Shell and cluster structures in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>Ne</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mn>20</mml:mn> </mml:mmultiscripts> </mml:math> in the variation of multiple bases o

We investigate the structures of $^{20}\mathrm{Ne}$ in the variation of the multiple bases of the antisymmetrized molecular dynamics (AMD). In this method, the multiple AMD bases are superposed and optimized simultaneously in the total-energy variation. This scheme is beneficial for describing the various configurations in $^{20}\mathrm{Ne}$. In the results, we confirm the shell and cluster structures in the ${K}^{\ensuremath{\pi}}={0}_{1\ensuremath{-}4}^{+}$ bands, such as the deformed states in the ${K}^{\ensuremath{\pi}}={0}_{1,4}^{+}$ bands with the $\ensuremath{\alpha}$ cluster development, and the spherical shell-like states in the ${K}^{\ensuremath{\pi}}={0}_{2}^{+}$ band, the latter of which is difficult to describe in the previous AMD calculations imposing the quadrupole deformation. We evaluate the monopole and quadrupole transitions in these states. The negative parity states of $^{20}\mathrm{Ne}$ with ${K}^{\ensuremath{\pi}}={0}^{\ensuremath{-}}$ and ${2}^{\ensuremath{-}}$ are discussed in relation to the shell and cluster structures. As a result, six kinds of the ${K}^{\ensuremath{\pi}}$ bands in $^{20}\mathrm{Ne}$ are described comprehensively in the microscopic framework of nuclei.