Probing the Size of Neutron and Proton Single-Particle Orbitals from Nucleon Knockout Reactions
The size of neutron and proton single-particle orbitals of $^{52}$Ca, $^{53}$Ca, $^{54}$Ca, and $^{55}$Sc were investigated via nucleon knockout reactions at $\sim$ 230 MeV/nucleon. The determination method is based on the measured fragment momentum distributions in $(p,pn)$ and $(p,2p)$ reactions, which are shown to be sensitive to the spatial extension of the wave function of the knocked-out nucleon, interpreted within the distorted wave impulse approximation (DWIA) framework. A systematic sensitivity study is carried out for the $(p,pn)$ recoil-momentum distribution method and is presented in this work. The experimental momentum distributions are compared to state-of-the-art mean field and $ab$ $initio$ in-medium similarity renormalization group and self-consistent Green's function calculations in combination with DWIA reaction theory calculations. Based on this work, the 1$p$ neutron orbitals are consistently found $0.48-0.78$ fm larger than the $0f_{7/2}$ neutron orbitals in $^{52-54}$Ca, while the size evolution of the valence proton orbitals remains inconclusive due to the large associated statistical uncertainties.