Elastic scattering measurements for the ${}^{10}\mathrm{C}+{}^{208}\mathrm{Pb}$ system at $E_{\text{lab}}=66$ MeV

Background: The influence of halo structure of ${}^6\mathrm{He}$, ${}^8\mathrm{B}$, ${}^{11}\mathrm{Be}$, and ${}^{11}\mathrm{Li}$ nuclei in several mechanisms such as direct reactions and fusion is already established, although not completely understood. The influence of the ${}^{10}\mathrm{C}$ Brunnian structure is less known.

Purpose: To investigate the influence of the cluster configuration of ${}^{10}\mathrm{C}$ on the elastic scattering at an energy close to the Coulomb barrier.

Methods: We present experimental data for the elastic scattering of the ${}^{10}\mathrm{C}+{}^{208}\mathrm{Pb}$ system at $E_{\mathrm{lab}}=66$ MeV. The data are compared to the three- and the four-body continuum-discretized coupled-channels calculations assuming ${}^9\mathrm{B}+p$, ${}^6\mathrm{Be}+\alpha$, and ${}^8\mathrm{Be}+p+p$ configurations.

Results: The experimental angular distribution of the cross sections shows the suppression of the Fresnel peak that is reasonably well reproduced by the continuum-discretized coupled-channels calculations. However, the calculations underestimate the cross sections at backward angles. Couplings to continuum states represent a small effect.

Conclusions: The cluster configurations of ${}^{10}\mathrm{C}$ assumed in the present work are able to describe some of the features of the data. To explain the data at backward angles, experimental data for the breakup and an extension of theoretical formalism towards a four-body cluster seem to be in need to reproduce the measured angular distribution.

Figure 1

Sketch of the detection system for the measurements, composed by one $\mathrm{\Delta }E\text{−}E$ telescope, placed at forward angles, and an $E$-detector at backward angles. The $E$-detectors are $128\times 128$ DSSSD and the $\mathrm{\Delta }E$ is a $16\times 16$ thin DSSSD. A third DSSSD (monitor) was placed at $0^{\circ }$ to monitor the beam axis.

Figure 2

The $\mathrm{\Delta }E\text{−}E$ plot for particle identification. A small fraction of ${}^{10}\mathrm{B}$ is observed due to sparks in the Wien filter of MARS separator during the acquisition runs.

Figure 3

Example of total energy spectrum for ${}^{10}\mathrm{C}$ particles scattered by ${}^{208}\mathrm{Pb}$ at (a) ${30}^{\circ }\le {\theta }_{lab}\le {35}^{\circ }$, (b) ${105}^{\circ }\le {\theta }_{lab}\le {115}^{\circ }$, and (c) ${135}^{\circ }\le {\theta }_{lab}\le {140}^{\circ }$. In panels (a) and (b), the elastic peak is represented by a single Gaussian curve. In panel (c), data points were adjusted to a two-Gaussian curve with the same standard deviation. The green dotted and violet dashed-dot curves correspond to elastic and the contribution from $2^{+}$ state in ${}^{10}\mathrm{C}$ and $3^{-}$ in ${}^{208}\mathrm{Pb}$, respectively.

Figure 4

Elastic scattering angular distribution for the ${}^{10}\mathrm{C}+{}^{208}\mathrm{Pb}$ system at $E_{lab}=66$ MeV (black circle points). The points in blue triangles correspond to data for ${}^{12}\mathrm{C}+{}^{208}\mathrm{Pb}$ system at 64.9 MeV from Ref. [37]. The solid curves were obtained by fitting the parameters of the optical potential.

Figure 5

Reduced reaction cross section for the several projectiles on ${}^{208}\mathrm{Pb}$ target. The universal fusion function (UFF) is also shown in the plot as a lower bound to the reduced reaction cross sections.

Figure 6

Comparison between data and coupled-channels calculations for the elastic angular distribution for the ${}^{10}\mathrm{C}+{}^{208}\mathrm{Pb}$ system at $E_{\mathrm{lab}}=66$ MeV. The no-coupling and the coupled-channel calculations are represented by dotted black and solid orange curves, respectively.

Figure 7

Comparison between data and 3b-CDCC calculations considering the ${}^9\mathrm{B}$ $+$ $p$ (green curves) and ${}^6\mathrm{Be}+\alpha$ (blue curves) cluster configurations in (a) linear scale and (b) log scale. The no-coupling calculation, presented in the previous subsection, is also included (dotted black curve). See text for details.

Figure 8

Comparison between data and $4b$-CDCC calculation considering the ${}^{10}\mathrm{C}$ nucleus has a ${}^8\mathrm{Be}+p+p$ cluster. The one-channel and full couplings results are represented by dashed and solid red curves, respectively. For reference, the no-coupling (dotted black curve) and the $3b$-CDCC assuming the ${}^9\mathrm{B}+p$ configuration (dot-dashed green curve) are also included.

Figure 9

Reaction cross sections as a function of the total angular momentum ($J$) as obtained from optical model fitting (OM), 3b-CDCC (${}^6\mathrm{Be}+\alpha$ and ${}^9\mathrm{B}+p$) and 4b-CDCC $({}^8\mathrm{Be}+p+p)$ calculations.