  The proton-induced $\alpha$ knockout reaction has been utilized for decades
to investigate the $\alpha$ cluster states of nuclei, of the ground state in
particular. However, even in recent years, it is reported that the deduced
$\alpha$ spectroscopic factors from $\alpha$ knockout experiments and reaction
analyses with a phenomenological $\alpha$ cluster wave function diverge
depending on the kinematical condition of the reaction. In the present study we
examine the theoretical description of the $^{20}$Ne($p$,$p\alpha$)$^{16}$O
cross section based on the antisymmetrized molecular dynamics and the distorted
wave impulse approximation by comparing with existing experimental data. We
also investigate the correspondence between the $\alpha$ cluster wave function
and the $\alpha$ knockout cross section. The existing
$^{20}$Ne($p$,$p\alpha$)$^{16}$O data at 101.5 MeV is well reproduced by the
present framework. Due to the peripherality of the reaction, the surface region
of the cluster wave function is selectively reflected to the knockout cross
section. A quantitatively reliable $\alpha$ cluster wave function, $p$-$\alpha$
cross section, and distorting potentials between scattering particles,
$\alpha$-$^{16}$O in particular, are crucial for the quantitative description
of the ($p$,$p\alpha$) cross section. Due to the peripherality of the reaction,
the ($p$,$p\alpha$) cross section is a good probe for the surface $\alpha$
amplitude.
