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Properties of $K^π=0^+_1$, $K^π=2^-$, and $K^π=0^-_1$ bands of $^{20}$Ne probed via proton and alpha inelastic scattering

The $K^π=0^+_1$, $K^π=2^-$, and $K^π=0^-_1$ bands of $^{20}$Ne are investigated with microscopic structure and reaction calculations via proton and $α$ 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 $K^π=0^+_1$ and $K^π=0^-_1$ bands have $^{16}\textrm{O}+α$ cluster structures, whereas the $K^π=2^-$ band shows a $^{12}\textrm{C}+2α$-like structure. Microscopic coupled-channel calculations of proton and $α$ scattering off $^{20}$Ne are performed by using the proton-nucleus and $α$-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 $α$ scattering at $E_α=104$--386 MeV. Transition properties from the ground to excited states are discussed by reaction analyses of proton and $α$ inelastic processes. Mixing of the $K^π=2^-$ and $K^π=0^-_1$ 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 $K^π=0^-_1$ cluster component in the $K^π=2^-$ band plays an important role in the transition properties.