Elastic scattering for the ${}^8\mathrm{B}$ and ${}^7\mathrm{Be}+{}^{208}\mathrm{Pb}$ systems at near-Coulomb barrier energies

The elastic scattering of the weakly bound radioactive nuclei ${}^8\mathrm{B}$ and ${}^7\mathrm{Be}$ from a ${}^{208}\mathrm{Pb}$ target was measured for the first time in the energy range around the Coulomb barrier. The data were analyzed using the optical model and the continuum discretized coupled channels (CDCC) formalisms. The reaction cross sections extracted from the optical model fits clearly indicate a remarkably enhanced reaction probability for the very weakly bound ${}^8\mathrm{B}$ ($S_p=137.5\mathrm{keV}$) compared to similar mass nuclei interacting with the same target nucleus. CDCC calculations assuming a ${}^3\mathrm{He}+{}^4\mathrm{He}$ cluster model well described the ${}^7\mathrm{Be}$ experimental elastic scattering angular distributions, whereas the use of a ${}^7\mathrm{Be}+p$ cluster model of ${}^8\mathrm{B}$ with an inert ${}^7\mathrm{Be}$ core gave a relatively poor description of the corresponding experimental data, suggesting that this model may be too simplistic and the possibility of core excitation should not be ignored.

Figure 1

(a) $\mathrm{\Delta }E-E_{\mathrm{res}}$ correlation plot for the ${}^8\mathrm{B}+{}^{208}\mathrm{Pb}$ reaction at 50 MeV collected by telescope A, covering the polar angle range ${\theta }_{\mathrm{lab}}=[+8^{\circ },+{40}^{\circ }]$. The ${}^7\mathrm{Be}$ and ${}^3\mathrm{He}$ contaminant beams are clearly visible on the plot. (b) Same as (a) after imposing an RF gate on the incoming ${}^8\mathrm{B}$ beam (see text for additional details).

Figure 2

As in Fig. 1, but for telescope F, located in the backward hemisphere (${\theta }_{\mathrm{lab}}=[-{134}^{\circ },-{166}^{\circ }]$).

Figure 3

Elastic scattering angular distribution for the ${}^8\mathrm{B}+{}^{208}\mathrm{Pb}$ system at a beam energy of 50 MeV. Error bars are statistical only. The curve represents an optical model fit to the data; see text for more details.

Figure 4

$\mathrm{\Delta }E-E_{\mathrm{res}}$ correlation plots for the ${}^7\mathrm{Be}+{}^{208}\mathrm{Pb}$ reaction at 40.5 MeV registered by telescope A, ${\theta }_{\mathrm{lab}}=[+{52}^{\circ },+{85}^{\circ }]$ (a), telescope B, ${\theta }_{\mathrm{lab}}=[+{95}^{\circ },+{128}^{\circ }]$ (b), and telescope F, ${\theta }_{\mathrm{lab}}=[-{138}^{\circ },-{167}^{\circ }]$ (c). In addition to the elastic scattering peaks the kinematic loci related to the isotopes of hydrogen and helium produced by the interactions between the beam and the target are clearly visible.

Figure 5

Quasielastic differential cross section for ${}^7\mathrm{Be}+{}^{208}\mathrm{Pb}$ at beam energies of 42.2 MeV (red triangles), 40.5 MeV (black circles), and 37.4 (blue squares). Errors bars are statistical only. The curves represent optical model fits to the data; see text for details.

Figure 6

Elastic scattering angular distribution for the ${}^8\mathrm{B}+{}^{208}\mathrm{Pb}$ system at a beam energy of 50 MeV. The solid curve denotes the result of the full CDCC calculation while the dashed curve denotes that of the no-coupling case.

Figure 7

Quasielastic scattering angular distributions for the ${}^7\mathrm{Be}+{}^{208}\mathrm{Pb}$ system at beam energies of 42.2 (a), 40.5 (b), and 37.4 (c) MeV. The solid curves denote the results of the full CDCC calculation while the dashed curves denote those of the two-channel case; see text for details. The dotted curve at 37.4 MeV denotes the quasielastic scattering predicted by a full CDCC calculation using the same ${}^3\mathrm{He}+{}^{208}\mathrm{Pb}$ optical model potential as at 42.2 and 40.5 MeV.

Figure 8

Total reaction cross sections for the ${}^8\mathrm{B}, {}^7\mathrm{Be}, {}^6\mathrm{Li}, {}^7\mathrm{Li}$, and ${}^8\mathrm{Li}+{}^{208}\mathrm{Pb}$ systems extracted from optical model fits plotted on the dimensionless scale according to the formalism of Canto et al. [73].