Investigation of $\alpha$ clustering with knockout reactions

Our goal is to reveal how the $\alpha$ cluster amplitude is probed through $\alpha$ knockout reactions depending on reaction conditions, e.g., the incident energy. We consider $^{20}$Ne($p$,$p\alpha$)$^{16}$O and $^{120}$Sn($p$,$p\alpha$)$^{116}$Cd at 100-400 MeV within the distorted wave impulse approximation (DWIA) framework. We introduce a masking function which shows how the reaction amplitude in the nuclear interior is suppressed and defines the probed region of the $\alpha$ cluster wave function. It is clearly shown by means of the masking function that the $\alpha$ knockout reaction probes the $\alpha$ cluster amplitude in the nuclear surface region, which is the direct measure of well-developed $\alpha$ cluster states. A simplified form of the masking function is introduced and the incident energy dependence of the masking effect is investigated. $\alpha$ knockout reaction can probe the $\alpha$ cluster amplitude in the nuclear surface region by choosing proper kinematics owing to the masking effect originated from absorptions of distorting potentials, and is a suitable method to investigate how $\alpha$ cluster states are spatially developed.