Elastic scattering of ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$ at near-barrier energies

The elastic scattering of the radioactive nucleus ${}^7\mathrm{Be}$ from a ${}^{28}\mathrm{Si}$ target was studied at four near-barrier energies: 13.2, 17.2, 19.8, and 22.0 MeV ($E/V_C=1.14$, 1.48, 1.71, and 1.90). Angular distribution measurements were performed at each energy with the multidetector array EXPADES in conjunction with two Parallel-Plate Avalanche Counters (PPAC) to enable beam ray reconstruction of the events. The data are analyzed in a double-folding framework and the energy evolution of the optical potential as well as the total reaction cross sections are deduced and discussed.

Figure 1

Schematic view of the experimental setup which includes six of the eight modules of the EXPADES array [45, 46]. Each module-telescope comprises two DSSSD detectors as explained in the text. Telescopes T1 and T6 were set at $\pm {27}^{\circ }$, T2 and T5 at $\pm {69}^{\circ }$, and T3 and T4 at $\pm {111}^{\circ }$, spanning the following angular ranges: $\sim {13}^{\circ }$ to ${41}^{\circ }$ and $\sim {14}^{\circ }$ to ${40}^{\circ }$ for the forward detectors, $\sim {54}^{\circ }$ to ${85}^{\circ }$ for the middle telescopes, and $\sim {96}^{\circ }$ to ${126}^{\circ }$ for the backward telescopes.

Figure 2

An energy spectrum for elastic scattering of ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$ at 22 MeV and ${\theta }_{\mathrm{lab}}=17.5^{\circ }$, collected by one strip of detector T6 (see Fig. 1).

Figure 3

Angular distribution for the elastic scattering of ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$ at 13.2 MeV ($E/V_C=1.137$), denoted by the red stars, compared with previous data [12] for ${}^7\mathrm{Li}+{}^{28}\mathrm{Si}$ at 10 MeV ($E/V_C=1.152$), denoted by the green circles. The dot-dashed red line denotes the best-fit OMP calculation while the solid blue line denotes the result of a CDCC calculation.

Figure 4

Angular distribution for the elastic scattering of ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$ at 17.2 MeV ($E/V_C=1.483$), denoted by the red stars, compared with previous data [12] for ${}^7\mathrm{Li}+{}^{28}\mathrm{Si}$ at 13 MeV ($E/V_C=1.497$), denoted by the green circles. The dot-dashed red line denotes the best-fit OMP calculation while the solid blue line denotes the result of a CDCC calculation.

Figure 5

Angular distribution for the elastic scattering of ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$ at 19.8 MeV ($E/V_C=1.707$), denoted by the red stars, compared with previous data [12] for ${}^7\mathrm{Li}+{}^{28}\mathrm{Si}$ at 15 MeV ($E/V_C=1.73$), denoted by the green circles. The dot-dashed red line denotes the best-fit OMP calculation while the solid blue line denotes the result of a CDCC calculation.

Figure 6

Angular distribution for the elastic scattering of ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$ at 22 MeV ($E/V_C=1.90$), denoted by the red stars, compared with previous data [12] for ${}^7\mathrm{Li}+{}^{28}\mathrm{Si}$ at 16 MeV ($E/V_C=1.84$), denoted by the green circles. The dot-dashed red line describes the best-fit OMP calculation while the solid blue line denotes the result of a CDCC calculation.

Figure 7

The energy evolution of the optical model parameters: $N_R$ and $N_I$, obtained in a BDM3Y1 framework (see text) for ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$, denoted by the red stars, compared with the optical model parameters for ${}^7\mathrm{Li}+{}^{28}\mathrm{Si}$ [12], denoted by the green circles. The dot-dashed line corresponds to a dispersion relation analysis for ${}^7\mathrm{Li}$ performed previously [12]. See text for an explanation of the solid green line.

Figure 8

Sensitivity analysis for the elastic scattering data at 19.8 MeV.

Figure 9

Reduced total reaction cross sections for weakly bound projectiles on light targets. Previous data from Refs. [37, 59, 60, 61, 62, 63] are compared with the present data and the prediction from Ref. [54] for light targets, denoted by the solid black line.

Figure 10

Elastic scattering data for ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$ at 13.2 MeV (top panel) and 17.2 MeV (bottom panel) compared with one-channel, two-channel, and CDCC calculations.

Figure 11

Elastic scattering data for ${}^7\mathrm{Be}+{}^{28}\mathrm{Si}$ at 19.8 MeV (top panel) and 22 MeV (bottom panel) compared with one-channel, two-channel, and CDCC calculations.