the best fit of the experimental data for the elastic scattering angular distributions for 11 B + 232 Th system.
To reduce the ambiguities of the best fitted parameters of the optical potential, the strong sensitive radius R S r and R S i corresponding to the real and imaginary potential were determined. For this purpose the radius parameters were kept fixed and the depth parameters of the real and imagi-  Figure 2. Several potential that produce similar fits of the data, for 65 MeV. The crossing point are the derived real (a) and imaginary (b) sensitivity radii for 11 B + 232 Th system. nary potentials were fitted by varying the diffuseness from 0.67 to 0.75 fm, in step of 0.02 fm for all energies of 11 B + 232 Th system. The strong sensitive radii [8] were determined, where the real and imaginary part of different optical potentials that fitted the data cross each other as shown in Fig. 2 (a) and 2(b) for 65 MeV for 11 B + 232 Th system. The real sensitive radii values were observed to be in the range of 12.4 to 11.3 fm with a average of R S r = 11.57 fm and for the imaginary sensitive radii values range from 12.7 to 13.5 fm with a average value of R S i = 13.34 fm. A mean sensitive radius of R s = 12.45 fm for 11 B + 232 Th system (average between R S r = 11.57 fm and R S i = 13.34 fm) was obtained to derive energy dependence of real and imaginary potential. In the analysis for this system the values of radius parameters for real and imaginary parts were kept fixed at 1.06 fm for all the calculations. A similar fitting procedure can also be found in the literature [2,7] for 11 B + 209 Bi system. The corresponding values of the energy dependence of the real and imaginary potentials for the 11 B + 232 Th system are shown in Fig. 3. The error bars in Fig. 3 represent the range of deviation of the potential corresponding to a χ 2 variation of one unit.
: 0H9 9 0H9 ( ODE 0H9 % 7K D E Figure 3. Energy dependence of the real and imaginary parts of the optical potential obtained for the 11 B + 232 Th system at an average radius R s = 12.45 fm.

Total Reaction Cross Section
The fusion cross sections have been calculated for 11 B + 232 Th system by using CCFULL code [9]. The energy range used in the calculation was 52 to 65 MeV, in steps of 1 MeV. In the present work, the total reaction cross sections derived from experimental elastic scattering data analysis for 11 B + 232 Th system was compared with the calculated fusion cross sections as shown in Fig. 4 (a). The total reaction cross sections obtained from optical model ECIS code. In order to eliminate the projectile size effect on the reaction cross sections for 11 B + 232 Th system, the "reduction" method was used. This method was proposed by Gomes et al. [10] and has been well implemented by others [4,5,11,12]. The reduced cross section values were calculated at all energies for the system. In this 7K D Figure 4. Total fusion cross section (σ f us ) (by CCFULL) and total reaction cross section (σ R ) for 11 B + 232 Th system as a function of the bombarding energy in 4 (a). Reduced total reaction cross section vs reduced projectile energy for the 6,7 Li + 232 Th and 11 B + 232 Th reactions using the prescription given in Ref. [10] in 4 (b). method, the quantities σ R / (A 1/3 P + A 1/3 T ) 2 vs E c.m. (A 1/3 P + A 1/3 T )/Z P Z T are plotted, where P and T represent the projectile and target respectively, and σ R is the total reaction cross section. As shown in Fig. 4 (b), it can be seen that total reduced reaction cross section of 11 B + 232 Th system is smaller than 6,7 Li + 232 Th system.

Summary and Conclusions
The elastic-scattering angular distribution measurements have been carried out for the 11 B + 232 Th system at several bombarding energies from below to well above the Coulomb barrier. The experimental data have been analyzed using the ECIS code forms of phenomenological optical potentials. The relevant parameters that gives best fit to the elastic scattering angular distribution, were obtained through a χ 2 -minimization procedure. The enhanced reaction cross sections have been observed at sub-barrier energies for 6,7 Li + 232 Th systems [5] in comparison to the 11 B + 232 Th system. This may be an indication that 11 B has a lower breakup probability as compared to 6,7 Li projectiles.