Extracting three-body breakup observables from continuum-discretized coupled-channels calculations with core excitations

Background: Core-excitation effects in the scattering of two-body halo nuclei have been investigated in previous works. In particular, these effects have been found to affect in a significant way the breakup cross sections of neutron-halo nuclei with a deformed core. To account for these effects, appropriate extensions of the continuum-discretized coupled-channels (CDCC) method have been recently proposed.

Purpose: We aim to extend these studies to the case of breakup reactions measured under complete kinematics or semi-inclusive reactions in which only the angular or energy distribution of one of the outgoing fragments is measured.

Method: We use the standard CDCC method as well as its extended version with core excitations, assuming a pseudostate basis for describing the projectile states. Two- and three-body observables are computed by projecting the discrete two-body breakup amplitudes, obtained within these reaction frameworks, onto two-body scattering states with definite relative momentum of the outgoing fragments and a definite state of the core nucleus.

Results: Our working example is the one-neutron halo ${}^{11}\mathrm{Be}$. Breakup reactions on protons and ${}^{64}\mathrm{Zn}$ targets are studied at 63.7 MeV/nucleon and 28.7 MeV, respectively. These energies, for which experimental data exist, and the targets provide two different scenarios where the angular and energy distributions of the fragments are computed. The importance of core dynamical effects is also compared for both cases.

Conclusions: The presented method provides a tool to compute double and triple differential cross sections for outgoing fragments following the breakup of a two-body projectile and might be useful to analyze breakup reactions with other deformed weakly bound nuclei, for which core excitations are expected to play a role. We have found that, while dynamical core excitations are important for the proton target at intermediate energies, they are very small for the Zn target at energies around the Coulomb barrier.

Figure 1

Differential breakup cross sections of ${}^{11}\mathrm{Be}$ on protons at 63.7 MeV/nucleon, with respect to the outgoing ${}^{11}\mathrm{Be}^{*}$ c.m. scattering angle and the neutron-core relative energy intervals $E_{\mathrm{rel}}=0–2.5$ MeV (top) and $E_{\mathrm{rel}}=2.5–5$ MeV (bottom). The contributions corresponding to the considered outgoing core states are also shown. See text for details.

Figure 2

Differential energy distribution following the breakup of ${}^{11}\mathrm{Be}$ on protons at 63.7 MeV/nucleon. Solid and dashed (red) lines correspond to the full ($0^{+}+2^{+}$) and the $2^{+}$ contribution of the XCDCC calculation, while the dot-dashed line (green) represents the result without dynamic core excitation. The arrow indicates the energy of the ${}^{10}\mathrm{Be}\left(2^{+}\right)+n$ threshold.

Figure 3

Calculated laboratory-frame double differential cross section for the ${}^{10}\mathrm{Be}$ fragments emitted in the process ${}^{11}\mathrm{Be}+p$ at 63.7 MeV/nucleon when four different scattering angles are considered. The blue solid and red dashed lines refer to the contributions from the different core states.

Figure 4

Calculated differential energy cross section, as a function of the ${}^{10}\mathrm{Be}$ energy in the laboratory frame, for the reaction ${}^{11}\mathrm{Be}+p$ at 63.7 MeV/nucleon. The solid (blue) and dashed (red) lines describe those calculations when the $I=0$ or $I=2$ state of the core is adopted.

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 $E_{\text{lab}}=28.7$ MeV. The solid line (blue) is the calculation when the core ground state, $I=0$, is selected in Eq. (25) after integration over ${\mathrm{\Omega }}_v$ and $E_c$. The dashed line (red) refers to the $2^{+}$ contribution. A single-particle calculation, omitting the core deformation, is also shown as a dot-dashed curve (green). Experimental data are from Ref. [28].

Figure 6

Calculated ${}^{10}\mathrm{Be}$ differential energy cross section for the reaction ${}^{11}\mathrm{Be}+{}^{64}\mathrm{Zn}$ at 28.7 MeV. The solid (blue) and dashed (red) lines represent the contributions with $I=0$ or $I=2$ as the core states in the two-body distributions (24) after integration over ${\mathrm{\Omega }}_K$. The dot-dashed (green) line considers the same calculation without core deformation, assuming a single-particle model for the projectile within the standard CDCC framework. The arrow indicates the energy of the ${}^{10}\mathrm{Be}\left(2^{+}\right)+n$ threshold.

Figure 7

Calculated laboratory frame ${}^{10}\mathrm{Be}$ cross section energy distributions for the process ${}^{11}\mathrm{Be}+{}^{64}\mathrm{Zn}$ at 28.7 MeV with different laboratory angles in Eq. (25). Under the XCDCC framework, we study both the $0^{+}$ (blue solid curve) and the $2^{+}$ (red dashed curve) contributions, while the standard CDCC method provides the distributions without core deformation (green dot-dashed curve).

Figure 8

Calculated laboratory frame ${}^{10}\mathrm{Be}$ differential energy cross section for the breakup reaction ${}^{11}\mathrm{Be}+{}^{64}\mathrm{Zn}$ at 28.7 MeV. The blue solid and red dashed lines account for the components obtained with the different core states in the XCDCC calculation. The distribution computed with the standard CDCC method (no deformation) is also shown (green dot-dashed curve).