Distortion effects on the neutron knockout from exotic nuclei in the collision with a proton target

Background: Reaction theory plays a major role in the interpretation of experimental data and one needs to identify and include accurately all the relevant dynamical effects in order to extract reliable structure information. The knockout of a nucleon (neutron/proton) from a high energy exotic nucleus projectile colliding with a proton target allows to get insight on the structure of its valence and inner shells.

Purpose: We aim to clarify the role of the distortion on the calculated observables for nucleon knockout, in particular, the dependence of the calculated observables on the binding energy ${\epsilon }_b$ and angular momentum $L$ of the knockout particle, and on the mass of the projectile core, $A_c$. We consider mainly the knockout of a neutron that may be either in the valence or in the inner shell of the projectile nucleus.

Method: Exact three-body Faddeev/Alt-Grassberger-Sandhas (Faddeev/AGS) calculations are performed for the nucleon knockout from stable and exotic nuclei in the collision of 420 MeV/u projectile beams with a proton target. Results are compared with plane-wave impulse approximation (PWIA) calculations.

Results: The Faddeev/AGS formalism accurately predicts: (i) a systematic nearly logarithmic dependence of the distortion parameter on the separation energy; (ii) roughly linear dependence of the ratio of the full to the PWIA cross section on the asymmetry parameter; (iii) a distinct behavior between the calculated transverse core momentum distribution from the PWIA and full Faddeev/AGS exact approach which indicates that distortion effects do not modify fully exclusive observables through a common renormalization factor.

Conclusions: To extract structure information on deeper shells one needs to include distortion effects accurately. A systematic analysis enables to estimate the total cross section for knockout of a nucleon from a given shell of nuclei at/away the stability line of the nuclear landscape. The comparison with experimental results may provide understanding on the used interaction and structure model.

Figure 1

Single and double scattering diagrams for breakup in the Faddeev scattering framework, as described in the text.

Figure 2

Triple scattering diagrams for breakup in the Faddeev scattering framework as described in the text.

Figure 3

Convergence of the total cross section with the valence neutron-core orbital angular momentum $L_{\max }^{n\text{−}C}$, the proton target-core orbital angular momentum $L_{\max }^{p\text{−}C}$, and the total three-particle angular momentum $J_{\max }$. The values shown correspond to the ${}^{14}\mathrm{C}\otimes n\left(2s_{1/2}\right)$ system with ${\epsilon }_b=-1.22\mathrm{MeV}$, but are illustrative of all systems.

Figure 4

Calculated fully converged and PWIA core ground state transverse momentum $p_x$ distributions at 420 MeV/u for different values of the mass of the core.

Figure 5

Core ground state transverse momentum $p_x$ distributions at 420 MeV/u for a system with a neutron-core binding energy ${\epsilon }_b=-4.50\mathrm{MeV}$ and different angular momenta. The solid and dashed lines represent the calculated fully converged and the PWIA observables, respectively.

Figure 6

Core ground state transverse momentum $p_x$ distributions at 420 MeV/u for different values of the $n$-core binding energy with the angular momentum $L=0$. The solid and dashed lines represent the calculated fully converged and PWIA scattering observables, respectively.

Figure 7

Calculated total cross section, full, and $p\text{−}n$ single scattering, as a function of the separation energy of the knockout neutron, in logarithmic scale, for different values of the angular momentum (top); the corresponding distortion parameter (middle); ratio parameter as a function of the asymmetry parameter (bottom).

Figure 8

Core ground state transverse momentum $p_x$ distributions at 420 MeV/u for the $n$-core binding energies ${\epsilon }_b=-0.5\mathrm{MeV}$ (left) and ${\epsilon }_b=-15\mathrm{MeV}$ (right), and angular momenta $L=0,1,2$. The solid and dashed lines represent the full and $p–n$ single scattering observables renormalized by the ratio parameter between the full and the PWIA total cross section described in the text.