Continuum-discretized coupled-channels calculations with core excitation

The effect of core excitation in the elastic scattering and breakup of a two-body halo nucleus on a stable target nucleus is studied. The structure of the weakly bound projectile is described in the weak-coupling limit, assuming a particle-rotor model. The eigenfunctions and the associated eigenvalues are obtained by diagonalizing this Hamiltonian in a square-integrable basis (pseudostates). For the radial coordinate between the particle and the core, a transformed harmonic oscillator (THO) basis is used. For the reaction dynamics, an extension of the continuum-discretized coupled-channels (CDCC) method, which takes into account dynamic core excitation and de-excitation due to the presence of noncentral parts in the core-target interaction, is adapted to be used along with a pseudostates (PS) basis.

Figure 1

Schematic sketch of the weakly bound projectile composed by a core $\left(c\right)$ and a valence particle $\left(v\right)$. To study the scattering of the composite projectile with an inert target, within a three-body model, the relevant coordinates are the relative coordinate of the valence particle with respect to the core $\left(\vec{r}\right)$ and that between the center of mass of the projectile and the target $\left(\vec{R}\right)$. Note that the valence-target and core-target coordinates (${\vec{r}}_v$ and ${\vec{r}}_c$, respectively) can be written in terms of $\vec{r}$ and $\vec{R}$.

Figure 2

Differential breakup cross sections, with respect to the outgoing ${}^{11}\mathrm{Be}{}^{*}$ c.m. scattering angle, for the breakup of ${}^{11}\mathrm{Be}$ on protons at 63.7 MeV/nucleon. Top and bottom panels correspond to the neutron-core relative energy intervals $E_{\mathrm{rel}}=0$–2.5 MeV and $E_{\mathrm{rel}}=2.5$–5 MeV, respectively.

Figure 3

Energy dependence of the core excitation effects in the breakup of ${}^{11}\mathrm{Be}$ on protons. The top, middle, and bottom rows correspond to the bombarding energies 10, 64, and 200 MeV/nucleon, respectively. The left and right panels are for the neutron-core energy intervals $E_{\mathrm{rel}}=0$–2.5 MeV and $E_{\mathrm{rel}}=2.5$–5 MeV, respectively. In each panel, the solid line is the full XCDCC calculation, whereas the dotted line is the XCDCC calculation without deformation in the $p+{}^{10}\mathrm{Be}$ potential.

Figure 4

Quasielastic differential cross section, relative to Rutherford, for the scattering of ${}^{11}\mathrm{Be}$ on ${}^{64}\mathrm{Zn}$ at $E_{\mathrm{lab}}=28.7$ MeV. The dot-dashed line (red online) is the standard CDCC calculation, without core excitation, from Ref. [54]. The solid line (blue online) is the XCDCC calculation. The dotted line is the XCDCC calculation neglecting the coupling to the breakup channels. Experimental data are from Ref. [52].

Figure 5

Differential cross section, as a function of the laboratory angle, for the ${}^{10}\mathrm{Be}$ fragments resulting from the breakup of ${}^{11}\mathrm{Be}$ on ${}^{64}\mathrm{Zn}$ at $E_{\mathrm{lab}}=28.7$ MeV. The dashed line (red online) is the standard CDCC calculation, without core excitation, from Ref. [54]. The solid line (blue online) is the XCDCC calculation. Experimental data are from Ref. [52].

Figure 6

Quasielastic differential cross section (top) and breakup differential cross section (bottom) for ${}^{11}\mathrm{Be}$ on ${}^{64}\mathrm{Zn}$ at $E_{\mathrm{lab}}=28.7$ MeV, compared with XCDCC calculations, for different choices of the ${}^{10}\mathrm{Be}+{}^{64}\mathrm{Zn}$ potential. See text for further details.

Figure 7

Breakup differential cross section for ${}^{11}\mathrm{Be}$ on ${}^{208}\mathrm{Pb}$ at $E_{\mathrm{lab}}=69$ MeV/nucleon, integrated in the $n\text{−}{}^{10}\mathrm{Be}$ relative energy up to 5 MeV. The data are from Ref. [60]. The lines are XCDCC calculations described in the text. The full calculation (solid line) has been convoluted with the experimental angular resolution for a meaningful comparison with the data.

Figure 8

Dipole strength distribution for ${}^{11}\mathrm{Be}$ deduced from Coulomb breakup experiments (diamonds [58], squares [59], and circles [60]) and from the PRM model of Ref. [36]. The latter has been convoluted with the energy resolution corresponding to the experiment of Ref. [60].