Two-proton momentum correlation from photondisintegration of $alpha$-clustering light nuclei in the quasi-deuteron region

The proton-proton momentum correlation function is constructed in three-body photo-disintegration channels from $^{12}$C and $^{16}$O targets in the quasi-deuteron regime within the framework of an extended quantum molecular dynamics model. Using the formula of Lednicky and Lyuboshitz (LL) for the momentum correlation function, we obtain a proton-proton momentum correlation function for the specific three-body photon-disintegration channels of $^{12}$C and $^{16}$O targets, which are assumed to have different initial geometric structures, and extract their respective emission source sizes for the proton-proton pair. The results demonstrate that constructing a proton-proton momentum correlation is feasible in photo-nuclear reactions, and it is sensitive to the initial nuclear structure. For future experimental studies investigating the $alpha$-clustering structures of light nuclei, the present work can be used to shed light on the performance and correlation function analysis of ($gamma$,pp) or (e,$e$pp) reactions.