Distinction between elastic scattering of weakly bound proton- and neutron-rich nuclei: The case of ${}^8\mathrm{B}$ and ${}^{11}\mathrm{Be}$

Experimental data show that the elastic scattering cross sections of the neutron-rich nucleus ${}^{11}\mathrm{Be}$ are greatly reduced by the coupling effects from the breakup channels, while those of the proton-rich nucleus ${}^8\mathrm{B}$ are not. Such difference is found to persist in results of systematic calculations of ${}^8\mathrm{B}$ elastic scattering from ${}^{208}\mathrm{Pb}$ at 60 and 170.3 MeV and from ${}^{64}\mathrm{Zn}$ at 32 and 86 MeV, and ${}^{11}\mathrm{Be}$ elastic scattering from ${}^{208}\mathrm{Pb}$ at 55 and 143 MeV and from ${}^{64}\mathrm{Zn}$ at 29 and 66 MeV with the continuum-discretized coupled channel (CDCC) method. The Coulomb and centrifugal barriers experienced by the valence proton in the ground state of ${}^8\mathrm{B}$, which do not exist for the valence neutron in the ground state of ${}^{11}\mathrm{Be}$, are found to be the reason for such differences in the angular distributions of elastic scattering cross sections of these two weakly bound nuclei.

Figure 1

CDCC calculation of the elastic scattering of ${}^{11}\mathrm{Be}$ from ${}^{64}\mathrm{Zn}$ at $E_{\text{c.m.}}=24.9$ MeV and its comparison with experimental data [11]. The results with and without taking into account the breakup coupling effects are designated as “BU” and “no BU,” respectively.

Figure 2

The same as Fig. 1 but for the elastic scattering of ${}^8\mathrm{B}$ from ${}^{208}\mathrm{Pb}$ at 170.3 MeV [14].

Figure 3

Results of CDCC calculations for differential cross sections of elastic scattering as ratios to the Rutherford cross sections for ${}^8\mathrm{B}$ [panels (a)–(d)] and ${}^{11}\mathrm{Be}$ [panels (e)–(h)] from ${}^{64}\mathrm{Zn}$ and ${}^{208}\mathrm{Pb}$ at low and higher energies. The incident energies are indicated in the figures.

Figure 4

Single-particle wave functions, $u\left(r\right) \left({\int }_0^{\infty }{u}^2\left(r\right)dr=1\right)$, of the valence proton in the ground state of ${}^8\mathrm{B}$ with and without the Coulomb $\left(V_{\mathrm{C}}\right)$ and centrifugal potentials $\left(V_{\mathrm{cf}}\right)$. The corresponding total potentials $V_1,V_2+V_{\mathrm{C}}$, and $V_3+V_{\mathrm{C}}+V_{\mathrm{cf}}$ are also shown, where $V_1,V_2$, and $V_3$ represent the nuclear potentials refitted to reproduce the experimental binding energy of the valence proton in the ground state of ${}^8\mathrm{B}$ without $V_{\mathrm{C}}$ and $V_{\mathrm{cf}}$, with $V_{\mathrm{C}}$ only, and with both $V_{\mathrm{C}}$ and $V_{\mathrm{cf}}$, respectively. For clearness of the figure, $V_2$ and $V_3$ are not plotted. The binding energy of this proton is indicated as the thin dotted line.

Figure 5

Results of CDCC calculations for the angular distributions of ${}^8\mathrm{B}$ elastic scattering from ${}^{64}\mathrm{Zn}$ at 32 MeV with all barriers (solid curve), with only the centrifugal barrier (dashed curve), and with no barriers (dotted curve).