Core-excitation effects in three-body breakup reactions studied using the Faddeev formalism

Background: Previous studies of $(d,p)$ reactions in three-body (proton, neutron, nuclear core) systems revealed a nontrivial effect of the core excitation: the transfer cross section cannot be factorized into the spectroscopic factor and the single-particle cross section obtained neglecting the core excitation. This observable, up to a kinematic factor, is the angular distribution of the core nucleus in the $(p,d)$ reaction.

Purpose: The study of the core excitation effect for the most closely related observable in the $(p,pn)$ three-body breakup, i.e., the core angular distribution, is the aim in the present work.

Methods: Breakup of the one-neutron halo nucleus in the collision with the proton is described using three-body Faddeev-type equations extended to include the excitation of the nuclear core. The integral equations for transition operators are solved in the momentum-space partial-wave representation.

Results: Breakup of ${}^{11}\mathrm{Be}$ nucleus as well as of model $A=11p$-wave nuclei is studied at beam energies of 30, 60, and 200 MeV per nucleon. Angular and momentum distributions for the ${}^{10}\mathrm{Be}$ core in ground and excited states is calculated. In sharp contrast to $(p,d)$ reactions, the differential cross section in most cases factorizes quite well into the spectroscopic factor and the single-particle cross section.

Conclusions: Due to different reaction mechanisms the core excitation effect in the breakup is very different from transfer reactions. A commonly accepted approach to evaluate the cross section, i.e., the rescaling of single-particle model results by the corresponding spectroscopic factor, appears to be reliable for breakup though it fails in general for transfer reactions.

Figure 1

Semi-inclusive differential cross sections for ${}^{11}\mathrm{Be}(p,pn){}^{10}\mathrm{Be}$ reactions at $E/A=30$, 60, and 200 MeV as functions of the ${}^{10}\mathrm{Be}$ core c.m. scattering angle. Predictions of models with CX, displayed by solid (dashed-dotted) curves for $0^{+}$ ($2^{+}$) final states of the ${}^{10}\mathrm{Be}$ core, and without CX, the latter rescaled by $\mathrm{SF}\left(0^{+}\right)=0.854$ and displayed by dotted curves, are compared. In addition to the results based on the KD optical potential, the ones based on the Watson parametrization are shown at 60 MeV as thin curves.

Figure 2

Core excitation effect for the core angular distribution in breakup (solid curve) and transfer (dashed-dotted curve) reactions, resulting from the proton-${}^{11}\mathrm{Be}$ collision at $E/A=60$ MeV.

Figure 3

Transverse (left) and longitudinal (right) core momentum distributions for ${}^{11}\mathrm{Be}(p,pn){}^{10}\mathrm{Be}$ reactions at $E/A=30$, 60, and 200 MeV. Curves are as in Fig. 1.

Figure 4

Semi-inclusive differential cross sections for the breakup of $p$-wave model nuclei as functions of the core c.m. scattering angle at $E/A=60$ and 200 MeV. Predictions of models with CX, displayed by solid (dashed-dotted) curves for $0^{+}$ ($2^{+}$) final states of the core, are compared with rescaled results of the SP model. Thin (thick) curves correspond to the neutron separation energy $S_n=0.5$ MeV (5.0 MeV) with $\mathrm{SF}\left(0^{+}\right)$ being 0.771 (0.731). KD optical potential is used.

Figure 5

Transverse core momentum distributions for the breakup of $p$-wave model nucleus with 5.0 MeV binding energy in the collision with proton at $E/A=60$ and 200 MeV. Curves are as in Fig. 4.