Effect of Coulomb breakup on the elastic cross section of the ${}^8\mathrm{B}$ proton-halo projectile on a heavy, ${}^{208}\mathrm{Pb}$ target

We investigate the role of the breakup channel in the elastic and breakup cross sections, in collisions of proton-halo nuclei. For this purpose, we perform continuum discretized couple channel (CDCC) calculations for the ${}^8\mathrm{B}+{}^{208}\mathrm{Pb}$ system and evaluate polarization potentials. One-channel calculations including the polarization potential are shown to reproduce very well the elastic cross sections obtained by CDCC calculations. We also study the individual contributions of the Coulomb and the nuclear couplings to the cross sections. To complement our study, we compare the effects of the breakup channel in proton-halo and neutron-halo nuclei, performing calculations treating ${}^8\mathrm{B}$ as a ${}^7\mathrm{B}+n$ core-nucleon system, with an artificially low breakup threshold. When only the nuclear breakup is considered, this approach can reasonably describe the elastic scattering.

Figure 1

Elastic scattering of ${}^8\mathrm{B}$ on ${}^{208}\mathrm{Pb}$ at 170.3 MeV. The solid line and the dashed line correspond, respectively, to CDCC calculations taking into account all couplings and to a one-channel calculation with all couplings switched off. The data are from Ref. [24].

Figure 2

Elastic angular distributions for different cutoff values in the multipole expansion of the interaction, ${\lambda }_{\max }$. The curves correspond to results of the CDCC calculations for ${\lambda }_{\max }=1$, 2, 3, 4, and 5. The one-channel calculations (thin solid lines) consider only the expectation value of the interaction, calculated for the elastic channel. To enhance the differences among the lines, we restrict the $y$ axis to values between 0.7 and 1.0. For the same reason, we use different angular regions for $E_{\mathrm{lab}}=60$ MeV (a) and $E_{\mathrm{lab}}=44$ MeV (b) in the $x$ axis. Further details can be found in the text.

Figure 3

Influence of Coulomb and nuclear couplings on elastic angular distributions. The figure shows results of one-channel calculations (thin solid lines) and of CDCC calculations with different couplings. The thick solid lines take into account all couplings, and the dashed and the dotted lines are restricted to nuclear and to Coulomb couplings, respectively.

Figure 4

Influence of the breakup threshold ($Q$) of ${}^8\mathrm{B}$ on the elastic angular distribution. See the text for details.

Figure 5

Contributions from the Coulomb and the nuclear couplings to the breakup cross sections at energies around the Coulomb barrier. For details see the text.

Figure 6

Contributions from the Coulomb and the nuclear couplings to the breakup cross sections at energies around the Coulomb barrier. For details see the text.

Figure 7

Real (a) and imaginary (b) parts of the breakup polarization potentials for the ${}^8\mathrm{B}+{}^{208}\mathrm{Pb}$ system. The polarization potential was obtained with long-range absorption. See the text for details.

Figure 8

Comparison of the elastic cross section of the CDCC calculation (solid line) and the cross section obtained with a one-channel calculation including the polarization potential (dashed line).

Figure 9

Ground state wave function of the relative motion of the halo nucleon with respect to the core. The solid and the dotted lines correspond respectively to the $p-{}^7\mathrm{Be}$ cluster structure with $Q_{\mathrm{p}}=0.137$ MeV, and to the $n-{}^8\mathrm{B}$ structure with $Q_{\mathrm{n}}=0.60$ MeV.

Figure 10

Comparison of elastic scattering cross sections obtained with CDCC calculations adopting the proton-halo configuration for ${}^8\mathrm{B}$ and adopting the neutron-halo configuration with artificially low separation energies. See the text for details.

Figure 11

Similar to Fig. 10 but here the curves represent elastic breakup cross sections.

Figure 12

Same as the previous figure but here the calculations took into account only nuclear couplings, as in the work of Kumar and Bonnacorso [40].

Figure 13

Similar to Fig. 13 but here the calculations took into account only nuclear couplings.