  The $K^\pi=0^+_1$, $K^\pi=2^-$, and $K^\pi=0^-_1$ bands of $^{20}$Ne are
investigated with microscopic structure and reaction calculations via proton
and $\alpha$ inelastic scattering off $^{20}$Ne. Structures of $^{20}$Ne are
calculated with variation after parity and total angular momentum projections
in the antisymmetrized molecular dynamics(AMD). The $K^\pi=0^+_1$ and
$K^\pi=0^-_1$ bands have $^{16}\textrm{O}+\alpha$ cluster structures, whereas
the $K^\pi=2^-$ band shows a $^{12}\textrm{C}+2\alpha$-like structure.
Microscopic coupled-channel calculations of proton and $\alpha$ scattering off
$^{20}$Ne are performed by using the proton-nucleus and $\alpha$-nucleus
potentials, which are derived by folding the Melbourne $g$-matrix $NN$
interaction with AMD densities of $^{20}$Ne. The calculation reasonably
reproduces the observed cross sections of proton scattering at $E_p=25$--35 MeV
and $\alpha$ scattering at $E_\alpha=104$--386 MeV. Transition properties from
the ground to excited states are discussed by reaction analyses of proton and
$\alpha$ inelastic processes. Mixing of the $K^\pi=2^-$ and $K^\pi=0^-_1$ bands
is discussed by detailed analysis of the $0^+_1\to 3^-_1$ and $0^+_1\to 3^-_2$
transitions. For the $3^-_1$ state, mixing of the $K^\pi=0^-_1$ cluster
component in the $K^\pi=2^-$ band plays an important role in the transition
properties.
