Manifestation of the divergence between antisymmetrized-molecular-dynamics and container pictures of ${}^9$Be via ${}^9$Be($p,pn$)${}^8$Be knockout reaction

We propose a new approach to probe the spatial extension of the valence neutron orbital in the ${}^9$Be nucleus via the ${}^9$Be($p,pn$)${}^8$Be knockout reaction. This property of the nuclear molecular orbital has not been established in previous experimental studies and divergence exists between the theoretical descriptions of ${}^9$Be from different perspectives, $\mathit{\text{i.e.}}$, the antisymmetrized molecular dynamics and the container pictures of cluster dynamics. These pictures are represented by two different well-proven microscopic models, the antisymmetrized molecular dynamics (AMD) and Tohsaki-Horiuchi-Schuck-R"{o}pke (THSR) wave functions. The corresponding reduced width amplitudes (RWAs) in the ${}^8$Be$+n$ channel are extracted from both the AMD and THSR wave functions, and they are found to describe drastically different valence-nucleon motion, which shows the theoretical ambiguity in describing the $\pi$-orbitals in ${}^9$Be. Using the RWAs as input, the physical observables of the ${}^9$Be($p,pn$)${}^8$Be knockout reaction are predicted by the distorted-wave impulse approximation (DWIA) framework. The magnitudes of the triple-differential cross sections (TDX) are found to be highly sensitive to the RWA input. It is concluded that the ${}^9$Be($p,pn$)${}^8$Be knockout reaction could provide a feasible probing for the subtle differences between several structure models manifesting through the spatial extension of the $\pi$-orbital in the ${}^9$Be nucleus.